Computational fluid dynamics simulation of gas dispersion in complex facilities using Kit Fox field experiments:Validation and statistical evaluation

Narjes Hemati Alam,Eslam Kashi,Razieh Habibpour

Department of Chemical Technologies,Iranian Research Organization for Science and Technology,P.O.Box 33535111,Tehran,Iran

Keywords:Gas dispersion simulation Computational fluid dynamics Complex terrain Obstructed flow

ABSTRACT Gas release and its dispersion is a major concern in chemical industries.In order to manage and mitigate the risk of gas dispersion and its consequences,it is necessary to predict gas dispersion behavior and its concentration at various locations upon emission.Therefore,models and commercial packages such as Phast and ALOHA have been developed.Computational fluid dynamics(CFD)can be a useful tool to simulate gas dispersion in complex areas and conditions.The validation of the models requires the employment of the experimental data from filed and wind tunnel experiments.It appears that the use of the experimental data to validate the CFD method that only includes certain monitor points and not the entire domain can lead to unreliable results for the intended areas of concern.In this work,some of the trials of the Kit Fox field experiment,which provided a wide-range database for gas dispersion,were simulated by CFD.Various scenarios were considered with different mesh sizes,physical conditions,and types of release.The results of the simulations were surveyed in the whole domain.The data matching each scenario was varied by the influence of the dominant displacement force (wind or diffusivity).Furthermore,the statistical parameters suggested for the heavy gas dispersion showed a dependency on the lower band of gas concentration.Therefore,they should be used with precaution.Finally,the results and computation cost of the simulation could be affected by the chosen scenario,the location of the intended points,and the release type.

1.Introduction

The release and dispersion of gas in a chemical plant can be a serious problem.Whether the gas is toxic or flammable,it is a risk for the residential population residing near the plant and the facility itself.In any industry,predicting the transport path of gas is a necessary feature of any good risk analysis and management plan.Different methods can be used to predict this path and its concentration.A number of researchers have utilized empirical models[1]to predict the gas dispersion path,and in the last two decades,computational fluid dynamics (CFD) simulations have become more popular[2,3].Some field experiments have also been carried out that provide reliable data for improving the relations and equations as well as evaluating new methods and simulations.A large body of data,which include different gases,various scenarios,and diversity of physical conditions,have been derived from various field experiments:Kit Fox [4],Thorney Island,MUST,EMU-L[5],Coyote series trials [6] and Prairie Grass [7].Some procedures have been established for loss prevention purposes in chemical industries.The dispersion models DEGADIS [8] and SLAB [9],as well as some commercial software packages such as Phast and ALOHA,have been developed and are the most widely used models in safety engineering applications[10].Even so,the majority of the available commercial tools cannot expose the obstacles in more complicated environments.

Sklavounos and Rigas[11]used CFX codes for a close estimation of risk in a gas release accident.Predicting the path of gas dispersion was carried out in the presence of obstacles that represented the buildings and plant facilities.In the past decade,the computation costs for CFD codes were significant in comparison with the commercial models mentioned above.The use of CFD codes for the simulation of gas dispersion in complex geometry conditions,e.g.,the presence of an obstacle,has become more popular with the optimization of computer speed and computation costs[12,13].For instance,Fluidyn-PANACHE used CFD tools for the simulation of pollution dispersion in atmospheric flows on a mediumrange scale [10,14].Dasgotraet al.[15],Donget al.[16],and Liuet al.[17] modeled large scale areas with CFD.With an increasing interest in using CFD in the simulation of gas dispersion,CFD models are applicable in risk analysis and management.de Souzaet al.[18]used CFD to classify the hazardous area for a subsonic leakage of hydrogen.Quantitative risk assessment for a complex terrain with CFD was carried out by Rumet al.[19].

In order to compare the simulation results with the experimental data,some factors should be considered.Hannaet al.[20] suggested statistical evaluation as one method to evaluate the models and simulation of gas dispersion,which was used by a different researcher.Some researchers investigated the simulation and modeling of the dispersion of dense gas in the atmosphere,but their results only included certain monitor points [12,21].It appears that the use of such results for validation can lead to some doubt.This study addressed these dubieties,which have not been previously discussed in the literature,by simulating the different conditions of gas releases such as plume and puff and comparing the results of the same computational strategies on different gas dispersion conditions.The Kit Fox experiment trials were used to validate the data extracted from these simulations.The simulation parameters,such as mesh size and temperature effect,were investigated.The effect of diffusivities on the simulation results was surveyed.The different locations and times of the duration of the dispersion were discussed to validate the results.

2.Numerical Methods and Model Validation

2.1.Governing equations and boundary conditions

The fundamental equations and relations used for computing fluid motion,which are used by ANSYS CFX [22],are explained below.These equations are derived from applying Newton’s second law of motion.The respective continuity and momentum equations for isothermal-Newtonian fluid are [23]:

where

whereUrepresents the velocity vector;ρ is viscosity;andp,μ,μeffandBrespectively describe the pressure,the viscosity,the effective of the medium,and the sum of the body forces.In addition,the general form of Navier-Stokes is:

In practice,the flow is turbulent,and all the flow variables fluctuate in diverse paths.For solving the fluid turbulence’s effect,some different methodologies have been developed.The Reynolds time-averaging procedure is one such method.The Reynoldsaveraged Navier-Stokes (RANS) equations are used for this procedure.

The time-averaged form of the momentum equation (Eq.(2))for a constant density is:

One of the simple and effective models for solving the turbulence flow is thek-ε model.In thek-ε model [24],the Reynold stresses are illustrated with the terms of turbulent viscosity (μt).The other terms used in the characterization of the turbulence fluctuation are turbulent kinetic energy (k) and rate of dissipation (ε)[25,26].

and the constants are:

Some additional equations should also be considered.One of the most useful equations is the conservation mass of species,which describes the transportation of the surveyed species such as the hazardous ones:Yiis the concentration ofith species andJiis the diffusion flux of speciesithat arises due to the concentration gradient;it is expressed in terms of Fick’s law.

These partial differential equations (PDE) have no known overall analytical solution.However,they could be individually solved numerically.The finite volume method (FVM) is used to solve equations in ANSYS CFX [22].

Q,F,V,andArepresent the vector of conserved variables,the vector of fluxes,the volume of the control volume element,and the surface area of the control volume element,respectively.

2.2.Statistical validation

Some models overpredict the gas concentration,and some underpredict the value.For example,HEGADAS3,which was developed based on wind tunnel observations made by Petersen [22],overpredicted more than four times.On the other hand,PANACHE underpredicts the maximum concentration of dense gas [23].Therefore,the models and software packages used to predict the path and concentration of dense gas in a gas dispersion should be evaluated.One evaluation process used by Hannaet al.[28]was statistical evaluation.

Some of the values calculated for the statistical evaluation are given in the following equations:

whereCois the observed concentration,Cpthe predicted concentration,MG is the geometric mean,VG is the geometric variance,NMSE is the normalized mean square error,FB is the fractional bias,and FAC2 is the fraction of C within a factor of two of C.

As described by Chang and Hanna[29],in a perfect model,MG,VG,R,and FAC2 would be equal to 1.0 while FB and NMSE would be 0.As a matter of fact,there is no such thing as a perfect model in air quality modeling.Note that since FB and MG only measure the systematic bias of a model,it is possible for a model to have predictions completely out of the range of the observations and still have an FB=0.0 or MG=1.0 because of canceling errors.

Hannaet al.[28]suggested that the models with statistical values such as FAC2>0.5,-0.3

2.3.Kit Fox field experiment

In this work,the simulations were validated by the Kit Fox field experiment data.The Kit Fox field experiment was carried out in August 1995 as part of a cooperative research project coordinated by the Petroleum Environmental Research Forum (PERF) Dispersion Modeling Project 93-16,which was carried out by Briggset al.[30].This experiment took place at the Nevada Test Site(NTS),which is a flat dry lake.

Two sets of artificial roughness were used to replicate the roughness found in the industrial facilities.The first set was named URA(Uniform Roughness Array),which used flat boards to build an obstacle with a 20 cm height and 80 cm width.These obstacles covered an area of 120 m by 314 m.These boards were arranged with 2.4 m lateral and 2.4 m longitude spacing.The URA obstacles were made with a roughness length of around 1 to 2 cm.The second set was called ERP (Equivalent Roughness Pattern) and consisted of 2.4 m×2.4 m flat boards.It was used to represent an oil refinery or the chemical plant roughness,and its scale was about 1/10 of an industrial plant and its surroundings.These boards were arranged with an 8.5 m lateral spacing and 6.1 m crosswind spacing;they covered an area that was 39 m wide and 85 m long.The gas used in this experiment was CO2at ambient temperature,which was released from a 1.5 by 1.5 m source area located on the ground.

The experiment included 52 trials.The trials were designated with two numbers:the first one indicated the day,and the second showed the order of the release.The CO2flow rates were 20 and 25 seconds for instantaneous release(puff)and 120 to 450 seconds for continuous release(plume).According to Hannaet al.[31],around 35 Irwin spires were located at the entrance of the field in order to make the turbulent boundary layer.

The gas concentration was measured at four perpendicular cross planes to the wind direction at distances of 25 m,50 m,100 m,and 225 m from the source of release.The observation of gas in each plane was done at different heights and widths.The meteorological data were collected by an EPA tower and eight MET towers at different heights,which are shown in Fig.1.The data from the EPA and MET was reported every 10 seconds.

The Kit Fox field experiment provided a wide-range database for the evaluation of different dense gas dispersion models and software packages.The dispersion models are used in risk assessment and hazard analysis.

3.Simulation Procedure

3.1.Geometry

This study attempted to simulate the geometry as close as possible to those of the Kit Fox field trials.The ERP obstacles were simulated as a flat square object that were the same size as those in the Kit Fox experiment.The roughness of the URA was set in the boundary conditions,and no object was used in their place.The scheme of the Kit Fox field experiment in these simulations is shown in Fig.2.In order to discretize the domain of simulation,tetrahedron elements were used.Also,a 25 layer inflated structured layer of elements was created near the ERP objects and the ground around it.The scheme of the mesh format of simulations is shown in Fig.3.The number of elements is discussed in the scenarios.

3.2.Boundary conditions

The boundary conditions of a simulation should be totally defined to get the most reliable and accurate results.The boundary conditions used in these simulations are expressed below:

●Inlet

The wind enters the domain from the inlet surface of the domain.The wind speed can play an important role in the dispersion and dilution of released gas.It varies with time and height.So,for the inlet condition,the wind speeds were set as profiles of the height and time.Fig.4 shows the wind profiles:(a)for the scenarios (1–5),(b) scenario 6,(c) scenario 7 during the simulation time at three heights(0.25,4,and 24 m),and(d)vertical profile of wind speed at the time of 200 s in the scenarios.The dense gas concentration in the inlet flows was considered to be equal to zero.

●Sides,Up and Outlet

Two sides were defined for the domain separately.For Side 1,the inlet condition was also demonstrated because the wind direction in the experiment did not completely match thexdirection,and the wind entered into the domain at an angle that varied in each scenario.For Side 2,the conditions were defined as open with no pressure gradient.The condition for the up side and outlet was an opening with a zero-pressure gradient.

Fig.1.Plot plan of the Kit Fox site,the meteorological towers,and the concentration monitoring arcs,the source,the ERP array,and the URA array.The EPA meteorological tower is of the figure at a location given by Downrange 102 m and Crossrange 177 m reported by WRI [4].

Fig.2.Scheme of Kit Fox simulation domain in CFX (x(-112,225) m, y (-60,60) m, z (0,25) m).

Fig.3.Scheme of simulation mesh.

●Ground

The ground’s roughness was set to 0.02 m,which was equal to the roughness of the URA obstacle in the Kit Fox experiment.

●ERP The ERP obstacles in these simulations were defined as a wall with no roughness and slip.

●Source

The CO2had a normal boiling point equal to 186.25 K.It existed in the gaseous phase at ambient temperature and pressure.The gas was released from the source square with an area of 1.5 m×1.5 m,with no elevation from the ground.The flow rates were from 3.6 up to 4 kg?s-1.The release time differed from 20 s to 180 s for the scenarios.The values for each scenario are presented in Table 1.

●The physical properties

The other physical properties of the experiments,such as ambient pressure,ambient temperature,relative humidity,turbulence closure,and atmospheric stability,were reported by Hannaet al.[31].The values of the parameters are listed in Table1.

Based on the two types of gas release,those with a time of release of less than 50 seconds are considered as puff releases,while all the others are plume release.

3.3.Scenarios

The simulations were arranged in different scenarios.One of the most important assumptions for all the scenarios was that there was no chemical reaction between the gas and air.For all the scenarios,the time step was set to 0.1 s.The ambient pressure and relative humidity that could affect the reference density of the air were extracted from the Kit Fox experiment data for each scenario.All the scenarios were simulated in the same geometry(see Fig.2).

The basis of the simulations in this study was the Kit Fox trial 5–3.This trial could be categorized as a plume type release.In each scenario,gas was released from the source for a period of time and modeled.Prior to this gas release,the wind stream condition was simulated and the gas was modeled for developing a more accurate simulation result.

Scenario 1 is the simulation of trial 5–3 with a coarse mesh size.The maximum and minimum mesh size was 1 m and 0.2 m,respectively.The minimum mesh size was used around the obstacles and the source in all the scenarios.It had around 3.3 million elements.The ambient temperature was considered as a constant value.Scenario 2 was also based on trial 5–3.This case was simulated using a finer mesh with around 12 million elements;the minimum mesh size was 0.17 m and the maximum 0.9 m.The diffusivity of the gas was taken into consideration.

Scenario 3,which was also based on trial 5–3,had the same mesh size as scenario 2.The diffusivity of the gas in the air was ignored.Scenario 4 was similar to scenario 2,with a difference in that the ambient temperature was floating.As can be seen in Table 1,in one of the scenarios,the ambient temperature is assumed to be variant,and the temperature profile against time is added to the simulations in different heights.Fig.5 shows the ambient temperature profiles at five altitudes (0.5,2,4,8 and 24 m) for scenario 4.In scenario 5,a finer mesh was investigated.

Table 1 The properties of the simulation scenarios (1 atm=101325 Pa)

To study the replication and reliability of the results,two more scenarios were simulated.Scenario 6 was based on trial 5–8 and another gas released plume.The last case was scenario 7,which simulated a puff release based on trial 3–7.These two simulations had the same mesh as scenarios 2,3,and 4.

The mentioned scenarios were considered to compare the effect of the floating temperature and to find the dominant force in mass transfer.This comparison can help to select the best scenario to optimize the calculation costs and time.

Fig.4.Wind speed at z=0.5,4 and 24 m during simulation time for:(a) scenarios (1–5),(b) scenario 6,(c) scenario 7,and (d) vertical wind speed profile at 200 s.

The vertical and horizontal contour plot of CO2concentration for scenario 3 is shown in Fig.6.The horizontal contours were taken in 150 s after the gas release at thez=1 m and the vertical contours aty=0 m.

3.4.Additional details

In this section,complimentary information regarding the modeling and simulation is presented.The simulations were performed on a computer system with the following features:16.0 GB RAM,Intel?processor,core i7TM,and CPU@ 4.00 GHz.The simulation times are reported in Table 1.The accuracy for all the residuals is 1×10-4.

4.Results and Discussion

4.1.Mesh size effect

Fig.5.Ambient temperature at z=0.5,2,4,8,and 24 m during simulation time for scenario 4.

In the CFD simulation of such problems,mesh size is one of the most important parameters.Because of the size of the domain of simulation,with a volume of over 1 ×106m3,mesh sizes should be properly chosen to optimize the computation time and cost.Therefore,the mesh sizes were set between 0.15 to 1 m.The use of a very fine mesh without considering the right time step can cause divergence in the solution.Also,fine mesh increases the number of equations that should be solved and the time needed to solve them.On the other hand,a coarse mesh can reduce the accuracy of the solution.

The difference between the three scenarios (1,3,5) was their different mesh size as well as node and element numbers;the results are shown in Fig.7 for two points:(a) P2111 (50,7,0.5)and (b) P2001 (50,0,0.5).Scenario 1 had a coarse mesh size and included around 3 million elements,scenario 3 had around 12 million elements,and scenario 5 had around 19 million elements as well as the finest mesh size of all the scenarios.The significant difference between the maximum concentrations of CO2in the results of scenario 1 and the experimental data was obvious.In scenario 3,the results of the simulation were more consistent with the experimental data.It showed that increasing the number of elements up to the same as in scenario 3 could lead to more accurate results.Although the difference between the results of scenario 3 and 5 is not significant,the simulation time of scenario 5 was considerably longer.The study of other monitor points also supported the same results.The mesh size of scenario 3 provided the proper calculation cost and accuracy.Therefore,the mesh size of scenario 3 was used in the other scenarios and investigations of different parameters.

4.2.Diffusion and monitors location

In order to investigate the influence of diffusivity,scenarios 2 and 3 were compared.In scenario 2,it was assumed that the diffusion of gas in the air was negligible in comparison with the convection of gas.One of the most noticeable results of these two scenarios was that the value of simulation by each of these cases showed an acceptable match to the experimental data in some monitor points;therefore,neither could be chosen as the proper scenario for gas dispersion in the whole domain.

Fig.6.Contours of CO2 concentration for scenario 3 were taken in 150 s after gas release,(a) horizontal plot at z=1 m and (b) vertical plot at y=0 m.

Fig.7.CO2 concentration against time(s) for simulation scenario 1,scenario 3,scenario 5 and Kit Fox experiment:(a) in P2111 (50,7,0.5),(b) in P2001 (50,0,0.5).

As previously mentioned,the monitors were located at four distances from the source.The first line of monitors was located at 25 m in thex-direction.Lines 2,3,and 4 of the monitors were located at 50,100,and 225 m,respectively.In the crosswind direction,the location of the monitors can be divided into three groups:the monitors located on the centerline (y=0 m),the monitors under the centerline(y<0),and those above the centerline(y>0).

In comparing scenarios 2 and 3,different monitors in different locations are distinct from each other.In the first line wherex=25 m,Fig.8 shows the simulation data in P1932 (25,-12,0.6).The result obtained by scenario 3 followed the experiment data more precisely than scenario 2;it created a maximum in a closer concentration value to the maximum value,and the time of reaching the first maximum was close to the experimental data.On the other hand,scenario 3 simulated closer values to the experimental data in P1003(25,0,1.2),whereas the data from scenario 2 were also acceptable,as shown in Fig.9.Different results can be noticed for P1132 (25,12,0.6) in Fig.10,and the value created by scenario 3 had no applicable match with the experiment.

Based on the y position of the monitors,similar results for the second line of monitors (x=50 m) occurred.In some points,scenario 3 provided better accuracy than scenario 2.A comparison of the results in different lines in Fig.11 (P2931 (50,-21,0.5)),Fig.12 (P2124 (50,14,4)),and Fig.13 (P2004 (50,0,5)) showed that scenario 2 created acceptable data,especially in the centerline and above it.

For the monitors under the centerline,such as P3922(100,-16,1.2)shown in Fig.14,scenario 3 created better data in comparison with scenario 2 in the third line (x=100 m) of the monitors.The same effects were illustrated in the fourth line,especially for the monitors not located in the centerline.For instance,the results of scenario 2 and scenario 3 for P4921 (225,-30,0.6) are shown in Fig.15.

Two other scenarios from the Kit Fox experimental trials were simulated to investigate the repeatability and reliability of the analysis of scenarios 2 and 3.Scenario 6 was simulated from trial 5–8 as a plume release;scenario 7 was based on trial 3–7 as a puff release.Scenario 6 led to accurate results in comparison with scenario 7 for P4121(225,30,0.6).The results of the data of scenario 2 were converged to the value of the experiment (see Fig.16).As shown in Fig.17,the same result was gained for P4001 (225,0,0.6).Fig.18 shows that the simulation based on convection with ignoring the diffusivity led to more acceptable results for scenario 6 in P1132 (25,12,0.6).

Fig.8.CO2 concentration against time for scenario 2,scenario 3 and Kit Fox experiment in P1932 (25,-12,0.6).

Fig.9.CO2 concentration against time for scenario 2,scenario 3 and Kit Fox experiment in P1003 (25,0,1.2).

Fig.10.CO2 concentration against time for scenario 2,scenario 3 and Kit Fox experiment in P1132 (25,12,0.6).

Fig.11.CO2 concentration against time for scenario 2,scenario 3 and Kit Fox experiment in P2931 (50,-21,0.5).

Fig.12.CO2 concentration against time for scenario 2,scenario 3 and Kit Fox experiment in P2124 (50,14,4).

Fig.13.CO2 concentration against time for scenario 2,scenario 3 and Kit Fox experiment in P2004 (50,0,5).

Fig.14.CO2 concentration against time for scenario 2,scenario 3 and Kit Fox experiment in P3922(100,-16,1.2).

When investigating these monitors,some common parameters were considered.It appears that for the monitoring points that are close to the ground or out of the gas plum,the diffusion controls the mass transfer.This was especially outstanding when these monitors were closer to the source,and the dispersion of the gas was mostly affected by diffusivity.For the monitors located in the wind direction or centerline and in a higher position or a farther location,scenario 2 developed acceptable data.A comparison of the results of these two scenarios showed that the dominant force of mass transfer in various locations of a field could affect the path of gas dispersion.Considering the data from scenarios 6 and 7,the dominant force in the plume releases in the simulations was convection.It seems that the diffusion in these cases could lead to accumulative computational error and divert the results of the simulation from the experimental.Therefore,the diffusivity equation can be ignored to optimize the calculation cost in simulation.Nevertheless,diffusivity should be considered in puff release.

Fig.15.CO2 concentration against time for scenario 1,scenario 3 and Kit Fox experiment in P4921(225,-30,0.6).

In many works,which are validated by the Kit Fox or other field experiments,the results of just one point or little points are reported and provide the basis for the simulation or models evaluated [10,22].Considering the above discussion,it seems that this format of validation is not reliable because some models or simulations can lead to the same results as the experimental data in some points,but they get a varied result in most of the points.

4.3.Temperature effect

The temperature effect and possibility of elimination of the dependent equations on temperature were surveyed to optimize the simulation cost.As mentioned before,the difference between scenarios 3 and 4 was the floating temperature for scenario 4.Scenarios 3 and 4 were compared with the experimental data from the Kit Fox to investigate the floating temperature effect.A comparison of the data of one monitor point (P1003 (25,0,1.2)) is shown in Fig.19.

It is observable that the difference between these two scenarios is not very significant.In addition,the change in the temperature during the release time,the development of the gas cloud,and the dilution of the gas in the air do not have a meaningful effect on the gas concentration.This may occur because the time of release and dispersion are too short.Based on this result,the effect of the changes in the temperature during the simulation timing can be ignored,thus reducing the computation cost.

4.4.Statistical evaluation

The MG and VG statistical parameters may be overly influenced by low values near the instrument thresholds and are undefined for the zero values.These types of values are common in dispersion modeling.Therefore,Chang and Hanna [29] recommended that a minimum lower bound should be assumed when calculating MG and VG.The statistical values for the overall domain of scenario 3 duringt=50 s andt=200 were (this time duration was chosen to ignore the zero values in statistical computation)) MG=1.24,NMSE=0.248,VG=2.235059,FB=-0.192,and FAC2=0.76.Previously,it was discussed that a simulation scenario could lead to an acceptable range of results in some points and out of range results in others.Anfossiet al.[32],Mazzoldiet al.[14],and Xinget al.[23] reported only the values for just a few points in their works and did not include the whole domain of simulations.However,considering the nature of these values,when only the value is reported without any description,it could be considered dubious(when the lower bound and rounding values are unknown or not considered,it could affect the interpretation of the data).Therefore,another parameter that should be considered is the monitors’threshold.It appears that the accuracy of the monitors was 1×10-6,and there were no digits after the decimal point.On the other hand,the use of decimals in simulations is very common.Therefore,some assumptions should be considered.The other factor is the accuracy of the data extracted from the simulation.How the low value bound of data,which are used for calculating the statistical parameters such as VG and MG,are chosen can affect these values.For investigating this effect,the statistical values were discussed point by point during the simulation time.As shown in Table 2,the value of the threshold affected the MG and VG.

Fig.16.CO2 concentration against time (s) for simulation (a) scenario 2,(b)scenario 6,(c) scenario 7,and Kit Fox experiment in P4121(225,30,0.6).

Fig.17.CO2 concentration against time (s) for simulation (a) scenario 2,(b)scenario 6,(c) scenario 7 and Kit Fox experiment in P4001(225,0,0.6).

Fig.18.CO2 concentration against time(s)for simulation scenario 2,scenario 6 and Kit Fox experiment in P1132(25,12,0.6).

Fig.19.CO2 concentration against time(s)for simulation scenario 4,scenario 3 and Kit Fox experiment in P1003 (25,0,1.2).

As mentioned above,the value of MG and VG are not acceptable for data near zero.This fact is evident in Table 2,where choosing a different lower bound for the data can change the MG value considerably.As an example,a change in the lower bound caused an extreme change in the MG for monitor points such as P4111 (seeFig.20),where the simulation data is well matched with the experimental data,but the MG and VG values are nearer the acceptable value.

Table 2 Statistical evaluation

Fig.20.CO2 concentration against time(s) for simulation scenario 2 and Kit Fox experiment in P4111 (225,15,0.6).

5.Conclusions

The Kit Fox trials 5–3,5–8,and 3–7 were simulatedviaANSYS CFX.For simulation purposes,different scenarios were assumed.The differences between the scenarios included a different node and element number,simplifying the mass transfer phenomena without setting the gas diffusivity,and assuming constant domain temperature against floating temperature.Also,to confirm the repeatability and reliability of the result analysis,two other Kit Fox trials were simulated.The results showed that the mesh size could play an important role in the accuracy of the CFD simulation results that could justify the computation cost of the simulation.The finer mesh was not always the best choice because solving it could be time-consuming;also,based on the purpose of the simulation,e.g.,risk assessment,a solution that is close to the experimental data could be acceptable.

Another important result of this study was that the data extracted from one simulation showed an acceptable match to the experiment data in one or more monitoring points andvice versa,while in some other points,they are not even close.After the simulation of any of the scenarios,their validity should be investigated on all the desired points and not only certain ones.In regard to the monitoring places,it appears that diffusion controls the dispersion of the gas in the points which are close to the ground or placed in the opposite direction of the wind.For the monitors pointed in the wind direction and in the last line,the wind force played a role.It seems that in these points,the accumulative error of computation can diverse the results of simulation when diffusivity was considered.The temperature was another parameter considered in this study.Based on the results,the change in temperature had a slight effect on the gas dispersion simulation,and it could be assumed that the temperature was constant.Some statistical equations for validating the simulations and models with experimental data were also presented.MG and VG are very sensitive to the value near zero,which is very common in gas dispersion simulation and modeling.Changing the value of the lower bound in their calculation can change them notably.Finally,for validating the models,it is suggested that the statistical validation be reported for the desired observation points based on the geometry and distances.Furthermore,other turbulent methodologies such as LES and DNS could be investigated.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The author appreciates the support provided by the Iranian Research Organization for Scientific and Technology (IROST) in conducting this research.

Nomenclature

Athe surface area of the control volume,m2

Coobserved concentration

Cppredicted concentration

FAC2 the fraction of C within a factor of two of C

FB the fractional bias

gigravitational acceleration,m?s-2

Jithe diffusion flux of the species

kturbulent kinetic energy,m2?s-2

NMSE the normalized mean square error

Ppressure,N?m-2

Qvector of conserved variables

Uvelocity vector,m?s-1

uivelocity,m?s-1

Yithe concentration ofith species

ε dissipation of turbulent kinetic energy,m2?s-2

ρ fluid density,kg?s-1

μ viscosity,Pa?s

μeffeffective viscosity,Pa?s

μtturbulent viscosity,Pa?s

λ coefficient of viscosity,kg?m-1?s-1

δijkronecker delta

σkturbulent Prandtl numbers fork

σεturbulent Prandtl numbers for ε