ANL/ES-25 L, .& IL« *'»• 3 i L-S 3 iCj ^ i — I L - 3 -.JLd TEMPERATURE AND VELOCITY MEASUREMENTS1^^__ AND PREDICTIVE MODEL COMPARISONS IN THE NEAR-FIELD REGION OF SURFACE THERMAL DISCHARGES R. A. Paddock, A. J. Policastro, A. A. Frigo, D. E. Frye, and J. V. Tokar i \r hbution by any holder of this document oj ,/tfHrMsn gnvemTS TO^oragn companies and foreiqn s u ds i cSlIif w lAlr'f bMftlWfit1 ry.r, ottkkUaiiiiitiiUtUUUi ..ihouLd b^coord^iiJkjwi th the' Ofressto^uncsio Energy Co - ;m > ion Prepared for the U.S. ATOMIC ENERGY COMMISSION Division of Reactor Research and Development under Contract W-31-109-Eng-38 The facilities of Argonne National Laboratory are owned, by the United States Govern¬ ment. Under the terms of a contract (W-31 -109-Eng-38) between the U. S. Atomic Energy Commission, Argonne Universities Association and The University of Chicago, the University employs the staff and operates the Laboratory in accordance with policies and programs formu¬ lated, approved and reviewed by the Association. MEMBERS OF ARGONNE UNIVERSITIES ASSOCIATION The University of Arizona Carnegie-Mellon University Case Western Reserve University The University of Chicago University of Cincinnati Illinois Institute of Technology University of Illinois Indiana University Iowa State University The University of Iowa Kansas State University The University of Kansas Loyola University Marquette University Michigan State University The University of Michigan University of Minnesota University of Missouri Northwestern University University of Notre Dame The Ohio State University Ohio University The Pennsylvania State University Purdue University Saint Louis University Southern Illinois University The University of Texas at Austin Washington University Wayne State University The University of Wisconsin -NOTICE- This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the United States Atomic Energy Commission, nor any of their employees, nor any of their contractors, subcontrac¬ tors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately-owned rights. Printed in the United States of America Available from U.S. Atomic Energy Commission Technical Information Center P.O. Box 62 Oak Ridge, Tennessee 37830 Price; Printed Copy $7.60 ANL/ES-25 Heat Rejection and Utilization (UC-12) ARGONNE NATIONAL LABORATORY 9700 South Cass Avenue Argonne, Illinois 60439 £2 B- I (o 5^.3 TEMPERATURE AND VELOCITY MEASUREMENTS AND PREDICTIVE MODEL COMPARISONS IN THE NEAR-FIELD REGION OF SURFACE THERMAL DISCHARGES A & 3 /? AjL/ £ S-2 S by R. A. Paddock, A. J. Policastro, A. A. Frigo, D. E. Frye, and J. V. Tokar Center for Environmental Studies * October 1973 Digitized by the Internet Archive in 2018 with funding from University of Illinois Urbana-Champaign Alternates https://archive.org/details/temperaturevelocOOpadd 3 TABLE OF CONTENTS ABSTRACT I. INTRODUCTION. II. EXPERIMENTAL TECHNIQUE . III. DESCRIPTIONS OF POWER PLANTS. A. Point Beach Nuclear Power Plant, .................. B. Palisades Nuclear Power Plant .................... IV. RESULTS OF FIELD MEASUREMENTS ............. V. EXTRACTION OF JET CHARACTERISTICS FROM FIELD MEASUREMENTS. ........................... VI. MATHEMATICAL MODELING OF NEAR-FIELD REGION OF SURFACE THERMAL DISCHARGES ............ A. Motz-Benedict Model ........................... B. Stolzenbach-Harleman Model. ..................... C. Prych Model. ................................ D. Pritchard Model .............................. VII. MODEL COMPARISONS TO DATA. .................... A. Jet Trajectories .............................. B. Centerline Temperature Decay and Temperature Half¬ widths ..................................... C. Centerline Velocity Decay and Velocity Half-widths. ...... D. Temperature and Velocity Half-depth ................ E. Isotherm Areas... F. Decay of Centerline Temperature and Velocity with Depth . . G. Variation of Temperature and Velocity Width with Depth . . . VIII. SUMMARY AND CONCLUSIONS ...................... A. Field-data Acquisition... B. Data-smoothing Technique ... Page 13 14 16 19 19 19 22 66 73 74 78 83 85 88 88 95 102 104 112 115 119 123 123 123 4 TABLE OF CONTENTS Page C. Analytical Model; Field-data Comparisons. 124 1. Pritchard Model. 124 2. Motz-Benedict Model. 124 3. Stolzenbach-Harleman Model. 126 4. Prych Model. 127 IX. RECOMMENDATIONS FOR FUTURE RESEARCH. 128 A. Field-data Acquisition. 128 B. Data-smoothing Technique. 128 C. Analytical Model; Field-data Comparisons. 128 APPENDIXES A. Previous Program Reports . .. 130 B. Preliminary Feasibility Study. 133 C. FORTRAN Listing for Fitting Procedure .. 138 D. Fitting Parameters and Results. 152 ACKNOWLEDGMENTS ...... 167 REFERENCES 168 5 LIST OF FIGURES No. Title Page 1. Boat with Current Meter Used in Jet-regime Studies.. 16 2. Motorola Mini-Ranger Range Positioning System. .. 16 3. Bendix Q-15 Geomagnetic Ducted Current Meter ............ 17 4. Aerial View of Point Beach Nuclear Power Plant. ........... 20 5. Aerial View of Palisades Nuclear Power Plant ............. 21 6. Approximate Depth Contours near Point Beach Outfall ........ 23 7. Approximate Depth Contours near Palisades Outfall. ......... 24 8. Jet-regime Study for 0.5-m Depth at Point Beach Power Plant (Unit 1): May 1 8, 1 972, 1 11 5 -1440 Hours . . . . ... 25 9. Jet-regime Study for 1.0-m Depth at Point Beach Power Plant (Unit l): May 18, 1972, 1 115-1440 Hours ............. 26 10. Jet-regime Study for 1.5-m Depth at Point Beach Power Plant (Unit l): May 18, 1972, 1115-1440 Hours ............. 27 11. Jet-regime Study for 2.0-m Depth at Point Beach Power Plant (Unit 1): May 1 8, 1 972, 1 11 5 -1440 Hours ............ . 28 12. Jet-regime Study for 2.5 -m Depth at Point Beach Power Plant (Unit l): May 18, 1972, 1 115-1440 Hours ............. 29 13. Jet-regime Study for 3.0-m Depth at Point Beach Power Plant (Unit l): May 18, 1972, 1 115-1440 Hours ............. 30 14. Jet-regime Study for 0.5-m Depth at Point Beach Power Plant (Unit l): May 23, 1972, 0945-1700 Hours ............. 31 15. Jet-regime Study for 1.0-m Depth at Point Beach Power Plant (Unit l): May 23, 1972, 0945-1700 Hours ............. 32 16. Jet-regime Study for 1.5-m Depth at Point Beach Power Plant (Unit l): May 23, 1972, 0945-1700 Hours ............. 33 17. Jet-regime Study for 2.0-m Depth at Point Beach Power Plant (Unit l): May 23, 1972, 0945-1700 Hours ............. 34 18. Jet-regime Study for 2.5-m Depth at Point Beach Power Plant (Unit l): May 23, 1972, 0945-1700 Hours .. 35 19. Jet-regime Study for 3.0-m Depth at Point Beach Power Plant (Unit l): May 23, 1972, 0945-1700 Hours .. 36 20. Jet-regime Study for 0.5-m Depth at Point Beach Power Plant (Unit l): July 13, 1972, 1308-1706 Hours ... . 37 6 LIST OF FIGURES No. Title Page 21. Jet-regime Study for 1.0 -m Depth at Point Beach Power Plant (Unit l): July 13, 1972, 1308-1706 Hours ... 38 22. Jet-regime Study for 1.5-m Depth at Point Beach Power Plant (Unit l): July 13, 1972, 1308-1706 Hours .. 39 23. Jet-regime Study for 2.0-m Depth at Point Beach Power Plant (Unit l): July 13, 1972, 1308-1706 Hours.. .. 40 24. Jet-regime Study for 2.5-m Depth at Point Beach Power Plant (Unit l): July 13, 1972, 1308-1706 Hours .. 41 25. Jet-regime Study for 3.0-m Depth at Point Beach Power Plant (Unit l): July 13, 1 972, 1308-1706 Hours ............. 42 26. Jet-regime Study for 0.5-m Depth at Point Beach Power Plant (Unit l): September 9, 1972, 1045-1420 Hours ......... 43 27. Jet-regime Study for 1.0-m Depth at Point Beach Power Plant (Unit l): September 9, 1972, 1045-1420 Hours ......... 44 28. Jet-regime Study for 1.5-m Depth at Point Beach Power Plant (Unit l): September 9, 1972, 1045-1420 Hours . .. 45 29. Jet-regime Study for 2.0-m Depth at Point Beach Power Plant (Unit l): September 9, 1972, 1045-1420 Hours .. 46 30. Jet-regime Study for 2.5-m Depth at Point Beach Power Plant (Unit l): September 9, 1972, 1045-1420 Hours ......... 47 31. Jet-regime Study for 3.0-m Depth at Point Beach Power Plant (Unit l): September 9, 1972, 1045-1420 Hours ......... 48 32. Jet-regime Study for 0.5-m Depth at Palisades Power Plant: June 14, 1972, 1000-1348 Hours ....................... 49 33. Jet-regime Study for 1.0-m Depth at Palisades Power Plant: June 14, 1972, 1000-1348 Hours ....................... 50 34. Jet-regime Study for 1.5-m Depth at Palisades Power Plant: June 14, 1972, 1000-1348 Hours... 51 35. Jet-regime Study for 2.0-m Depth at Palisades Power Plant: June 14, 1972, 1000-1348 Hours.. 52 36. Jet-regime Study for 2.5-m Depth at Palisades Power Plant: June 14, 1972, 1000-1348 Hours .. 53 37. Jet-regime Study for 0.5-m Depth at Palisades Power Plant: July 19, 1972, 0922-1414 Hours.... . 54 7 LIST OF FIGURES No. Title Page 38. Jet-regime Study for 1.0 -m Depth at Palisades Power Plant: July 19, 1972, 0922-1414 Hours ... 55 39. Jet-regime Study for 1.5-m Depth at Palisades Power Plant: July 19, 1972, 0922-1414 Hours ....................... 56 40. Jet-regime Study for 2.0-m Depth at Palisades Power Plant: July 19, 1972, 0922-1414 Hours ....................... 57 41. Jet-regime Study for 2.5-m Depth at Palisades Power Plant: July 19, 1972, 0922-1414 Hours ....................... 58 42. Jet-regime Study for 3.0-m Depth at Palisades Power Plant: July 19, 1972, 0922-1414 Hours ....................... 59 43. Jet-regime Study for 0.5-m Depth at Palisades Power Plant: October 10, 1972, 1025-1550 Hours ..................... 60 44. Jet-regime Study for 1.0-m Depth at Palisades Power Plant: October 10, 1972, 1025-1550 Hours ..................... 61 45. Jet-regime Study for 1.5-m Depth at Palisades Power Plant: October 10, 1972, 1025-1550 Hours ..................... 62 46. Jet-regime Study for 2.0-m Depth at Palisades Power Plant: October 10, 1972, 1025-1550 Hours ..................... 63 47. Jet-regime Study for 2.5-m Depth at Palisades Power Plant: October 10, 1972, 1025-1550 Hours ..................... 64 48. Jet-regime Study for 3.0-m Depth at Palisades Power Plant: October 10, 1972, 1025 -1550 Hours ..................... 65 49. Centerline Excess-temperature and -velocity Decays Resulting from Fits to Point Beach Jet Data at 0.5-m Depth .... 70 50. Half-widths of Temperature and Velocity Distributions Resulting from Fits to Point Beach Jet Data at 0.5-m Depth .... 70 51. Centerline Temperature Excess and Velocity Excess as a Function of Depth Resulting from Fits to Point Beach Jet Data. . . 71 52. Half-widths of Temperature and Velocity Distributions as a Function of Depth at s = 150 m, Resulting from Fits to Point Beach Jet Data .. 71 53. Geometrical Characteristics of Jet Assumed in Stolzenbach- Harleman Model.. 79 54. Velocity and Temperature Characteristics of Jet Assumed in Stolzenbach-Harleman Model ......................... 81 8 LIST OF FIGURES No. Title Page 55. Definition Sketch for Coordinate System and Jet Region Assumed in Prych Model.. 84 56. Centerline Trajectories Resulting from the Fitting Procedure and Model Calculations for Point Beach: May 18, 1972. ....... 90 57. Centerline Trajectories Resulting from the Fitting Procedure and Model Calculations for Point Beach: May 23 s 1972. 90 58. Centerline Trajectories Resulting from the Fitting Procedure and Model Calculations for Point Beach: July 13, 1972. ....... 91 59. Centerline Trajectories Resulting from the Fitting Procedure and Model Calculations for Point Beach: September 9, 1972 .... 91 60. Centerline Trajectories Resulting from the Fitting Procedure and Model Calculations for Palisades: October 10, 1972. ...... 92 61. Idealized Surface Profile of Excess Temperature ©/ 0 O , and Velocity u/u 0 across Bent Jet near Orifice ................ 92 62. Bottom Depth at Palisades Outfall for Three Dates of Jet Studies .... 94 63. Centerline Temperature Excess and Velocity Decays Resulting from the Fitting Procedure and Model Calculations for Point Beach: May 18, 1972 ... 96 64. Centerline Temperature Excess and Velocity Decays Resulting from the Fitting Procedure and Model Calculations for Point Beach: May 23, 1972 .......................... 96 65. Centerline Temperature Excess and Velocity Decays Resulting from the Fitting Procedure and Model Calculations for Point Beach: July 13, 1972 .......................... 97 66 . Centerline Temperature Excess and Velocity Decays Resulting from the Fitting Procedure and Model Calculations for Point Beach: September 9, 1972. .. 97 67. Centerline Temperature Excess and Velocity Decays Resulting from the Fitting Procedure and Model Calculations for Palisades: October 10, 1972 ....... 98 68 . Half-widths of Temperature and Velocity Distributions Resulting from the Fitting Procedure and Model Calculations for Point Beach: May 18, 1972.... 99 69. Half-widths of Temperature and Velocity Distributions Resulting from the Fitting Procedure and Model Calculations for Point Beach: May 23, 1972..... 100 9 LIST OF FIGURES No. Title Page 70. Half-widths of Temperature and Velocity Distributions Resulting from the Fitting Procedure and Model Calculations for Point Beach: July 13, 1972. 100 71. Half-widths of Temperature and Velocity Distributions Resulting from the Fitting Procedure and Model Calculations for Point Beach: September 9, 1972 . 101 72. Half-widths of Temperature and Velocity Distributions Resulting from the Fitting Procedure and Model Calculations for Palisades: October 10, 1972. 101 73. Half-depths of Temperature and Velocity Distributions Resulting from Model Calculations for Point Beach: May 18, 1972. 104 74. Half-depths of Temperature and Velocity Distributions Resulting from Model Calculations for Point Beach: May 23, 1972. 104 75. Half-depths of Temperature and Velocity Distributions Resulting fropa Model Calculations for Point Beach: July 13, 19 72. 105 76. Half-depths of Temperature and Velocity Distributions Resulting from Model Calculations for Point Beach: September 9, 1972 . 105 77. Half-depths of Temperature and Velocity Distributions Resulting from Model Calculations for Palisades: October 10, 1972 . 112 78. Isotherm Areas Resulting from the Fitting Procedure and Model Calculations for Point Beach: May 18, 1972 . 113 79. Isotherm Areas Resulting from the Fitting Procedure and Model Calculations for Point Beach: May 23, 1972 . 113 80. Isotherm Areas Resulting from the Fitting Procedure and Model Calculations for Point Beach: July 13, 1972 . 114 81. Isotherm Areas Resulting from the Fitting Procedure and Model Calculations for Point Beach: September 9, 1972 . 1 14 82. Isotherm Areas Resulting from the Fitting Procedure and Model Calculations for Palisades: October 10, 1972 . 115 83. Idealized Decay of Temperature Excess and Velocity Excess with Depth. 118 10 LIST OF FIGURES No. Title Page 84. Centerline Temperature Excess and Velocity Excess as a Function of Depth at 150 m from Outfall Resulting from the Fitting Procedure and Model Calculations for Point Beach: May 18, 1972. 1 17 85. Centerline Temperature Excess and Velocity Excess as a Function of Depth at 150 m from Outfall Resulting from the Fitting Procedure and Model Calculations for Point Beach: May 23, 1 972. 117 86 . Centerline Temperature Excess and Velocity Excess as a Function of Depth at 150 m from Outfall Resulting from the Fitting Procedure and Model Calculations for Point Beach: July 13, 1972. 1 18 87. Centerline Temperature Excess and Velocity Excess as a Function of Depth at 150 m from Outfall Resulting from the Fitting Procedure and Model Calculations for Point Beach: September 9, 1972 . 1 18 88 . Centerline Temperature Excess and Velocity Excess as a Function of Depth at 150 m from Outfall Resulting from the Fitting Procedure and Model Calculations for Palisades: October 10, 1972 . 1 19 89. Half-widths of Temperature and Velocity Distributions as a Function of Depth at 150 m from Outfall Resulting from the Fitting Procedure and Model Calculations for Point Beach: May 18, 1972. 120 90. Half-widths of Temperature and Velocity Distributions as a Function of Depth at 150 m from Outfall Resulting from the Fitting Procedure and Model Calculations for Point Beach: May 23, 1972. 120 91. Half-widths of Temperature and Velocity Distributions as a Function of Depth at 150 m from Outfall Resulting from the Fitting Procedure and Model Calculations for Point Beach: July 13, 1972. 121 92. Half-widths of Temperature and Velocity Distributions as a Function of Depth at 150 m from Outfall Resulting from the Fitting Procedure and Model Calculations for Point Beach: September 9, 1972 . 121 93. Half-widths of Temperature and Velocity Distributions as a Function of Depth at 150 m from Outfall Resulting from the Fitting Procedure and Model Calculations for Palisades: October 10, 1972 . 122 11 LIST OF FIGURES No. Title Page 94. Station Locations for Jet-regime Study: November 3, 1971, 1245-1605 Hours. 133 95. Jet-regime Study for 2-ft Depth at Point Beach Power Plant (Unit l): November 3, 1971, 1245-1605 Hours. 134 96. Jet-regime Study for 4-ft Depth at Point Beach Power Plant (Unit l): November 3, 1971, 1245-1605 Hours. 135 97. Jet-regime Study for 6 -ft Depth at Point Beach Power Plant (Unit l): November 3, 1971, 1245-1605 Hours. 136 12 LIST OF TABLES No. Title Page I. Instrument Accuracy. 18 II. Summary of Characteristics of Jet Models. 75 III. Summary of Characteristics of Complete-field Models. 76 IV. Data and Parameters Used for Model Calculations for Point Beach and Palisades. 89 V. Determination of Temperature and Velocity Half-depths at Each Station Location from Point Beach Data of May 18, 1972 . . 107 VI. Determination of Temperature and Velocity Half-depths at Each Station Location from Point Beach Data of May 23, 1972 . . 108 VII. Determination of Temperature and Velocity Half-depths at Each Station Location from Point Beach Data of July 13, 1972 . . 109 VIII. Determination of Temperature and Velocity Half-depths at Each Station Location from Point Beach Data of September 9, 1972 . 110 IX. Determination of Temperature and Velocity Half-depths at Each Station Location from Palisades Data of October 10, 1972 . Ill TEMPERATURE AND VELOCITY MEASUREMENTS AND PREDICTIVE MODEL COMPARISONS IN THE NEAR-FIELD REGION OF SURFACE THERMAL DISCHARGES by R. A. Paddock, A. J. Policastro, A. A. Frigo, D. E. Frye, and J. V. Tokar ABSTRACT Simultaneous temperature and velocity measurements were made in the near-field regionof the surface thermal dis¬ charge at the Point Beach Unit 1 and Palisades Nuclear Power Plants on Lake Michigan. Data collected include measurements of temperature and velocity at the 0.5-, 1.0-, 1.5-, 2.0-, 2.5-, and 3.0-m depths, along with measurements of ambient lake and meteorological conditions. Bottom depth was also measured at various locations. Four such surveys were made at the Point Beach plant, three at the Palisades plant. To examine the jet features from the above surveys and facilitate a comparison with analytical model predictions, a computer program was written to smooth the data, extracting such jet characteristics as trajectory, centerline temperature decay and temperature half-widths, centerline velocity decay and velocity half-widths, temperature and velocity half-depths, and isotherm areas. Four near-field analytical models oftenused in environ¬ mental impact evaluations of power-plant surface discharges are compared to the jet characteristics determined from the smoothed jet data. The Pritchard model compares rather well with these limited data and is often conservative when model-data discrepancies exist. The Stolzenbach-Ha rleman and Prych models predict too rapid a temperature and velocity decay ac¬ companying too great a lateral spread. The Motz-Benedict model is too sensitive to an entrainment coefficient E with lit¬ tle consistent data available for its determination for accurate prediction. Recommendations for future research, encompassing the field-data acquisition, the smoothing procedure, and the presently available models are included. I. INTRODUCTION Under the auspices of the U.S. Atomic Energy Commission, the Argonne Center for Environmental Studies has been studying the physical effects of heated condenser discharges from steam-electric power plants on the Great Lakes since FY 1970. Appendix A lists the reports published under this program to the present. Two of the primary objectives of this program have been and continue to be the acquisition of reasonably complete prototype thermal-plume field data and the verification of analytical predictive plume models. To this end, field data in the jet regime of two nuclear power plants on Lake Michigan have been collected and compared to models, with the results reported herein. The jet regime (the near field) is that region of the discharge in which the heated effluent enters the receiving body of water possessing a velocity and temperature disparity with respect to the receiving body. Thus, as a heated effluent enters an ambient environment from a particular plant outfall, viscous shear between the effluent and the ambient fluid creates turbulence in the contact region. This turbulence works its way both inward toward the jet centerline and outward toward the ambient fluid, with a resultant net out¬ ward flux of momentum and heat away from the jet axis. Within this regime of the discharge, it is the mechanical mixing action induced by the kinetic energy of the discharge itself that dominates the eddy transport mechanisms. At some distance from the outfall, the kinetic energy of the discharge will be sufficiently dissipated to allow the natural turbulence existing within the am¬ bient receiving water, together with buoyant forces, to dictate plume disper¬ sion. It is nominally assumed that the effluent is no longer jetlike in character when this situation is reached. From a regulatory point of view, the jet regime is of particular in¬ terest. It is often within this region that outfall architects must design their discharges to meet thermal wate r-quality criteria that limit the temperature rise in the thermal plume beyond a prescribed distance from the point of discharge. This is commonly referred to as a mixing-zone limitation. Some states have adopted very restrictive mixing-zone criteria; others have none at all. Therefore, depending on the nature of the receiving body, the size of plant, and a multitude of different factors including the thermal criteria, each plant outfall design is more or less tailored to the particular siting situation. On the Great Lakes, the predominant outfall design happens to be a shoreline, open, rectangular discharge canal. Several more recent plant designs have used more sophisticated offshore multiorifice submerged discharges, called diffuse rs. The literature contains numerous models that attempt to predict the behavior of shoreline canal discharges. Some of these models are qualitative in nature; others profess to be quantitative as well. One thing all these models have in common is that none has been generally verified with prototype field data. To compound the problem, a survey of the literature reveals surprisingly little actual jet-regime field data with which models can be tested. Since there 15 is such a paucity of data in the jet regime, a field program was developed by the Center for Environmental Studies specifically to acquire prototype data near canal-type discharges. This program has been partially described in Refs. 21 and 25 of Appendix A. A description of experimental methods and detailed information concerning the results of seven jet studies obtained during 1972 are presented herein. Since it would have been difficult to compare the field data directly to results obtained from analytical models, a data-smoothing technique was de¬ veloped to help in this endeavor. The smoothing method was primarily devel¬ oped to glean as much information from the experimental data as possible, considering the limited number of data points collected using the present field technique. A complete description of the smoothing method appears in Sec. V. While one should recognize that the smoothing method has some obvious limi¬ tations and biases, it nevertheless has worked out quite well for the purposes for which it was designed. Lastly, the results of the smoothing procedure are compared to four ana¬ lytical models that have been used, in some cases quite extensively, for pre¬ dictive purposes. These comparisons and a discussion of them appear in Sec. VII. Note that the success or apparent lack of success displayed by a particular model should not, at this point, be considered as a total test of the model. Many more data comparisons under different outfall situations must be made before any model can be realistically evaluated. In summary, this report brings together details concerning the acqui¬ sition, smoothing, and model analysis of a relatively unique set of jet-regime plume field data. We hope this report will stimulate more interest than has been shown in the literature in attempting to validate existing predictive models. In our opinion, too many predictive models existing in the literature have not been adequately tested. Much reliable field data is just now becom¬ ing available, and it should be the immediate goal of those interested in ap¬ plying predictive models to test these models with actual field data. Only in this way can we hope for a positive improvement in the existing state of the art. II. EXPERIMENTAL TECHNIQUE A two- or three-point mooring -|-m (18 - ft) cathedral-hull fiberglass Fig. 1. Boat with Current Meter Used in Jet-regime Studies system was used to hold Argonne's boat, the R. V. Aha, steady while ob¬ taining simultaneous temperature and velocity measurements in the near¬ field region of the thermal plume (see Fig. l). Anchors were located on either side of the plume, and for re¬ gions very near the outfall, a third line was sometimes attached to the outfall itself. Transects across the plume centerline were then made at various distances from the outfall. The posi¬ tion of the boat was held relatively constant at the various measuring stations, and the position of each station was determined by using a Motorola Mini-Ranger range position¬ ing system (Fig. 2). This positioning system consists of two shore-based transponders with a receiver-transmitter unit and range console on board the boat that displays the range information Fig. 2. Motorola Mini-Ranger Range Positioning System 17 from each transponder. The boat's position can then be found by trilateration. The Mini-Ranger is powered by 110 V ac (available from a 24-V dc high- efficiency Flitetronics PC 16 Air¬ craft Static Inverter). The usable range of the system with omnidirec¬ tional antennas is about 16 km. A Bendix Q-1 5 geomagnetic ducted current meter (Fig. 3), with an attached YSI thermistor, was used to measure the velocity and tempera¬ ture of the discharge waters. The Q-1 5 has a five-bladed impeller that rotates in both directions and is en¬ closed in a duct. The ducted assembly is aligned with the current by a vane of adjustable length. The effects of wave and boat motion are nulled out by electronic averaging (over about 2 5 sec) of the number of turns of the impeller and by the presence of the duct. Current speed and direction are displayed on deck by means of a readout unit, Bendix Model No. S-232, which is connected to the current meter through a four-conductor cable. The current meter is powered by six 9- V batteries. The meter was lowered over the side of the boat and suspended at 0.5-m intervals to a depth of 3.0 m or to the bottom. The first time the experiment was being conducted, it was discovered that time variations in velocity and temperature occur. Thus, in order to obtain average values of velocity and temperature along with any variation, strip chart recorders were connected to the current- meter and thermistor outputs. Fig. 3. Bendix Q-15 Geomagnetic Ducted Cur¬ rent Meter. ANL Neg. No. 190-568-11. Note at this point that a variety of factors inherent in making measure¬ ments in the jet regime may cause uncertainties in the data. These problems must be understood if proper use is to be made of the data. An important aspect of the experimental uncertainty is the short-term variations in the velocity and temperature of the discharge jet (see Ref. 30). The cause of these variations is not clear at present, but they may be due to eddies created at the interface between the jet and the ambient water, to surging which is apparent in the discharge canal, or to other factors. These fluctua¬ tions appear to have periods ranging from a few seconds to a few minutes. 18 Since point-by-point measurements in the jet were typically made over a period of 1-2 min, it is apparent that an unrepresentative value might be ob¬ tained at a given point. The scale of the short-term temperature fluctuations is on the order of several Centigrade degrees or less; the velocity variations are on the order of 50% of the mean value or less. These fluctuations were not present at all locations. A more typical value for the uncertainty in the temperature measurement is ±0.5C°; a typical value for the uncertainty in the current speed is ±20%. Another source of uncertainty, in terms of data analysis, is the ambi¬ guity attached to the values of ambient current and temperature. These num¬ bers, necessarily assumed to be constants throughout the measurement (which lasted from 3 to 7 hr), vary not only in time but in space as well. Ambient- current measurements were typically made at a single location (at several depths) before and after the jet-regime measurements. Here again, current fluctuations in time and position may lead, for a variety of reasons, to an un¬ representative value for ambient-cur rent speed. (Direction of the current is thought to be more definite.) Ambient-cur rent speeds as reported may have an uncertainty of 20- 50%; lower current speeds are the most uncertain. On some occasions, ambient-temperature measurements are as difficult to pin down as ambient-cur rent speed and are somewhat more important in terms of the analysis to be described. We chose the ambient temperature to be the water temperature (at the appropriate depth), which appeared not to be in¬ fluenced by the discharge water, yet was in the vicinity of the discharge. Un¬ fortunately, on days when upwelling, downwelling, shoreline heating, or other disturbing phenomena occurred, the reported values of ambient water tempera¬ ture may have an uncertainty of as much as 1-2C°. In the face of the previously discussed uncertainties in the data, in¬ strumentation accuracy may not be very important, but for completeness, Table I lists the instrument specifications. Of special interest in terms of velocity measurements is the fact that, while a ducted current meter is used to null out disturbing vertical motion, shielding of the impeller occurs if the duct is not aligned with the flow. The importance of this remains unclear, but because the meter continuously averages the speed over a 25-sec period, any shielding would result in lower values for current speed. TABLE I. Instrument Accuracy Instrument Sensor Accuracy Threshold Range Time Constant Resolution Remarks Bendix 0-15 Current Meter Speed: impeller ±4% of full scale 3 cm/sec 0-1.0 knot, low scale 0-5.0 knots, high scale 25 sec; low scale 2.5 sec: high scale 1 cm/sec; low scale 5 cm/sec; high scale Direction; compass with vane ±12° - 0-360° 5° Vane has adjustable length. 0.3-3.0 m Temperature Recorder 9 Thermistor +0.5C° 0-30°C -2.5 sec 0.2C° Consisting of a Rustrak Model No. 2133 temperature recorder and YSI No. 409 thermistor probe Temperature Recorder^ Thermistor a0.2C° - 0-50°C -2.5 sec 0.1C° Consisting of YSI No. 709 probe and digital readout built at Argonne Motorola Mini-Ranger +3 m 0.1-35 km 1 m Accuracy applies to each range meas¬ urement. System accuracy varies with position of transponders relative to boat For most of these measurements. +3 m would apply. a Used in temperature measurements up to and including July 19, 1972. b Used in temperature measurements after July 19, 1972. 19 III. DESCRIPTIONS OF POWER PLANTS The jet regimes of the thermal plumes were surveyed at two power plants located on Lake Michigan. The power plants studied were the Point Beach Nuclear Power Plant, operated by the Wisconsin Electric Power Company and the Wisconsin Michigan Power Company, and the Palisades Nuclear Power Plant, operated by Consumers Power Company. Brief descriptions of these plants follow. A. Point Beach Nuclear Power Plant The Point Beach Nuclear Power Plant is in the town of Two Creeks, Wisconsin, on the western shore of Lake Michigan. (Figure 4 is an aerial view of the plant.) The plant is a two-unit steam-generating station. The nuclear reactors for each unit are pressurized light-water-moderated and -cooled systems. Each unit has a gross capacity of 523 MWe and a net ca¬ pacity of 505 MWe. The water intake for the plant consists of a circular crib 533 m from the shore. Cooling water for the operation of the power plant is drawn from Lake Michigan and passes through the cooling condensers at a maximum rate of 25.1 m 3 /sec for full-power operation of each individual unit of the plant. The water is returned to the lake about 50 m offshore through two 10.7-m-wide discharge flumes (one flume per unit). Water depth in the flumes is about 4.2 m. During most of the field year, the second unit was not operational. Late in the summer, however, the second unit was operating at about 12% power and 50% of its rated discharge flow. B. Palisades Nuclear Power Plant The Palisades Nuclear Power Plant is near the city of South Haven, Michigan, on the eastern shore of Lake Michigan. (Figure 5 is an aerial view of the plant.) This plant uses a pressurized-water reactor to produce a maxi¬ mum gross output of 714 MWe. During the 1972 field year, the plant was oper¬ ating at a net generating capacity of about 420 MWe. The cooling water is taken from Lake Michigan through an intake crib located 6.1 m below the lake's sur¬ face, 1.8 m from the lake bottom, and 1000 m from the shoreline. For the Palisades plant, as presently constructed, the cooling water passes through the cooling condenser at a maximum flow rate of 25.6 m 3 /sec and is returned to Lake Michigan, via a 32.9-m-long discharge canal at the shoreline. The canal is 11.3 m wide at the shoreline outlet and diverges to a width of 28.3 m at the point of discharge. At this point, the water has an average depth of about 2.1 m. 20 Fig. 4. Aerial View of Point Beach Nuclear Power Plant. ANL Neg. No. 190-499. 21 Fig. 5. Aerial View of Palisades Nuclear Power Plant 22 IV. RESULTS OF FIELD MEASUREMENTS During the 1972 field year, seven jet-regime studies were conducted at the two power plants described in Sec. III. Specifically, these studies were at the Point Beach Nuclear Power Plant Unit 1 on May 18, May 23, July 13, and September 9, 1972, and at the Palisades Nuclear Power Plant on June 14, July 19, and October 10, 1972. In addition, one survey was conducted late in the 1971 field year (November 3, 1971) as a preliminary feasibility study of the technique (see Appendix B). Data collected include measurements of velocity and temperature in the near-field region of the thermal plume at the 0.5-, 1.0-, 1.5-, 2.0-, 2.5-, and 3.0-m depths, along with measurements of ambient lake and meteorological conditions. Bottom depth was also measured at various locations. From the bottom-depth data, approximate depth contours were drawn near the outfalls and are shown in Figs. 6 and 7. The points indi¬ cate positions at which data were taken.* Results of the jet-regime measure¬ ments are shown in Figs. 8-48 for the dates indicated. The figures show station locations at which jet velocities and temperatures were measured. The velocity is represented vectorially at each station location. In addition, the current speed, current direction, and temperature at each station are listed in a table on each figure. Current direction is given in degrees as measured from magnetic north. Also listed on the figures are the ambient lake and meteorological data, as well as the plant operating data. Tempera¬ ture and velocity centerlines and widths are shown in most cases. The widths represent the lateral distance from the centerline at which the ap¬ propriate parameter has reached a value halfway between the centerline value and the ambient value. The mathematical fitting technique used to obtain the centerlines and widths is described in Sec. V. Centerlines and widths are not shown for any depths for the jet-regime studies conducted at the Palisades Plant on June 14 and July 19, 1972. Typically, the Palisades outfall produces a very wide jet, and the data on these dates did not lend themselves to the type of analysis necessary for determining centerlines and widths. ♦Dotted lines indicate estimated contours for which no data were available. 23 60s Fig. 6. Approximate Depth Contours near Point Beach Outfall. ANL Neg. No. 190-878. SHORE 24 Fig. 7. Approximate Depth Contours near Palisades Outfall. ANL Neg. No. 190-880 25 STATION NUMBER CURRENT SPEED (cm/sec) CURRENT DIRECTION (°) TEMPERATURE (°C) 1 0 - 11.0 2 0 - 11.2 3 NOT MEASURED 4 21.1 115 14.0 5 26.1 80 14.5 6 16.7 105 11.1 7 0 - 12.7 8 0 - 13.3 9 40.6 125 14.5 10 44.5 120 13.0 11 0 - 10.5 12 0 - 10.6 13 9.5 95 11.0 14 58.4 105 16.7 15 36.1 125 16.0 16 27.8 140 16.0 . 17 12.8 145 13.8 18 9.5 125 13.4 19 67.8 95 17.7 /(VELOCITY) ^ 5 / (TEMPERATURE) / / TEMPERATURE WIDTH VELOCITY WIDTH / PLANT & METEOROLOGICAL DATA PLANT LOAD: 495 MWe DISCHARGE FLOWRATE 24.7 m 3 /sec OUTFALL TEMPERATURE 17.7°C INTAKE TEMPERATURE 6.7«C AMBIENT WATER TEMPERATURE 9.2 • 9.6°C DRY BULB TEMPERATURE: 10.7 - 12.2°C RELATIVE HUMIDITY 75% WIND SPEED & DIRECTION 0 - 3.0 m/sec. 110° AMBIENT CURRENT SPEED & DIRECTION 0 LAKE SURFACE CONDITIONS CALM, 0 - 0.2 m WAVES SKY CONDITIONS: CLEAR 100 VELOCITY SCALE - cm/sec 100 150 DIMENSION SCALE • melers Fig. 8. Jet-regime Study for 0.5-m Depth at Point Beach Power Plant (Unit 1): May 18, 1972, 1115-1440 Hours. ANL Neg. No. 190-761 Rev. 1. 26 STATION NUMBER CURRENT SPEED (cir./sec) CURRENT DIRECTION (°) TEMPERATURE CC) 1 0 - 9.7 2 0 - 11.0 3 6.1 145 12.6 4 16l7 140 14.0 5 22.2 85 13.5 6 9.5 110 10.6 7 LAKE BOTTOM 8 0 - 13.1 9 36.1 110 14 4 10 41.7 no 13.9 11 0 - 9.7 12 0 - 8.5 13 8.3 no 10.3 14 47.3 95 16.0 15 30.6 100 14.5 16 22.2 115 14.7 17 12.2 135 13.6 18 0 - 13.3 19 65 2 95 17.7 -TEMPERATURE WIDTH - VELOCITY WIDTH PLANT & METEOROLOGICAL DATA PLANT LOAD. 495 MWe DISCHARGE FLOW RATE 24 7 ni 3 /sec OUTFALL TEMPERATURE !7.7°C NTAKE TEMPERATURE 6 7°C AMBIENT WATER TEMPERATURE 8 5°C DRY BULB TEMPERATURE 1C 7 - 12 2°C RELATIVE HUMIDITY 75% WIND SPEED & DIRECTION 0-3.0 m/sec 110° AMBIENT CURRENT SPEED & DIRECTION 0 LAKE SURFACE CONDITIONS CALM. 0 - 0.2 m WAVES SKY CONDITIONS CLEAR 100 200 VELOCITY SCALE -cm/sec 50 100 150 J DIMENSION SCALE meters Fig. 9. Jet-regime Study for l.O-m Depth at Point Beach Power Plant (Unit 1): May 18, 1972, 1115-1440 Hours. ANL Neg. No. 190-895. 27 STATION NUMBER CURRENT SPEED (cm/sec) CURRENT DIRECTION (°) TEMPERATURE (°C) 1 NOT MEASURED 2 8.9 10 10.4 3 NOT MEASURED 4 10.6 135 13.2 5 23.9 85 12.6 6 0 - 9.7 7 LAKE BOTTOM 8 0 - 12.1 9 33.4 115 15.0 10 29.5 100 13.4 11 NOT MEASURED 12 0 - 8.3 13 8.3 170 8.4 14 50.0 105 16.2 15 22.2 105 15.0 16 11.3 125 14 4 17 5.6 115 13.2 18 0 - 12.5 19 62 3 95 17.7 > - TEMPERATURE WIDTH — VELOCITY WIDTH PLANT & METEOROLOGICAL DATA PLANT LOAD. 495 MWe DISCHARGE FLOWRATE 24 7 m 3 /sec OUTFALL TEMPERATURE 17 7°C INTAKE TEMPERATURE 6 7°C AMBIENT WATER - TEMPERATURE 8 3°C DRY BULB TEMPERATURE 10.7 - 12.2°C RELATIVE HUMIDITY 75% UNO SPEEO & DIRECTION 0 -3 0 m/sec. 110° AMBIENT CURRENT SPEED & DIRECTION 0 LAKE SURFACE CONDITIONS CALM, 0 - 0.2 m WAVES SKY CONDITIONS: CLEAR 100 200 J VELOCITY SCALE • cm/sec 100 L 150 DIMENSION SCALE meters Fig. 10. Jet-regime Study for 1.5-m Depth at Point Beach Power Plant (Unit 1): May 18, 1972, 1115-1440 Hours. ANL Neg. No. 190-893. 28 SMTION NUMBER CURRENT SPEED icn/sec CURRENT DIRECTION TEMPERATURE (°Ci 1 0 - 99 2 8.3 15 8.3 0 - 10.8 4 6.7 135 10 4 5 19.5 80 12.5 6 0 - 9.2 7 LAKE BOTTOM 8 LAKE BOTTOM 9 21 7 90 14.5 10 25.0 125 11.5 11 0 - 8.3 12 LAKE BOTTOM 13 LAKE BOTTOM 14 50 0 105 15.0 15 278 110 14.2 16 10 0 110 13.3 17 0 - 124 18 0 - 11 9 19 58 9 95 177 - TEMPERATURE WIDTH - VELOCITY WIDTH PLANT 8 METEOROLOGICAL OAT4 PLANT LOAD. 495 MWe DISCHARGE FLOW RATE 24.7 m 3 /sec OUTFALL TEMPERATURE !7.7»C INTAKE TEMPERATURE 6 7'C AMBIENT WATER TEMPERATURE 7.7 8.3'C ORY 3ULB TEMPERATURE' 1C7-12.2'C RELATIVE HUM'ICITY 75V WIND SPEED 8 DIRECTION 0 3 0 m sec. 110' AMBIENT CURRENT SPEED 8 DIRECTION 0 LAKE SURFACE CONDITIONS CALM. 0 0.2 m WAVES SKY CONDITIONS CLEAR 0 100 200 VELOCITY SCALE cm/sec Si’ 100 150 DIMENSION SCALE meteis Fig. 11. Jet-regime Study for 2.0-m Depth at Point Beach Power Plant (Unit 1): May 18. 1972, 1115-1440 Hours. ANL Neg. No. 190-899. 29 STATION NUMBER CURRENT SPEED (cm/sec) CURRENT DIRECTION C) TEMPERATURE CC) 1 NOT MEASURED 2 7.8 35 7.8 3 0 - 9.0 4 0 - 12.0 5 15.6 80 11.1 6 0 8.8 7 LAKE BOTTOM 8 LAKE BOTTOM 9 16.7 95 13.2 10 17.8 130 10.0 11 LAKE BOTTOM 12 LAKE BOTTOM 13 LAKE BOTTOM 14 LAKE BOTTOM 15 LAKE BOTTOM 16 LAKE BOTTOM 17 67 « 12.8 18 LAKE BOTTOM 19 556 95 ,7, 2 - TEMPERATURE WIDTH - VELOCITY WIDTH PLANT & METEOROLOGICAL DATA PLANT LOAD 495 MWe DISCHARGE FLOW RATE 24 7 m 3 /sec OUTFALL TEMPERATURE 17 7°C INTAKE TEMPERATURE 6.7°C AMBIENT WATER TEMPERATURE 7.6 - 7.8°C DRY 3ULB TEMPERATURE 10 7 12 ?°C RELATIVE HUMIDITY 75% ' WIND SPEED & DIRECTION 0 • 3.0 m/sec. 110°C AMBIENT CURRENT SPEED & DIRECTION 0 LAKE SURFACE CONDITIONS CALM, 0 - 0.2 m WA\£ SKY CONDITIONS: CLEAR 0 100 200 VELOCITY SCALE cm/sec C 50 100 150 DIMENSION SCALE meters Fig. 12. Jet-regime Study for 2.5-m Depth at Point Beach Power Plant (Unit 1): May 18, 1972, 1115-1440 Hours. ANL Neg. No, 190-898. 30 STATION NUMBER CURRENT SPEED (cm/sec) CURRENT DIRECTION (°) TEMPERATURE CC) 1 0 - 8.0 2 LAKE BOTTOM 3 NOT MEASURED 4 NOT MEASURED 5 NOT MEASURED 6 NOT MEASURED 7 LAKE BOTTOM 8 LAKE BOTTOM 9 LAKE BOTTOM 10 LAKE BOTTOM 11 LAKE BOTTOM 12 LAKE BOTTOM 13 LAKE BOTTOM 14 LAKE BOTTOM 15 LAKE BOTTOM 16 LAKE BOTTOM 17 LAKE BOTTOM 18 LAKE BOTT OM 1) 518 | 95 | 17 7 PLANT & METEOROLOGICAL DATA 12 1*3 15 16/ PLANT LOAD. 495 MWe DISCHARGE FLOW RATE 24 7 ni 3 /sec OUTFALL TEMPERATURE !7.7*C INTAKE TEMPERATURE 6.7°C AMBIENT WATER TEMPERATURE 7.5 - 7 7°C DRY 3ULB TEMPERATURE 1G.7 - I2.2°C RELATIVE HUMIDITY 75% 100 150 DIMENSION SCALE meters Fig. 13. Jet-regime Study for 3.0-m Depth at Point Beach Power Plant (Unit 1): May 18, 1972, 1115-1440 Hours. ANL Neg. No. 190-889. 31 STATION NUMBER CURRENT SPEED (cm sec) CURRENT DIRECTION (°) TEMPERATURE (°C) 1 7.2 0 14 9 2 23 3 140 188 3 69.5 110 20.8 4 75.1 110 21.1 5* 83 4 110 20.9 6 * 52.8 no 20 7 7 12.8 70 16.5 8 9.5 80 194 9 19.5 90 15.6 10 66 7 90 20 7 11 55.6 90 19 8 12 25.0 130 17.4 13 0 - 15.6 14 40.6 100 19.8 15 50.0 80 19.3 16 44 5 75 20.1 17 23.9 55 17.5 18 5.0 315 14.5 19 5.6 120 16.7 20 23 4 120 18 6 21 36.1 80 19.6 22 20.6 90 16.3 23 in 75 166 24 0 - 14.3 25 18.9 75 16.6 26 19.5 90 17.3 27 21.1 no 18.3 28 2.8 160 166 29 7.8 200 16.7 •VELOCITY VECTOR NCT SHOWN £ (VELOCITY) { (TEMPERATURE) PLANT & METEOROLOGICAL DATA PLANT LOAO. 497 MWe DISCHARGE FLOW RATE 25.1 m 3 sec OUTFALL TEMPERATURE 21 6°C INTAKE TEMPERATURE: 11 1°C AMBIENT WATER TEMPERATURE 14 3°C DRY BULB TEMPERATURE 14 5°C RELATIVE HUMIDITY. 83 # * WIND SPEED & DIRECTION 0-15m/sec, AMBIENT CURRENT SPEED & DIRECTION LAKE SURFACE CONDITIONS CALM SKY CONDITIONS CLEAR 100 JL 200 VELOCITY SCALE cm sec 50 L 100 150 J DIMENSION SCALE melees Fig. 14. Jet-regime Study for 0.5-m Depth at Point Beach Power Plant (Unit 1): May 23, 1972, 0945-1700 Hours. ANL Neg. No. 190-760 Rev. 1. 32 (TEMPERATURE) STATION NUMBER CURRENT SPEEO (cm sec) CURRENT DIRECTION (°) TEMPERATURE (°C) 1 0 - 148 2 26.1 140 188 3 72.3 125 20.8 4 66.7 110 21.0 5 66.7 110 209 6 48.9 90 20.3 7 7.2 100 13.8 8 5.6 70 19.6 9 12.2 80 14 1 10 69.5 90 20 6 11 38 9 110 19.6 12 12.2 100 16.5 13 5.6 20 15.6 14 34.5 90 18.2 15 41.7 80 19.8 16 41.7 85 19.2 17 19.5 50 17 0 18 8.3 320 14.0 19 0 - 16.1 20 24.5 100 18 6 21 36.1 90 19.2 22 15.6 80 14.8 23 0 - 15.0 24 0 - 12.6 25 11.7 70 15.3 26 17.8 90 17.3 27 139 120 16.8 28 0 - 15.7 29 6.7 185 15.8 -TEMPERATURE WIDTH - VELOCITY WIDTH PLANT & METEOROLOGICAL DATA PLANT LOAD. 497 MWe DISCHARGE FLOWRATE 25.1 m 3 sec OUTFALL TEMPERATURE 21 6°C INTAKE TEMPERATURE 11 1°C AMBIENT WATER TEMPERATURE 12 6°C DRY BULB TEMPERATURE 14 5°C RELATIVE HUMIDITY: 83% WIND SPEEO& DIRECTION 0 - 15 m/sec, 120° AMBIENT CURRENT SPEED & DIRECTION 0 LAKE SURFACE CONDITIONS CALM SKY CONDITIONS CLEAR 100 i VELOCITY SCALE cm sec 100 DIMENSION SCALE meters Fig. 15. Jet-regime Study for l.O-m Depth at Point Beach Power Plant (Unit 1): May 23. 1972, 0945-1700 Hours. ANL Neg. No. 190-891. 33 / / STATION NUMBER CURRENT SPEED (cm sec) CURRENT DIRECTION (°) TEMPERATURE CC) 1 0 - 14.7 2 18.9 110 17.2 3 77 8 135 20.8 4 61.2 100 21.1 5 61.2 100 21.0 6 42.8 100 19.8 7 9.5 150 12.7 8 7.2 75 18.8 9 9.5 220 14.3 10 47.3 90 19.7 11 23.9 70 17.8 12 5.6 90 15.9 13 10.0 350 14.7 14 29.5 70 18.7 15 50.0 95 18.6 16 434 90 18.7 17 5.6 75 14 9 18 5.6 305 13.7 19 0 - 15.0 20 20.6 100 17.8 21 30.0 90 18.8 22 6.7 115 13.8 23 0 - 13.8 24 0 13.5 25 9.5 80 14.7 26 12.2 80 168 27 9.5 120 15.8 28 0 - 14.9 29 0 - 15.1 / - TEMPERATURE WIDTH - VELOCITY WIDTH PLANT & METEOROLOGICAL DATA PLANT LOAT), 497 MWe DISCHARGE FLOW RATE 25.1 m 3 sec OUTFALL TEMPERATURE 21.6°C INTAKE TEMPERATURE 11 1°C AMBIENT WATER TEMPERATURE 12.CC DRY BULB TEMPERATURE 14 5°C RELATIVE HUMIDITY. 83°« WIND SPEED & DIRECTION 0 15 m/sec. 120° AMBIENT CURRENT SPEED & DIRECTION 0 LAKE SURFACE CONDITIONS CALM SKY CONDITIONS CLEAR 0 100 200 VELOCITY SCALE cm sec . 0 50 100 150 DIMENSION SCALE meters Fig. 16. Jet-regime Study for 1.5-m Depth at Point Beach Power Plant (Unit 1): May 23. 1972, 0945-1700 Hours. ANL Neg. No. 190-906. 34 STATION NUMBER CURRENT SPEED (cm/sec' CURRENT DIRECTION (•' TEMPERATURE CO 1 LAKE BOTTOM 2 12.2 90 17 1 3 61 2 no 209 4 61.2 100 21.1 5 69.5 100 21.0 6 350 no 184 7 8.9 150 125 8 13.9 no 16.1 9 LAKE BOTTOM 10 400 85 19.5 11 31.7 100 19.3 12 9.5 30 15.3 13 11.1 340 14.4 14 20.6 60 173 15 27.8 105 19.0 16 356 90 18.7 17 0 - 14.3 18 2.8 315 13.7 19 5.0 340 140 20 17.8 85 176 21 26 7 90 18 1 22 2.8 160 13.3 23 0 - 12.8 24 0 - 11 6 25 0 - 14 1 26 6.7 70 15.1 27 0 - 14.7 28 0 - 12.8 29 0 - 13 3 / (VELOCITY) /(TEMPERATURE) . /9 -TEMPERATURE WIDTH - VELOCITY WIOTH PLANT & METEOROLOGICAL DATA PLANT LOAD. 497 MWe DISCHARGE FLOW RATE: 25.1 m 3 sec OUTFALL TEMPERATURE 216°C INTAKE TEMPERATURE 11 1°C AMBIENT WATER TEMPERATURE 11.6«»C DRY BULB TEMPERATURE 14.5°C RELATIVE HUMIDITY 83 0 « WIND SPEED & DIRECTION 0 - 1.5 m/sec; 120° AMBIENT CURRENT SPEED & DIRECTION 0 LAKE SURFACE CONDITIONS: CALM SKY CONDITIONS CLEAR 100 200 VELOCITY SCALE - cm sec 0 50 100 150 DIMENSION SCALE meters Fig. 17. Jet-regime Study for 2.0-m Depth at Point Beach Power Plant (Unit 1): May 23, 1972, 0945-1700 Hours. ANL Neg. No. 190-894. 35 STATION NUMBER CURRENT SPEED (cm sec) CURRENT DIRECTION ( # i TEMPERATURE (•C) 1 LAKE BOTTOM 2 13.9 100 16.8 3 45.6 110 20.6 4 47 3 110 21.0 5 72.3 100 21.0 6 350 110 17.6 7 7.8 140 12.4 8 LAKE BOTTOM 9 LAKE BOTTOM 10 44.5 90 19.3 11 24.5 60 17.3 12 14.5 20 15.3 13 7.2 350 14.1 14 LAKE BOTTOM 15 NOT MEASURED 16 24 5 85 176 17 0 - 12.3 18 LAKE BOTTOM 19 LAKE BOTTOM 20 15.0 75 17.3 21 16.7 75 17.1 22 5.6 200 11.6 23 5.6 225 11.3 24 0 - 11.3 25 0 - 13.3 26 0 - 14 8 27 0 - 14.7 28 0 - 12.8 29 0 - 12.8 (TEMPERATURE) - TEMPERATURE WIOTH ■ ■ ■ ■ VELOCITY WIDTH PLANT & METEOROLOGICAL DATA PLANT LOAD. 497 MWe DISCHARGE FLOW RATE 25.1 m 3 sec OUTFALL TEMPERATURE 21 6°C INTAKE TEMPERATURE 11 1°C AMBIENT WATER TEMPERATURE 11 3°C DRY BULB TEMPERATURE 14 5°C RELATIVE HUMIDITY: 83 c « WIND SPEED & DIRECTION 0-1.5 m/sec. AMBIENT CURRENT SPEED & DIRECTION LAKE SURFACE CONDITIONS. CALM SKY CONDITIONS: CLEAR VELOCITY SCALE cm sec 120 ° 0 0 50 100 150 DIMENSION SCALE melets Fig. 18. Jet-regime Study for 2.5-m Depth at Point Beach Power Plant (Unit 1): May 23, 1972, 0945-1700 Hours. ANL Neg. No. 190-892. 36 / STATION NUMBER CURRENT SPEED (cm sec' CURRENT DIRECTION (°. TEMPERATURE CD 1 LAKE BOTTOM 2 LAKE BOTTOM 3 43.9 80 19.3 4 528 95 20.9 5 50.0 100 208 6 18.3 120 16 4 7 LAKE BOTTOM 8 LAKE BOTTOM 9 LAKE BOTTOM 10 LAKE BOTTOM 11 NOT MEASURED 12 LAKE BOTTOM 13 LAKE BOTTOM 14 LAKE BOTTOM 15 NOT MEASURED 16 NOT MEASURED 17 NOT MEASURED 18 LAKE BOTTOM 19 LAKE BOTTOM 20 6J 85 16.3 21 16.7 75 16 1 22 2.8 190 11.2 23 5.6 225 11 6 24 0 - 10.8 25 0 - 12.1 26 0 - 14.3 27 0 - 14 3 28 0 - 12.8 29 0 - 12.6 (TEMPERATURE) -TEMPERATURE WIDTH - VELOCITY WIDTH PLANT & METEOROLOGICAL DATA PLANT LOAO. 497 MWe DISCHARGE FLOW RATE 25.1 m 3 sec OUTFALL TEMPERATURE 21i°C INTAKE TEMPERATURE ll.CC AMBIENT WATER TEMPERATURE 10 8°C DRY BULB TEMPERATURE 14.5°C RELATIVE HUMIDITY: 83°« WIND SPEED & DIRECTION 0-1.5 m/sec. 120° AMBIENT CURRENT SPEED & DIRECTION 0 LAKE SURFACE CONDITIONS CALM SKY CONDITIONS: CLEAR 100 VELOCITY SCALE cm/sec 0 50 100 150 I_I_I_I DIMENSION SCALE meteis Fig. 19. Jet-regime Study for 3.0-m Depth at Point Beach Power Plant (Unit 1): May 23. 1972, 0945-1700 Hours. ANL Neg. No. 190-890. 37 STATION NUMBER CURRENT SPEED (cm/sec) CURRENT DIRECTION (°) TEMPERATURE (°C) 1 19.5 180 17.0 2 62.3 no 19.0 3 67.8 95 20.2 4 51.1 80 18.5 5 17.8 65 16.7 6 5.6 60 16.5 7 30.0 80 16.7 8 44.5 95 18.8 9 51.1 110 19.2 10 23.4 125 17.0 11 8.9 135 17.0 12 6.7 75 15.3 13 26.1 115 16.3 14 30.0 120 16.5 15 24.4 140 16.0 16 13.9 170 15.5 17 11.1 145 15.7 (TEMPERATURE) — — — TEMPERATURE WIDTH - VELOCITY WIDTH PLANT & METEOROLOGICAL DATA PLANT LOAD 500 MWe DISCHARGE FLOW RATE 24.3 - 25 1 m 3 'sec OUTFALL TEMPERATURE 20.3°C INTAKE TEMPERATURE: 10.0°C AMBIENT WATER TEMPERATURE: 13.0 - 13.5°C DRY BULB TEMPERATURE 17.3 - 18 0°C RELATI VE HUMIDITY: 80°c WIND SPEED & DIRECTION 0 - 2.0 m/sec; 135° AMBIENT CURRENT SPEED & DIRECTION 6.6 cm sec, 180°#1215hrs 2.2 cm sec, 245°# 1720 hrs LAKE SURFACE CONDITIONS CALM 0 - 0.1 m WAVES SKY CONDITIONS: CLEAR 100 200 VELOCITY SCALE • cmsec 100 150 DIMENSION SCALE • meters Fig. 20. Jet-regime Study for 0.5-m Depth at Point Beach Power Plant (Unit 1): July 13, 1972, 1308-1706 Hours. ANL Neg. No. 190-762 Rev. 2. 38 STATION NUMBER CURRENT SPEED (cm/sec) CURRENT DIRECTION C) TEMPERATURE (°C) 1 12.2 115 16 7 2 62.3 110 19 0 3 600 95 20.0 4 37.3 80 18 0 5 14.5 130 16.7 6 2.2 325 16.0 7 20.6 90 15.5 8 42.3 95 18 3 9 40.0 110 18.3 10 19.5 115 16.3 11 5.0 160 162 12 2.2 115 14.0 13 16.7 120 15.0 14 22.2 120 15.0 15 16.7 145 14.7 16 3.9 195 14.0 17 106 145 13.7 (TEMPERATURE) TEMPERATURE WIDTH VELOCITY WIDTH PLANT & METEOROLOGICAL DATA PLANT LOAD 500 MWe DISCHARGE FLOW RATE 24 3 25 1 m 3 /sec OUTFALL TEMPERATURE 20 3°C INTAKE TEMPERATURE 10.0°C AMBIENT WATER TEMPERATURE 12 2 • 12.7°C DRY BULB TEMPERATURE 17 3 18 0°C RELATIVE HUMIDITY 80% WIND SPEED & DIRECTION 0 - 2 0 m/sec. 135° AMBIENT CURRENT SPEED & DIRECTION 6 6 cm sec. 180°• 1215 hrs 2 2 cm sec, 245° • 1720 hrs LAKE SURFACE CONDITIONS CALM 0 - 0 1 m WAVES SKY CONDITIONS CLEAR 100 200 J_I VELOCITY SCALE • cm sec 100 I 150 DIMENSION SCALE meters Fig. 21. Jet-regime Study for l.O-m Depth at Point Beach Power Plant (Unit 1): July 13, 1972, 1308-1706 Hours. ANL Neg. No. 190-900 Rev. 1. 39 STATION NUMBER CURRENT SPEED (cm/sec) CURRENT DIRECTION (°) TEMPERATURE (°C) 1 12.2 45 16.0 2 32.2 110 17.0 3 67.8 95 18.5 4 40.0 90 18.5 5 14.5 180 16.0 6 0 - 15.5 7 16.7 125 15.2 8 36.7 95 17.7 9 37.3 110 18.3 10 11.1 115 16.0 11 3.9 250 15.7 12 6.7 145 12.5 13 111 125 14.5 14 13.3 130 14.0 15 9.5 150 13.5 16 0 - 12.7 17 6.7 150 12.5 t (VELOCITY) £ !3 ^ (TEMPERATURE) TEMPERATURE WIOTH VELOCITY WIOTH / / 4 PLANT & METEOROLOGICAL DATA PLANT LOAD 500 MWe DISCHARGE FLOW RATE 24 3-25 1 m 3 /sec OUTFALL TEMPERATURE 20 3°C INTAKE TEMPERATURE 10.0°C AMBIENT WATER TEMPERATURE 11 4 - 11 7°C DRY BULB TEMPERATURE 17 3 18 0°C RELATIVE HUMIDITY 80% WIND SPEED & DIRECTION 0 - 2.0 m/sec; 135° AMBIENT CURRENT SPEED & DIRECTION 6 6 cm sec. 180° * 1215 hrs 2 2 cm/sec. 245° © 1720 hfs LAKE SURFACE CONDITIONS CALM O-Olm WAVES SKY CONDITIONS CLEAR 0 100 200 VELOCITY SCALE - cm sec 50 100 150 DIMENSION SCALE meters Fig. 22. Jet-regime Study for 1.5-m Depth at Point Beach Power Plant (Unit 1): July 13, 1972, 1308-1706 Hours. ANL Neg. No. 190-903 Rev. 1. 40 STATION NUMBER CURRENT SPEED (cm/sec) CURRENT DIRECTION C) TEMPERATURE (°C) 1 16.7 25 14.5 2 40.0 110 18.5 3 77.8 95 19.5 4 30.0 100 17.5 5 LAKE BOTTOM 6 11.1 185 14.3 7 13.9 170 13.5 8 33.4 95 17.7 9 28.9 125 16.5 10 6.7 40 15.0 11 LAKE BOTTOM 12 5.6 180 11.5 13 8.3 135 140 14 11.1 150 13.3 15 11 170 12.3 IS 5.6 320 11.7 17 1.1 180 11.5 -TEMPERATURE WIDTH - VELOCITY WIDTH PLANT & METCOROLOGICAL DATA PLANT LOAD 500 MWe DISCHARGE FLOW RATE 24 3 • 25 1 m 3 'sec OUTFALL TEMPERATURE 20 3°C INTAKE TEMPERATURE 10 0°C AMBIENT WATER TEMPERATURE 11.0 - 11 6°C DRY BULB TEMPERATURE 17 3 18 0°C RELATIVE HUMIDITY 80% WIND SPEED & DIRECTION 0 2 0 m/sec. 135° AMBIENT CURRENT SPEED & DIRECTION 6 6cm/sec. 180°• 1215 2.2 cm/sec. 245° *1720 LAKE SURFACE CONDITIONS CALM 0 0 1m WAVES SKY CONDITIONS: CLEAR 100 200 J VELOCITY SCALE - cm sec 100 JL 150 J DIMENSION SCALE • melers Fig. 23. Jet-regime Study for 2.0-m Depth at Point Beach Power Plant (Unit 1) July 13. 1972, 1308-1706 Hours. ANL Neg. No. 190-905 Rev. 1. 41 STATION NUMBER CURRENT SPEED (cm/sec) CURRENT DIRECTION C) TEMPERATURE ( # C) 1 20.0 15 12.7 2 23.4 70 15.0 3 51.1 95 19.0 4 LAKE BOTTOM 5 LAKE BOTTOM 6 12.2 180 12.0 7 13.9 195 12.0 8 31.7 95 17.7 9 13.9 150 15 5 10 10.0 30 11.7 11 LAKE BOTTOM 12 3.9 180 11.3 13 3.9 175 12.5 14 5.6 190 12.0 15 1.1 230 11.3 16 5.6 330 11.0 17 0 - 10.7 ^VELOCITY) l (TEMPERATURE) -TEMPERATURE WIDTH - VELOCITY WIDTH PLANT & METEOROLOGICAL OATA PLANT LOAD 500 MWe DISCHARGE FLOW RATE 24 3 - 25 1 m 3 sec OUTFALL TEMPERATURE 20 3°C INTAKE TEMPERATURE 10 0°C AMBIENT WATER TEMPERATURE 10 6 - 11 3°C DRY BULB TEMPERATURE 17 3 - 18 0°C RELATIVE HUMIDITY 80^ WIND SPEED & DIRECTION 0-2.0m'sec, 135° AMBIENT CURRENT SPEED & DIRECTION 9 4 cm sec. 180° • 1215 hrs 5.5 cm/sec. 180° # 1720 hrs LAKE SURFACE CONDITIONS CALM 0 0.1 m WAVES SKY CONDITIONS: CLEAR 200 VELOCITY SCALE • cm sec 100 150 j DIMENSION SCALE - meters Fig. 24. Jet-regime Study for 2.5-m Depth at Point Beach Power Plant (Unit 1): July 13, 1972, 1308-1706 Hours. ANL Neg. No. 190-896 Rev. 1. 42 STATION NUMBER CURRENT SPEEO (cm sect CURRENT DIRECTION (°> TEMPERATURE CC) 1 LAKE BOTTOM 2 150 35 15.0 3 LAKE BOTTOM 4 LAKE BOTTOM 5 LAKE BOTTOM 6 LAKE BOTTOM 7 LAKE BOTTOM 8 LAKE BOTTOM 9 LAKE BOTTOM 10 LAKE BOTTOM 11 LAKE BOTTOM 12 2.8 185 11.3 13 7.2 205 11.5 14 5.6 290 11.0 IS 1.1 250 11.0 16 3.9 330 11.0 w 0 - 10.3 PLANT l METEOROLOGICAL DATA PLANT LOAD' 500 MWe OISCHARGE FLO* RATE 24 3 - 25.1 m 3 /sec OUTFALL TEMPERATURE 20 3”C INTAKE TEMPERATURE 10.0-C AMBIENT *ATER TEMPERATURE 10.3 - 11 1* ORY BULB TEMPERATURE: 17.3 • 18.0-C 100 150 J DIMENSION SCALE - meters Fig. 25. Jet-regime Study for 3.0-m Depth at Point Beach Power Plant (Unit 1) July 13. 1972, 1308-1706 Hours. ANL Neg. No. 190-875 Rev. 1. 43 (VELOCITY) STATION NUMBER CURRENT SPEED (cm/sec) CURRENT DIRECTION (°) TEMPERATURE (°C) 1 8.3 220 17.2 2 25.0 70 19.6 3 55.6 90 23.0 4 55.6 110 23.8 5 41.7 105 21.0 6 11.1 110 19.1 7 9.5 20 18.8 8 26.7 80 20.5 9 27.8 115 20.7 10 29.5 115 20.2 11 23.9 145 20.1 12 8.9 165 20.0 13 13.3 110 19.3 n 12.8 75 19.5 15 12.2 110 19.9 16 6.7 no 19.6 17 0 - 18.9 (TEMPERATURE) / -— TEMPERATURE WIDTH - VELOCITY WIDTH PLANT & METEOROLOGICAL DATA PLANT LOAD: 493 MWe DISCHARGE FLOWRATE: 24.7 m 3 /sec OUTFALL TEMPERATURE: 24.5°C INTAKE TEMPERATURE: 13.9°C AMBIENT WATER TEMPERATURE: 16.3 • 16.6°C DRY BULB TEMPERATURE: 14.4 - 16.7°C RELATIVE HUMIDITY: 74 89% WIND SPEED & DIRECTION 0-6.0 m/sec, 135° AMBIENT CURRENT SPEED & DIRECTION: 15.0 cm/sec; 180° • 0950 hrs 0 • 1440 hrs LAKE SURFACE CONDITIONS: SLIGHT CHOP; 0-0.3m WAVES SKY CONDITIONS: CLEAR 0 100 I L VELOCITY SCALE ■ cm/sec ISO DIMENSION SCALE • meters Fig. 26. Jet-regime Study for 0.5-m Depth at Point Beach Power Plant (Unit 1): September 9, 1972, 1045-1420 Hours. ANL Neg. No. 190-763 Rev. 1. 44 / / / / / / / / STATION NUMBER CURRENT SPEED 'cm sect CURRENT DIRECTION TEMPERATURE (°C> 1 7.8 200 16.3 2 13.9 90 19.5 3 47.3 85 22.8 4 38.9 90 21.5 5 27.8 no 20.5 6 2.8 90 18.6 7 2.8 30 18.3 8 228 80 19.9 9 22.2 no 19.2 10 21.1 115 19.8 11 19.5 125 19.5 12 3.9 180 18.5 13 2.2 125 17.8 14 0 - 17.7 15 7.2 125 18.2 16 6.7 125 18.1 17 0 - 18.9 13 / -TEMPERATURE WIDTH - VELOCITY WIDTH PLANT S METEOROLOGICAL DATA PLANT LOAD 493 MWe — __ __ DISCHARGE FLO* RATE: 24,7 m 3 /sec OUTFALL TEMPERATURE 24VC INTAKE TEMPERATURE I3.9“C AMBIENT WATER TEMPERATURE: 15.2 • 15.5-C DRY BULB TEMPERATURE: 14 4 • 16.7“C RELATIVE HUMIDITY: 74 -89* WINDSPEED& DIRECTION: 0 - 6.0 m/sec, 135- AMBIENT CURRE NT SPEED & DIRECTION 15.0 cm/sec. 180“ » 0950 hrs 0 - 1440 hrs LAKE SURFACE CONDITIONS SLIGHT CHOP 0 0 3 m WAVES SKY CONDITIONS CLEAR 0 100 200 I 1 VELOCITY SCALE cm sec 5C 100 150 DIMENSION SCALE meters Fig. 27. Jet-regime Study for l.O-m Depth at Point Beach Power Plant (Unit 1) September 9, 1972, 1045-1420 Hours. ANL Neg. No. 190-904. 45 / / / STATION NUMBER CURRENT SPEED (cm sec) CURRENT DIRECTION (°) TEMPERATURE (°C) 1 LAKE BOTTOM 2 8.3 110 19.6 3 41.7 100 21.3 4 41.7 100 22.2 5 26.1 100 18.1 6 9.5 340 18 4 7 / 0.6 35 17.7 8' 13.9 90 18 8 / 9 14.5 105 18.8 ' 10 10.6 145 17.9 11 11.1 135 18.3 12 2.8 220 16.8 13 0 — 16.0 14 0 — 15.9 15 2.8 170 15.8 16 1.7 170 16.8 17 0 - 18.3 / (TEMPERATURE) TEMPERATURE WIDTH VELOCITY WIDTH PLANT & METEOROLOGICAL DATA PLANT LOAD 493 MWe DISCHARGE FLOW RATE 247 m 3 /sec OUTFALL TEMPERATURE 24.5°C INTAKE TEMPERATURE 13.9"C AMBIENT WATER TEMPERATURE 14 4 14 6"C DRY BULB TEMPERATURE. 14 4 16 7“C RELATIVE HUMIOITY 74 89% WIND SPEED & DIRECTION 0 6.0 m/sec, 135" AMBIENT CURRENT SPEEDS DIRECTION 15 0 cm/sec, 180-• 0950 his 0 # 1440 hrs LAKE SURFACE CONDITIONS: SLIGHT CHOP, 0-0 3 m WAVES SKY CONDITIONS: CLEAR 200 VELOCITY SCALE cm sec 0 L 5C 10C DIMENSION SCALE meters 150 Fig. 28. Jet-regime Study for 1.5-m Depth at Point Beach Power Plant (Unit 1): September 9, 1972, 1045-1420 Hours. ANL Neg. No. 190-897. 46 STATION NUMBER CURRENT SPEED icm seci CURRENT DIRECTION n TEMPERATURE (°C) 1 LAKE BOTTOM ? LAKE BOTTOM 3 44.5 100 21.8 4 44.5 80 21.6 5 15.0 110 17.7 6 15.0 340 16.7 7 6.7 165 16.6 8 1.7 100 179 9 0.6 115 17.6 10 12.2 135 17.7 11 0.6 135 16.7 12 5.6 325 16.1 13 0 - 15.5 14 0 - 14.8 15 1 . 1 ' 180 14.8 16 / 0 - 15.7 17 ✓ 2.2 180 16.1 » / / / / / (TEMPERATURE) TEMPERATURE WIDTH VELOCITY WIDTH PLANT & METEOROLOGICAL DATA PLANT LOAD: <93 MWe DISCHARGE FLOW RATE 24 7 m 3 /sec OUTFALL TEMPERATURE 24.5-C INTAKE TEMPERATURE 13 9“C AMBIENT WATER TEMPERATURE M l • 14 4°C DRY BULB TEMPERATURE: 14 4 • 16.7-C RELATIVE HUMIDITY 74 89% WIND SPEED S DIRECTION: 0 • 6.0 m/sec; 135" AMBIENT CURRENT SPEEDS DIRECTION: 15 0 cm/sec. 180”»0950hrs 0 # 1440 Ins LAKE SURFACE CONDITIONS: SLIGHT CHOP, 0 0.3 m WAVES SKY CONDITIONS: CLEAR 100 200 J_I VELOCITY SCALE cm sec 0 L 50 100 150 DIMENSION SCALE meters Fig. 29. Jet-regime Study for 2.0-m Depth at Point Beach Power Plant (Unit 1): September 9, 1972, 1045-1420 Hours. ANL Neg. No. 190-902. 47 STATION NUMBER CURRENT SPEED (cm seci CURRENT DIRECTION (°> TEMPERATURE (°C) 1 LAKE BOTTOM 2 LAKE BOTTOM 3 LAKE BOTTOM 4 LAKE BOTTOM 5 LAKE BOTTOM 6 L/KE BOTTOM 7 7.2 165 15.6 8 6.1 165 15.6 9 0 - 16.2 10 4 4 180 16.2 11 5.6 •290 15.1 12 6.7 345 14.6 13 0 - 149 14 0 - 14.6 15 1.7 215 14 6 16 4 4 235 14.6 17 3.9 200 15.1 / / I l \ / 9 / -TEMPERATURE WIDTH PLANT LOAD 493 MWe DISCHARGE FLOW RATE 24 7 m 3 sec OUTFALL TEMPERATURE 24 5°C INTAKE TEMPERATURE 13 9*C AMBIENT WATER TEMPERATURE 13 9 14 3°C DRY BULB TEMPERATURE 14 4 • 16 7«C RELATIVE HUMIDITY 74 89% WIND SPEED & DIRECTION 0-60m sec, 135° AMBIENT CURRENT SPEED & DIRECTION 11 1 cm/sec, 2.8 cm/sec; 180°# 0950 hrs 170° • 1440 hrs LAKE SURFACE CONDITIONS SKY CONDITIONS CLEAR SLIGHT CHOP, 0 -0 3M WAVES 100 200 VELOCITY SCALE cm, sec 0. 50 100 150 DIMENSION SCALE melets Fig, 30. Jet-regime Study for 2.5-m Depth at Point Beach Power Plant (Unit 1): September 9, 1972, 1045-1420 Hours. ANL Neg. No. 190-885. 48 STATION NUMBER CURRENT SPEED (cm/sec) CURRENT DIRECTION C) TEMPERATURE (°C) 1 LAKE BOTTOM 2 LAKE BOTTOM 3 LAKE BOTTOM 4 LAKE BOTTOM 5 LAKE BOTTOM 6 LAKE BOTTOM 7 7.2 180 14.9 8 LAKE BOTTOM 9 LAKE BOTTOM 10 LAKE BOTTOM 11 LAKE BOTTOM 12 LAKE BOTTOM 13 0 — 14.6 14 0 - 14.5 15 1.7 245 14.5 16 2.8 235 14.5 17 0 - 14.5 1*5 7 9 10 PLANT S METEOROLOGICAL DATA PLANT LOAD 493 MWe DISCHARGE FLO* RATE: 24 7 m 3 /sec OUTFALL TEMPERATURE: 24.5»C INTAKE TEMPERATURE 13 9°C AMBIENT WATER TEMPERATURE 13 8 14 3»C DRY BULB TEMPERATURE 14 4-16.7°C 0 SO 100 150 DIMENSION SCALE - meters Fig. 31. Jet-regime Study for 3.0-m Depth at Point Beach Power Plant (Unit 1) September 9. 1972, 1045-1420 Hours. ANL Neg. No. 190-888. 49 STATION NUMBER CURRENT SPEED (cm sec) CURRENT DIRECTION C) TEMPERATURE (°C) 1 33.9 285 22.3 2 25.6 300 22.9 3 31.1 320 22.9 4 16.7 335 22.4 5 24.5 345 23.0 6 22.2 350 20.4 7 21.1 320 20.9 8 24.5 320 22.2 9 23.4 340 21.7 10 19.5 355 21.8 11 19.5 10 22.0 12 18.3 355 20.2 13 15.0 10 19.9 14 18.3 10 16.8 15 20.0 360 20.9 16 47.3 320 23.5 17 69.5 320 23 5 18 61.2 320 23.6 19 55.6 330 23.6 PLANT & METEOROLOGICAL DATA PLANT LOAD 405 MWe DISCHARGE FLOW RATE 25 6 m 3 sec OUTFALL TEMPERATURE 23 6-C INTAKE TEMPERATURE 13 9-C AMBIENT WATER TEMPERATURE 16.8°C DRY BULB TEMPERATURE 20.5-C RELATIVE HUMIDITY 80% WIND SPEED & DIRECTION 6 3 msec, 220- AMBIENT CURRENT SPEED & DIRECTION 26.7 cm/sec, 020- LAKE SURFACE CONDITIONS CHOPPY 0 5 10 m WAVES SKY CONDITIONS; CLOUDY 12 \ 13 1 0 100 200 VELOCITY SCALE • cm/sec 0 SO 100 DIMENSION SCALE meteis Fig. 32. Jet-regime Study for 0.5-m Depth at Palisades Power Plant: June 14,1972,1000-1348 Hours. ANL Neg. No. 190-757 Rev. 1. iso 50 STATION NUMBER CURRENT SPEED (cm/sec) CURRENT DIRECTION C) TEMPERATURE CC) 1 21.1 310 22.4 2 17.8 310 22.7 3 16.7 310 22.7 4 13.3 20 21.6 5 17.8 345 226 6 22.2 360 23.3 7 21.7 330 19.7 8 21.1 325 21.3 9 16.7 340 20 6 10 13.3 15 19.8 11 13.3 70 16.1 12 18.3 360 176 13 16.1 10 16.8 14 189 15 165 IS 10.0 360 17.8 16 44.5 340 236 17 61.2 325 23 5 18 50.0 300 236 19 55.6 330 236 PLANT & METEOROLOGICAL DATA PLANT LOAD «5 Mi* DISCHARGE FLO* RATE 25 6 aVuc OUTFALL TEMPERATURE 23VC INTAKE TEMPERATURE 13V C AMBIENT (ATEN TEMPERATURE II l*C DRY BULB TEMPERATURE 2t.S*C RELATIVE HUMIDITY IM UNO SPEEO I DIRECTION 6.3 b/mc; 220* AMBIENT CURRENT SPEED l DIRECTION 26 7 ca/scc. 020* LAKE SURFACE CONDITIONS CHOPPY. 0.5 • 1.0 m NAVES SKY CONDITIONS CLOUOY 12 \ 0 100 200 I_I_I VELOCITY SCALE - cm/sec 0 50 100 150 I_I_I_I DIMENSION SCALE ■ meters Fig. 33. Jet-regime Study for 1.0-m Depth at Palisades Power Plant: June 14, 1972, 1000-1348 Hours. ANL Neg. No. 190-872. 51 STATION NUMBER CURRENT SPEED (cm sec) CURRENT DIRECTION ( # ) TEMPERATURE (°C) 1 18.3 315 21.7 2 16.7 325 21J 3 14.5 35 22.2 4 15.6 55 21.3 5 11.1 360 22.6 6 20.6 360 23.3 7 22.2 355 18.3 8 22.2 355 19.1 9 11.7 345 17.3 10 9.5 45 16.0 11 LAKE BOTTOM 12 16.7 15 16.2 13 14.5 360 16.5 14 18 9 20 16.3 15 1.1 20 16 4 16 25.0 320 23.5 17 55.6 325 23.5 18 55.6 300 23.6 19 44.5 325 23.6 PLANT & METEOROLOGICAL DATA PLANT LOAD 405 MWe DISCHARGE FLOW RATE 25 6 m 3 sec OUTFALL TEMPERATURE 23 6°C INTAKE TEMPERATURE 13 9°C AMBIENT WATER TEMPERATURE 16.0°C DRY BULB TEMPERATURE 20 5°C RELATIVE HUMIDITY 80 # . WIND SPEED & DIRECTION 6 3 m sec. 220° AMBIENT CURRENT SPEED & DIRECTION 26.7 cm/sec. 020° LAKE-SURFACE CONDITIONS CHOPPY. 05 10 m WAVES SKY CONDITIONS CLOUDY 0 100 200 I_I_I VELOCITY SCALE • cm/sec 0 50 100 150 I_I_I_I DIMENSION SCALE meins Fig. 34. Jet-regime Study for 1.5-m Depth at Palisades Power Plant June 14, 1972. 1000-1348 Hours. ANL Neg. No. 190-879. 52 STATION NUMBER CURRENT SPEEO (cm sec) CURRENT DIRECTION C) TEMPERATURE CC) 1 21 1 10 21.5 2 13.9 10 21.5 3 139 90 21.7 4 LAKE BOTTOM 5 LAKE BOTTOM 6 LAKE BOTTOM 7 20.0 10 17.3 8 22.2 20 17.3 9 1.1 350 16.4 10 LAKE BOTTOM 11 LAKE BOTTOM 12 139 20 15.8 13 156 360 16.4 14 178 15 16 2 15 LAKE BOTTOM 16 LAKE BOTTOM 17 LAKE BOTTOM 18 LAKE BOTTOM 19 47 3 330 | 236 PUNT 4 METEOROLOGICAL OATA PUNT LOAD 405 MWe OISCHARGE FLO* RATE 25 6 m 3 sec OUTFALL TEMPERATURE 23 6" C INTAKE TEMPERATURE 13 9”C AMBIENT *ATER TEMPERATURE 15.8°C DRY BULB TEMPERATURE.. 20,5°C REUTIVE HUMIDITY. 80S WIND SPEEO & DIRECTION 6 3 m sec, 220“ AMBIENT CURRENT SPEED & DIRECTION 26 7 cm/sec. 020° LAKE SURFACE CONDITIONS CHOPPY. 0 5 10 m WAVES SKY CONDITIONS CLOUDY 12 1 0 100 200 I_I_I VELOCITY SCALE - cm/sec 0 50 100 150 I_I_I-i DIMENSION SCALE meters Fig. 35. Jet-regime Study for 2.0-m Depth at Palisades Power Plant: June 14,1972,1000-1348 Hours. ANL Neg. No. 190-877 Rev. 1. 53 STATION NUMBER CURRENT SPEED (cm sec) CURRENT DIRECTION C) TEMPERATURE (°C) 1 LAKE BOTTOM 2 LAKE BOTTOM 3 LAKE BOTTOM 4 LAKE BOTTOM 5 LAKE BOTTOM 6 LAKE BOTTOM 7 LAKE BOTTOM 8 LAKE BOTTOM 9 LAKE BOTTOM 10 LAKE BOTTOM 11 LAKE BOTTOM 12 11.7 35 15.6 13 111 15 162 14 13.9 15 16 2 15 LAKE BOTTOM 16 LAKE BOTTOM 17 LAKE BOTTOM 18 LAKE BOTTOM 19 LAKE BOTTOM PLANT & METEOROLOGICAL DATA PLANT LOAD 405 MWe DISCHARGE FLOW RATE 25 6 m 3 sec OUTFALL TEMPERATURE 23 6°C INTAKE TEMPERATURE 13 9°C AMBIENT WATER TEMPERATURE 15.6°C ORY BULB TEMPERATURE 20 5°C RELATIVE HUMIDITY 80** WINO SPEED & DIRECTION 6 3 m sec, 220° AMBIENT CURRENT SPEED & DIRECTION 24.5 cm/sec. 020° LAKE SURFACE CONDITIONS CHOPPY. 0 5 10 m WAVES SKY CONDITIONS CLOUDY 13 1 0 100 200 I_I_I VELOCITY SCALE cm/sec 0 SO 100 ISO DIMENSION SCALE meleis Fig. 36. Jet-regime Study for 2.5-m Depth at Palisades Power Plant: June 14, 1972, 1000-1348 Hours. ANL Neg. No. 190-887. 54 STATION NUMBER CURRENT SPEED (cm/sec) CURRENT DIRECTION C) TEMPERATURE ( # C) 1 1.7 230 26 5 2 21.1 285 27.0 3 34.5 280 28 5 4 19.5 295 28.7 5 16.7 325 29.0 6 3.3 18 28.2 7 8.3 280 26.0 8 19.5 275 27,0 9 16.7 300 27.0 10 14.5 330 28.0 11 11.7 330 27.5 12 6.7 255 25.0 13 156 280 26.8 14 15.6 290 25.5 15 11.7 300 25.5 16 12.2 300 25.8 17 10.6 305 26 6 18 545 300 286 19 72.3 315 28.7 20 61.2 300 28.7 7 •- 10 v 11 v PLANT t METEOROLOGICAL OATA PLANT LOAD 420 MWe DISCHARGE FLOW RATE. 25.6 m 3 /sec OUTFALL TEMPERATURE 28 7*C INTAKE TEMPERATURE 20 0”C AMBIENT WATER TEMPERATURE 23.5 - 2«.5*C DRY BULB TEMPERATURE 22.7 - 25.6” C RELATIVE HUMIDITY: 86% WIND SPEED & DIRECTION: 0 • 2.0 m/sec; 135“ AMBIENT CURRENT SPEED & DIRECTION 8.6 cm/sec, 180” LAKE SURFACE CONDITIONS: CALM SKY CONDITIONS: CLOUOY 12 «■ 13 — 14 — 15 - 16 — 17- 0 100 200 VELOCITY SCALE - cm/sec 0 50 100 DIMENSION SCALE • melers Fig. 37. Jet-regime Study for 0.5-m Depth at Palisades Power Plant: July 19.1972,0922-1414 Hours. ANL Neg. No. 190-758 Rev. 1. 150 55 PLANT & METEOROLOGICAL DATA PLANT LOAD 420 MWe DISCHARGE FLOW RATE 25 6 m 3/ sec OUTFALL TEMPERATURE 28.7°C INTAKE TEMPERATURE 20 0*C AMBIENT WATER TEMPERATURE 22.1 • 23.7-C DRY BULB TEMPERATURE 22 7 25 6°C RELATIVE HUMIDITY 86% WIND SPEED & DIRECTION 0 2 0 m/sec. 135° AMBIENT CURRENT SPEED & DIRECTION 8.6 cm/sec. 180- LAKE SURFACE CONDITIONS CALM SKY CONDITIONS: CLODUY 12 • 13 • 16* 0 100 200 VELOCITY SCALE • cm/sec 0 50 100 DIMENSION SCALE • meters Fig. 38. Jet-regime Study for l.O-m Depth at Palisades Power Plant: July 19, 1972, 0922-1414 Hours. ANL Neg. No. 190-873. iso N \ STATION NUMBER CURRENT SPEED (cm sec) CURRENT DIRECTION (°) TEMPERATURE CC) 1 LAKE BOTTOM 2 .AKE BOTTOM 3 6 7 300 27.5 4 15.6 295 28.4 5 4 4 320 27.6 6 LAKE BOTTOM 7 3.3 200 22.5 8 56 190 222 9 1.1 235 22.3 10 0.6 280 22.0 11 0 - 22.0 12 0 - 22.0 13 3.3 250 21.5 14 2.2 270 21.6 15 1.7 270 224 16 11 240 22.0 17 2.8 270 23.1 18 345 300 28.7 19 57.0 345 28 7 20 48 8 300 28 7 8 t 9» PUNT & METEOROLOGICAL DATA PUNT LOAD 420 Mle DISCHARGE FLOW RATE 25 6 m 3, sec OUTFALL TEMPERATURE 28.7*C INTAKE TEMPERATURE 20 0°C AMBIENT WATER TEMPERATURE 21.3 • 22.5*C DRY BULB TEMPERATURE 22 7 - 25 6*C REUTIVE HUMIDITY 86% WIND SPEED & DIRECTION 0 2 0 m sec, 135° AMBIENT CURRENT SPEED & DIRECTION 8 6 cm /sec. 180° UKE SURFACE CONDITIONS CALM SKY CONDITIONS: CLOUDY 0 L 13. 0 100 200 1_I_I VELOCITY SCALE ■ cm/sec 50 100 DIMENSION SCALE meteis ISO Fig. 39. Jet-regime Study for 1.5-m Depth at Palisades Power Plant July 19. 1972, 0922-1414 Hours. ANL Neg. No. 190-884. 57 N il STATION NUMBER CURRENT SPEED (cm/sec) CURRENT DIRECTION (•) TEMPERATURE (°C) 1 LAKE BOTTOM 2 LAKE BOTTOM 3 8.3 30 J_26.0 4 LAKE BOTTOM 5 LAKE BOTTOM 6 LAKE BOTTOM 7 4 4 180 220 8 5.6 180 22.3 9 1.7 235 22.3 10 4 4 200 22.0 11 0.6 250 21.6 12 0 21.5 13 2.2 255 21.4 14 1.1 220 21.5 15 1.7 200 21.4 16 3.9 215 21.8 17 2.8 205 22.0 18 LAKE BOTTOM 19 48 9 330 28.3 20 51.5 300 28 7 10 . PLANT & METEOROLOGICAL DATA PLANT LOAO 420 MWe DISCHARGE FLOW RATE 25 6 m 3 /sec OUTFALL TEMPERATURE 28.7°C INTAKE TEMPERATURE 20.0°C AMBIENT WATER TEMPERATURE 21,4°C DRY BULB TEMPERATURE: 22 7 25 6°C RELATIVE HUMIDITY 86% WIND SPEED & DIRECTION 0 2.0 m/sec, 135° AMBIENT CURRENT SPEED & DIRECTION 8.6 cm/sec, 180° LAKE SURFACE CONDITIONS CALM SKY CONDITIONS CLOUDY 0 100 200 I I J VELOCITY SCALE - cm/sec 0 50 100 150 I_I_I_I DIMENSION SCALE • meters Fig. 40. Jet-regime Study for 2.0-m Depth at Palisades Power Plant: July 19.1972.0922-1414 Hours. ANLNeg.No. 190-871 Rev. 1. 58 STATION NUMBER CURRENT SPEED i cm sed CURRENT DIRECTION TEMPERATURE (°C> 1 LAKE BOTTOM 2 LAKE BOTTOM 3 LAKE BOTTOM 4 LAKE BOTTOM 5 LAKE BOTTOM 6 LAKE BOTTOM 7 LAKE BOTTOM 8 22 140 21 8 9 3 3 170 22 1 10 5 6 185 22 0 11 0 6 220 21.5 12 0 6 205 21 0 13 11 255 21 0 14 1 1 185 21 4 15 1 1 190 21 0 16 2.8 210 21 8 17 3.3 205 21.5 18 LAKE BOTTOM 19 LAKE BOTTOM 2C LAKE BOTTOM II • PLANT & METEOROLOGICAL DATA PLANT LOAD 420 MWe DISCHARGE FLOW RATE 25 6 m 3 sec OUTFALL TEMPERATURE 28 7°C INTAKE TEMPERATURE 20 0°C AMBIENT WATER TEMPERATURE 21 0°C DRY BULB TEMPERATURE 22 7 25 6°C RELATIVE HUMIDITY 86 3 « WINO SPEEO & DIRECTION 0 20 in sec. 135° AMBIENT CURRENT SPEED & DIRECTION 5 0 cm'sec. 200° LAKE SURFACE CONDITIONS CALM SKY CONDITIONS CLOUDY 13. 0 100 200 VELOCITY SCALE cm sec 0 50 100 DIMENSION SCALE meters 150 Fig. 41. Jet-regime Study for 2.5-m Depth at Palisades Power Plant: July 19, 1972, 0922-1414 Hours. ANL Neg. No. 190-881. N STATION NUMBER CURRENT SPEED (cm sec) CURRENT DIRECTION r> TEMPERATURE (°C) 1 LAKE BOTTOM 2 LAKE BOTTOM 3 LAKE BOTTOM 4 LAKE BOTTOM 5 LAKE BOTTOM 6 LAKE BOTTOM 7 LAKE BOTTOM 8 LAKE BOTTOM 9 LAKE BOTTOM 10 LAKE BOTTOM 11 LAKE BOTTOM 12 2.2 180 20.8 13 2.2 170 20.6 14 2.2 155 210 15 1.1 185 210 16 2.2 210 21.5 u 2.2 200 21.0 18 LAKE BOTTOM 19 LAKE BOTTOM 20 LAKE BOTTOM 8 • 9 • N PLANT & METEOROLOGICAL DATA PLANT LOAD 420 MWe DISCHARGE FLOW RATE 25 6 m 3 sec OUTFALL TEMPERATURE 28.7“C INTAKE TEMPERATURE 20 0-C AMBIENT WATER TEMPERATURE 20.6°C DRY BULB TEMPERATURE 22 7 25 6°C RELATIVE HUMIDITY 86% WIND SPEED & DIRECTION 0 2.0 m/sec, 135° AMBIENT CURRENT SPEED & DIRECTION 5.0 cm/sec, 200“ LAKE SURFACE CONDITIONS CALM SKY CONDITIONS: CLOUDY 12 • 15 • 0 100 200 VELOCITY SCALE - cm/sec 0 50 100 DIMENSION SCALE meteis 150 J Fig. 42. Jet-regime Study for 3.0-m Depth at Palisades Power Plant July 19, 1972, 0922-1414 Hours. ANL Neg. No. 190-882 Rev. 1, 20 and R-p and K-j are two dimen¬ sionless free parameters to be determined by fitting to the field data. The case for which R-p = 1.0 and Kp, = 0.0 corresponds to a jet centerline that is directed straight out from the outfall. Positive values of Krp correspond to the jet bending to the left, and negative values corre¬ spond to bending to the right. The quantity Rrpj5 0 determines the initial angle of the centerline at the origin (discharge). The velocity excess (assumed parallel to the centerline) at a lateral distance T| from the velocity centerline is given by the following expression: u e (T|, s ) = u CE (s)(y where Pb 0 u 0 B for s £ —— B 2 and W u (s) = Db 0 + 6s. 68 These velocity-excess equations have the same form as the expressions for the temperature excess, except that u 0 is the outfall velocity averaged over the entire outfall. The velocity centerline has a form analogous to that for the temperature centerline: K x cu = 5 cos ( R uM - § 2 sin (R u 3o) and K u y cu = 5 sin (R u E>o) + 5 2 cos (R U P„). The parameters B, j3, D, 6, R u , and K u are determined by fitting to the data. The temperature and velocity functions described above, each with only six free parameters, are fairly restrictive. However, due to the limited amount of data available, it was felt that more general functions with more free parameters would be unwarranted. As a consequence, only the general trends of the resulting fitted function can be considered significant. The details are artifacts of the functions chosen. The fitting procedure was carried out on the computer by a minimiza¬ tion technique. The root-mean-square deviations of the functions from the data are defined as follows: (a T ;A,o,C, y,R T ,K T ) = N I i=i ( 0 Di" 0 Fi) N - 6 -,1 /2 and (o u ;B, j3,D, 6,R U ,K U ) where N is the number of data points, is the measured temperature excess at the ith data point, is the temperature excess calculated from the function, u^. is the component of the measured velocity excess parallel to the velocity centerline, and u^' is the velocity excess calculated from the function. The 6 in the denominator is introduced to account for the six degrees of freedom associated with the six free parameters of the fitting function. The final values of the parameters were then chosen to be those values that minimize CTj and c u . The FORTRAN program JETFIT used for this fitting procedure is listed in Appendix C. The sets of measurements taken during the four jet studies at the Point Beach outfall and one of the studies at the Palisades outfall (Octo¬ ber 10, 1972) were each fitted independently. The measurements of the other two Palisades surveys did not lend themselves to this fitting procedure because the limited number of data points did not appear to characterize a major portion of the jet region; i.e., the jet seems to be significantly wider than the region surveyed. The parameters resulting from the fitting procedure and a tabulation of the deviations of the fitted functions from the measurements are included in Appendix D. The average deviation of the function from the data varied from about 0.2 to 1.1 C°, with an overall average deviation for all five studies of 0.7C°. The average velocity deviation varied from 1 to 8 cm/sec, with an overall average deviation of 4 cm/sec. These overall average deviations correspond to about 7% of the average initial temperature excess and outfall velocity, respectively. Figures 8-48 show the temperature and velocity centerlines and the temperature and velocity half-widths resulting from this fitting procedure, along with the actual field measurements. Note that the field measurements were made in groups corresponding approximately to perpendicular transects of the jet. Some of the fitting results for the Point Beach studies are shown together in Figs. 49-52 so that they may be compared with each other. The circles on the curves of 0 C / 9 0 , plotted as a function of distance from the outfalls (Fig. 49), indicate the approximate location of the measurement groupings. The results for the one Palisades case are presented in Sec. VII along with the model comparisons. Figure 49 shows the centerline temperature and velocity decays resulting from the fits to the measurements taken at a depth of 0.5 m for all four Point Beach dates. The drop-off rates are approximately the same for each survey and for both temperature and velocity, except for the velocity results of July 13, 1972. This difference is presently unexplained. Indeed, the differences shown in the figures, with that one exception, are probably within the errors associated with the experimental measurements and the fitting procedure. On all four dates, the power plant was operating at essen¬ tially the same power level and discharge flow rate. The temperature dis¬ tribution across the outfall has been measured and found to be quite uniform. Therefore, the excess temperature ratio 0 C / 9 0 plotted in the upper half of Fig. 49 must be 1.0 at s = 0. This restriction was not placed on the fitting function, and so not much significance should be attached to the details con¬ tained in the first 100 m of the fitting results. The initial velocity distri¬ bution at the Point Beach outfall has also been measured.* It was not found to be uniform. In fact, velocities as much as 60% above the average outfall velocity were observed. This fact shows up in the lower half of Fig. 49, where the velocity ratio exceeds 1.0 for small values of s. Again, not much significance should be attached to the details of the results in this initial 100 -m region. Figure 50 presents the corresponding temperature and velocity half¬ widths for the same four dates. It is evident that the temperature distribu¬ tion is wider than the velocity distribution. Indeed, on the average, it is approximately twice as wide. *A typical outfall velocity distribution for Point Beach appears in ANL/ES-16 (Ref. 19 of Appendix A). Measurements on several other dates exist and will be published in the future. 70 °n / 3 n Fig. 49. Centerline Excess-temperature and -velocity Fig. 50. Half-widths of Temperature and Velocity Distri Decays Resulting from Fits to Point Beach Jet butions Resulting from Fits to Point Beach Jet Data at 0.5-m Depth. ANL Neg. No. 190-950. Data at 0.5-m Depth. ANL Neg. No. 190-961. 71 (SJ343LU) J-M (SJStauj) n M Fig. 51. Centerline Temperature Excess and Velocity Excess as aFunc- Fig. 52. Half-widths of Temperature and Velocity Distributions as tion of Depth Resulting from Fits to Point Beach Jet Data a Function of Depth at s = 150 m, Resulting from Fits to (normalized to the 0.5-m results). ANL Neg. No. 190-953. Point Beach Jet Data. ANL Neg. No. 190-945. Figure 51 shows the centerline temperature and velocity excesses as a function of depth relative to the 0.5-m results. Because of the nature of the functional form chosen, these quantities are independent of distance from the outfall after the initial region, which was always less than about 100 m. Within the accuracy of these results, the excesses are fairly constant with depth. However, the temperature data of September 9, 1972, do show an exception. Because there is no clear drop-off with depth, a characteristic depth of the jet could not be extracted from the JETFIT results. Figure 52 shows the widths as a function of depth at a distance of 150 m from the outfall. This distance was chosen because it lies approxi¬ mately in the middle of the range for which measurements were made. These widths show a decreasing trend, tending toward zero at a depth of 2.5-3.0 m. The temperature widths are approximately constant for the first 1.0-1.5 m and then decrease while the velocity widths decrease more uniformly. In summary, the Point Beach jet studies indicate that the centerline excess temperature and excess velocity ratios decay at about the same rate, with jet longitudinal distance, for all four dates and for depths down to 2 m or more. This decay, beyond about the first 50 m, is characterized by In the above expression, 4.2 is the average value of O' and g for all cases except for the 0.5-m velocity results of July 13, 1972, and the 1.5 -, 2.0 - , and 2.5-m temperature results of September 9, 1972. The average deviation of the actual values of O' and $ from this value of 4.2 is 0.7. The tempera¬ ture half-widths at the 0.5-m depth grow at a rate of 3-6 m for each 10 m from the outfall; the velocity half-widths grow at only about 2 m per 10 m. Both these rates decrease with depth, tending toward zero at about 2.5-3.0 m. 73 VI. MATHEMATICAL MODELING OF NEAR-FIELD REGION OF SURFACE THERMAL DISCHARGES The utility of analytical near-field, surface-discharge models is pri¬ marily centered around three considerations. The first of these is a desire to assess, and therefore avoid, possible recirculation of heated water into the plant intake. The second is the necessity to develop an appropriate dis¬ charge design to satisfy temperature standards. The third is a desire to help predict possible biological effects relating to changes in the physical and chemical properties of the water. Most presently operating power plants use a surface channel or canal to discharge their heated condenser-cooling water, and many new plants still plan for similar discharge designs. Since thermal discharges of cooling water from power plants will undoubtedly increase greatly in both magnitude and number during the next decade, the adequacy of predictive models for such discharges becomes an important factor in design. Table II summarizes the basic characteristics of 15 near-field analytical models 1-15 for surface thermal discharges presently available in the literature. Table III summarizes those complete-field models 16-24 that have separate jet-regime analyses. Due to limitations of time and space, the field of 24 models had to be narrowed down considerably. Con¬ sidered in this report and compared with the Point Beach Unit 1 and Palisades data are the more promising and widely used models of Pritchard (Model No. 1), Motz and Benedict, Stolzenbach and Harleman, and Prych. Some of the reasons for not including comparisons with the other models are as follows: 1. Hoopes et al.: model too sensitive to the main parameter, wind speed; generally unsatisfactory comparison with earlier data taken at Point Beach (Ref. 21 of Appendix A). 2. Hayashi and Shuto: mainly historical nature of model; no jet entrainment simulated in this model. 3. Wada (Model No. l) : computer program unavailable. 4. Carter: mainly historical nature of model; jet model based on hydraulic data taken in too small a basin; improved data appeared recently in Ref. 25. 5. Koh and Fan (2D Model): no lateral entrainment simulated in this two-dimensional (longitudinal, vertical) model; as with the Wada Model No. 2, it is basically a tool to develop greater physical insight. 6. Koh and Fan (axisymmetric model): discharge outfall assumed in this model is circular, not rectangular as exists at Point Beach and Palisade s. 7. Barry and Hoffman: model authors prefer to make changes in model development before further application. 8. McLay et al.: modification on Hoopes et al. model which includes a region of flow establishment and a constant spreading rate; not used because of generally unsatisfactory experience with computer code. 9. Stefan: no region of flow establishment, which severely restricts application of model; also, model comparison with Stefan's tank data not satisfactory (possibly due also to stratification of ambient water in tank). 10. Paul and Lick: new model with computer code incomplete at time of present study. 11. Engelund and Pedersen: model applicable only for surface dis¬ charges having large initial densimetric Froude numbers. 12. Waldrop and Farmer: model is of too recent an origin. 13. Wada (Model No. 2): no computer code available; no lateral en¬ trainment simulated in this two-dimensional (longitudinal, vertical) model. 14. Sundaram et al.: mainly historical nature of model; jet- trajectory formulas not applicable until reasonably distant from outfall. 15. Elliott and Harkness: model authors are presently improving their near-field analysis. 16. Giles et al. : model authors will be making further (though minor) modifications in the model; the hybrid computer required for model application is too large for Argonne facilities. 17. Loziuk et al.: model authors are presently modifying the hydraulics of their jet analysis; computer code presently unavailable. 18. Brady and Geyer: model is of too recent an origin for application in this report. 19- Till: model is of too recent an origin. 20. Pritchard (Model No. 2): model is of too recent an origin. The four analytical models to be considered in this report and com¬ pared with the present field data are summarized next. A. Motz - Benedict Model Motz and Benedict have developed a two-dimensional model for the velocity and temperature distribution of a heated surface jet. 5 Ambient receiving-water turbulence and buoyancy are assumed to be of minimal influence with regard to plume dynamics and heat transfer within the jet regime. The authors built their integral analysis upon the framework es¬ tablished primarily by Morton, 26 Fan, 27 Hoopes et al., 1 and Carter. 4 Con¬ servation equations of mass, x and y momentum, and energy, along with two equations of jet bending, lead to a system of six ordinary differential equations which must be solved numerically to yield the jet trajectory, centerline temperature and velocity, and profile width. The Motz - Benedict model assumes that only two factors affect the flux of momentum at any TABLE II. Summary of Characteristics of Jet Models (ANL Neg. No. 190-990 Rev. 1) 75 COffVTER PROGRAM i 1? “8 * 8 -i 8 “8 1 8 "8 8 I2 1 i ss i s 8 I 8 8 2 2 2 8 2 8 8 2 8 8 81 j 8 2 I 2 • 2 2 8 2 8 2 8 2 2 8 RECIRCULATION OF PLUME WATER s s 8 2 2 2 2 2 2 2 2 2 8 2 8 DIRECT WIND STRESS EFFECTS E s 2 2 2 "2 2 2 2 "2 8 2 2 2 ' AMBIENT STRATIFICATION INTERACTION s s 2 2 2 2 2 2 2 2 2 2 2 2 8 Bsl g u. ~ □ am le l ■°S s 2 8 8 2 2 2 8 8 2 8 8 8 8 s s B 8 8 8 8 8 8 8 8 8 8 8 8 2 8 SURFACE HEAT LOSS B 8 8 2 8 8 8 8 8 8 8 8 8 2 8 is \ 2 8 2 2 2 2 8 2 2 2 2 H s 2 8 ii B 2 2 8 8 2 2 8 8 8 8 8 2 8 8 1 2 8 8 2 2 8 8 8 8 2 8 8 8 2 8 sii 2 2 8 2 2 2 2 2 2 2 2 2 8 8 8 3 2 i i B 8 8 8 8 8 8 8 8 8 8 8 8 8 8 i 5 £ 2 5 Q | 1 \ 8 2 2 \ 2 2 2 2 2 2 2 8 2 1 | B 8 2 8 8 8 8 2 8 ‘B 8 8 2 8 2 1 2 2 8 2 2 2 2 8 2 Is 2 2 8 2 8 w s 2 2 2 2 2 2 2 2 2 2 2 2 2 2 INITIAL MIXING (JET REGIME) B 8 8 8 8 8 8 8 8 8 8 8 8 8 8 | 5 % s 8 u e 2 2 8 8 8 8 8 8 8 8 8 8 ip 1 B 8 8 8 8 2 8 8 8 8 8 8 8 8 8 1 \ 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 di Cl 1 1 2 I s G 1 1 9 5 1 § I si 4 tul s 5 1 I5 3 1 1 ! 1 i ! YET MAY BE EASILY WRITTEN FRCM MDDEL EQUATIONS. TABLE III. Summary of Characteristics of Complete-field Models (ANL Neg. No. 190-989 Rev. 1) 76 77 lateral slice of the jet: The first is the entrainment of lateral crossflow momentum, and the second is a net pressure force caused by eddying of the ambient fluid in the lee of the jet and by distortion of the jet boundaries. Explicit expressions must be assumed for both the entrainment function (to determine mass and momentum conservation) and the drag force per unit length (to determine momentum conservation). The assumed form of the entrainment velocity is Vj _ = E(U - U a cos 0), whe re v^ = inflow velocity (of entrainment), U = local jet centerline velocity, U a = ambient current velocity, 0 = local angle between jet centerline and ambient current, and E = entrainment coefficient. The form of the assumed drag force is ^D^a z s ^ n ^ D where Fq = drag force operating normal to jet axis, Cq = experimentally determined drag coefficient, and z = jet depth. This form for is based on the assumption that the interaction of the jet with the ambient current can be treated as if the jet were a solid body and the resulting pressure gradients can be represented by a drag force. Utilization of the model requires the specification of the drag and entrainment coefficients, and E, respectively. In the region of established flow, the authors make similarity assump¬ tions for velocity and temperature: u(s, 71) = U(s) exp(-7) 2 /b 2 ) and T'(s, T]) = T(s) exp( -T) 2 /b 2 ) 78 where u = local jet velocity, T' = local jet temperature, U = jet centerline velocity, T = jet centerline temperature, s = distance along jet centerline, T] = lateral distance from jet centerline, and b = characteristic width of lateral profiles. The assumed forms for u, T', v^, and Fq are used in the integral equations of conservation to yield the jet characteristics in the established flow regime. To account for the zone of flow establishment, Motz and Benedict have developed phenomenological relationships for the length of the region of flow establishment (s^) and the initial angle of the jet at the end of the region of flow establishment ({3 0 ). These relationships are based on a series of laboratory hydraulic studies. No details of the temperature and velocity distribution in the region of flow establishment were determined, only its length and final angle with the shore. These studies yielded values for s^, and E in terms of the ratio A of ambient to initial jet velocity and the actual initial angle of the jet with respect to shore, j3g. (The authors, however, recommend a value for of 0.5 be used for most cases.) Also needed is the width of the jet at the end of the region of flow establishment, 2b 0 . The authors suggest a value calculated by equating the heat flux at the point of discharge with the heat flux at the end of flow establishment. The actual width at the point of discharge is denoted by 2bg. B. Stolzenbach-Harleman Model The mathematical model of Stolzenbach and Harleman 9 predicts the distributions of temperature and velocity within a completely determined jet structure for a near-field region, defined by the predominance of initial jet momentum over the effects of ambient lake turbulence. Wherever possible, the model synthesizes previous knowledge of buoyant and nonbuoyant jets. The heated discharge is assumed to be structured in its physical characteristics as well as its assumed velocity and temperature distribution, basically like a classical, turbulent, non¬ buoyant jet. Just as for nonbuoyant jets, the authors assume an initial core region void of shear followed by the main turbulent region. The basic jet structure assumed by Stolzenbach and Harleman appears in Fig. 53. 79 Fig. 53. Geometrical Characteristics of Jet Assumed in Stolzenbach-Harleman Model Using an integral method as in most jet analyses, velocities and tem¬ peratures at each longitudinal cross section are presumed to be related to centerline values by similarity profiles. Figure 54 illustrates the similarity profiles assumed. These are represented mathematically by u = u c (x)Fy(y)F z (z) - V cos 0 and AT - AT c (x)T (y)T (z), whe re y u, AT = local value of velocity and temperature excess, x,y,z = longitudinal, lateral, and vertical coordinates, V cos 0 = component of ambient velocity normal to jet, F y = T = y 1.0, 0 < 1 y 1 C s, F y VJJ II T = y t(C y ). s < |y| < b + s, F = T = o, b + s < 1 y 1, y y F„ = T = 1.0, -r < z < 0, z z F z = f(G z ). T z = t(c z >. -r - h < z < -r F z = T z = 0, z < -h - r. y I - s r y • / 28 \ The form of the similarity functions (from Abramovich ) are f = (1 - G 3 ' 2 ) 2 , and t = l - c 3/2 . The variables b, s, h, and r are defined in Figs. 53 and 54. Horizontal and vertical entrainment of ambient fluid is related to the jet centerline velocity by appropriate entrainment coefficients. The lateral- entrainment coefficient is determined by nonbuoyant jet theory alone and is constant; the vertical-entrainment coefficient is related to the local tem¬ perature gradient by the local Richardson number, using the experimental results of Ellison and Turner, 29 and is chosen to reduce to the nonbuoyant value when no density gradients exist. 81 Fig. 54. Velocity and Temperature Characteristics of Jet Assumed in Stolzenbach-Harleman Model Buoyant convection is incorporated through the pres sure-gradient terms in the equations of motion and through the vertical-entrainment coefficient. Buoyancy effects generally reduce vertical entrainment and enhance lateral spreading. To treat the interaction of these complex phenomena encompassing jet momentum, entrainment, buoyancy, and ambient crosscurrent, the authors developed their model from the steady, time-averaged differential equations of mass, momentum, and conservation of heat energy by dropping negligible terms, assuming a form for some of the unknown variables, and finally integrating the simplified equations over the four assumed regions of the jet longitudinal cross section. Boundary conditions for the differential equations of mass, momentum, and energy (along with jet geometry) required assumptions for the boundary values of heat and mass fluxes as well as for internal lateral and vertical velocity distributions. The set of conservation differential equations for a buoyant deflected jet are integrated over the jet cross section. The continuity and x-momentum equations are each integrated over all of the four regions defined in Fig. 53, yielding eight equations. The y-momentum equation is integrated over half the (symmetric) cross section to yield the ninth equation. The tenth is a jet-bending equation obtained from equating the rate of entrainment of lateral momentum to the rate of jet deflection. (No drag force on the jet is assumed.) In this manner, the coupled flow and energy equations reduce to a system of simultaneous, first-order, nonlinear ordinary differential equa¬ tions in the single variable x (longitudinal distance along jet centerline from the outfall), which are then solved numerically. The solution to the model equations yields three-dimensional temperature and velocity pre¬ dictions as well as the jet physical characteristics. The complete solution may be written in nondimensional form as T - T a " To - T a u u 0 / K V \ > functions [ IF 0 . A, -, —, and ^ pc p u 0 u 0 / iet characteristics = whe re IFn =—'— — • = discharge densimetric Froude Number, /Ap„ y — sh ° A = h 0 /b 0 = discharge-channel aspect ratio, K r - = surface-heat-los s parameter, pc p u 0 V = ambient crossflow velocity (possibly a function of offshore distance), u 0 = channel outlet velocity, a 0 = angle of discharge with respect to shoreline, T a = uniform lake water temperature, T 0 = initial discharge temperature, Apo = density difference between discharged and ambient water, 83 and p a = density of ambient lake water, g = acceleration due to gravity, 2b 0 = width of discharge canal, h 0 = depth of discharge canal, K = surface-heat-transfer coefficient, p = density of water, c = specific heat of water. P Thus the only site-dependent input parameters required are: IFq, A, K V pc p u 0 ’ u 0 and ct 0 . C. Prych Model 1 ? The Prych model is based on a three-dimensional integral analysis of a turbulent, buoyant, horizontal, surface jet into a large, deep, uniform, turbulent flowing receiving water. Integral equations of conservation are written for mass, horizontal x and y momentum, and energy, as well as equa¬ tions for the jet trajectory. Figure 55 illustrates the coordinate systems and the jet region. The model uses Gaussian similarity assumptions for tem¬ perature and velocity: t(s,n,z) = T'(s) exp[-n 1 2 /B 2 (s)] exp[-z 2 /H 2 (s )] u(s,n,z) = U(s) exp[ -n 2 /B 2 (s)] exp[ -z 2 /H 2 (s )] + V cos 9(s), whe re t, u = local values of temperature excess and velocity, s, n z T 1 (s), U(s) B(s), H(s) and curvilinear coordinates along jet centerline parallel and perpendicular to the jet trajectory, respectively, vertical distance from receiving-water surface, centerline values of excess temperature and excess velocity, local characteristic width and depth of jet, = component of ambient velocity parallel to jet trajectory. V cos 9 84 Fig. 55. Definition Sketch for Coordinate System and Jet Region Assumed in Prych Model. ANL Neg. No. 190-1045. The rate of increase of the local jet flow due to incorporation of am¬ bient water is included in the model by simulating entrainment due to jet mix¬ ing and also entrainment caused by turbulence in the ambient fluid. Horizontal and vertical rates of entrainment are calculated separately for both processes and are then summed. Prych computes jet entrainment in a manner similar to Stolzenbach and Harleman. Most notable is the requirement that the entrain¬ ment coefficient decreases with increasing fluid stability in the density- stratified jet. Prych calculates the contribution of ambient mixing to horizontal and vertical entrainment as 3.5e/a, where e is the ambient turbulent diffusion coefficient (horizontal or vertical) and a is the standard deviation of the lateral distribution of a tracer (excess temperature) in a two-dimensional jet. Prych assumes a = 2 s/H for the vertical direction. Four force terms appear in the x- and y-momentum equations: 1. Ambient momentum flux in the direction of the ambient current. 2. Pressures due to the density differential between the fluid in the jet region and the ambient fluid. This force is assumed hydrostatic and is calculated by integrating the excess pressure force: APo g — (s, n, z 1 o ) dz 1 over each vertical cross-sectional face. 3. A form drag on the jet due to the pressure difference between offshore and lee sides of the jet, represented by F d = Hv|v| sin 2 0, where = form-drag coefficient. This force is computed in the same way one computes form drag on a solid body. 85 4. Interfacial shear stress between the jet fluid and the underlying ambient fluid. Prych approximates this force by modifying an expression for the shear stress at the base of a turbulent boundary layer on a smooth, flat, solid surface. Once the basic conservation equations are integrated over the jet cross section using the above assumptions, a system of ordinary differential equa¬ tions results that are solved for jet trajectory, jet width, jet depth, and jet- centerline temperature and velocity. A separate region of flow establishment is included with the same forces simulated as described previously. The basic input parameters to the model are: and Q 0 = discharge flow rate from the outfall, T 0 = excess temperature of jet (above ambient) at the outfall, 0 O = angle of discharge velocity vector with positive x axis, 2b 0 = width of outfall, h 0 = depth of outfall, V = ambient-current velocity (assumed constant), AP 0 = difference in density between ambient water and water from outlet, K = surface-heat-transfer coefficient, E 0 = jet-entrainment coefficient (horizontal), Cq = form-drag coefficient, Cp = (interfacial) shear-stress coefficient. D. Pritchard Model t 1 7 Pritchard's model is basically a synthesis of previous theoretical - and phys ical-modeling results for buoyant and nonbuoyant jets, complemented by results the author has gleaned from field data obtained from existing power plants sited on bays, estuaries, and large lakes. The model is simple and considers plume dispersion to be governed solely by momentum-jet entrainment, turbulent diffusion, and surface heat loss. An integral technique is used in which the plume velocity and excess temperature (above ambient) are assumed to have, at each longitudinal posi¬ tion, a "tophat" distribution laterally and vertically. Buoyancy-induced convective motions are not explicitly considered. No ambient current is assumed to exist in the theoretical development; yet, the author expects that the predicted centerline-temperature decay and areas within isotherms will still be accurate in the presence of a current less than 10% of the initial discharge velocity. In the model, environmental changes are reflected solely in the surface-heat-transfer coefficient, K. Entrainment is accounted for by the specification of a fixed inverse spreading-rate parameter, n, normally taken to be about 6. The lake bottom is assumed to have no effect other than upon the author's choice of a plume depth and, when necessary, upon the length and depth of an initial region of vertical entrainment. The model handles both the jet and far-field regions; it predicts a two-dimensional temperature field and areas within isotherms down to a 0.56C° (l.OF 0 ) temperature excess. The parameters required for the appli¬ cation of this model are: b 0 = width of rectangular outfall, h 0 = depth of rectangular outfall, Qjl* = excess heat-rejection rate of power plant based on 9 0 , 9 0 = initial excess temperature of the jet, and K = surface-heat-loss coefficient. In spite of the simplifications made in the model development, the author claims the model to be conservative in many respects and simple to apply. The author's theoretical development is carried out in four consecutive stages: 1. Horizontal spreading is considered, neglecting vertical diffusion and surface heat loss to the atmosphere. A two-dimensional temperature field is determined for the jet and far-field regions by the integral equations of conservation. Centerline temperature and velocity is found to drop off as 1 / VW in the jet regime, where s is the distance along the centerline after a constant region of flow establishment of length 6b 0 . For the far-field region, excess temperature is assumed to drop off as l/s. 2. Vertical entrainment is then considered independent of horizontal spreading and surface heat loss. The depth is assumed constant, except pos¬ sibly for a small region in the vicinity of the outfall, where the depth grows slowly in a linear fashion. When vertical spreading is assumed to occur, a correction of the two-dimensional temperature field is made to account for the additional dilution. For Lake Michigan, Pritchard suggests that vertical *Qj_j would be identically equal to the total condenser heat-rejection rate if the condenser intake temperature were identically equal to the ambient temperature. spreading be allowed for until the plume depth reaches 3.05 m (10 ft). For a greater initial depth, the jet is assumed to remain at that constant depth throughout the complete field. 3. A second correction of the temperature field may be needed, depending on the temperature of the water entrained into the plume. Due to possible recirculation of condenser cooling water, the diluting water mixed into the plume may have an excess temperature above ambient. Once this additional correction on the temperature field is made, the areas within isotherms can then be calculated for the condition of mixing alone. 4. Surface heat losses are then included in the analysis as a cor¬ rection to the areas derived in stage 3. This surface-heat-loss correction yields the final two-dimensional temperature field and the isotherm areas. VII. MODEL COMPARISONS TO DATA Table IV summarizes the basic discharge and environmental parame¬ ters required for application of the analytical models to the four Point Beach cases and the single Palisades case. Parameters such as entrainment and drag coefficients were chosen, based upon the recommendations of the model authors. In some cases (especially with the Motz-Benedict model), no clear- cut choice exists for some of the required parameters. This problem is discussed in more detail in Sec. VIII.C.2 below. The data, JETFIT - smoothed results and model predictions are dis¬ cussed and compared with respect to some of the major jet characteristics in the following paragraphs. A. Jet Trajectories Figures 56-60 show the jet trajectories resulting from JETFIT and the four model predictions. Before the analytical models are compared to the jet trajectory data, a few comments should be made regarding the JETFIT trajectories themselves. Figure 56 shows the jet centerline to bend gradually toward the north-shore direction (negative x direction). In a similar fashion, Fig. 57 shows the jet to bend gradually toward the south-shore direction (positive x direction). In both cases, the ambient current has been assigned a nominal value of zero, based on field measurements. Possible causes of the seemingly anomalous behavior may be combinations of the following: 1. A small but undetectable ambient current, directed north on May 18 and south on May 23, may have been present. The threshold of the instrument used for measuring ambient current is about 3.0 cm/sec; con¬ sequently, any current below or near this value is virtually undetectable. Further, the ambient-current conditions were measured at a limited number of specific locations. A small current could possibly have been detected at some other location, since near-shore current measurements are known to be spatially and temporally unsteady. 2. Local gyres might exist in the region of the outfall. The intru¬ sion of the 33-m discharge structure into a small ambient-current field will cause local eddies and gyres to form in the vicinity of the discharge. Data taken near the outfall may be influenced by them. Also, a return current on the lee side of the jet (when an ambient current exists) or on both sides of the jet (when no ambient current is present) is required to provide water to the jet as it disperses due to jet entrainment and ambient mixing. When an ambient current exists, the region between the outer boundary of the jet on the lee side and the shoreline will be likely to contain eddies of continually recirculating water. 3. Lake-bottom irregularities in the vicinity of the discharge might influence the jet trajectory. The contours in Fig. 6 represent average values Point Beach Unit No. 89 a> ■3 = CJ U o > eg to I «J I ONNNONf O O nO fO O • no o . o in -f- o eg . . HOIPJOO 1—< eg lo 000 o > % ii m u X ctJ _ - to eg „ • f"- LO .NO • • • ^ to • • O -Of Of • ^ HlOHH f ON NlON H a o eg NO ^ o e s • lo to 10 r-H eg lo 000 •s . Z ° F a a eg o H NO lO N . . • tO f"- • o • o lo h lo • cn IHf-ONNlONH a o cnj >Of o LO O to fH eg lo 000 > a § H F t r- t^. 1^. t"- » . eg o • • • io N • O -Of Nf • ^ IrIf nONHION n a o eg NOf o LO o LO H eg lo OOO ss r 0 0 sa ■2.S C55ii-S^ .Q JO 0 >T 3 O- Cjfl LO LJ 0 > rH ft 00 to y f 3 ^ 133 •a bo 00 o' oZ !J J • 8-8 *-» 4 J LO tO 4-» d> 0) c I I 0 ) § So U, U-, lm < f3 ^ U . E £ *-> -r-< u3 uJ C <4-4 < 0) < 4 -| > 4 -> 4 -* E y ctj ctj E O I -3 U J ttb 0 A 2 W'p(s) - Cb 0 + Ys, and A, Ot , C, and Y are fitted parameters. It is clear from Figs. 63-67 that the temperature excess near the outfall from the data-smoothing procedure can be different from 0 O . This corresponds to A / 1. The values of A, Ot, and length of region of flow establishment s 0 = Ot /A 2 (in units of the outfall width) for the four Point Beach dates con¬ sidered are: May 18 May 23 July 13 September 9 A 0.84 0.84 0.92 0.79 ot 3.8 5.6 6.2 4.5 So 5.38 7.95 7.32 7.22 The values of s 0 do compare with values in the range from 5 to 7 usually quoted in the literature. However, the above Point Beach numbers certainly reflect insufficiencies in the data and inadequacies in the fitting procedure; consequently, much significance should not be attached to them. Since 0 ^ 0 O (i.e., A 4 l) at the outfall, one should not place much significance on the results of the fitting procedure for the first 50-100 m. It may have been more profitable to have A fixed at 1.0 and introduce a new parameter e as the power of ocb 0 /s in the formula for 0 c (s). (The present formulation restricts e to a value of 1 / Z.) The fit would then involve ot, e, C, and Y- It is not expected, however, that the present JETFIT results would be altered significantly if such changes were implemented in the fitting func¬ tion. One further comment: The results of JETFIT for the jet character¬ istics most generally agreed with what one would expect from visual examination of the data along each transect of the jet. This gives additional confidence to the JETFIT results. 96 °9/°e °n/ 3 n 0 e/°e ° n / 3n Fig. 63. Centerline Temperature Excess and Velocity Decays Result- Fig. 64. Centerline Temperature Excess and Velocity Decays Result¬ ing from the Fitting Procedure and Model Calculations for ing from the Fitting Procedure and Model Calculations for Point Beach: May 18, 1972. ANL Neg. No. 190-952. Point Beach: May 23, 1972. ANL Neg. No. 190-949. 97 0 8/°e °n/ 3 n Fig. 65. Centerline Temperature Excess and Velocity Decays Result- Fig. 66. Centerline Temperature Excess and Velocity Decays Result¬ ing from the Fitting Procedure and Model Calculations for ing from the Fitting Procedure and Model Calculations for Point Beach: July 13, 1972. ANL Neg. No. 190-958. Point Beach: September 9, 1972. ANL Neg. No. 190-951. 98 Fig. 67. Centerline Temperature Excess and Velocity Decays Result¬ ing from the Fitting Procedure and Model Calculations for Palisades: October 10, 1972. ANL Neg. No. 190-960. The Pritchard model appears most accurate and also conservative for the four Point Beach cases of Figs. 63-66. Both JETFIT and the Pritchard model have centerline temperature decay rates proportional to the -l/l power of the centerline distance; hence, both curves become parallel as s increases. The Motz - Benedict model gives reasonably conservative predictions for the no-current cases of May 18 and May 23 where the entrainment coefficient was chosen to be 0.05. (Benedict recommends 0.04 for a 90° outfall and suggests a slight increase for an off-90° discharge.) The model does poorly on July 13 and September 9, apparently due to the choice of entrainment coefficient. The authors' recommendation for the value of the entrainment coefficient for cases with ambient current less than 0.2u 0 is not clear. The model overpredicts temperature decay for both these cases. The Stolzenbach-Harleman and Prych models both predict a much greater temperature decay than the data indicate. When no current exists, the Stolzenbach-Harleman decay is initially very abrupt, 99 yet tends to level off after about 125 m; the centerline temperature data eventually drop below the model results. For the current cases of July 13 and September 9, the centerline decay of Stolzenbach and Harleman is more regular, yet is too rapid. The Prych model predicts too great a temperature decay, yet does so at a rather regular rate of decrease, seemingly independent of an ambient current. Moreover, Prych predicts lower temperatures than Stolzenbach and Harleman, at least within the first 200-250 m from the outfall. Beyond this point, the two models run nearly parallel. Figures 68-72 show the widths of the excess temperature distribu¬ tions resulting from JETFIT and the model calculation. (Note that the linearity of the JETFIT results is a consequence of the linear form assumed in the fitting function.) A very rapid rate of lateral spreading is apparent for the Prych and Stolzenbach-Harleman models. Both models require an assumed form for a lateral spreading velocity that is instrumental in determining the Fig. 68. Half-widths of Temperature and Velocity Distributions Result¬ ing from the Fitting Procedure and Model Calculations for Point Beach: May 18, 1972. ANL Neg. No. 190-947. 250 1-1-1-R—7-1-1-1-1-1 250 100 Fig. 69. Half-widths of Temperature and Velocity Distributions Result- Fig. 70. Half-widths of Temperature and Velocity Distributions Result¬ ing from the Fitting Procedure and Model Calculations for ing from the Fitting Procedure and Model Calculations for Point Beach: May 23, 1972. ANL Neg. No. 190-946. Point Beach: July 13, 1972. ANL Neg. No. 190-942. 2501-1-1-1-7—i-7-1-1-1--»-1 250 Fig. 71. Half-widths of Temperature and Velocity Distributions Result- Fig. 72. Half-widths of Temperature and Velocity Distributions Result¬ ing from the Fitting Procedure and Model Calculations for ing from the Fitting Procedure and Model Calculations for Point Beach: September 9. 1972. ANL Neg. No. 190-941. Palisades: October 10, 1972. ANL Neg. No. 190-959. 102 lateral extent of the jet. Both models, on the basis of present results, used assumptions that were apparently too theoretical in nature and apparently require calibration with some empirical data to yield more accurate results. The overextended lateral spread of these two jet solutions is a probable cause of the extremely rapid centerline temperature decay required by energy conservation at each jet cross section. The Motz-Benedict model predicts a jet that is by far too narrow for all four Point Beach cases. The model is very sensitive to the particular choice for the value of some of the input parameters, in particular, the entrainment coefficient and the jet width at the end of the region of flow establishment. A more judicious choice for these parameters would un¬ doubtedly improve the comparisons. However, when this model is used as a predictive tool, it is difficult, at present, to know what values to choose other than those recommended by the authors of the model. Pritchard predicts rather accurate temperature decays and widths, except for the temperature width on September 9- The wider width of the data might well be due to the second unit operating at 12% power on that date, adding to the temperature excesses on the offshore side of the plume. The Palisades results are quite interesting (Figs. 67 and 72). As expected, the temperature does not drop off until about 175 m downstream, due to the larger region of flow establishment resulting from the wider out¬ fall at Palisades. Again, Prych and Stolzenbach and Harleman are still too optimistic in their temperature-decay predictions and too wide in their lateral jet spreading. Pritchard predicts too great a temperature decrease and too narrow a jet. This is probably due to his method of handling vertical entrain¬ ment, which is very sensitive to the difference between the outfall depth and the critical mixing depth of the lake. Vertical entrainment is not a factor in Pritchard's predictions for Point Beach. Motz and Benedict are conserva¬ tive in temperature decay for Palisades due to the large region of flow estab¬ lishment (5.2 times the full width of the outfall). Lateral widths are again very much underpredicted. C. Centerline Velocity Decay and Velocity Half-widths Figures 63-67, for u c /u 0 derived from JETFIT, indicate a significant deviation of the initial jet velocity from the calculated average channel ve¬ locity. For July 13, velocity measurements near the channel outlet indeed verified a velocity greater than u 0 for the first meter depth. Other measure¬ ments, on different dates, all showed values greater than u 0 . The Stolzenbach-Harleman and Prych models predict too rapid a velocity-centerline decay. In each case, the Stolzenbach-Harleman model predicts an increase in velocity after the jet leaves the outlet up to 60 m along the centerline. This is possible for discharges having very low den- simetric Froude numbers. A light fluid, discharged over a heavier fluid, 103 accelerates laterally as well as longitudinally due to hydrostatic pressure gradients. For low densimetric Froude numbers (near 1.0) such buoyant accelerations become dominant. Although increases in velocity are possible, increases in temperature are never realistic. If such hydrostatic pressure gradients were removed or neglected in the model, a momentum jet would occur. For discharges having high densimetric Froude numbers, lateral accelerations greatly dominate longitudinal ones and consequently allows such longitudinal gradients to be neglected. The densimetric Froude num¬ bers for the four Point Beach cases are about Z.4, which may be a little large for the above floating-plume phenomenon to occur. For the stagnant- lake cases of Figs. 63 and 64, the Prych model has a sharp decrease in velocity within 1Z5 m of the outfall and then tends to level off. The Stolzenbach-Harleman model is more regular in its rapid velocity decline, crossing the Prych curve for u c /u 0 at about 170 m from the outfall. The ambient-current cases realize a more regular velocity decline, with the Prych model giving consistently lower velocities. The Motz-Benedict and Pritchard models appear adequate for both stagnant-lake cases of May 18 and May Z3, and the current case of September 9- The data of July 13 reveal higher velocities than predicted by any of the models. An apparent defect in the Motz-Benedict model is the assumption of decay of lateral velocity to zero, even where an ambient current exists. A more realistic assumption would require a decay superimposed on U a cos P (the component of the ambient current parallel to the local jet centerline). Velocity widths as predicted by the Prych and Stolzenbach-Harleman models are much too large for the four Point Beach dates (Figs. 68-71). This again reflects on their assumptions of lateral spreading velocity. The Prych predictions are consistently larger than those of Stolzenbach and Harleman. The Stolzenbach-Harleman predictions appear too sensitive to ambient cur¬ rent; the Prych predictions seem very insensitive. Pritchard has no predic¬ tions for velocity width. Examining the data reveals that the temperature width is approximately twice the size of the velocity width for any fixed date at Point Beach. The Palisades data indicate a very slow velocity decline after a rather rapid drop in the first 50 m (see Fig. 67). This rapid drop might be due to the long, diverging discharge channel. Irregularities in the velocity distribu¬ tion across the channel (lake water entering the channel at the north end combined with significant channel-depth irregularities) may be a contributing factor. No model for velocity decay appears adequate for Palisades on October 10. Velocity widths of Prych and Stolzenbach and Harleman are again too large, and the Motz-Benedict predictions, although more reasonable, are too small (see Fig. 7Z). Due to site-dependent irregularities (diverging outfall, shallow bottom), Palisades is not the ideal site to evaluate near-field models, albeit a real site. 104 D. Temperature and Velocity Half-depth Figures 73-76 compare the predictive models with respect to half-depth. The half-depth is the vertical distance at which the excess temperature and/or excess velocity drop to one-half the local surface-centerline value. Also shown is an indication of the location of the lake bottom. No data are plotted, since the vertical profile information was insufficient to define a half-depth in most cases. Either the 3.0-m limit or the lake bottom was reached before the half¬ depth or the temperature or velocity distribution was reached. VELOCITY -/ \ ir"\ % > i / \\i i / ■ A 3 W 0) J Q 4 V ~\ \: " \ 'k.- VELOCITY TEMPERATURE 5 — 6 - STOLZENBACH-HARLEMAN PRITCHARD a MOTZ-BENEDICT LAKE BOTTOM - PRYCH V 50 100 150 200 s (meters) 250 300 350 400 Fig. 74. Half-depths of Temperature and Velocity Distributions Result¬ ing from Model Calculations for Point Beach: May 23, 1972 105 3 k_ Q) 00 g g eg Vf (V) 9 9 9 9 9 O to vO 00 r-* r oo to to rg to o r rg to OY to to rg o o o o o o o o o CN1 9 9 £ eg 12 lo g g ir. JO ~ CO ^ il 9 5 „ 3 9 9 9 9 9 OO >-< rg p_ OY rH H" LO Cg rH C*g -H rH rH l o LO OO I s ** o o o o o o 9 3 Cl 9 X U Cti UJ 4-* (T3 if) V) > LO o LO o LO o ^ Oh si o rH rH rg rg to 4-> •rH o rH rH rg rg to TABLE VI. DETERMINATION OF TWERATURE AND VELOCITY HALF-DEPTHS AT EACH STATION LOCATION FRCM THE POINT BEACH DATA OF MAY 23, 1972 108 TABLE VII. DETERMINATION OF TEMPERATURE AND VELOCITY HALF-DEPTHS AT EACH STATION LOCATION FROM THE POINT BEACH DATA OF JULY 13, 1972 109 cQl wl cq I Si n I zl 2l O I hh| Hi <1 Hi COl e- e- LO rH LO rH e- rH vO to rH eg rH rH o o rH to 1 to l vO LO 00 to LO vO to O) r- rH eg rH rH o o rH to l to 1 vO 1 LO o LO rH to r- vO 00 CT> rH CT) rH to CM eg rH o LO oo eg to to rH i i LO OO vO to O c- to rH to rH to CM eg eg H LO 00 to eg rH 1 a s to to OO H o cr> o LO 00 LO to s . to eg to to H CM eg eg vO to eg i LO £ eg £ i ! § 12 to oo rH LO e- e- to LO eg vO CM 1 LO CM H rH o o eg »H rH eg eg H 1 o o § rH H rH o o to 3 LB o OO LO a a W CO CQ < H" O vO £ Q O o rH vO o rH O vO LO rH £ i ■— 1 eg vO to to tO cr> vo oo to LO eg e- vO tO to to lo rg o e- to eg 00 rH to rH rH oo LO o LO LO vO VO vO rH 00 to o oo oo *3- H CO W W CQ to 1-t Q UJ "O h C Uh 03 • H CO H CO w w CQ S 1 ■ s -a -H CM <* •'CO vO 5 eg .35 LO oo rH to eg 00 rH H- to to to rH rH to eg rH LO LO CM LO 00 LO 00 vO a LB N to to rH or rH rH 1 "d to to LO H - LO vO oo • • o to CT) vO vO LO e» a e- oo oo vO LO LO eg to H 03 5 (/) 4-* O LO vO LO rH 03 to LO vO OO H- 0) O r* rt H- to eg (/) o 00 O a a a O eg e- a 00 h- S I O i lu o H O z F < O Cu m m ^ £ h Q < ■ > UJ t— H PL, CO S co£ i: H t-H II I co cy co S W H X - PJ LO fea £ ga a i ^ LO CO h : o i c/o £ £ I §1 TABLE VIII. DETERMINATION OF TEMPERATURE AND VELOCITY HALF-DEPTHS AT EACH STATION LOCATION FROM THE POINT BEACH DATA OF SEPTEMBER 9, 1972 no oc\ wl ml si ZD | zl zl ol HH | Hi <1 Hi CO I r- vO f-. GY o CM LO r-H ^P o r-H (SI to to CM r-H o O O r-H CM i i i i i NO to GY NO rsi ^p LO ^p LO t-H to CM Csl r-H O CO to o o ^p i i i LO vO o ■^p 00 LO c- VO t-H to to r-H o o gy to o o r-H i i i (VI LO LO r- ^p r-H (VJ to (VI t-H to (VI r-H O o (VJ o o o o r-H 1 1 1 to o vO vO ^P O LO r-H (VI to (SJ i-H to (VI t-H r-H r-H o i-H O o o i-H i 1 1 (VJ to *pp o (VI (VI OO r-H rH • • • • • • • • • • to to (VI (SJ o r-H r-H (VJ to (VJ i i i i t-H 00 to GY NO (VI O to *3- r-H • • • • • • • • • • to to (VJ i-H r-H to vO o LO r-H r-H 1 1 o gy vO LO NO to o r-H o (VJ r-H • • • • • • • • • • to to to fsj LO (VI vO r-H t-H 1 GY ^3- ^P O ^P LO tO to (VJ NO t-H OO CM to oo cm o CM rH r-H I O (VI 00 r-^ to r-H GY (VJ 00 • • • • • • • • • ^P rp rp to r-H LO Csl to O O Csl (VI r-H r^ LO *rp to TABLE IX. DETERMINATION OF TEMPERATURE AND VELOCITY HALF-DEPTHS AT EACH STATION LOCATION FROM THE PALISADES DATA OF OCTOBER 10, 1972 1 1 1 vD (NJ to o o tO o oo eg lo eg o eg vO LO vO e- LO CTi tO eg o o o eg lo eg to to lo 9 to e- o to 9 o \D eg LO o LO to 9 O o 9 00 eg eg or pH eg 9 vO t"- o o o 00 00 -3- eg eg i—i o o ■'d- cn oo e- o o o 00 e- o oo OLOOtOtOt^- to 1—I rH O O to VO 00 'C* O eg o to o eg co O' oc\ pjI CQ I Si ^1 Si Si Ol ►H I HI <1 Hi col lo o oo g 2 2 LO to o LO LO to 2 2 O rH LO LO 00 g g g oo vO eg 9 9 9 9 9 OO LO f" rH rH rH I I I 9 9 9 to o e- g 2 2 eg o o H o eg oo 2 2 9 lo eg lo eg rH ^ 3 3 3 3 9 § LO o PJ CQ 2 H CO PJ PJ PQ H LO rH tO 2 ^ ^ e- lo 0^ 9 9 9 9 lo eg o eg vo 2 2 9 to or e- eg rH *2 °I 9 9 9 3 eg eg II II 91 E—' S w S *-h PJ 9 9 9 3 °2 9 9 9 9 to H co < I O jC d4 rS e- o lo to 3 9 3 9 ■H- v£> to 2 2 9 vO eg o o e- v£> LO 9 9 9 oo to lo 2 2 2 \D rj- to E LO o E o 9 9 E o eg Q> > a> rj 5 CJ o to in O 9 3 9 9 0 0*399 O eg eg lo o> o 2 2 9 'CT> cO O 0° ^ o 9 2 9 -C ^ tO ’H- L) rH rH o o O O E o eg to eg eg 9 9 E LO E E E O lo o eg eg to PJ Q CO CO I SI w ■ w & fe 1 £! U. n °2 £9 POINTS OF IRREGULAR VERTICAL EXCESS-VELOCITY VARIATION: 18-25. FROM POINTS 7-17, THE VELOCITY HALF-DEPTH OF THE STRATIFIED JET MAY BE ESTIMATED AS 0.5-1.5 METERS. 112 Fig. 77. Half-depths of Temperature and Velocity Distributions Result¬ ing from Model Calculations for Palisades: October 10, 1972 three-dimensional Prych and Stolzenbach-Harleman models predict a buoyant surface jet, with only the Stolzenbach-Harleman temperature half-depth reach¬ ing the bottom. On a point-by-point basis (see Figs. 43-48), the temperatures at Stations 9, 11. 14, and 1 5 do not decline to half their near-surface values before the lake bottom is reached. All other points indicate a 1.0- to 1.5-m temperature half-depth. It is inferred from the data that the jet hugs the bottom for the first 125 m and then rises to a 1.0- to 1.5-m half-depth as the bottom drops away and jet buoyancy becomes predominant. A point-by-point analysis of the velocity data indicates no real trend. The bottom was usually encountered on the first two transects before the half-depth was reached. The velocity half-depth appears to be 1.0-1.5 m otherwise. The variation of ve¬ locity data with depth at Palisades is just too erratic for any consistent con¬ clusions. This also was true for the Palisades data of June 14 and July 19. E. Isotherm Areas Isotherm areas were calculated based upon the temperature-distribution function resulting from the fit to the data by JETFIT. The data were not suf¬ ficiently detailed to contour isotherms and determine areas directly. Conse¬ quently, the JETFIT area calculations should be used with caution. It is encouraging, however, to note that isotherm areas for the four dates at Point Beach are approximately the same; this is to be expected, since plant conditions were nearly the same and ambient currents were weak, if present at all. These isotherm areas, along with the model predictions, are presented in Figs. 78-82. 113 o o o o o o ( Z W) V3UV i 4— 1 •r»4 U-. c* GO •1-^ Ci4 G -J O •H 2 4—» a < a . o 1-4 G pG o T3 (U 0) CO O 4-* o c 1-4 •H Oh o bO Oh C 4-4 •H 4-> £ ( Z W) V3HV No. 190-939. Neg. No. 190-938. 114 O 05 l 4-* U4 X> a 03 D o E o X> c 03 3 u X w a a c a> O oo c 3 CO (.D) °e (39S/UJ3) from the Fitting Procedure and Model Calculations for from the Fitting Procedure and Model Calculations for Point Beach: May 18, 1972 Point Beach: May 23, 1972 118 (oD) °Q (33S/W0) 3 n oo c , TP a 03 3 o 03 u *3 TP o c 1/5 u, u 0) c C r 3 a) Uh U 03 03 (D CQ E c o CL 00 oo •H Uh TP C 03 5 c C 3 (U b-, U «> N 00 3 C —> Uh CJ « S 3 CQ 4-J ^ E s 2 O id CL CO CO 00 • H Uh UP) (D3S/UU3) 3 fl 119 Fig. 88. Centerline Temperature Excess and Velocity Excess as a Function of Depth at 150 m from Outfall Resulting from the Fitting Procedure and Model Calculations for Palisades: October 10, 1972 G. Variation of Temperature and Velocity Width with Depth Each mathematical model predicts a constant velocity and temperature width with depth. The two-dimensional models do so by the nature of their two- dimensionality, the three-dimensional models by definition of their lateral and vertical profiles. The Stolzenbach-Harleman and Prych models assume, for any cross section of the jet normal to the centerline, the same decay laterally independent of depth, as well as identical decay vertically, irrespective of lateral distance. Consequently, the widths must maintain a constant value with depth. The data, however, show a more lens-shaped profile, indicating that the temperature and velocity widths decrease with depth (see Figs. 89-92). The local centerlines (with depth) do not coincide, yet are sufficiently close to indi¬ cate that such vertical profile results may be meaningful. From the figures, the temperature width appears to be uniform with depth for about 1.5 m and then decreases abruptly; the velocity width appears constant for a shorter depth distance (0.5-1 m) before decreasing toward zero. 120 (SJ3iaai) ± /v\ (sjatauj) n M Fig. 89. Half-widths of Temperature and Velocity Distributions as a Function Fig. 90. Half-widths of Temperature and Velocity Distributions as a Function of Depth at 150 m from Outfall Resulting from the Fitting Procedure of Depth at 150 m from Outfall Resulting from the Fitting Procedure and Model Calculations for Point Beach: May 18, 1972 and Model Calculations for Point Beach: May 23, 1972 121 (SJ3J9UJ) 1 m (SJ3tauj) n M Fig. 91. Half-widths of Temperature and Velocity Distributions as a Function Fig. 92. Half-widths of Temperature and Velocity Distributions as a Function of Depth at 150 m from Outfall Resulting from the Fitting Procedure of Depth at 150 m from Outfall Resulting from the Fitting Procedure and Model Calculations for Point Beach: July 13, 1972 and Model Calculations for Point Beach: September 9, 1972 The Palisades data (see Fig. 93) are insufficient and irregular, due again perhaps to the shallow lake depths in the discharge vicinity as well a the nonuniformity of the diverging discharge. 300 250 200 QJ £ 150 100 50 250 200 | 150 100 50 T T. T. T. ■~l -STOLZENBACH-HARLEMAN ■ M0TZ- BENEDICT ■PRITCHARD -PRYCH • FIT TO DATA 20 2 5 -z (meters) 4 5 Fig. 93. Half-widths of Temperature and Velocity Distributions as a Function of Depth at 150 m from Outfall Resulting from the Fitting Procedure and Model Calculations for Palisades: October 10, 1972 123 VIII. SUMMARY AND CONCLUSIONS A. Fiel d-data Acquisition The experimental technique described in Sec. II for making meas¬ urements in the jet regime represents a compromise between speed and com¬ pleteness. More data in a shorter period of time are needed for a more accurate comparison with model predictions. Given the manpower and equip¬ ment limitations under which the work was done, the technique reported on in this report gives reasonable results in terms of number of data points versus time of measurement. The data obtained in this manner reflect the gross features of the jet regime, but have two limitations: 1. Since the temperature and velocity at a point in the jet are not constant, a single measured value of each may not accurately define these parameters at a point. 2. The measurements are not made simultaneously. Typically, they are collected over a period of 3-7 hr during which time factors affecting the jet may change. B. Data-smoothing Technique The fitting procedure described in Sec. V was used to extract the gross features of the temperature and velocity distributions from the field measurements. Some procedure of this type is necessary because the data consist of measurements at isolated points in the temperature and velocity fields. The functional forms used in this study were chosen for several rea¬ sons. One reason is their similarity to the forms resulting from the simple yet fairly widely used jet analyses of Pritchard 17 and Motz and Benedict. 5 Another reason is that preliminary examination of the Point Beach data in¬ dicated that such forms might represent the available data fairly well. Finally, it was thought that for this initial attempt at data fitting, simple forms with limited numbers of free parameters would be appropriate. Clearly, unless the actual functional forms are known, any fitting procedure of this type will have limitations and biases. The results of the present fitting procedure can be considered to be a successful first attempt. It is difficult to assess the goodness of fit in a mean¬ ingful, quantitative way; therefore a point-by-point tabulation has been included in Appendix D. The average deviations of the fitted function from the data for any particular set of measurements never exceeded 1 .1 C° for temperature and 8 cm/sec for velocity. These values correspond to 12 and 14% of the initial excess temperature and average outfall velocity, respectively. Certainly at least the gross behavior of the near-field temperature and velocity distribu¬ tions has been accounted for with the present fitting procedure. 124 C. Analytical Model; Field-data Comparisons The results of the model-data comparisons are summarized here for each model evaluated. 1. Pritchard Model The Pritchard model compared best with the Point Beach Unit 1 and Palisades jet data presented in this report. Model-data discrepancies usually indicated conservative predictions on the part of the model. The suc¬ cess of Pritchard's model for these cases is due in part to the persistent efforts of the author in calibrating the model with field and hydraulic data. Also, the field data used by Pritchard in the development of his model were generally from plants with similar discharge and environmental character¬ istics to Point Beach and Palisades. This basically empirical or phenomenological model is not ex¬ pected to perform well when buoyancy is significant (initial densimetric Froude number less than about 2) or when the dilution capacity of the re¬ ceiving water is significantly restricted by lateral or bottom boundaries. The model is also weak in its treatment of vertical mixing; the model has scarcely been tested for prototype situations in which vertical entrainment is significant. Although the model is too simplistic to handle the major compli¬ cations that may be important in certain field cases (buoyancy, cross currents, etc.), it might well give good results for cases of the higher-velocity dis¬ charges (i.e., larger densimetric Froude number problems) for the critical case of a stagnant lake. Further verification work for this model is desirable at different sites describing a variety of geometric, kinematic, and dynamic conditions. « 2. Motz-Benedict Model The Motz-Benedict recommendations for the choice of entrain¬ ment coefficient E apparently vary over too large a range for the data ob¬ served at Point Beach and Palisades. The recommended value of 0.05 for the stagnant-lake case gave a reasonably good approximation for centerline temperature and velocity decay. Values of E for A (ratio of ambient velocity to initial jet velocity) between 0 and 0.2 were determined by a linear interpo¬ lation from the known values of 0.05 (A = 0) and 0.4 (A = 0.2). This appeared to us to be as good an approximation for E as any in the presence of the wide scatter in the Motz-Benedict data from which E is to be determined. The results indicate that smaller values of E for the cases of nonzero ambient crosscurrents would have been more appropriate. Temperature and velocity decays would not have been as rapid and plume widths would have been larger. The most sensitive parameters are E and r = b 0 ,/bo. Data for the determination 125 of E have much scatter; data for r have not been determined. The inade¬ quacies of this simple, two-dimensional model are briefly summarized as follows: a. Buoyant forces, as well as vertical entrainment, are ignored in the model development. For densimetric Froude numbers less than about 2, buoyant spreading is quite important; for densimetric Froude numbers ex¬ ceeding about 5, a substantial amount of vertical entrainment may be expected. Consequently, the types of discharges for which the model may be used is limited. The entrainment coefficient, determined from data fitting, must actually account for spreading due to buoyancy as well as from jet entrainment. b. The choice of a coefficient of entrainment must be based on inconsistent data as expressed above. Data presented by Motz and Benedict show considerable variation in the value of entrainment coefficient from situ¬ ation to situation. Particularly for lake data, the value of E is shown to be extremely small, -0.04, in relation to riverine situations where E is about an order of magnitude larger. A particularly interesting contrast is afforded when one compares 5 the Motz-Benedict laboratory data for a 90° discharge to the Romberg-Ayres lake data. Although most of the initial conditions are similar, the entrainment coefficients are different by about a factor of 10. Part of the problem probably lies with the fact that Motz and Benedict ana¬ lyzed lake data from locations in which prominences (breakwaters, for ex¬ ample) were present. A second difficulty is that the limited field results indicated that the entrainment coefficient remained essentially constant at a particular location with changing values of A; this behavior is consistent with the laboratory findings showing E to be relatively independent of A for each site. Here, turbulent intensity of the ambient current (see item e below) may be a significant factor that was ignored. c. We believe the model is actually restricted to small ambient currents. The simulation assumes that the jet velocity approaches zero at large distances normal to the jet centerline. The assumption of Gaussian profiles for temperature and velocity and the assumption of equal rates of entrainment on offshore and lee sides of the jet are not valid for ambient currents that are not very small. d. The model does not simulate unequal rates of spread for momentum and heat, as has been observed to be significant in the Point Beach and Palisades data. The Prych and Pritchard models also do not distinguish between these rates of spread. e. The model does not treat turbulent intensity in the crossflow, due to the assumption that such turbulence and its effect on mixing are neg¬ ligible. Although some account of this effect may be made in the choice of entrainment coefficient, any such treatment would be only qualitative in nature. The other models do not treat this phenomenon adequately either; the Prych model does include ambient turbulence in terms of a horizontal and vertical ambient eddy-thermal diffusivity. 126 Deficiencies a and b could eventually be fatal to the model. Im¬ proved predictions might be obtained by determining the free parameters E = entrainment coefficient, r = b 0 /bo and s = ratio of lateral spread of heat to that of momentum for each set of data available, with the hope that a consistent trend (or corre¬ lation) might develop as the initial densimetric Froude number, initial angle of jet discharge with the current, velocity ratio A, and w (ambient stream width/discharge width) vary. 3. Stolzenbach-Harleman Model The Stolzenbach-Harleman model generally compared poorly with the jet data of Point Beach and Palisades. Centerline temperature and velocity decay were predicted to be too rapid; the lateral spread of the jet was much too great. The model does not consider jet interaction with the lake bottom, which does occur to some degree near the outfall. Such interaction should provide some increase in lateral spread due to restricted dilution at the jet- lake bottom interface. The predicted lateral spread, however, greatly ex¬ ceeded the observed spread, even with bottom effects assisting that lateral growth. Surprisingly, the model tends to underpredict lateral spread in the region of flow establishment. These poor comparisons of model to data may be traced, in part, to the model assumption on lateral-spreading velocity, which was based more on physical intuition than on any data. A second major fault of the model lies in the presumed jet struc¬ ture based upon nonbuoyant jet theory. First, the four-zone, rectangular jet structure may not be valid for buoyant jets. In particular, the cross section of a buoyant jet is normally taken to be lens-shaped rather than rectangular, as supposed by the model. The assumed division of the jet into four distinct regions necessitates that interregional velocities be specified. The forms of these velocities are unknown and therefore must be guessed. Stolzenbach and Harleman also require that no turbulent momentum transfer occurs between regions of the jet or between the jet and ambient water. This is tantamount to dropping the Reynolds stress terms in the equations of motion or, equiva¬ lently, dropping the turbulent-diffusion mechanism. As a consequence, turbu¬ lent jet diffusion had to be artificially simulated through the entrainment coefficient and similarity forms for temperature and velocity. In any case, some calibration of the model to actual field and hydraulic data might have provided better predictions. Aside from the largely theoretical criticisms of the model, there are practical difficulties in actually obtaining a numerical solution to the set 4 * 127 of ordinary differential equations. Due to the complexity of the set, derivatives must be found by solving a linear set of algebraic equations before applying a Runge-Kutta scheme. For many cases, the matrix, which must be reduced, is nearly singular and much precision is lost in solving for the derivatives. Among the problems that may be encountered in using the code are: a. Width predictions may decrease by as much as 50% with each o rde r-of-magnitude reduction in the error criteria until the program finally fails'. b. The program may not run for cases of (1) Low initial densimetric Froude number. (2) Low aspect ratio. (3) Initial angles greater than 90°. c. Numerical underflows must be suppressed for successful completion of many runs. d. Differences in machine precision due either to differences in word structure or to differences in the operating system may cause differences of up to 5% . 4. Prych Model The Prych predictions have the same problems as those of Stolzenbach and Harleman: a. Too rapid a decay in centerline temperature and velocity. b. Too great a lateral spread. The Prych model also compares poorly with the Point Beach and Palisades data. We suspect that a major difficulty with the theoretical development is in the assumption for a late ral-spreading velocity based upon the analogy to the celerity of a density front of a uniform depth with a uniform density differ¬ ence. This model for lateral spreading is apparently incorrect as simulated. Also, the hydrostatic pressure force is simulated to act in the longitudinal di¬ rection only. Pressure forces in reality act longitudinally and laterally, with an approximate hydrostatic distribution vertically. The as sumption of a fictitious late ral-spreading velocity was made to remedy that omission. The adequacy of the Prych simulation of ambient turbulence and shear stresses has not been verified. Calibration of the model and its empirical coefficients with hydraulic or prototype data might have improved predictions. As with the Stolzenbach-Harleman model, the Prych model is ap¬ plicable for small or zero ambient currents due to the assumption of similarity for temperature and velocity profiles, as well as equal entrainment on offshore and lee sides of the jet. The computer code developed by Prych operates well (model equations are simpler than those of Stolzenbach and Harleman); this makes it easier for future alteration, manipulation, and calibration of the model. 128 IX. RECOMMENDATIONS FOR FUTURE RESEARCH A. Field-data Acquisition Other techniques, such as fixed instrument arrays, aerial photography and aerial infrared imagery, and nonstationary measurement systems, may prove worthwhile in future measurements in the jet regime. These techniques or combinations of techniques may make it possible to overcome the limita¬ tions inherent in the fixed-boat method described here, but will probably also result in increased complexity of the measurement and significant monetary commitment. B. Data-smoothing Technique To extract as much information as possible from the data, the most general functional forms practicable should be used. This would require more free parameters and a more involved and lengthy fitting process. Future at¬ tempts to extend this method of data analysis might include some of the following: 1. Instead of Gaussian lateral profiles, a function that allows for a flat region near the jet centerline might be chosen. This could then simulate the core region included in the Stolzenbach-Harleman analysis. 2. The form of the centerline temperature excess should be such as to require that it extrapolate to the measured excess at the outfall (s = 0). The present form does not have this property. 3. In the present procedure, the rate of dropoff of the centerline temperature and velocity excesses is fixed as being inversely proportional to the one-half power of s, the distance from the outfall. Instead of this being restricted to the one-half power, it could be left as a free parameter to be de¬ termined by fitting to the data. The more recent phenomenological model by Pritchard 24 has employed this form for centerline decay of temperature. 4. Additional parameters could be added to the expressions for the widths to allow them to vary quadratically with s instead of linearly. The alternatives are limitless, and only through repeated attempts at a fitting pro¬ cedure can it be determined whether significant improvements are possible. C. Analytical Model; Field-data Comparisons 1. An attempt should be made to calibrate the Motz-Benedict, Stolzenbach-Harleman, and Prych models to field and hydraulic data.* The Pritchard model (No. l) should be further tested with field data from other sites as well as available data from physical hydraulic models. The new nu¬ merical models of Brady and Geyer, Paul and Lick, and Waldrop and Farmer *'Work is presently underway by Dr. M. Shirazi at the Pacific Northwest Environmental Research Laboratory at Corvallis to improve the Stolzenbach-Harleman and Prych models by calibration with data. At this writing, a successful modification and calibration of the Prych model appears imminent. 129 look promising, and attempts should be made at verification with prototype field data. The new phenomenological model of Pritchard (No. 2), based upon 52 sets of model and prototype data, also looks promising and should be verified. 2. Considerably more data are required from more ideal or classical types of discharge structures for verification. The Palisades data had too many irregularities (rough shallow bottom and diverging discharge channel) for adequate model evaluation for those integral-type models studied in this report. Data are required for model verification (for both integral and nu¬ merical models), which include a wide range of densimetric Froude numbers, aspect ratios, bottom slopes, angle of discharge, ambient currents, etc., to provide a fair and wide variety of test situations for the models. Only when this large body of data (physical model or preferably prototype field data) be¬ comes available will it be possible to fully and fairly evaluate and improve, or develop, better models. From our verification efforts supplemented by the work done by Dr. M. Shirazi at the Pacific Northwest Water Laboratory of the EPA, we recommend that: 1. The Stolzenbach-Harleman and Prych models not be used as they exist in their present form for those cases when significant bottom interaction is expected. However, the vast majority of prototype situations do have some bottom interaction. 2. The Motz - Benedict model be used for stagnant ambient water case only (with an entrainment coefficient on the order of 0.04) 3. The Pritchard model be used for stagnant receiving water only. Further analytical work is necessary to modify the Prych and Stolzenbach- Harleman models so they can be used for shallow water surface discharges. Additional work in model calibration is necessary before a viable form of the Motz - Benedict model can be achieved for ambient currents. More verifica¬ tion work on the Motz - Benedict (no current) and Pritchard models would be useful. 130 APPENDIX A Previous Program Reports 1. J. G. Asbury, Effects of Thermal Discharges on the Mass/Energy Balance of Lake Michigan , ANL/ES-1 (July 1970). 2. E. Silberman and H. Stefan, Physical (Hydraulic) Modeling of Heat Dispersion in Large Lakes: A Review of the State of the Art, ANL/ES-2 (Aug 17, 1970). 3. J. G. Asbury, R. E. Grench, D. M. Nelson, W. Prepejchal, E. P. Romberg, and P. Siebold, A Photographic Method for Determining Velocity Distri ¬ butions within Thermal Plumes , ANL/ES-4 (Feb 1971). 4. J. G. Asbury and A. A. Frigo, A Phenomenological Relationship for Pre¬ dicting the Surface Areas of Thermal Plumes in Lakes , ANL/ES-5 (Apr 1971). 5. I. K. Abu-Shumays, D. L. Phillips, and S. M. Prastein, "Thermal Plume Data Acquisition, Documentation and Initial Analysis," Proceedings of the 14th Conference of the International Association of Great Lakes Research, Toronto, Ontario, April 19-21, 1971, p. 495. 6. G. P. Romberg, W. Prepejchal, and D. M. Nelson, "Thermal Plume Measurements," Proceedings of the 14th Conference of the International Association of Great Lakes Research, Toronto, Ontario, April 19-21, 1971, p. 625. 7. G. E. Birchfield, Wind-driven Currents in a Large Lake or Sea , ANL/ES-6 (July 1971). 8. J. V. Tokar, Thermal Plumes in Lakes: Compilations of Field Experience , ANL/ES-3 (Aug 1971). 9,. R. E. Nakatani, D. Miller, and J. V. Tokar, "Thermal Effects and Nuclear Power Stations in the U.S.A.," International Atomic Energy Agency Transactions, Vienna, 1971, IAEA-SM- 146/30 , p. 561. 10. J. G. Asbury and A. A. Frigo, "A Phenomenological Relationship for Predicting the Surface Area of Thermal Plumes in Lakes," Transactions of the American Nuclear Society, 1971 Winter Meeting, October 17-21, 1971, Volume 14, No. 2, p. 461. 11. B. M. Hoglund, D. Nelson, and S. Spigarelli, "The Anatomy of a Thermal Plume and its Biological Implications," Transactions of the American Nuclear Society, 1971 Winter Meeting, October 17-21, 1971, Volume 14, No. 2, p. 462. 12. A. J. Policastro and J. V. Tokar, Heated Effluent Dispersion in Large Lakes: State-of-the-Art of Analytical Modeling: Part 1. Critique of Model Formulations, ANL/ES-1! (Jan 1972). 131 13. T. H. Hughes and G. E. Birchfield, A Compilation of the Average Depths of Lake Michigan and Lake Ontario on a Two-minute Grid, ANL/ES-10, (Jan 1972). 14. J. E. Draley, The Treatment of Cooling Waters with Chlorine, ANL/ES-12 (Feb 1972). 15. A. A. Frigo, "Prediction of Surface Plume Areas Associated with Heated Discharges into Large Lakes --A Phenomenological Model," Proceedings of the 15th Conference of the International Association of Great Lakes Research, Madison, Wisconsin, April 5-7, 1972, p. 583. 16. B. M. Hoglund and S. A. Spigarelli, "Studies of the Sinking Plume Phenomenon," Proceedings of the 15th Conference of the International Association of Great Lakes Research , Madison, Wisconsin, April 5-7, 1972, p. 614. 17. A. J. Policastro, "State-of-the-Art of Analytical Modeling of Heated Effluent Dispersion in Large Lakes," Proceedings of the 15t h Conference of the International Association of Great Lakes Research , Madison, Wisconsin, April 5-7, 1972, p. 652. 18. Center for Environmental Studies and Environmental Statement Project, Summary of Recent Technical Information Concerning Thermal Dis- charges into Lake Michigan, Argonne National Laboratory for the Envi¬ ronmental Protection Agency Region V, Enforcement Branch, Contract Report 72-1 (Aug 1972). 19. A. A. Frigo and D. E. Frye, Physical Measurements of Thermal Dis - charges into Lake Michigan: 1971, ANL/ES-16 (Oct 1972). 20. A. J. Policastro, "Heated Effluent Dispersion in Large Lakes: State-of- the-Art of Analytical Modeling, Surface and Submerged Discharges," paper presented and published in Session Notes of the Topical Conference , Water Quality Considerations: Siting and Operating of Nuclear Power Plants, Atomic Industrial Forum, Inc. (Oct 1972). 21. A. J. Policastro and R. A. Paddock, Analytical Modeling of Heated Surface Discharges with Comparisons to Experimental Data, paper presented at the 1972 Annual Meeting of AIChE, November 26-30, 1972, to be published (Heat T ransfer Symposium Series, 1973). 22. A. J. Policastro, Thermal Discharges into Lakes and Cooling Ponds, paper presented at ASCE Water Resources Conference, Washington, D.C. (Feb 1973). 23. R. A. Paddock, J. V. Tokar, and A. J. Policastro, "Analysis of DataTaken in the Near-Field Region of a Surface Thermal Discharge with Compari¬ sons to Analytical Model Predictions, " paper presented at 16th Conference of the International Association of Great Lakes Research, Huron, Ohio (Apr 1973). 1 32 24. D. E. Frye, A. A. Frigo, and B. M. Hoglund, "Data Collection and Reduc¬ tion Techniques Used for Investigating Thermal Discharges," paper pre¬ sented at 16th Conference of the International Association of Great Lakes Research , Huron, Ohio (Apr 1973). 25. A. A. Frigo, D. E. Frye, and P. Siebold, "Temperature and Velocity Measurements in the Near-Field Region of Thermal Plumes," paper pre¬ sented at 16th Conference of the International Association of Great Lakes Re search, Huron, Ohio (Apr 1973). 26. A. J. Policastro and W. Dunn, Chapter 13: "Heated Surface Discharges-- Mathematical Models and Similarity Principles," Chapter 14: "Heated Surface Discharges--Application and Verification of State-of-the-Art Near-Field Models," Heat Disposal in Power Plant Siting, Joint Center for Graduate Study, Richland, Wash., August 20-24, 1973. 133 APPENDIX B Preliminary Feasibility Study On November 3, 1971, a preliminary feasibility study of the technique for studying the temperature and velocity profiles was made near the outfall of the Point Beach Nuclear Power Plant (Unit 1). A three-point mooring sys¬ tem was used to hold the boat steady while simultaneous temperature and velocity measurements were obtained in the near-field region. Anchors were located on either side of the plume and attached to the stern cleats of the boat, and a bowline was attached to the center of the outfall. Transects across the plume centerline were then made at about 8, 27, and 73 m from the outfall by pulling the boat from one side anchor to the other. The position of the boat was held relatively constant, and transits were used to obtain the location of each station. (Station locations for this jet study are shown in Fig. 94.) A Bendix Q-15 current meter with a YSI thermistor attached was used to measure current velocity and water temperature. The meter was lowered over the side and suspended at 2-ft intervals to a depth of 10 ft or to the bottom. The lake depth was 4.1 m at the outfall and decreased in depth to 2 1 m at a point 73 m from the outfall. Fig. 94. Station Locations for Jet-regime Study: November 3, 1971, 1245-1605 Hours. ANL Neg. No. 190-573. The data with the range of variability are plotted in Figs. 95-97 for three different depths. Drawings for the 8- and 10 - ft depths were not made because data were not available at all stations. The temperature at a given AMBIENT 134 ./ j§ *07“ f *3 / «r> <0 J, $ * n 3 O x° s>, uj uj C -5! *- D . Z < r- cr i UJ ■ oc uj _ D OC 5 H D UJ < I- *- 0C< f r _ < ' a z o 5*< uj 5 > in ^ £ < CD =>£5 o?< z UJ uj o oc oc - <<£ oc oc = uj uj Q a. cl 55* UJ UJ 0 »- H- Q UJ gd a) uj — j —j a. DDtfl m 03 _ >t- z oc UJ i dSJ • J o o Z ^ M O 00 ^ o OC uj tr u 3 , < O^u, « * * <55 •g 2. o r—I C ^ S 1 j2 o CL O* 0) £ o CL O CTJ N tr- 03 T3 a *-» c/o e CO s d) I > S Z UO DO •H Ll AMBIENT 135 136 •a S > c- XJ O'} 3 rH CO X> 00 E o 2 0) o o o o r> o o o o o o o r> o o o r» o r» o o o o o o o o o r» r> o r> r> o r> o o r» o o o o r> o o o o o o o 138 APPENDIX C FORTRAN Listing for Fitting Procedure The FORTRAN listing of the computer code JETFIT used for the jet data fitting procedure appears below. ********************************************************************** PROGRAM JETFIT ****************************************************************,******<3 PROGRAM FITS A FUNCTION (CALLED ‘JET-FUNCTION') WITH 12 PARAMETERS TO JET STUDY DATA. THE FUNCTION YIELDS TEMPERATURE AND VELOCITY CENTERLINESt CENTERLINE DECAYS AND WIDTHSU/2). THE C J NCT T ON ‘JET-FUNCTION* USES GAUSSIAN PROFILES, A QUADRATIC FORM FOR THE CENTERLINE TRAJECTORIES, A CENTERLINE DECAY OF TEMPERATURE AND VELOCITY THAT FALLS OFF AS THE INVERSE OF THE SQUARE ROOT OF THE DISTANCE FROM THE OUTFALL, AND WIDTHS WHICH INCREASE LINEARLY WITH DISTANCE. INPUT - CARD 1 (20A4) TITLE CARD 2 ( 21 5,5F 10. 5) NPTS = NO. OF DATA POINTS (STATIONS) (<=60) NLEVEL = NO. OF LEVELS (DEPTHS) AT WHICH DATA WAS TAKEN (<=6» ANGN = ANGLE OF NORTH W.R.T. + X-AXIS (DEG.) BO = FULL WIDTH OF OUTFALL (FT.) 8ETA0 = ANGLE OF OUTFALL W.R.T. +X-AXIS (DEG.) TO = OUTFALL TEMPERATURE (DEG.-C) UO = AVERAGE OUTFALL SPEED (CM./SEC.) CARD 3 (6F10.5) AMTEMP(1 TO NLEVEL) * AMBIENT TEMPERATURE AT EACH LEVEL (DEG.-C) CARD 4 (6F10.5) AMCUR(1 TO NLEVEL) = AMBIENT CURRENT (CM./SEC.) (ASSUMFD TO BE PARALLEL TO THE +X-AXIS) CARD 5 (6F10.5) CON(1 TO NLEVEL) = FACTOR WHICH SETS THE CONVERGENCE CRITERION FOR THE SEARCH TYPE FIT BASED ON THE DELTA'S FOR EACH OF THE 12 PARAMETERS TO BE ENTERED BELOW. CONVERGENCE IS ASSUMED TO HAVE OCCURRED WHEN CHANGES IN THE PARAMETERS ARE ALL LESS THAN CON*DELTA(PARAMETER) • CARD 6 (6F10.5 ) ALIMT(1 TO NLEVEL) = MAXIMUM NUMBER OF ITERATIONS IN FITTING THE TEMPERATURE PART OF ‘JET-FUNCTION* (STEPS ARE PRINTED OUT IF AL IMT < 0.0). CARD 7 (6F10.5) ALIMVd TO NLEVFL ) = SAME AS ABOVE BUT FOR THE VELOCITY PART OF THE FUNCTION. CARD 8 (6F10 .5) o o o o o o o r> o o o to ooonooooi-joonoooooooooooooooooooooooooooooooooooo 139 PCltl TO NLFVEL) = FIRST GUFSS AT FIRST PARAMETER OF •JET-FUNCTION* (DIMENSIONLESS). CARD 9 (6FI0.5) DELP(1»1 TO NLEVEL) = SMALL CHANGE IN P(I) TO BE USED TO NUMERICALLY CALCULATE DERIVATIVES AND CONVERGENCE CRITERION. CARDS 10 THROUGH 31 (6F10.5) REST OF THE 12 DIMFNSIONLFSS PARAMETERS AND THEIR DELTA'S. FOLLOWING THESE 31 PRELIMINARY CARDS COMES THE DATA DECK (THIS DECK IS COMPATIBLE WITH THE DATA DECK FOR PROGRAM JETDAT EXCEPT THAT THE LAST BLANK CARD MUST BE REMOVED). CARD 1 (3F10.5) XP = X-COORDINATE OF STATION (FT.) YP = Y-CDORDINATF OF STATION (FT.) DEPTH = DEPTH OF WATER (M.) CARDS 2 (5F10.5) (DATA AT DIFFERENT LEVELS - TWO LEVELS PER CARD) TPMP(K) = TEMPERATURE AT K-TH LEVEL (DEG.-C) VEL(K) = SPEED (CM./SEC.) DIR(K) = DIRECTION OF CURRENT W.R.T NORTH (DEG.) TEMP(K+1) = VEL( K 4-1) = DIR(K4-1) = REPEAT FOR FACH STATION UP TO »NPTS* STATIONS (<=60). DETAILS OF 'JET-FUNCTION* A COORDINATE SYSTEM IS CHOSEN SUCH THAT THE +Y-AXIS IS DIRECTED IN THE OFF-SHOPE DIRECTION. THE +Z-AXIS IS DIRECTED VERTICALLY UPWARD, AND THF +X-AXIS IS SUCH AS TO BE ORTHOGONAL TO THE OTHER TWO AND SO AS TO FORM A RIGHT HANDED COORDINATE SYSTEM IN THE CONVENTIONAL SENSE (X,Y,Z). THE PARAMETERS OF 'JET-FUNCTION' ALONG WITH TYPICAL VALUES FOR SOME POINT REACH UNIT NO. 1 DATA ARE GIVFN BELOW. P( 1) = A ( 1.0) P(2 ) = ALPHA (4.0) P(3) = C (0.5) P(4) = GAMMA (0.33) P(5) = RT (1.0) P (6) = KT (RANGES FROM ABOUT -1.0 TO 4-1.0) P( 7) = B (1.0) P(8) = BF T A (4.8) P(9) = D (0.5) P(10) = DELTA (0.19) 0(11 ) = RV (1.0) P ( 12) = KV (RANGES FROM ABOUT -1.0 TO 4-1.0) TEMPERATURE papt of •jft-functION' CFNTERLINE TRAJECTORY- X=XSI*COS(RT*BETAO)-(0.01*KT/BO)*XS1**2*SIN(R T *BET AO) C Y=XSI*SIN(RT*BETA0)4(0.01*KT/B0)*XSI**2*C0S(RT*BETA0) 140 C c c c c c c c c c r c c c c c c c c c c c r, c c c c c c c c c c c c c c c c 93 91 92 93 94 95 WHERF XSI IS INTRODUCED ONLY DUE TO THE PARAMETRIC FORM OF THE EQUATIONS (PENDS LEFT FOR KT>0, BENDS RIGHT FOR K T<0) CFNTERLINF TEMPERATURE EXCESS RATIO- (TC-TA)/(TO-TA)=A IF SALPHA*BO WHERE S IS THE DISTANCE FROM THE OUTFALL MEASURED ALONG THE CENTERLINE TEMPERATURE WIDTH (TO 1/2 THE CENTERLINE VALUE!- WT/BO=C+GAMMA*S/BO VFLOCITY PART OF 'JET FUNCTION* THE CENTERLINE TRAJECTORY EQUATIONS HAVE THE SAME FORM AS THE ABOVE WITH KT REPLACED BY KV AND RT REPLACED BY RV. CENTERLINE VFLOCITY RATIO DECAY- UC/UO=B IF SBETA*BO WHERE UC IS VELOCITY IN EXCESS OF AMBIENT CURRENT VELOCITY WIOTH (TO 1/2 THE CENTERLINE VALUE)- WU/BO=DOELTA*S/BO WARN!NG: BE VERY CAREFUL OF ATTACHING ANY SIGNIFICANCE TO THE INDIVIDUAL VALUES OF THE PARAMETERS (P(l) - P(12)), THEY ARE USUALLY NOT UNIQUELY DETERMINED BY THE DATA. DO NOT USE THESE PARAMETERS TO EXTRAPOLATE TO VALUES OF S BEYOND (OP BEFORE) THE DATA. DIMENSION TITLE(20),CON(6),ALIMT(6),ALI MV(6) ,P(12,6) ,DEPTH(60),BT( 16) ,BV(6),EPSB(6),AREA(6) COMMON/HAVE/DELP(12»6),TEMP(60,6 »,VEL(60,6),DIR(60,6),XP(60),YP(60 1 ) ♦ AMTEMP(6 ), AM CUP. (6), BET A 0,BO,ANGN,TO,UO,NPTS,DR f RD,K EXTERNAL FTSIG EXTERNAL FVSIG DR=0.0174532925 R D = 57.2 95780 IMAX= 27 FORMAT STATEMENTS - FORMAT(20A4) FORMAT! 21 5 »5F10.5) FORM AT(6F10.5) FORMAT(3 FI0•5) FORMAT!•1PP0GRAM JETFIT*,//,* JET STUDY - INPUT DAT A•,/♦5X,20A4,// 1 ) FORMAT(* NUMBER OF STATIONS = *, 13, /, ' NUMBER OF LEVELS =', 12, 1/, • ANGLE OF NORTH W.R.T. +X-AXIS = • , F8.2, * DEG.*, /, • FULL WI 2DT H OF OUTFALL =*♦ F7.2, * FT.», /, • ANGLE OF OUTFALL W.R.T. +X-A 3X1S =', F7.2,' DEG.*, /, • OUTFALL TEMPERATURE (TO) =', F7.2, ' DE 4G.-CS /, • AVERAGE OUTFALL VELOCITY (UO) =• , F7.2, • CM./SEC.*, / 5/, • LEVEL*, 2X» * AM B • TEMP.*, 2X, 'A MB• CURRENT*, 2X, 'CONV. FACT 6 OP• , 2 X, 'LIMIT(TEMP)*, 2X, •LIMIT(V EL)', /, 10X, •(DEG.-C)•, 4X, 7MCM./SFC. ) *, /) 141 96 F0PMAT(4X, !2, 5X, F7.2, 6X, F8.2, 6X f F8.5, 6X, F7.1, 5X, F7.1) 97 FORMAT(///»' INITIAL PARAMETERS OF JET-FUNCTION (ALL ARE DIMENSION 1LFSS )',//* * LEVEL',8X,'P(1)',8X,'P(2)',8X,'P(3)',8X,'P(4)',8X,'P(5 2 )• ,8X,» P(6) ' ,/) 98 FORMAT!4X,I 2) 99 F0RMAT(6X,6(2X,F10.6) ) 900 FORMAT!//,' LEVEL•,8X,•P(7)',8X,•P(8)•,8X,*P(9 ) •,7X, *P!101'»7X,•P( 1111 *,7X,'P(12)•, /) 901 FORMAT(•10ATA DECK'//,5X,20A4,//, 1 STATI ON',14X,•X',11X,»Y*,3X,•DE 1PTH* »2X »' LEVEL*,4X,'TEMP.',7X, •SPEED*,2X, •DIRECTION*,/♦18X,MET.)• 2, 7X»' (FT.)'»4X, MM.)•,8X,•(DEG.-C1•,2X,'(CM./SEC.) • ,5X,'(DEG.)',/) 902 FORM AT(5X t 13, 5X, F10.2, 2X, F10.2, 2X, F6.2) 903 F0RMAT(48X, 12, 5X, *-', 8X, *-*, 7X, '-') 904 FORMAT! 48X, 12, 2X, F 7. 2,5X, F 7. 2,4X, F 7. 2) 905 FORMAT(•1LEVEL*,12,3X,'(TEMPERATURE FIT)*,//,5X,20A 4,//I 906 FORMAT!//,• FINAL TEMPERATURE RESULTS F0R',I2,'-TH LEVEL',//,8X,'S 1TGMA =', F8•3,' AFTER*,16,* ITERATIONS.',//) 907 F0RMAT(10X,»P(* ,12 ,* I =*,F10.6) 908 FORMAT!•1C0MPARISON OF DATA AND FIT RESULTS FOR THE*,I2,'-TH LEVEL 1.*,//,5X,20A4,//,2X,'STATION',1IX,*X',1IX,•Y',2X,'TEMP.(DATA)•,2X, 2'TEMP.(CALC.)• ,3X,* BET AT(CALC.)•,2X,•SPEED(DATA)',2X,'SPEED!CALC.» 3',3X,'BETAV(CALC.)•,/,16X,'(FT.)*,7X,»(FT.)•,5X,'(DFG.-C)•,6X,»(DE 4G.-C)',°X,•(DEG.)',3X,•(CM./SEC.)',4X,'(CM./SEC.)',9X,'(DEG.)•,/) 909 FORMAT(6X,I3,2X,F10.2,2X,F10.2,6X,F7.2,7X,F7.2,8X,F7.2,6X,F7.2,7X, 1F7.2,8X,F7.2) 910 FORMAT(//,• TABLE OF JET-FUNCTION (TEMPERATURE PART)',//,9X,•XSI', 111X,'S',10X,'XC*,10X,•YC',2X,'(TC-TA)/(TO-TA>•,2X,'H(1/2)/BO•,5X,• 2BFTA',/,7X,'(FT.)',7X,'(FT.)*,7X,*(FT.)',7X,'(FT.)•,31X,'(DEG.)•,/ 3) 911 FORMAT(2X,F10.2,2X,F10.2,2X,F10.2,2X ,F10.2 , 9X,F8.4,3X,F8.3,2X,F7. 12) 912 FORMAT!//,• TABLE OF JET-FUNCTION (VELOCITY PART)',//,9X,•XSI',1IX 1, 'S', 10X, 'XC ', 10X, 'YC • ,4X, 'UC/UO* ,2X,« (UC + UA) /UO' ,2X ,' W( 1/2 )/B0' ,5 2X,'BETA*,/,7X,*(FT.)•,7X,•(FT.)«,7X,'(FT.)',7X,'(FT.)',35X,'(DEG.) 3* , /) 913 FORMAT! 2X,F10.2, 2X,F10.2,2X,F10.2,2X,E10.2,2X,F7.4,4X,F8.4,3X,F8.3 1 ,2X,F7.2) 914 FORMAT!/,• TOO MANY DATA POINTS.',/) 915 FORMAT!/,• TOO MANY LEVELS.',/) 916 FORMAT(•1LEVEL*,12,3X,'(VFLOCITY FIT)',//,5X,20A4,//) 917 FORMAT!//,• FINAL VELOCITY RESULTS FOR', 12, '-TH LEVEL', //, 8X, l'SIGMA =', F8.3, • AFTER', 16, • ITERATIONS.', //) 918 FORMAT!•1APPP0XIMATE EXCESS TEMPERATURE ISOTHERM AREAS AND JET DEP 1THS.', //, 5X, 20A 4, ///, 2X, 'TEMP. EXCESS', 6X, 'AREA!ACRES ) - L 2EVEL',/,6X,'(C-DEG.)', IIX, '1', 11X, *2', 11X, *3', 11X, '4', 11X 3, '5', 11X, *6', /) 919 FORMAT! 7X,F7.2,6(2X,F10.4) ) 920 FORMAT(////, 11X, 'S', 2X, 'TEMP. EXCESS', 4X, 'DEPTH', 6X, 'E TA(F IT.) - LFVEL', /, 7X, '(FT.)', 6X, '(C-DEG.)', 2X, '(LEVEL)', 9X, • 21', 9X» *2', 9X, *3', 9X, '4', 9X, *5', 9X, *6', /) 921 FORMAT(2X,F10.2,7X,F7.2 , 2X , F7.3, 6(2X, F8.2)) 922 FORMAT!////, 11X, 'S', 3X, 'VEL. EXCESS', 4X, 'DEPTH', 6X, 'ETA(FT 1.) - LFVEL', /, 7X, '(FT.)', 4X, •(CM./SEC. ) • , 2X, '(LEVEL)', 9X, 2*1', 9X, '2', 9X, '3', 9 X, *4', 9X, '5', 9X, *6', /) 923 FORMAT!//, ' GOODNESS OF FIT:', /, 20X, 'TEMPERATURE', F8.2, • *', 1/, 20X, 'VELOCITY', F11.2, • ?• ) C C R FAD IN DATA 33 RFAD(5,90»END=30)(TITLF(I), 1=1,20) REAO(5,91) NPTS,NLEVFL,ANGN,80,BETAO,TO,U0 IF(NPTS-60)1,1,31 1 IF(NLFVFL-6)7,7,32 142 7 RFAD(5,92) !AMTEMP!K),K = 1,6) RF AD (5,92) (AMCUR(K),K = 1,6) RF AD(5 » 92 ) (CON(K),K=1,6) READ ( 5, 92 ) (ALIMT(K),K=1,6) RFAD(5,92) (AL IMV(K ),K = 1,6) HO 2 J =1»12 R EAP(5» °2) (P(J,K) ,K=1,6) RF AD(5,92) (DELP(J,K),K=1»6) 2 CONTINUF DO 6 1=1,NPTS 3 R FAD(5 * 93) XP(I),YP(I),DEPTH(II IF ( XPII ).NE. 0. 0) GOTO 4 IF(YP( I ).NE.0.0) GOTO 4 IF(OEPTH(I).NE.O.O) GOTO 4 GOTO 3 4 ANUM=NLEV EL ANUM=ANUM/2.0+0.75 M=ANUM N=2*N DO 5 K=1»N,2 5 READ!5,92) TPMP(I ,K ) , VEL(I,K>,DIR( I , K) ,TEMP!I,K+l), VEL(I,K+l),DIR( 1 I,K + l) 6 CONTINUE c C PRINT OUT DATA C WRITE(6» 94) (TITLEU ) ,1*1,20) WRITF(6,95 ) NPTS,NLEVEL,ANGN,BO*BETAOtTO,UO DO 8 K = 1 , NLE VE L 8 WRITE(6 » 96) K,AMTEMP(K),AMCUR(K),CON(K),ALIMT(K),ALI MV(KI WRITEI6 ,97 ) DO 9 K = 1 ,NLEVEL WRITEI 6,98 ) K WRIT F(6 ,99 ) (P(J,K),J=1,6) WRITE(6 »99) (DFLP!J,K),J=1,6) 9 CONTINUE WR I TF(6 ,900) DO 10 K=l,NLEVEL WR ITE(6,98) K WR I TE(6 ,99) (P(J,K),J=7,12) WRITE!6,99) (DELP(J,K) ,J = 7,12) 13 CONTINUE WRIT E(6,901) (TITLE!I),1=1,20) DO 11 1=1,NPTS WRITE(6,902 ) I,XP(I ),YP(I),DEPTH!I) DO 11 K=1,NLEVEL IF!TEMP(I,K) ) 13,14,14 13 IE(VEL( I ,K))15,14,14 15 WR I TF ( 6,903 ) K GOTO 11 14 WRITE!6,904) K,TEMP!I,K),VEL( I,K),DIR(I,K) 11 CONTINUE C C START LOOP THROUGH LEVELS (COMPLETE ONE LEVEL AT A TIME). C DO 16 K=l,NLEVEL C TF(ALTMT(k ).EQ.O.O.AND.ALIMV(K).EQ.O.O) GOTO 16 M = 6 C C FIT TO TEMPERATURE DATA. C SI GT = 0. 0 143 OELMAX=0.0 no 17 J=1,M BT 22, 23,23 22 IF(V C L(I,K))21,23,23 23 CALL TEMVEL(XP(I ) ,YPII) , BT , BO , BET AO, RT , BET AT ) T=RT*TO-RT*AMTEMP(K)+AMTEMP(K) BETAT=BETAT*RD A 1 = A 1+(TEMP(I,K)-AMTEMP(K)1**2 CALL T EMVEL(XP(I),YP(I),BV,BO,BETAO,RV,BETAVI OEVBET=(ANGN-DIRtI,K))*DR-PETAV VD=VEL-> is) o r> o o r> o r» o t— i\» o oc~»or»oooor>r» 149 RETURN 3 CUBRT = 0. 0 RETURN FND * * * * 4c * * * * * * * * * * 4c * * * * * * ** * * * *** * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * C c SUBROUT INF FTSIG(M,BT,SIGT,G,ITER) ***********************************************ft********************** ROUTINE CALCULATES THE STANOARD DEVIATION OF THE TEMPERATURE DATA FROM ’JET-FUNCTION' WITH PARAMETERS BT. ON CERTAIN CALLS, THE DERIVITIVFS OF THIS DEVIATION WITH RESPECT TO EACH PARAMETER IS ALSO CALCULATED. DIMENSION BT(6),G<6),BB<6) COMMON/HAVE/DELP<12,6),TEMP(60,6),VEL(60 ,6),01RC60,6),XP<60),YP(60 1),AMTPMPC&),AM CUP (6)»BETAO,BO,ANGN,TO,UO,NPTS,DR»RD »K CALL TSIG(BT,SIGT) IFt ITER.EQ.2 ) RETURN DO I J = 1,M DO 2 1=1,M BB(I)=BTtI) BR( J)=BT< JHDELPC J,K) CALL TSIGIBB,SIGP> BB(J)=BT(J)-DEL P(J » K ) CALL TSIG(BB,SIGM) G(J)=0.5*(SIGP-STGM)/DELPIJ,K) RFTURN END ********************************************************************+*£ C SUBROUTINE FVSIG(M,BV,SIGV,G,ITER) C **********************************************************************^ ROUTINE DOES THE SAME THING AS FTSIG EXCEPT FOR THE VELOCITY PART OF 'JET-FUNCTION* AND THE VELOCITY DATA. DIMFNSTON BV<6),G<6),BB<6) COMMON/HAVE/DFLP(12,6),TEMP(60,6),VEL( 60, 6 ), D IR ( 60,6) , XP < 60) , YP( 60 1),AMTFMP(6),AMCUR(6),BET AO,BO,ANGN,TO,UO,NPTS,DR,RD,K CALL VS IG(BV,SIGV ) IF(ITER.EQ.2) RFTURN DO 1 J=1,M DO 2 1=1,M BB ( I )=BV( I ) BB(J)=BV(J )+DELP(J*-M,K ) CALL VSIG(BB,SIGP) BB(J)=BV(J)-DELP r> o o o o o r> i\» t— r> o <-> r> o o o r> i\> »— o oooo 150 ROUTINE CALCULATES THE STANDARD DEVIATION OF THE TEMPERATURE DATA FROM 'JET-FUNCTION* OF PARAMETERS BT. DIMENSION BT(6 I COMMON/HAVE/DELP(12,6),TEMP(60,6 I,VEL(60,6),DIR<60,6),XP(601, YPt 60 l), AMT EMP(6 ),AMCURI6),BET AO,BO,ANGN,TO,UO,NPTS,DR,RD,K SIGT=0.0 ANUM=0.0 DO 2 1=1,NPTS IF(TEMP(I,K)>2,1,1 CALL TFMVFL(XP(I>,YP(I),BT,BO,BETAO,RT,RBETA) SIGT=SIGT*(TEMP( I , K)-RT*TO + PT*AMTEMP