key: cord-0821924-bxog9j4h
authors: Yang, Yi; Zhang, Huihui; Lai, Alvin CK.
title: Lagrangian modeling of inactivation of airborne microorganisms by in-duct ultraviolet lamps
date: 2020-11-21
journal: Build Environ
DOI: 10.1016/j.buildenv.2020.107465
sha: c0de261a28e8a48fbdbcfdf55601647936cc99cf
doc_id: 821924
cord_uid: bxog9j4h

There has been increasing interest in modeling the UV inactivation on airborne microorganisms via the Lagrangian approach as a result of its outstanding features in calculating UV dose with particle trajectory. In this study, we applied the Lagrangian method to model the disinfection performance of in-duct UV lamps on three bacteria: Pseudomonas alcaligenes, Salmonella enterica and Escherichia coli, respectively. For modeling, the airborne bacteria's inactivation was determined by critical survival fraction probability (CSFP) and maximal bearable UV dose (MBUD) methods, respectively. The results indicated that Lagrangian modeling utilizing the MBUD method needs to appropriately evaluate the maximal UV dose (D(mb)), which is bearable for airborne microorganisms. The disinfection efficacy obtained by using the CSFP method agreed well with experimental measurements. Within the Lagrangian framework, the recommended empirical value for critical survival fraction (F(sc)) was 0.4 for modeling the disinfection efficacy of in-duct UV lamps. Besides, the disinfection efficacies of in-duct UV lamps with full luminous length on P. alcaligenes and E. coli were 100% with Re within the range of 4.11 × 10(4) to 8.22 × 10(4). Moreover, the present numerical model was also applied for further validation with inactivation measurements of in-duct UV lamps performed by the U.S. Environmental Protection Agency (EPA). Based on the results, the UV disinfection efficacies obtained by the present modeling method had a closed agreement with EPA experimental results. It deserved to pay more investigations on the optimal value of F(sc) in further for accurately applying Lagrangian modeling on air UV disinfection.

Over the past two decades, the prevalence of respiratory diseases has extremely threatened 2 public health security and negatively impacted society and economic development. Among these 3 diseases are influenza, tuberculosis (TB), severe acute respiratory syndrome (SARS) in 2003, 4 middle east respiratory syndrome (MERS) in 2012 and novel coronavirus disease (COVID-19) 5 pandemic [1] [2] [3] [4] . Recently, the World Health Organization (WHO) reported that COVID-19 has 6 caused more than 770,866 deaths worldwide until 18 Aug 2020 [5] . However, there is no 7 effective treatment for this emerging virus so far [6] . It has been demonstrated that respiratory 8 illness virus transmitted through aerosol transmission and mainly infected people via 9 close-contact, respiratory droplet, saliva and droplet nuclei [1-2; 7-9] . Active preventive measures 10 are necessary to cut off the aerosol transmission of respiratory illness virus. Individual 11 protection such as facemask is usefully suggested to cut off airborne pathogen transmission 12 between an infected person and healthy person [10] , whereas sterilization technologies are also 13 necessary to reduce the risk of infection. 14 Recently, different disinfection approaches, have been investigated such as ultraviolet 15 germicidal (UVGI) lamp, negative ionizer and cold plasma, for inactivating airborne pathogens 16 in heating, ventilation, and air conditioning (HVAC) systems [11] [12] [13] [14] . Although an HVAC system 17 delivers comfortable humidity and air temperature in the indoor environment, it may also 18 become airborne pathogens source by a poor corresponding maintenance [15] [16] . Based on 19 previous works, it was found that the UV lamp installed in the HVAC system significantly 20 results in fewer work-related symptoms among office people [17] [18] . Recent studies indicated that 21 J o u r n a l P r e -p r o o f airborne microorganisms was described to consider particle instantaneous fluctuating turbulent 1 velocity utilizing stochastic methods. The instantaneous fluctuating turbulent velocity obeyed 2 the Gaussian probability distribution assumption which was defined as 3

where v ur is air instantaneous fluctuating velocity vector, ζ represents normally distributed 5 random number, and k denotes turbulent kinetic energy. 6 2.1 Lagrangian model 7

By integrating the force balance on airborne microorganisms, the trajectory of airborne 8 microorganisms was described and the force balance equation was expressed as [43] : 9 ( ) ( ) ( ) ( )

The terms in the right part of Eq. (2) represent the Stokes' drag force, gravity, Brownian force 11 and Saffman's lift force, respectively. v r is air velocity, b v r represents the airborne 12 microorganism velocity and F d is written as 13

where μ is the molecular viscosity of air, ρ denotes the air density, ρ b is airborne microorganism 15 where λ represents the molecular mean free path, λ = 66 × 10 -9 m, g ur is the gravity vector, δ ij 19 J o u r n a l P r e -p r o o f denotes the Kronecker delta function and 1

T is the absolute air temperature, ν represents the kinematic viscosity, k B denotes the Boltzmann 3 constant, k B =1.38×10 -23 m 2 kgs -2 K -1 and d ij is the deformation tensor. 4

The boundary condition of Eq. (2) was adjusted with "escaped" for ventilation duct inlet and 5 outlet, and it was "trapped" for ventilation duct wall and UVGI lamp wall, respectively. 6

The UV dose was given as 7

where D represents the UV dose received by airborne microorganisms, Jm -2 , t i , and t p are time in 9 which airborne microorganisms enter the ventilation duct and arrive present location, 10 respectively. I r (x, y, z) is the spatial irradiance at spatial location (x, y, z) and I r (x, y, z) is 11 predicted through a mathematical model introduced in our previous works [44] . Figure 1  12 represents the predicted spatial irradiance of half and full luminous length of in-duct UVGI lamp. 13 Spatial irradiance (I r (x, y, z)) includes emissive irradiance from UVGI lamp and diffuse 14 irradiance reflected from the duct wall. It should be noted that the predicted spatial irradiance 15 can be also regarded as equivalent to fluence rate that is defined to evaluate the UV power per 16 unit area at a specific point from all directions incoming UVC rays [45] [46] [47] . The prediction was 17 already validated in our previous works [44] . During the simulation process, Eq. When airborne microorganisms expose to irradiance, the survival fraction (F s ) is an exponential 6 function [19, 29] and it is written as 7

where Z represents the susceptibility of airborne microorganisms and is also termed Z value, 9 m 2 /J. F s is also the ratio of the number of airborne microorganisms gathered in the sample plane 10 under in-duct UV lamp-on and lamp-off conditions. 1

The disinfection efficacy (η) of in-duct UVGI is evaluated with UVGI lamp off and on 2 experiments [19, 48] . Based on this method, the disinfection efficacy (η) can be calculated as, 3

, off sampling t t n ∑ are airborne microorganisms collected in sample plane 5 (y=1.4m) for in-duct UVGI lamp on and off circumstances, respectively. When airborne 6 microorganisms receive higher UV doses, the calculated F s of microorganisms will be lower. If 7 the UV dose received by microorganisms is lower than the critical survival fraction (F sc ), then 8 the airborne microorganisms will be regarded as inactivation. At last, fewer airborne 9 microorganisms will be counted in downstream and the disinfection efficacy will be higher. The percentage of airborne microorganisms eliminated by other mechanisms was defined as 2

where P j is the percentage of airborne microorganisms dealt with different mechanisms, φ k 4 represents the expression of various mechanisms, the expressions of P j and φ k are provided in 5 Experiments were performed to assess the disinfection of 1/2 and full luminous length of in-duct 13 UVGI on P. alcaligenes, E. coli and S. enterica with 9 m × 0.2 m × 0.2 m galvanized steel 14 ventilation duct system for Re from 4.11 × 10 4 to 9.58×10 4 (velocity 3 -7 m/s) in our previous 15 work before [19, 44] . The susceptibility constants of test bacteria and disinfection efficacy were In this study, simulation cases were set based on the experiments. In the numerical physical 8 model, the length of the ventilation duct was 3.2 m and one UVGI lamp was installed at the 9 location y = 1.05 m from the inlet. It was assumed that the airflow pattern has been fully 10 developed at the inlet. Figure 2 represents the computational grid style where 267,106 11 non-uniform structure grid cells were used in the simulation. The bare luminous tubes were 12 inserted from the left wall of the duct. For 1/2 luminous length lamp, luminous tubes were 13 covered with black tape from two sides and maintained only half luminous length tubes in the 1 center. Airborne microorganisms were assumed to be spherical with 1000 kg/m 3 density and 1.0 2 μm diameter. At first, by solving continuity, momentum, and turbulence equations, the airflow 3 field was obtained. The air velocity was monitored at the center of the duct in the process and by 4 the steady value, the modeling will stop. Then, irradiance was calculated with a mathematical 5 model coded into ANSYS Fluent solver with user-defined functions. The predicted spatial 6 irradiance was maintained in each numerical grid cell. The trajectory of airborne 7 microorganisms was obtained by integrating the Lagrangian force balance equations (Eq. (2)) 8 based on the computational airflow field and predicted irradiance. Survival fraction (F s ) and UV 9 dose (D) were calculated with the predicted irradiance saved in computational grid cells by 10 existing the tracked airborne microorganisms. Airborne microorganisms were injected from the 11 duct inlet surface at the beginning of each time-step. The injected numbers of airborne 12 microorganisms may affect computational time and numerical accuracy. To minimize the impact 13 of injected particle numbers, the disinfection efficacy of half luminous length in-duct UVGI 14 lamp on E. coli was modeled at Re = 8.22 × 10 4 (v =6 m/s) for injected numbers of 3404, 5106, 15 10212 and 49358, respectively. The disinfection efficacies are presented in Table 2 . The results 16 indicated that η obtained by three different injected numbers was within the range of 48.6% -17 48.9%, however, the disinfection efficacy of another injected number was 49.1%. The 18 disinfection efficacies were difficult to distinguish for different injected numbers. Ultimately, 19 5106 particle numbers were used to save computational resources and time. 20

To couple with the pressure and velocity, the SIMPLE algorithm was used. Using the second 21

Order Upwind scheme, the convection terms were discretized except the QUICK scheme for the 1 airborne bioaerosol transport equation. Then, Green-Gauss Cell-Based theorem was used to 2 calculate the gradient. The transient term was discretized with the First Order Implicit scheme. 3

The airborne microorganisms' motion equations were solved with the implicit and Runge-Kutta 4 scheme. The equations were numerically solved in unsteady-state with the time step of 0.1 s. 5

During the numerical simulation, the highest residual value was less than 10 -5 s and a high 6 residual value was always found in the dissipation rate (ε) equation. The effects of critical survival fraction (F sc ) were assessed for modeling the disinfection efficacy 15 of an in-duct UV lamp with two luminous lengths on E. coli at Re = 8.22 × 10 4 (v = 6 m/s). 16

The discrete data points in Figure 3 were the disinfection efficacy (η) of the in-duct UV lamp 17 obtained by the corresponding label F sc case. The range of the box chart was determined by the 1 25th and 75th percentiles of the disinfection efficacies' data. The upper and lower lines in the 2 box chart represent the maximum and minimum values, respectively. The results indicated that 3 there is a monotonous relationship between disinfection efficacy (η) and F sc . The reason is if F sc 4 was higher, airborne microorganisms were easily regarded as inactivated microorganisms and 5 they had a higher probability to be eliminated from the particle trajected list. Ultimately, fewer 6 airborne microorganisms can pass through the UV irradiance field to arrive at the sample plane, 7 hence, the higher disinfection efficacy will be resultant. Because the spatial irradiance was much 8 higher for UV lamp with full luminous length compared to the half luminous length, the 9 disinfection efficacy (η) of UV lamp with half luminous length was lower than the full luminous 10 case at the same F sc . The disinfection efficacy (η)was over 100% with F sc = 0.4 for full luminous 11 length case ( Fig. 3 (b) ) and η there is no significant difference after following a higher F sc case. different methods with Re = 4.11 × 10 4 -9.58 × 10 4 (velocity 3-7 m/s). 10

In Figure 4 , the results obtained with CSFP and MBUD methods are presented and compared 11 J o u r n a l P r e -p r o o f with experiment and Eulerian modeling results which were reported in our previous works [44] . It 1 was indicated that the disinfection efficacies (η) obtained by MBUD approaches were much 2 lower than others. However, the disinfection efficacies gained by the CSFP method were well 3 consistent with experiment value except at Re = 4.11 × 10 4 (v = 3 m/s) and they were slightly 4 better than the results from Eulerian modeling. Since the effects of Z-value and UV dose (Eq. 7) 5 were both considered for the calculation of F s in the CSFP method, there was a good agreement 6 between the results from the CSFP method and the experimental values. The results also 7 suggested that utilizing the MBUD method in the Lagrangian modeling needs to further consider 8 the individual discrepancy of airborne microorganisms for predicting the disinfection efficacy of 9 UV lamps. Namely, if Lagrangian modeling was used along with the MBUD method, optimal 10 value of D mb should be evaluated for the test airborne microorganisms at first. It is worth noting 11 that Eq. (7) is also one of the best ways to calculate D mb . If the D mb in the MBUD method is 12 calculated by Eq. (7) using the Z value of tested airborne microorganisms and the corresponding 13 F sc , then the results of the MBUD method will be equivalent to that of the CSFP method. Since airborne microorganisms spent a longer time in the duct, they have more chances for 4 irradiance exposure. Therefore, the values of D incremented along the airborne microorganism's 5 trajectory. Considering an inverse trend of the variation of F s , the airborne microorganisms 6 received more UV dose and lower survival fraction, ultimately. Under higher velocity of airflow, 7 airborne microorganisms will travel more quickly through the duct and they will receive a lower 8 UV dose. Therefore, more airborne microorganisms survived in Re = 8.22 × 10 4 than in Re = 9 4.11 × 10 4 . This is also in line with the decrement tendency of disinfection efficacy in Figure 4 . 10

The figure also represents the percentage of airborne microorganisms that dealt with other 11 mechanisms. A reduction was observed in the percentage of airborne microorganisms 12 inactivated by irradiance (P uv ) from 82.2% to 39.8% by increasing Re from Re = 4.11 × 10 4 to 13 Re = 8.22 × 10 4 . However, the percentage of particles escaped from the outlet (P e ) changed from 14 0% to 38.1%. The reason is the airborne microorganisms survived from irradiance inactivation, 15 which has a higher chance of elimination by ventilation air. 16 The disinfection of in-duct UV lamps with full luminous length on P. alcaligenes, E. coli and S. 1 enterica were assessed with F sc = 0.4 for various Re, respectively. Figure 6 shows the UV dose 2 (D) and survival fraction (F s ) with F sc = 0.4 and Re = 8.22 × 10 4 . The results showed that P uv 3 was 85.5%, 84.7% and 63.1% for P. alcaligenes, E. coli and S. enterica accordingly. Moreover, 4 their Z-values reported in our previous work [19] also reduced in the following order: 1.0 m 2 /J, 5 0.6 m 2 /J, and 0.39 m 2 /J. It can be stated that bacteria with higher Z-value was more sensitive to 6 irradiance. The percentage of S. enterica suspended in air (P s ) was 1.8%, which was the highest 7 value among the three test bacteria. Few airborne microorganisms suspended in the duct were 8 caused by the fact that airflow in the duct was a single-pass pattern without further disturbance. 9

Moreover, airborne microorganisms cannot stay for a long time in high airflow rate cases, and 10 for low airflow rates, they would easily receive enough UV dose for inactivation. The 1 disinfection efficacies of three test bacteria with different Re are shown in Figs. 7 -9. The 2 disinfection efficacies of P. alcaligenes and E. coli were nearly 100% for Re from 4.11 × 10 4 to 3 8.22 × 10 4 , however, η was lower for S. enterica and it reduced from 100% to 71.6%. This also 4 can be directly perceived from the nonexistence of P. alcaligenes and E. coli at downstream of 5 the sampling surface (y=1.4m) in Fig. 6 . Besides, the modeling accuracies of results of the 6 Lagrangian-CSFP method and Eulerian method were compared by using one-way analysis of 7 variance (ANOVA) compared to the experimental results. The probability values (P-values) of 8

Lagrangian-CSFP and Eulerian methods are 0.70 and 0.81 for half luminous length cases ( Fig.  9 4), 0.99 and 0.51 for full luminous length cases (Fig. 7 -9 ), respectively. The results indicated 10 that the Lagrangian CSFP method is relatively better than the Eulerian method for full luminous 11 length cases (larger P-value for Lagrangian than that for Eulerian), whereas it is just the reverse 12 for half luminous length cases. This may be due to the difference in UV dose estimations among 13 these two methods. The Lagrangian method integrates the UV dose along the movement 14 trajectories of airborne microorganisms and the microorganisms' trajectories can be highly 15 affected by the turbulent vortex. For half luminous length cases, airborne microorganisms 16 receive less UV dose than in full luminous length cases. Airborne microorganisms will have a 17 chance to arrive nearby the nonluminous part of the UV lamp and the integration may be 18 affected by turbulent eddy more obviously in this area. While the Eulerian method considers the 19 inactivation of UV irradiance as the sink term in microorganism transport equations. This sink 20 term is the product of Z value, spatial irradiance, and spatial concentration of airborne 21 microorganisms. Thus, the calculation of UV dose in the Eulerian method is not directly affected 1 by the flow pattern compared to the Lagrangian method. where n is the total number of particles sampled in-plane and D i represents the UV dose of 13 particle i. To calculate the average UV dose, it was supposed that airborne microorganisms were 14 immune to ultraviolet disinfection. The bacteria can travel through the duct without considering 15 ultraviolet inactivation and regardless of UV dose received by the bacteria. Therefore, the 16 average UV dose can represent the maximal strength of ultraviolet irradiance which they have 1 passed through based on the corresponding exposure time. However, airborne microorganisms 2 have diversities and higher Z-value airborne microorganisms were more vulnerable to ultraviolet 3 in real, they may be killed before arriving sample plane. Moreover, if the average UV dose was 4 estimated with high Z-value airborne microorganisms, the inactivation may be ultimately 5 underestimated. As shown in Figure 10 , by increasing the air velocity, UV dose linearly declined 6 since airborne microorganisms spent less time in-duct with higher air velocity. By reducing the 7 luminous length of the UV lamp by half, the average UV dose was almost one half of the full 8 luminous length case. 9

Although within the CSFP method, our experiment cases were well modeled with F sc =0.4, there 11 was still incompletely interpreting the reason for the optimal value of F sc , 0.4 by biological 12 theory. To further validate the method, the present model was applied to assess the experiment 13 cases of the U.S. Environmental Protection Agency's (EPA's) National Homeland Security 14

Research Center (NHSRC). The inactivation efficiency of an in-duct ultraviolet light system was 15 evaluated by NHSRC against airborne microorganisms [49] . Four UV lamps were inserted the 16 duct from side and perpendicular to airflow direction in the test, however, the ballast box was 17 left outside of the duct. Three microorganisms, Serratia marcescens, MS2 bacteriophage and 18

Bacillus atrophaeus were selected to examine. The other test conditions are provided in Table 3  19 and more details of the experiment can be found in the literature [49] . 20 Table 3 Conditions of EPA experiment case [49] . 21 [42, 50] . The duct was then meshed with 348, 400 non-uniform 2 structure computational grid cells. UV irradiance was predicted by our mathematical model [44] . 3

The emissive irradiance from UV lamp and reflection from the duct wall were considered in the 4 prediction. By achieving a steady flow field, 5600 particles were injected from the inlet surface 5 at the beginning of each time step. The average UV dose and disinfection efficiency were 6 calculated with airborne microorganisms in the outlet surface. Table 4 represents the comparison 7 of present modeling and EPA experiment measurement. Based on the table, the numerical results 8 of literature [42, 50] are also indicated. It was different from Section 3.3 that D avg in Table 3 where I ravg is the average spatial irradiance of duct, t f represents the time particle pass through 8 the duct, t f =V/Q, V is the volume of duct, Q denotes the airflow rate. The average spatial 9 irradiance (I ravg ) was calculated by a computer model that was developed to predict the emissive 10 irradiance and reflection of the duct wall. He also found that the reflection was important for 11 calculating the UV dose. 12

Eqs. 11-13 were different and applied on the basis of various input conditions. For comparing 13 their results, it is essential to keep the calculation conditions consistent. For EPA's calculation 14 (Eq. 12), the survival fraction of airborne microorganisms was closely dependent on the 15 sampling location. If the sample location was nearer the airborne nebulizer, the sampled 16 airborne microorganisms would receive a lower UV dose compared to sampling in a farther 17 downstream location. Of course, F s was higher for those microorganisms with a lower UV dose 18 at the end. In the experiment of EPA, the length of ventilation duct and the coordinates of their 19 sample location were not given, hence, the parameters of numerical cases cannot be exactly 20 equivalent to the experiment and there was a significant difference between the average UV 21 dose calculated by CFD method (Eq. 11) and EPA (Eq. 12). Although Capetillo et al. (2015) [42] 1 used an identical physical model, they did not state that their calculation was performed on the 2 basis of which airborne microorganisms. Table 4 indicates that the average UV dose obtained by 3 the present method with MS2 bacteriophage was very closed to the value of Capetillo et al. 4 (2015) [42] . The average UV dose was none with S. marcescens for both simulations in Table 4 . 5

Because D avg was the arithmetic mean (Eq. 11) of UV dose at the sample plane in downstream 6 of UV lamp in these works and the value of D avg was saved with the survival particle during 7 simulation, if airborne microorganisms were very sensitive to irradiance, they failed to pass 8 through UV lamp and ultimately cannot be sampled in downstream of the UV lamp. For 9 instance, Figure 11 (a) represents that none of S. marcescens was sampled at downstream of the 10 UV lamp and we cannot obtain the average UV dose from survival particle. The disinfection 11 efficacies obtained with the present work were in line with the results of the EPA experiment 12 well. Figure 11 also represents the numerical results of UV dose (D) and survival fraction (F s ) of 13 three test microorganisms for the EPA experiment case. It is indicated that the survival fraction 14 of S. marcescens was the fewest, however, the value of B. atrophaeus was the highest. Although 15 airborne microorganisms were uniformly injected from the inlet surface, the UV dose obtained 16 by each airborne microorganism was much different and depended on the distribution of 17 irradiance and the exposure time. 18

It should be emphasized that although the CSFP method was validated well with modeling the 19 above experiment cases, its optimal value F sc = 0.4 was empirical and cannot be directly 20 interpreted well with biotechnology. Unlike the MBUD methods, it is impossible for biological 21 experiment tests to quantificationally discover the optimal critical survival fraction to regard the 1 airborne microorganisms as inviable. Further studies are required since the Lagrangian method 2 was an optimal CFD method for modeling the UV disinfection process. 3 airborne microorganisms, Z was Z value of airborne microorganisms. 7 b Calculated by D avg =I ravg ·t f , where I ravg was average spatial irradiance of whole duct, t f was the 8 time particle pass through duct, t f =V/Q, where V was the volume of duct, Q was air flow rate. 9 c Calculated by D avg =(D 1 +D 2 +…+D i )/n, where n was the total number of particles sampled in 10 outlet plane, D i was the UV dose of particle i. 

The accurate prediction of the disinfection efficiency of UV lamps on airborne microorganisms 3 by CFD simulations is crucial and very helpful to develop its engineering application. In this 4 study, the Lagrangian method was used to assess the disinfection efficacy of an in-duct UV lamp 5 with half and full luminous length on P. alcaligenes, E. coli and S. enterica with Re from 4.11 × 6 10 4 to 9.58×10 4 (velocity 3 -7 m/s). The distribution of spatial UV irradiance in the ventilation 1 duct was predicted by a mathematical model based on the view factor method, as explained in 2 previous work. The results of disinfection efficacy predicted by simulations were compared with 3 the experimental measurements of our former works. Critical survival fraction probability and 4 maximal bearable UV dose were used as the bacteria viability judgment approaches and their 5 accuracy was studied in detail. 6

The results indicated that microorganisms' individual differences to UV irradiation should be 7 further considered for modeling the performance of in-duct UV lamps using the MBUD method. 8

Besides, the results obtained with the CSFP method were well matched with experiment data. It 9 was indicated that the optimal value of the survival fraction of airborne microorganisms (F s ) was 10 recommended as 0.4 based on our experiment data. Moreover, the percentage of airborne 11 microorganisms inactivated by UV irradiance reduced with Re. The disinfection efficacy of 12 in-duct UV lamp with full luminous length on P. alcaligenes and E. coli were almost 100% with 13 Re from 4.11 × 10 4 to 8.22 × 10 4 . There was a good consistency between the results obtained 14 from Lagrangian modeling and experiment data and they were relatively better compared to 15 Eulerian modeling. 16 CSFP method was also used to study EPA experiment cases with optimal empirical value 17 F sc =0.4. The average UV dose and disinfection efficacy obtained by the present method were 18 compared with the results of experiment measurement and previous CFD simulation works. The 19 results indicated that there was a slight difference between the average UV dose owing to the 20 difference in their calculation way and conditions. The disinfection efficacies obtained by the 21 present method were well-matched with the experiments. It is worth noting that the optimal 1 value of critical survival fraction probability requires further future investigations. 

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