IChemE SYMPOSIUM SERIES NO. 153 # 2007 IChemE

CFD MODELING FOR EMERGENCY PREPAREDNESS AND RESPONSE TOLIQUEFIED AMMONIA RELEASE

Michal Kisa, L’udovıt Jelemensky and Jan Stopka

Institute of Chemical and Environmental Engineering, Faculty of Chemical and Food Technology, Slovak University of

Technology, Radlinskeho 9, SK-812 37 Bratislava; e-mail: ludovit.jelemensky@stuba.sk

In the recent years, the CFD modeling has become a very useful tool for many research areas. This

is connected with the increasing power of desktop computers. Accordingly to that, the compu-

tations for which we needed supercomputers can be done on regular PCs. The ability of CFD to

predict fluid flow and concentration of dangerous gases is essential to the people working on

safety analysis. There were many programs developed for the prediction of dangerous gas cloud

spreading. Starting from very simple Gaussian models for the light gases (the density of gas is

less or equal to that of air) continuing with box models for heavy gases (the density of gas is

higher than that of air) and ending with complete solving 3D balance equations for mass, momen-

tum and energy (CFD). The use of CFD models has high potential to be a tool which can after some

adjusting and modification replace the experimental modeling or at least reduce the number of

experimental trials.

This work is concentrating on such adjusting of CFD parameters by using experimentally

obtained data from FLADIS experiments. FLADIS experiments were carried out by the Risø

National Laboratory (Rediphem database). The experimental trials were done on pressure liquefied

ammonia. Ammonia behaved as heavy gas due to the presence of liquid droplets and due to the heat

of evaporation of ammonia the flashing jet became much colder.

This paper will provide a comparison of the results obtained by the FLADIS field experiments

and the results of CFD modeling by Fluent 6.2. Meteorological conditions and source strength

were determined from experimental data and simulated using the CFD approach. The initial

two-phase flow was also included for the released ammonia. The liquid phase was modeled as dro-

plets using discrete particle modeling, i.e. Euler-Langrangian approach for continuous and discrete

phases. The second part of work was devoted to the inclusion of obstacles. Included were high

obstacles, which cannot be modeled with increasing surface roughness. From results is obvious

that such obstacles influence radically the dispersion of gas. The presence of wakes and cavities

behind the buildings also increases the residence time of toxic gases.

KEYWORDS: CFD modeling, gas dispersion, ammonia, turbulence, Schmidt number

INTRODUCTIONPotentially hazardous gases are very common in industrialand also in domestic uses. The term “hazardous” meansgas toxicity to the public or environment or flammabilityof the gas. Such gases are usually stored in highly pressur-ized vessels in liquefied state at ambient temperature. If anaccident happens and the stored gas is suddenly depressur-ized the resulting jet will consist of a gaseous vapourphase and a liquid phase containing particle dropletsmixed with air. Concentrations of the released gas arethen predicted by various types of models and the valuesobtained are used in the hazard and risk assessmentstudies or by authorities (e.g. fire department) in the caseof an accident.

The mostly used models are simplifications of theconservation equations for mass, momentum and energy.The models used in the mentioned area can be distinguishedon the basis of the density of the released gas into light gases(the density is equal to that of air) and heavy gases(the density is much higher than that of air). Gaussianmodels have been derived as an analytical solution from

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the diffusion equation and from observations made by theexperimental work, i.e. the concentration of released gas isfollowing the Gaussian distribution (Lees 1996). The dis-persion coefficients have been derived from experiments(Barrat 2001). Box models have been used for heavygases. In the simple box model the gas is assumed to be apancake-shaped cloud with properties uniform in the cross-wind and vertical directions. The model then containsrelations which describe the growth of radius and heightof an instantaneous release, or the crosswind width andheight of a continuous release, given for example in refer-ence (Spicer and Havens 1989). These simplifications donot allow to model complex geometries. They are derivedfor a flat plane geometry with no obstacles or a two-dimensional model with a simple obstacle.

Another model is the CFD approach, i.e. simul-taneous solving of balance equations (eqs. 1–4) of mass,momentum and energy (Bird et al.) given below. Theresults obtained by the CFD modeling are more accuratebecause the wind velocity is completely resolved in com-parison to the simpler models, where velocity is a single

IChemE SYMPOSIUM SERIES NO. 153 # 2007 IChemE

value or a function of height. This is clearer in the domainwith high obstacles. By using the CFD set of equationsany real hazardous situation including gas release in the pre-sence of buildings can be modeled (Venetsanos et al. 2003).Moreover, in the CFD model the second phase can beincluded. The gas phase (air – toxic gas) is modeled bythe mentioned balance equations, and the liquid phase(droplets generated by a sudden pressure drop of the super-heated liquid) can be modeled by the multiphase approach.It means that the second phase is modeled by the sameequations as the first phase or the droplets are modeled asdiscrete particles (Crowe et al. 1998).

The buildings or obstacles strongly influence the flowand thus also the dispersion of gases. Due to the wakes andcavities behind buildings the residence time of the toxicgas is higher, the turbulence is increased and the gas isspread faster in the crosswind direction.

Numerical simulations are very important for verify-ing the models with measured data. Delaunay (Delaunay1996) have performed numerical simulations of tracer gasexperiments carried out at Porte Maillot in Paris. Hannaet. al. (Hanna et al. 2004) have used FLACS software tosimulate the MUST experiment, Venetsanos et. al.(Venetsanos et al. 2003) worked on the modeling of theStockholm hydrogen gas explosion. All these works havevalidated the application of the CFD approach as a usefultool for predicting gaseous dispersion in the vicinity ofbuildings.

In the present work the dispersion of the liquefiedammonia release was simulated by the CFD approachusing the commercial software package Fluent 6.2.Ammonia was chosen because it is toxic and increasinglyused in the industry. Ammonia is usually stored inpressurized vessels in the liquid phase. After its release, atwo-phase flow occurs near the point of release formingan ammonia cloud which is denser than the ambient air.The temperature and the density gradually approachvalues of the ambient air and the cloud exhibits signs ofneutral or even lighter type of gas dispersion.

The dispersion of ammonia was modeled by thenumerically solved full set of conservation equations withadditional equations for turbulence and a discrete particlemodel for liquid particle droplets. The mixture phasewhich is composed of air and ammonia vapour is modeledby the Eulerian approach. The continuous phase and theliquid phase consisting of particle droplets with differentdiameters are modeled by the Lagrangian approach for thediscrete phase.

Data obtained by mathematical simulation werecompared to the experimental data from the FLADIS(Nielsen et al. 1997) field experiment. In this field exper-iment the release rates were approximately 0.5 kg . s21

unlike the most well-known field experiment DesertTortoise Series (Goldwire et al. 1985) with release ratesabout 100 kg . s21. These are much higher than those pre-sented in the FLADIS experiment. However, the smalleramounts of ammonia release occur more frequently inpractical situations. Other differences are lower ambient

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temperature and higher humidity, which are more represen-tative for the European climate, comparing to DesertTortoise Series. The FLADIS experiment was chosen alsobecause of its perfectly organized data and the free accessto them on the webpage.

Furthermore, the buildings or obstacles were placedin a computational domain to see the influence of obstacleson the dispersion.

GOVERNING EQUATIONSThe following Reynolds averaged Navier-Stokes equations(RANS) were used in CFD modeling in all three directionx, y, z (Fluent 2005) of mass, momentum, energy andspecies balances with mass Sm, enthalpy Sh, momentumSui and species source Sn,

@r

@tþ@

@xj

(ruj)¼Sm (1)

@

@t(rui)þ

@

@xj

(ruiuj)¼�@p

@xi

þ@

@xj

(mþmt)@ui

@xj

þ@uj

@xi

� �� �

þrgiþSui (2)

@

@t(rcpT)þ

@

@xj

uj(rcpT)� �

¼@

@xj

lþcpmt

Prt

� �@T

@xj

�X

i

hi J!

i

!

þSh (3)

@(rYn)

@tþ@(rujYn)

@xj

¼@

@xj

r Dn,mþmt

rSct

� �@Yn

@xj

� �þSn

(4)

(where Prt and Sct are turbulence characteristics of parti-cular transport phenomena, i.e. heat transport and masstransport, respectively) together with the k-e turbulenceclosure model (eqs. 5–7) used also in the work ofSklavounos and Rigas (Sklavounos and Rigas 2004), whoobtained a good agreement with experimental datathrough this model.

mt¼cmrk2

1(5)

@(rk)

@tþ@(rujk)

@xj

¼@

@xj

mþmt

sk

� �@k

@xj

� �þGk�r1 (6)

@(r1)

@tþ@(ruj1)

@xj

¼@

@xj

mþmt

s1

� �@1

@xj

� �þc11

1

kGk�c21r

12

k(7)

In eqs. 5–7 the constants are c11¼1:44,c21¼1:92,s1¼1:3,sk¼1:0,cm¼0:09.

For the discrete phase, the equation of motion isdefined as

dup

dt¼ FD(u� up)þ ~g

(rp � r)

rp

þ ~F (8)

IChemE SYMPOSIUM SERIES NO. 153 # 2007 IChemE

the enthalpy balance as

mpcp

dTp

dt¼ aAp(T1 � Tp)þ

dmp

dth fg (9)

where a, convective heat transfer coefficient, is obtainedfrom the Nusselt correlation reported in (Ranz and W. R.Marshall 1952; Ranz and W. R. Marshall 1952)

Nu ¼adp

l¼ 2:0þ 0:6Re

1=2d Pr1=3 (10)

and the mass balance as

Nn ¼ kc(Cn,s � Cn,1) (11)

where kc, mass transfer coefficient, is obtained from theNusselt correlation (Ranz and W. R. Marshall 1952;Ranz and W. R. Marshall 1952)

Nuc ¼kcdp

Dn,m

¼ 2:0þ 0:6Re1=2d Sc1=3 (12)

FLADIS EXPERIMENTField experiments with the dispersion of pressure liquefiedammonia were carried out in the Risø National Laboratory.The source was a flashing jet oriented in the horizontaldownwind direction with the source strength of 0.25–0.6 kg . s21 and duration in the range 3–40 min. Due toevaporation heat, the flash boiling ammonia jet becamemuch colder, and therefore heavier than the surroundingair. The main focus was to study the dispersion in all itsstages, i.e. heavy gas dispersion (measured gas concen-tration in 20 m distance) and then further downstream,where the flow developed into a plume of neutral buoyancy,the passive gas dispersion (measured gas concentration in70 m and 235 m distance). The main characteristics of thetrials used in this work are in Table 1.

The source was a 6.3 mm (4.0 mm for the trialFladis16) diameter nozzle pointing horizontally in theideal downwind x-direction with an elevation of 1.5 m.

Table 1. Main characteristics of the Fladis trials used

Trial

_m/kg . s21 f

w/m . s21 L/m

u10/m . s21 Stability

Fladis9 0.40 0.160 20 348 5.6 D

Fladis15 0.51 0.184 24 396.8 6.10 D

Fladis16 0.27 0.194 30 138 4.40 D

Fladis21 0.57 0.200 27 252.6 4.08 C

Fladis23 0.43 0.184 20 2112.3 6.74 D

Fladis24 0.46 0.186 22 276.9 5.03 C

Fladis25 0.46 0.186 22 2201.5 4.71 D

_m – release rate; f – vapour fraction; w – release velocity; L – Monin-

Obukhov length; u10 – wind velocity in the 10 m height

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BOUNDARY CONDITIONSThe boundary and meteorological conditions were identicalto the FLADIS experiment. The domain size used inmodeling was 280 � 200 � 100 m in x, y, z directions,respectively. Each emission was treated as a plume, i.e. acontinuous release.

Following boundaries for the continuous phase wereset according to Figure 1: no slip boundary condition onthe wall with standard wall function incorporated inFluent 6.2 with roughness length of 0.04 m and boundarylayer depth of 0.2 m, i.e. the distance of the first pointfrom the wall. Symmetry boundary condition was appliedon y and z planes.

The atmospheric stability class is represented by theinflow boundary condition for the velocity u ¼ u10(z=z10)n

and turbulent kinetic energy k and dissipation of turbulentkinetic energy 1 (Han et al. 2000). Power law velocityprofile was used according to the stability class reportedby Barrat (Barrat 2001). i.e. n ¼ 0:15 for the D class stab-ility and n ¼ 0:10 for the C class stability. On the outflowboundary, the Neumann boundary condition was applied.

For the liquid discrete phase, the initial temperaturewas also set to 239 K and the initial speed to the value,which corresponds to the velocity of the flow of liquefiedammonia through the orifice. The source of ammoniarelease was modeled as the source in the balance equationswithout exactly modeling the release from the pipe.Rosin-Rammler distribution for the diameter of droplets dis-tribution for the ammonia liquid discrete phase was applied(Johnson and Woodward 1999) as the mass fraction ofdroplets with diameter greater than diameter d

Yd ¼ e�(d= �d)b

(13)

with dmin ¼ 10mm, dmax ¼ 100mm, �d ¼ 50mm andb ¼ 2.5. The initial amount of liquid ml and vapour phasemv fractions was found from the enthalpy balance

f ¼mv

mv þ ml

¼cp(T0 � Tb)

Hvap

(14)

Figure 1. Boundary conditions. Length scales: x ¼ 280 m,

y ¼ 200 m, z ¼ 100 m

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SOLUTIONFluent 6.2 was used for solving 3D RANS. The used discre-tization scheme was the first order upwind and SIMPLEpressure-velocity coupling (Patankar 1980). Computationalgrids consisted of approximately 400 000 hexahedralvolume elements. Steady state runs were terminated after�400 iterations allowing a reasonable convergence to beachieved. The convergence criterion was set to residualsequal or less than 1024 for the continuity equation. Thetotal time for the steady states results was �45 minutes on2.8 GHz Intelw Pentium4 Processor with 1 GB of RAM.

RESULTS AND DISCUSSIONUnlike a wind tunnel simulation the atmospheric wind direc-tion and plume centerline position are not known a priori buthave to be determined by the observation. From the CFDmodeling (steady state) point of view it may be more rel-evant to find a typical instantaneous plume profile thanaverage of a meandering plume. Therefore, it is necessaryto determine the plume position from concentrationmeasurements. This can be done using the fixed frame ofreference, where local average concentration is calculated.Another alternative way is to find instantaneous positionof plume and then calculate the plume statistics, i.e.moving frame of reference. This moving frame of referenceexpresses more accurate the simulated results because itneglects the strong variation of wind direction. Themoving-frame analysis was used for the experimentaldata. Experimental concentrations were obtained by theinterpolation of experimental data with the assumptionthat the concentration profiles in the horizontal plane canbe approximated by the Gaussian profile equation reportedin (Nielsen 1996), with longitudinal (x-direction) variationof centerline concentration c0(x), horizontal plume spread-ing sy(x), lateral plume position y0(x), plume centre ofgravity �z(x).

c(x, y, z) ¼ c0(x) � exp �z

�z(x)

� � exp

½y� y0(x)�2

2s2y(x)

( )(15)

The statistical performance of the observed and pre-dicted data is given in Table 2. The statistical performance

Table 2. Comparison of observed and predicted data of

maximal concentration for trials in Table 1 with statistical

measures

FB MG VG MRSE NMSE

0 1 1 0 0

Heavy (20 m) 0.446 1.852 1.724 0.306 0.322

Neutral (70 m) 20.427 0.783 1.334 0.637 0.667

Far (235 m) 20.861 0.506 3.222 1.981 2.431

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measures are fractional bias (FB) with ideal value of 0

FB ¼Co � Cp

�Þ

0:5 Co þ Cp

�Þ

(16)

geometric mean bias (MG) with ideal value of 1

MG ¼ exp ln Co � ln Cp

� �(17)

geometric mean variance (VG) with ideal value of 1

VG ¼ exp ln Co � ln Cp

� �2 �

(18)

mean relative square error (MRSE) with ideal value of 0

MRSE ¼ 4Co � Cp

Co þ Cp

� �2 !

(19)

Normalized mean square error (NMSE) with idealvalue of 0

NMSE ¼Co � Cp

� �2

CoCp

(20)

where Co is the observed quantity and Cp is the predicted(modeled) quantity.

The perfect model should have ideal values of statisti-cal measures. Of course, because of the influence of randomatmospheric processes, there is no such thing as a perfectmodel in air quality modeling. Generally, it can be saidthat the heavy stage of dispersion the CFD model is under-estimating and overestimating the passive stage ofdispersion.

The results from the FLADIS experiments for thetrials are presented in Figure 2, where experimental and pre-dicted maximal (centerline) concentrations, Co and Cp,respectively, are depicted.

The results obtained from the numerical simulation oftrial Fladis9 are shown in Figure 3 for different turbulentSchmidt number ranging from 0.1 to 1.3.

The influence of different Schmidt numbers was usedbecause the turbulent Schmidt number generally used 0.7 iscorrect in the turbulent core. The turbulent Schmidtnumber is depended on the height within the boundarylayer, as reported by Koeltzsch (Koeltzsch 2000). Fromthis paper follows that the turbulent Schmidt number isnot constant throughout the atmospheric boundary layer.

Another problem is that heavy gases tend to suppressturbulent mixing within a cloud bellow that of ambient tur-bulence. Mainly the entrainment of ambient air to the cloudis neglected. This observation comes from the functionalform of the dispersion coefficient given by

K ¼ku�z

f Ri�ð Þ(21)

with Monin-Obukhov profile function for negative buoyancy

f ¼ 1þ 0:8Ri�ð Þ0:5 (22)

Figure 2. Centerline observed and predicted maximal concentrations for trials in Table 1 for three sensor arrays a) heavy (20 m),

b) neutral (70 m), c) far (235 m)

Figure 3. Influence of Schmidt number for trial Fladis9 for the centerline concentration

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and layer Richardson number

Ri� ¼g rc � r0

� �H

r0u2�

(23)

By inspecting these equations one can explain the sup-pressing feature of heavy gases. If the Ri number is calculated

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for heavy gas, high values are expected, i.e. negative buoy-ancy. This value is used to calculate f and then the dispersioncoefficient. With increasing heavy gas cloud concentration,the Ri number and also the f function are being increased.Then, with increasing concentration of heavy gas the dis-persion coefficient will decrease. In words of turbulence mod-eling, the turbulent Schmidt number is increasing and the

Figure 4. Crosswind observed and predicted concentrations for three sensor arrays a) heavy (20 m), b) neutral (70 m), c) far (235 m)

for a trial Fladis9

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values of higher Sct correlate well with the first phase of dis-persion. The passive stage of dispersion is better correlatedusing a smaller turbulent Schmidt number what correspondswith the Koeltzsch description that the turbulent Schmidtnumber is a function of height in the boundary layer.

From Figure 4 follows that the computed concen-trations for the turbulent Schmidt number of 0.7 are nar-rower compared to those obtained experimentally. Themaximal concentrations are computed relatively correctly.However, a closer look on Figure 2 shows that the crosswind concentration profiles are not well correlated. Asreported e.g. in (Hanna et al. 2004) the k-e model showsits weakness in a flat terrain with no obstacles where toomuch dissipation of turbulence was observed. The single

Figure 5. Computed a) and measured b) (interpolated) concentrati

1 ppm

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realization of wind direction in steady state cannot takeinto account the fluctuation of wind direction and the turbu-lence production which is generated by these fluctuations.This would typically lead to an over-prediction of thehazard distance (over-prediction of concentration). Buildingobstacles can ensure a sufficient production of turbulence.

Configurations with different types of obstacles werechosen to find out how the computed concentrations will beaffected. Geometry with different height, width, length andposition of obstacles was examined (taking into accountdifferent dimensions of the obstacles ranging from 10–50 � 10–20 � 8–15 m for all three directions and the pos-ition of obstacles). It is complex and irregular as can be seenin Figure 6.

on for trial Fladis9 with isolines 10000 3000 1000 300 100 30 10

Figure 6. Computed concentration with isolines 10000 3000

1000 300 100 30 10 1 ppm

Figure 6a. 3D realization for geometry with obstacles

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From Figures 6 is evident that the calculated isolinesare wider than without buildings. The turbulence (evoked bythe presence of buildings and streamlines of wind whichflows around the buildings) is influencing the concentrationisolines. Thus, the width of the cloud is not dominantlysensitive to the turbulent Schmidt number. The width ofthe cloud is also a function of the geometry. As can beseen from Figures 6 the isolines are wider and morechaotic in comparison with isolines without obstacles(Figure 5). Furthermore, it is evident, that ammonia will dis-perse in the places, which are not affected in the casewithout obstacles. The presence of obstacles has also aninfluence on the values of centerline concentrations.

This work shows that for complex geometries model-ing, CFD models can play an important role. The usuallyused models are approximated from the field experimentswhich are done in flat plane fields. Therefore, their appli-cation to the complex geometries is rather controversial.On the other hand, the CFD models are able to modelcomplex geometries but they are limited by the applicationof turbulence closure models. However, in the futureCFD models can be used after their validation against

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experimental data for replacing experimental modeling inthe known area of possible hazardous gas release.

ACKNOWLEDGEMENTThis work was supported by the Grant VEGA 1/1377/04 ofSlovak Scientific Grant Agency.

NOTATIONcp specific heat capacity J . kg21 . K21

C molar concentration mol . m23

d diameter of droplet particle mGk generation of turbulence

kinetic energykg . m21 . s23

h enthalpy J . kg21

hfg latent heat J . kg21

r density kg . m23

J species diffusion flux kg . m22 . s21

N molar flux of vapor mol . m22 . s21

p static pressure PaRe Reynolds numberY species mass fractionl thermal conductivity W . m21 . K21

m viscosity Pa . s

SUBSCRIPTSn speciesop operatings saturation1 ambientv vapour

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