239

Journal of Loss Prevention in the Process Industries 16 (2003) 341347www.elsevier.com/locate/jlp

Evaluation of a CFD porous model for calculating ventilation inexplosion hazard assessments

C.E. Fothergill ab, S. Chynoweth a, P. Roberts a,, A. Packwood ba Shell Global Solutions, P.O. Box 1, Chester, CH1 3SH, UK

b Department of Mechanical and Materials Engineering, University of Surrey, GU2 7XH, UK

Abstract

In the past, gas explosion assessment relied on worst case scenarios. A more realistic approach is to look at the probability ofexplosions and their likely severity. The most flexible way of investigating many different scenarios is to estimate a ventilationflow, feed this into a flammable volume calculation and then calculate the explosion severity. The procedure allows many parametersto be varied efficiently. A Computational Fluid Dynamics porous model is evaluated for modelling the ventilation flow throughcongested regions, including a new method that has been developed to derive the resistance. Comparison with velocity measurementsfrom a large scale model of an offshore module showed that overall the CFD model performs very well, especially consideringthat the homogenous porosity block does not model any of the internal obstructions and therefore would not predict any local floweffects. This gives confidence that the overall flow pattern is sufficiently close to the local flow patterns, to be used in explosionassessments. The porous approximation in CFX is found to underpredict the turbulence intensity in the obstacle array compared tothe explosion model EXSIM. Improving the turbulence prediction in the porous model would be valuable, so a relatively simplemethod of increasing the turbulence in porous regions is proposed. The CFD model will provide the non-uniform natural ventilationflowfields of complex regions for future explosion assessments at a hierarchy of levels. 2003 Shell Research Ltd. Published by Elsevier Science Ltd. All rights reserved.

Keywords: CFD; Porous model; Explosion assessment

1. Introduction

In the past, gas explosion assessment relied on worstcase scenarios. A more realistic approach is to look atthe probability of explosions and their likely severity.For instance, a gas release may not result in a uniformflammable mixture throughout the module; and thepressures created from a worst case explosion arisingfrom the ignition of a stoichiometric gas cloud extendingthrough the entire module have been proven to be higherthan those created by a realistic gas cloud (Johnson,Cleaver, Puttock, and Van Wingerden, 2002).

The most flexible way of investigating many differentscenarios is to estimate a ventilation flow, feed this intoa flammable volume calculation and then calculate the

Corresponding author. Tel.: +44-151-373-5893; fax: +44-151-373-5845.

E-mail address: [email protected] (P. Roberts).

0950-4230/03/$ - see front matter 2003 Shell Research Ltd. Published by Elsevier Science Ltd. All rights reserved.doi:10.1016/S0950-4230(02)00113-4

explosion severity (Fig. 1). The procedure allows manyparameters to be varied efficiently, unlike a single stepprocess where a CFD model could calculate theexplosion severity of one individual scenario directly,but each variation of the input parameters would involveanother computationally expensive simulation. A newmethod of modelling the ventilation flow through con-gested regions is evaluated here. This involves rep-resenting a congested region as a volume of homogenousporosity in the CFX-4 CFD model. The method chosento parameterise the porous region is described andassessed here. The results of the porous simulations arevalidated against full scale experimental measurementsand another CFD code, EXSIM(http://www.exsim.com).

2. Background

Three main methods are currently available for therapid calculation of ventilation flow; zone models, inte-

342 C.E. Fothergill et al. / Journal of Loss Prevention in the Process Industries 16 (2003) 341347

Fig. 1. Stages of an explosion calculation.

gral models and empirical approximations. These tech-niques are appropriate where the flow is expected to bespatially uniform (Grosso, 1992), but in more complexregions the flow field can contain significant areas ofnon-uniformity such as recirculation regions and thesecases need to be calculated using CFD. The large-scaleflow circulations and patterns within the module can bemodelled by representing the congestion in the moduleas a volume of homogenous porosity and resistance. Thisapproximation is used instead of fully resolving theobstacles because:

It is computationally more efficient, allowing a largenumber of confinement arrangements under a rangeof windspeeds to be modelled.

The results need to be applicable to any module, soone single internal arrangement would not be appro-priate as it would create specific flow patterns thatwould not be appropriate input for calculating flam-mable volumes.

The details of the flow inside the module are notrequired by simpler flammable volume models thatuse the ventilation velocity.

The evaluation of this method will be valuable formany applications.

Research concerning wakes behind surface mountedtwo-dimensional porous obstacles (Shiau, 2000; Lee &Kim, 1999; Raju, Garde, Singh SK & Singh N, 1988)has allowed the basic features of the perturbed flow tobe reasonably well understood. The large scale generalflow patterns inside a free-standing porous region inatmospheric flow has rarely been considered, the closestexamples being investigations into groups of buildings(Macdonald, 2000).

The flammable volume is calculated using a methodsuitable to the likely complexity of the problem. Simple

correlations can be used to arrive at the flammable vol-ume (Cleaver & Britter, 2001) if a characteristic venti-lation velocity is known. A more accurate method(Chynoweth, 2001) uses random walk theory. Many dif-ferent release scenarios can be calculated with one singleflow field as the basis, while the release location, orien-tation, flow rate and composition are all varied. Theefficiency of the technique means that many thousandsof simulations can be performed in order to construct astatistically sound picture of the probable flammable gasclouds. The explosion models use the flammable volumeinput, and range from simple empirical methods(Puttock, 1995) through phenomenological models(Puttock et al., 1998) to CFD models (Saeter, 1998). Themodel complexity required is case dependent and inmany situations it is appropriate to apply more thanone model.

3. Porous model in CFD

Geometry is represented as a porous region in CFXusing the Porosity Distributed Resistance (PDR) formu-lation of the governing equations. The model is a gener-alisation of the Navier-Stokes equations for fluid flowand of Darcys law commonly used for flows in porousregions (Miguel, van de Braak, Silva, & Bot, 2001). Thismethod was first proposed by Patankar and Spalding(1974). In the PDR method, the presence of obstructionsmodifies the governing equations in two ways. Firstly,the volume of the obstruction is represented in the con-trol volume in such a way that only the non-blockedareas are available for fluid flow. Secondly, obstaclesgive additional flow resistance which must be modelled.The modified Navier-Stokes momentum equation iswritten as

343C.E. Fothergill et al. / Journal of Loss Prevention in the Process Industries 16 (2003) 341347

t(brUi)

xj

(birUjUi)xj

(bisij) bpxi

Ri

where Ui is the mean velocity vector in the i-direction,b is the volume porosity, bi is the area porosity in the idirection, andRi b(RCi RFi|Ui|)UiRCx (kgs-1/m-3) is the resistance constant in the x-direc-tion and RFx (kg/m4) is the speed resistance factor in thex-direction. The linear resistance term RCx can be set tozero due to the highly turbulent nature of the flow.

The porous approximation has been used to modeltwo-dimensional porous fences (Takahashi, Du, Wu,Maki & Kawashima, 1998). Packwood (2000) used aresistance based on empirical data from Hoerner (1965)and tested the performance of a modified k- and theReynolds stress model for flow downstream of fences.Overall the much simpler, modified k- model workedsurprisingly well. The three-dimensional problem hasbeen largely neglected, although Speirs (1997) experi-mental study showed that the main flow features werecommon to both the two and three-dimensional cases.Another study of 3D volumes compared CFD PDRresults to experiments (Hoang, Verboven, De Baerde-maeker & Nicola, 2000) and found 26% error in theCFD simulations, but this was thought to be mostly dueto mesh quality.

Despite these studies, methods for representing com-plicated geometries as porous regions in CFD are notwell established. The value for resistance depends onboth the shapes of the blockages within a module andthe distribution of large volume and small volumeobstacles. The drag on the flow through a porous regioncan be estimated by calculating the drag due to eachindividual obstacle and then summing these values toarrive at the overall resistance.

The speed resistance factor RFi (kg/m4) equates to

RFi D

Vu2

where V is the total volume, u is the averaged flow speedand D is the drag. SI units are used throughout. The dragon an individual object can be written

D 12ru

2CDA

where r is density, CD is the drag coefficient, and A isthe frontal area. The effective drag of the entire moduleand all of its internal congestion was then taken to bethe sum of the drag of each obstacle:

D i

12ru

2C(i)D A(i)

where CD (i) and A (i) are values for an individualobstacle.Therefore,

D 12ru

2i

C(i)D A(i)

and

RFi 12rC(i)D A(i)

V

The formulation above uses CAD data to calculate theactual drag for four categories of obstruction, and eachof the shapes have different drag coefficients, availablein the literature (Munson, Young & Okiishi, 1998).

Implicit in the above formulation is the assumptionthat obstacles are sufficiently well spaced. This issue hasbeen addressed in another study using a resistance para-meter, (TNO, 1989) where corrections were made forobstacles lying in the wake of another obstacle. In Pack-woods (2000) simulations the main deficiency found isthat it overestimates the total resistance in cases wheregrids are closely spaced, due to the partial shieldingeffect of an upstream grid on a downstream one. A tech-nique which sums the drag of all of the obstacles withinthe module may similarly overpredict the overall resist-ance.

The Engineering Sciences Data Unit Item 74040(1974) provides a method for estimating the pressuredrop across tube banks which takes into account thespacing of the obstacles. This method was used to testthe effect of spacing. It assumes that all of the obstruc-tions are circular cylinders, and that the flow is con-strained to go through the tube matrix rather than aroundit. The resistance of an array of typical dimensions and1 m spacing were calculated using both the ESDUmethod and the method that sums the drag. A differenceof 7.5% was found in the ventilation. This is negligiblewhen considering the role of the ventilation figures inthe calculation of gas cloud size and explosion assess-ments, but indicates that the method could beimproved nonetheless.

4. Validation

The ability of the porous block approximation in theCFX code to represent flow through congested moduleswas evaluated using measurements from a full scalemodule and the results from another code, EXSIM(http://www.exsim.com). EXSIM is a CFD basedsoftware tool specifically designed for explosion model-ling, which models more of the complex geometrywithin a congested region.

Simulations were carried out of the flow through amodule of dimensions 28 m 12 m 8 m with onelong side, the adjacent short side and the top blocked.Five different wind speeds were modelled, ranging from2.77.8 m/s, and the same wind direction was used in


every case, with the wind impinging on the short blockedside of the module. Velocities from CFX were comparedat the locations where measurements were taken in themodule. The velocities for the different windspeeds werenon-dimensionalised by the ambient windspeed in eachcase. The non-dimensionalised values from each differ-ent wind speed simulation were then averaged to give asingle value at each location for the measurements andthe model.

The experimental programme was carried out in aJoint Industry Project with 11 participating companies(BG Technology, 1999). Velocities were measuredinside an experimental rig representative of an offshoremodule, in different wind speeds. The rig was on openland with trees and buildings in the vicinity. Ten anem-ometers were placed in two planes, one at eight m alongthe length of the rig, and the other at 20 m along thelength of the rig.

The domain in the CFX model extended five moduleheights around the module and 15 heights downwind, inaccordance with guidance found in Casey and Win-tergerste, (2000). The domain was divided into cells ona 0.5 m grid. The inlet velocity was fitted with a loglaw profile

U u ln zzoA surface roughness length of zo = 0.5 m, appropriatefor the location of the model, was used. The k - turbu-lence model was used, and turbulent kinetic energy atthe inlet was derived from wind tunnel measurements.The CAD data describing the module was used with themethod described above, which sums the drag of all theindividual obstacles. This gave the porosity and resist-ance of the porous block that represented the internalcongestion of the module, with porosity = 0.93 and Rx= 0.11kg/m4. Fig. 2 shows the congestion inside themodule.

The EXSIM model takes account of more of thedetails of the congestion, by using CAD data to calculatea porosity and resistance appropriate to the congestionin each cell on a coarse (1 m) grid to use in the PDRformulation. The k - turbulence model in EXSIMincludes turbulence source terms appropriate to flowthrough congested regions.

5. Results and analysis

The vector plot in Fig. 3 illustrates, in plan view, theresults of the CFX simulations with an ambient windspeed of 6.7 m/s. The ambient wind is approaching fromthe left hand side and impinging on the short blockedside. The flow leaves the module at the upwind end ofthe long open side due to the pressure reduction, and

Fig. 2. Geometry of experimental rig.

flow is entering at the downwind end to compensate forthis. Fig. 4, a, b, and c show the u, v, and w componentsof the velocity predicted and measured at the ten anem-ometer locations. The reversed flow shown in the vectorplot (Fig. 3) helps to explain why the u velocities pre-dicted by CFX are all negative. The CFX prediction ofthe velocity component is close to the experimentalvalues in almost every case. This is surprisingly goodbecause the CFD velocity is representative of the entirecell and so is an average over 0.5 m. The anemometerson the other hand are amongst the geometry of the mod-ule and measure the velocity at that point, which will beaffected by any nearby obstructions. Thus we would notexpect precise agreement with the measurements. A fewof the velocities are in the opposite direction to thosemeasured, which will be due to the effect of the localobstructions on the flow past the anemometers.

Turbulence predicted by CFX and EXSIM was alsocompared. The comparison was of the same arrangementwith two adjacent sides and the top blocked, and thewind impinging on the short blocked side. Fig. 5 a & bshow that the both the turbulent kinetic energy and theturbulent eddy dissipation predicted by CFX is muchlower than EXSIM. The coarser EXSIM mesh willaccount for part of the difference because small featuresthat could be resolved on the CFX mesh would be coun-ted as turbulent energy by EXSIM. The most importantreason for the difference in turbulence is that EXSIMuses a source term to increase turbulence in the wake ofobstacles. The increase in turbulence when flow


Fig. 3. Flow vectors in and around module from CFX.

Fig. 4. a,b,c. Comparison of non-dimensionalised u, v & w compo-nents of velocity.

Fig. 5. a,b. Turbulent kinetic energy (TKE) and turbulent eddy dissi-pation (TED) predicted by CFX and EXSIM.

impinges on an obstacle is significant, and its role as amechanism for increasing flame speed in explosions iswell established (Brandeis, 1985; Dorge, Pangritz &Wagner, 1976). EXSIM is primarily an explosion modelthat has been designed to capture these effects, andtherefore provides a more accurate prediction of turbu-lence than the CFX porous model. If the obstacles in thegeometry were resolved in CFX then the turbulencewould be predicted, but the CFX porous approximationpurely reduces the volume available for free flow, andadds resistance to the flow. The porous model in CFXwould benefit from improved turbulence predictionbecause of the effects on the mean flow, and becausethis would allow the flammable volumes to be calculatedmore accurately when using the random walk method.

While the best approach would be to define a source


term in the k - equations, this is complicated to do inCFX at the application level. One technique to improvethe turbulence prediction is to use a model similar tothat which is typically implemented at boundaries suchas inlets, based on the local velocity field and local tur-bulence length scale. This can be implemented in CFXusing an extra FORTRAN routine which can introducea source of any kind at any location within a domain.The turbulent kinetic energy k and the turbulent eddydissipation could be replaced by values calculatedlocally using the following:

k C1U2

e C2k3/2Ltpm

where Ltpm is the turbulent length scale in the porousmedia, akin to the interstice size, and C1 and C2 are con-stants. The values of these are problem specific, and assuch are difficult to recommend. One method of findingthe constant values would be to set up a model ofobstacles representing the porous region explicitly. Thelocal turbulence constants required to achieve similarlevels of turbulence in the porous media could then bedetermined.

6. Conclusions

A new method has been developed to derive the resist-ance that is used to modify the Navier-Stokes equationsin the Porosity Distributed Resistance formulation. Alarge scale model of an offshore module was simulatedusing CFX-4. Comparison with the measurementsshowed that overall the CFD model performs very well,especially considering that the homogenous porosityblock does not model any of the internal obstructionsand therefore would not predict any local flow effects.This gives confidence that the overall flow pattern is suf-ficiently close to the local flow patterns to be used inexplosion assessments.

The porous approximation in CFX is found to under-predict the turbulence intensity in the obstacle array. ThePDR formulation does not account for the significant tur-bulence created by obstacles, whereas the EXSIM k - turbulence model has been modified to capture theextra turbulence. Improving the turbulence prediction inthe porous model would be valuable, firstly because itwould provide more accurate inputs to random walkmethods of calculating flammable volume, and secondlybecause the turbulence itself can affect the mean flow.A relatively simple method of increasing the turbulencein porous regions is proposed, by locally specifying theturbulence to raise it to levels found when the obstaclesare modelled explicitly.

The CFD model can be used to provide the non-uni-

form natural ventilation flowfields of complex regionsfor future explosion assessments at a hierarchy of levels,whether simple approximate methods are adequate ormore complex methods are required to calculate theflammable volume, in addition to providing pressureboundary conditions for simple zone models.

Acknowledgements

Acknowledgements are given to the Engineering andPhysical Sciences Research Council and to ShellResearch for funding this work, and to the Joint IndustryProject for providing experimental results.

References

BG Technology (1999). Gas build up for high pressure natural gasreleases in naturally ventilated offshore modules. Large ScaleExperiments. British Gas Technology Report.

Brandeis, J. (1985). Effect of obstacles on flames. Combustion Scienceand Technology, 44, 6173.

Casey, M., & Wintergerste, T. (Eds.). (2000). Special interest groupon quality and trust in Industrial CFD best practice guidelines.European Research Community on Flow, Turbulence and Combus-tion.

Chynoweth, S. (2001). Dispersion in congested environments. Pro-ceedings, Major Hazards Offshore 2001, 27-28 November, London.

Cleaver, R. P. & Britter, R. E. (2001). A workbook approach to esti-mating the flammable volume produced by a gas release. TechnicalDiscussion Paper R406, Fire and Blast Information Group News-letter, Issue 29, July 2001.

Dorge, K. J., Pangritz, D., & Wagner, H. G. (1976). Experiments onvelocity augmentation of spherical flames by grids. Acta Astro-nautica, 3, 10671076.

ESDU (1974). Pressure loss during crossflow of fluids with heat trans-fer over plain tube banks without baffles. Engineering SciencesData Unit Item No. 74040.

Grosso, M. (1992). Wind pressure distribution around buildings: aparametrical model. Energy and Buildings, 18, 101131.

Hoang, M. L., Verboven, P., De Baerdemaeker, J., & Nicola, B. M.(2000). Analysis of the air flow in a cold store by means of compu-tational fluid dynamics. International Journal of Refrigeration,23(2), 127140.

Hoerner, S. F. (1965). Fluid dynamic drag. Published by the author,Library of Congress No. 64,19666.

Johnson, D. M., Cleaver, R. P., Puttock, J. P., & Van Wingerden, C.J. M., Investigation of Gas Dispersion and Explosions in OffshoreModules. Proceedings, 2002 Offshore Technology Conference,Houston, TX, 6-9 May 2002.

Lee, S., & Kim, H. (1999). Laboratory measurements and turbulencefield behind porous fences. Journal of Wind Engineering andIndustrial Aerodynamics, 80, 311326.

Macdonald (2000). A comparison of results from scaled field and windtunnel modelling of dispersion in arrays of obstacles. AtmosphericEnvironment, 32(22), 38453862.

Miguel, A. F., van de Braak, N. J., Silva, A. M., & Bot, G. P. A.(2001). Wind-induced airflow through permeable materials. Jour-nal of Wind Engineering and Industrial Aerodynamics, 89, 4547.

Munson, B. R., Young, D. F., & Okiishi, T. (1998). Fundamentals offluid mechanics. John Wiley and Sons Inc.

Packwood, A. R. (2000). Flow through porous fences in thick bound-


ary layers: comparisons between laboratory and numerical experi-ments. Journal of Wind Engineering and Industrial Aerodynamics,88, 7590.

Patankar, S. V., & Spalding, D. B. (1974). A calculation procedurefor the transient and steady-state behaviour of shell-and -tube heatexchangers. In N. H. Afgan, & E. V. Schundler (Eds.), Heatexchangers: design and theory sourcebook (pp. 155176).McGraw-Hill.

Puttock, J. S. (1995). Fuel gas explosion guidelinesthe congestionassessment method. Second European Conference on major Haz-ards Onshore and Offshore, IchemE, Rugby, UK p. 267.

Puttock, J. S., Yardley, M. R., & Cresswell, T. M. (1998). Predictionof vapour cloud explosions using the SCOPE model. Journal ofLoss Prevention in the Process Industries, 13, 419431.

Raju, R., Garde, R. J., Singh, S. K., & Singh, N. (1988). Experimental

study on characteristics of flow past porous fences. Journal of WindEngineering and Industrial Aerodynamics, 29, 155163.

Shiau, B. (2000). Experimental study of a turbulent boundary layerflow over a wind-break of semi-circular section. Journal of WindEngineering and Industrial Aerodynamics, 84, 247256.

Speirs, L. J. (1997). Wake dispersion on process plant: enhancing VOCemissions control. Engineering Doctorate Thesis, University ofSurrey.

Takahashi, S., Du, M., Wu, P., Maki, T., & Kawashima, S. (1998).Three dimensional numerical simulation of the flow over complexterrain with windbreak hedge. Environmental Modelling andSoftware, 13(34), 257265.

TNO Green Book (1989). Methods for the determination of possibledamage. Rijswijk, The Netherlands: TNO, (Chapter 1).

Evaluation of a CFD porous model for calculating ventilation in explosion hazard assessmentsIntroductionBackgroundPorous model in CFDValidationResults and analysisConclusionsAcknowledgements

References

239

Documents

Transcript of 239