C.J. Lea and H.S. Ledin- A Review of the State-of-the-Art in Gas Explosion Modelling

8/3/2019 C.J. Lea and H.S. Ledin- A Review of the State-of-the-Art in Gas Explosion Modelling

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A Review of the State-of-the-Artin GasExplosion ModellingHSLl2002102

Project Leader:C J LeaH SLedin MSc PhD DICFire and Explosion Group

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Summary

Objectives1. To iden tify organisations involved in gas explosion research in the U.K. ndEurope.2. To survey these organ isations, to determine their areas of current andproposedwork.3. To collate their responses in a report, which also provides an up to date literaturereview of g as explosion modelling.4. To critically assess the strengths andweaknesses of available gas explosionmodels.5. To recommend areas where fk th er work is needed to improve the accuracy ofthe gas explosion models.

Main FindingsI. There are a wide range of class of models available - from empirical andphenomenological, through to those which are C omputational Fluid D ynam ics(CFD) based. The latter category falls into two areas: 'simple' - many obstaclesnot resolved and 'advanced' - all obstacles resolved by the 3-D FD grid.2. Generally as one moves from em pirical to advanced CFD, odels become basedon m ore fundamen tal physics, are able to more accurately represent the rea lgeom etry, but require increasing resource to set-u p, run and interpret the results.3. Models in each class embody a number of simplifications and assumptions,limiting their ability to be used as reliable predictive tools ou tside their range ofvalida tion against test data. It appears that only those mo dels falling into'advanced' CFD class could in principle be capab le of being truly predictive toolsoutsid e their immediate range of validation. However, even here the existingmod els have limitations and require furtherdevelopment and testing before thiscapability is fu lly realised - which even then w ill currently be lim ited torelatively sim ple geometries by the required com puter resources.4. Many of the CFD-based explosion models in current use emp loy relatively crudeapproximations of the modelled geometry, relying on calibrated sub-grid m odels.5. Most of the 'simple' CFD codes and some of the 'advanced' CFD codes mostcommonly used for explosion prediction use simple, dated numerical schem es forboth the com putational grid and the finite differencing, which cou ld lead tosubstantial num erical errors.

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6. The combustion model used in CFD-based approaches to predict the reactionrates are also subject to a considerable degree of uncertainty. Models, whichemploy prescribed reaction rate, could be more sound than those re lying on anEddy Break-Up model, because the latter requires a resolution of the f lm e rontunlikely to be achieved in practice. Work is currently under way on theincorporation of detailed chemical kinetics into a gas explosion model, but it w illnot be feasible to use such a model on a real complex plant geom etry in theforeseeable future.

7. The simple eddy-viscosity concept is ubiquitous amongst the explosion codes formodelling turbulent transport, but this model o f turbulent transport is not strictlyapplicab le in high speed, cornbusting flows, leading to further possible errors.There is a move to full Reynolds stress turbulence models, these have e ither beenimplemented in research type codes - currently not available on general release,or have not been tested for explosions. 'There are numerical stability problemsassociated with Reynolds stress transport models which need to be addressed.8. The accuracy expected from, say phenomenologica~ nd 'simple' CFD models, isgenera lly fairly good (to within a factor of two), e.g. the models yield so lutionswhich are approximately correct, but, importantly, only fo r a scenario for w hichthe model parameters have been tuned. This limits the applicability of thesemodels as truly predictive tools.

Main Recomm endations

There is a range of modelling approaches available, each with their okm strengthsand weaknesses. In order to establish greater confidence in model predictions, itis clear that, for the future, improvements in the physics and the numerics arerequired, particularly for the CFD-based approaches. However, predictiveapproaches are needed now. It is thus important that the user be aware of theuncertainties associated with the different models. The followingrecommendations are essentially those needed to be taken on board by modeldevelopers and their funders. They primarily relate to CFD models, which, inprinciple, should offer the best hope of becoming truly predictive models of gasexplosions, with wide applicability,2. Ideally on e would replace the Cartesian grid 1PDR orosity / DistributedResistance) based CFDmodels by models that are capable of representing agiven geom etry more accurately. However, the likely time sca le for thenecessary advances in computing power and code efficiency which will possiblyallow geometries to be fully grid resolved is large, possibly of the o rder of tenyears or more. Until this is possible a hybrid approach has to be adopted,whereby body-fitted grids are used to represent the larger objects within theexplosion domain, with the PDR approach reserved for the regions that may notbe resolved by the grid. It is therefore recommended that methodolog ies aredeveloped to allow a seamless transition between resolved and PDR-representedsolutions as grids are refined. There should be a move away from fixed grid cell

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size, because such models will require constant re-calibration for new scenariosdue to physical and numerical errors associated with the large grid cell sizealway s needing to be com pensated. This situation cannot improve until there is amove to a more soundly based methodology.3. More work isneeded to establish the reliability of the com bustion models used.Presently, the majority of the explosion models investigated prescribe thereaction rate according to empirical correlations of the burning velocity.How ever, it should be recognised that these correlations are subject to a largeuncertainty. The eddy break-up combustion model should ideally not be used ifthe flam e front canno t be properly resolved or, the resulting errors should berecognised and quantified.4. Th e sensitivity of model predictions to the turbulence model used should beinvestigated. Turbulence modelling has not yet received muc h attention in the

field of explosion modelling. The commonly used two-equation, k-6model has anum ber of known failings i.e. do es not predict counter-gradient diffusion, butrema ins in use due to its economy and robustness. Large improvem ents inover-pressure prediction have been noted by including simp le terms into th e k-emo del, to account for compressibility effects. However, inclusion of the se termsis by no means universal. There is a wide range of advanced, non-linear k-emo dels now available. Ideally Reynolds stress transport mod elling should beused but the models require much work to ensure that improvem ents are notoffset by lack of num erical stability.

5, Model development should now be driven by repeatable, well defined, detailedexperim ents, focusing on key aspects of the physics of explosions. This tends toimply sm all or medium-scale experiments. Large-scale experiments are suitableas benchmark tests, but co de calibration on the basis of macroscopic propertymeasurem ents should be treated with caution, since it is quite possible to obtainapproximately correct answers but for the wrong reasons due to gross featuresswamping finer details. Detailed comparisons of flame speeds, speciesconcentrations, etc., should allow deficiencies in explosion model p hysics andnum erics to be identified, and solutions developed and tested.

6. There are no, or few, technical barriers to implementation of the abov e modelimprovements, beyond a willingness and need to do so.7. Perhap s the safest that can be advised at this point is that it would be unwise to' rely on the predictions of one model only, i.e. better to use a judicio uscombinationof mo dels of different types, especially if a model is being usedoutside its range of validation.

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Contents1 NTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..I Background 1

1.2. A Description of Gas Explosions . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1.3. Why Model Explosions? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.4. Model Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..5. Review Methodology 42.DESCRIPTION AND DISCUSSIONOF CURRENT MODELS . . . . . . . . . 72.7. Empirical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..1.1. htroduction 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..1.2. TNT Equivalency Method 72.1.3. TNO Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..1.4.Mulfi-Energy Concept 8

2.1.5.Baker-Strehlow Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.7.6. Congestion Assessment Method . . . . . . . . . . . . . . . . . . . . . 102. . .Sedgwick Loss Assessment Method . . . . . . . . . . . . . . . . . 1 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..2. Phenomenological Models 12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..2.f . ntroduction 12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..2.2. SCOPE 122.2.3.CLICHE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........... . 14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..3. CFD Models 172.3.I . ntroducfion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..3.2. EXSIM 18. . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . ..3.3.FLACS 20. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..3.4. AutoReaGas 22. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..4. Advanced CFD Models 24. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..4. 1 lnfroduction 24. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..4.2. CFX-4 24. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..4.3. COBRA 26. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..4.4. NEWT 27. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..4.5. REACFLOW 29. . . . . . . . . . . . . . . . . . . . . ..4.6. Irnperlal Col/ege Research Code 31

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .DISCUSSION 34. . . . . . . . . . . . . . . . . . . . . . . . . . . . ..1. Overview of ModelConstraints 34. . . . . . . ..2. Empirical Models = Main Capabilities and Limitations 36

3.3. Phenomenological Models. ain Capabilities and. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .imltations 373.4. Simple CFD Models. ain Capabilities and Limitations . . . . . . 37. . ..5. Advanced CFD Models Main Capabilities andLimitations 39. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..6. Model Accuracy 39. . . . . . . , . . . . . . . . . . . . . . . ..7.Recommendationsfor Future Work ; 42. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..7.1. Grld Improvements 42. . . . . . . . . . . . . . . . . . . ..7.2. Combustion Model Improvements 42. . . . . . . . . . . . . . . . . . . . ..7.3. Turbulence Model Improvements 43HEALTHAND SAFETY LABORATORYAn agency of the Health and SafetyExecutive


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3.7.4. Experimental Input to Model Development . . . . . . . . . . . . .433.7.5. Miscellaneous ssues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .CONCLUSION 445.REFERENCES . . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . .46

5.1. References Cited i n the Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . .465.2. References Used but not Cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

APPENDIX A . HEORETICAL DESCRIPTIONOF GASEXPLOSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 Conservation Equations 54A2.Turbulence Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56A3.Reaction Rate Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57A3.1. Turbulent Flame Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.2. Turbulent Reaction Rate 59. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4 Numerical Modelling 61

APPENDIX B = COMBUSTION MODEL IN SCOPE CODE . . . . . . . . . . . . .66APPENDIX C = COMBUSTION MODELS IN CFD CODES . . . . . . . . . . . . .68C l Exsim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

C2.FLACS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9C3.CFX-4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4 COBRA 73C5.NEWT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

APPENDIX D . lSCRETlSATlONOF PARTIAL DIFFERENTIAL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .QUATIONS 77D l. ntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 702.First-Order Discretisation Schemes . . . . . . . . . . . . . . . . . . . . . . . . 77D3.Second-Order Discretisation Schemes . . . . . . . . . . . . . . . . . . . . . 78

03.1. Central Differencing Scheme . . . . . . . . . . . . . . . . . . . . . . . . 7803.2. Total Variation Diminishing Schemes . . . . . . . . . . . . . . . . 78. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.References 79APPENDIX E. OMMUNICATIONS WITH CHRISTIAN

. . . . . . . . . . . . . . . . . . . . . . . . . . . .ICHELSEN RESEARCH 80. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .l. ntroduction 80. . . . . . . . . . . . . . .2.Comments from J.R.Bakke on 20 June 2001 80. . . . . . . . . . . . . . . . . . .3.Reply from 0 .R.Hansen on 9 July 2001 80

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Listof FiguresFigure 1 Example of a congested geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Figure 2 - Comparisonof calculated and measured maximum over-pressuresfor MERGE medium-scale experiments, (x)- COBRA predictions and ( 0 )EXSlM predictions; a) all experiments and b) experiments with maximumover-pressures below.I5bar, see also Popat et al. (4 996) 40. . . . . . . . . . . . . . . . . . .Figure 3 - Comparison of calculated and measured maximum over-pressuresfor MERGE large-scale experiments, (x ) - COBRA predictions, (o) EXSlMpredictions, ( 0 ) - FLACS predictions and (a) AutoReaGas predictions; a) allexperiments and b) experimentswith maximum over-pessures below 1 bar, seealso Popat et a/-(1996) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41FigureA1 - Schematic description of the flame reaction zone . . . . . . . . . . . . . . . . . 58FigureA2 - A non-orthogonal structured grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62. . . . . . . . . . . . . . . . . . . . .igure A3 - A multi-block, non-orthogonal structuredgrid 62. . . . . .igure A4 - An unstructured gridwith prismatic grid in the boundary layer 63. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .igure A5 - Control volume in one dimension 64

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1. INTRODUCTIONf.1. BackgroundThe aim of this review is to inform the Hazardous Installations Directorate about the currentstatus and future dire ction of gas exp losion numerical models presently in use. Gasexplo sions are a major hazard in both the on-shore and off-shore environm ents.The 1974explosion at the Nypro plant at Flixborough is one of the most serious accidents toafflict the chemical processing industry. The explosion at Flixboroughwas caused by theignition of a flamma ble cloud containing about 50 tons of cyclohexane, the cyclohexanerelease was probably d ue to the failure of a temporary pipe. The blast has been estimated tobe equivalent to about 16 tons of TNT, with the result that 28people were killed, 89 injured,the plant was totally destroyed , and dam age was caused to nearly 2000 properties external tothe site.In 1988 on the offsho re platform P iper Alpha a small explosion in a compressor mod ulecaused f ires wh ich resulted in the rupture of a riser. Most of the platform wa s subseque ntlydestroyed by fire, causing the death of 167people. The over-pressure generated by the initialexplosion has been estimated to be only 0.3 bar, Cullen (1990).This report desc ribes empirical models, phenomenological mod els and Com putational FluidDynamics (CFD) based models. Empirical models are the simplest way of estimatingdeflagration over-pressures. These models con tain correlations and con tain little or nophysics. Phenom enological models are simplified models which represent the major physicalprocesses in the explosion. CFD models involve numerical evaluation of the partialdifferential equations governing the explosion process and yield a great deal of informationabout the flow field. . .The report is further restricted to num erical models of deflagrations. Detonations are notincluded. A deflagration is the name given to the process of a flame travelling through acom bustible mixture where the reaction zone progresses through the medium by the processesof m olecular (and / or turbulent) diffusion of heat and mass. The burning velocity - i.e. thevelocity of the com bustion front relative to the unburnt gas is sub-sonic relative to the s p e dof sound in the unburnt gas. A detonation is a self-driven shock wave w here the reaction zoneand the sh ock are coincident. The combustion wave is propagating at super-sonic velocityrelative to the speed of sound in the unbumt gas. The chemical reaction is initiated by th ecom pressive heating caused by the shock, the energy released serving to d rive thecom pression wave. Propagation velocities of the combustion wave fo r a detonation can b e upto 2000 m s-1 with a pressure ratio across the detonation front of up to 20.This is a update and ex tension of the gas explosion model review by Brookes (1997).1.2. A Descriptionof Gas ExplosionsAn explosion is the sudden generation and expansionof gases associated with an increase intemperature and an increase in pressure capable of causing structural daniage. If there is onlya neg ligible increase in pressure then the combustion phenomena is termed a flash-fire.

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Gas explos ions are generally defined as either confined or unconfined. An explosion in aprocess vessel or building would be termed as confined. If the explosion is fully confined -i.e. if there is no venting and there is no heat loss, then the over-pressure will be high, up toabout eight times higher than the starting pressure. The pressure increase is determinedmainly by the ratio of the temperatures of the burnt and unburnt gases. Explosions inconfined bu t un-congested regions are generally characterised by low initial turbulence levelsand hence low flame speeds. If the region contains obstacles, the turbulence level in the flowwill increase a s the fluid flows past the objects, resulting in a flame acceleration. If thecon fining cham ber is vented, as is usually the case, then the rate of pressure rise and the ventarea become factors that will influence the peak pressure, The rate of pressure rise is linked tothe flam e speed, which in turn is a function of the turbulence present in the gas.The over-pressure generated by an unconfined explosion is a function of the flame speed,which in turn is linked to the level of turbulence in the medium through which the flameprogresses. As the flame accelerates the pressure waves generated by the flame front begin tocoalesce into a shock front of increasing strength. If the explosion occurs in a medium of lowinitial turbulence, is l l l y unconfined, and there are no obstacles present then the generatedover-pressure is very low. If obstacles are present then expansion-generated flow, created bythe combustion, of the unburnt gas passing through the obstacles will generate turbulence.This w ill increase the burning velocity by increasing the flame area and enhancing theprocesses of molecular d ifh sio n and conduction, and this will in turn .increase the expansionflowwhich will further enhance the turbulence. This cycle, so called Schelkchkinmechanism , continues generating higher burning velocities and increasing over-pressures.1.3. Why Model Explosions?Deflagrations are unwanted events. Models containing physical descrip tions of deflag rationsare a complem ent to experiments in risk assessments and or when designing or assessingmitigating features. The more complex models have the wherewithal to be applied to diversesituations, but must not therefore be assumed to be more accurate.The effects of an explosion depends on a number of factors, such as maximum pressure,duration of shock w ave interaction with structures, etc. These factors in turn depend on anumber of variables:

Fuel typeStoichiometry of fuel

a Ignition source type and location.a Confinement and venting (location and size)a Initial turbulence level in the plant

Blockage ratiosHEALTHAND SAFETY LABORATORY

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Size, shape and location-of obstaclesNum ber of obstacles (for a given blockage ratio)

9 Scale of experiment/plantThe reactivity of h e 1 has a profound effect on the overpressures generated in a givengeom etry. The least reactive gas is methane, while acetylene and especially hydrogen give riseto very h igh pressures.The stoichiometryof the gas cloud is also important. Lean mixtures produce low eroverpressures than rich or stoichiometric mixtures, while slightly rich m ixtures yield thehighest over-pressures for a given plant layout.Ignition source tyde also affects the strength of the exp losion; jet-type, or bang-box-type,ignition sources give rise to higher over-pressuresthan a planar o r point source. The locationof the ignition is also important, bu t must be viewed in conjunction with inform ation aboutthe plant geometry, e.g. how confined andor congested is the plant. Confinem ent leads topressure build-up and influences the way the flame front advances through the g eom etry..Venting is on e way of reducing the over-pressure generated by the com bustion. Strateg icallyplaced vents can greatly reduce the impact of a deflagration.Explosions situated in a quiescent environment will generally lead to lower over-pressuresthan those occuring in turbulent flow environments. This is du e to the enhanced burning rateexperienced by the flow.One can d efine a blockage ratio, which is measure of how congested the plant is. Explosionsin plants w ith large blockage ratios usually yield higher over-pressu res than sm all block ageratios,However, the size and shape of the obstacles are also important factors to take intoaccount. In g eneral, for a given blockage ratio, many small objects results in higher pressuresthan arger objects. Furthermore, the location of th e obstacles also affects the pressure. Themore tortuous rou te the flame has o travel through the domain, the highe r pressure is likely tobe produced, du e to turbulence enhancement of the burning velocity.Finally, the scale of experiment/plant is also an mpo rtant factor. Large-scale expe rimentsgenerally yield higher pressures than small-scale ones.This makes it difficult to predict, froma sm all-scale experim ent, what the pressures are likely to be in real plants.Ideally, explosion risks should be considered at the plant design stage, but for various reasonsthis might not be possible. Unfortunately accidents do happen, but research prog rammesconsisting of experiments and modelling should hopefully result in a better understanding ofwhy the accident happened and how the impact can be minimised or the risk of explosion bemitigated or elim inated completely. In most cases, a great number of scenarios needs to beinvestigated, which is one justification for developing and using mod els of varying degrees ofcomplexity.

,

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I4. Mode Requl ementsA number of factors influencing the strength of the deflagration were identified in theprevious section. A model should ideally take all these variables into account. In addition tothis, the m odel should contain appropriate physics, be able to deal with different fuels andambient conditions without special tuning of constants, and be easy to use. Furthermore, thecomputer code in which the model is implemented should be numerically accurate, d lo w foran accura te representation of the geometry, be easy to use and he run imes should be short.Some of these requirements are contradictory. Complex models are unlikely to run veryquickly. In some cases the understanding of the underlying physics is sketchy , at best,Turbulent prem ixed combustion i s an active area of research and new findingsmay find theirway into th e models currently in use. However, there are limitations in t er ns of computerresources. A real world plant is very complex, with a large number of pipes, tanks and otherequipment of various shapes and sizes, and it is not possible today to resolve all the featu resof the geometry - due to the demands on computer memory and processor speed. The flameacceleration due to turbulence generated when the flow has to make its way past obstacles ispartly down to a m ore intense combustion, but also an ncrease in flam e area. Most of theCFD odes do not allow for flame front tracking, neither would these codes be able toproperly resolve the flame fiont.However, the models currently in use do contain some physics and chemistry. In manysituations, the results of the simulations are in good agreement with experiments, but it isimportant to remember that the models have their limitations. The cho ice of model dependson the level of detail required,on the level of accuracy required, and ime available for thecalculations.The turbulence models implemented in the CFD codes can perform well for some types offlows, mainly high Reynolds number, isothermal, isotropic, incompressible flows. Thesemodels have no mechanism for modelling transition from lam inar to turbulent flow.Deflagrations in confined spaces might start in a quiescent environment. A transition fromlaminar to turbulent flow is a distinct possibility, which can contribute to inaccurate so lutions.1.5. Review MethodologyThis review was conducted by following three approaches. The HSL Sheffield InformationCentre was asked to carry out an on-line search seeking information on gas explosionmodelling. A number of key words and phrases, aswell as a large number of possibleauthors, were providedA paper based literature survey was conducted. Relevant reports and papers were collected,the reference lists of which were used to discover further useful sources of information. Thesurvey continued to 'fan out' in this manner, generating a large quantity of useful material.This search has been mainly used to provide the background to this report, but some recentinformation on certain models was also discovered in the open literature.

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CFX-4 2D and 3DCFD FiniteVolume2D and 3DCFD Finite

Unstrucfmed,1 Adaptive

HigherOrderTemporal and SpatialSecond OrderTemporal and Spatial

Implict Temporal,Second order (TVD)SpatialHigher Order

~ Temporal andSecond Order SpatialFirst or Second OrderITemporal and Spatial

Structured,Body-fitted Eddy Break-upand Thin FlameEmpiricalCorrelation

LaminaFlamelet andPDF TransportEddy Break-Wpand LaminarFlameletEddy Break-up

Unstructured,Cartesian,Cylindrical Polaror Hexahedral,Adaptive, PDRTreatmentofSub-Grid caleObjectsUnstructured,Adaptive

' Unstructured,Adaptive

Imperia1 2D CFD FiniteCollege VolumeResearchCodeNEWT 3D CFD FiniteVolumeREACFLOW 2D and 3DCFD FiniteVolume I I

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2. DESCRIPTION AND DISCUSSIONOF CURRENT MODELS2.1. Empirical Models2,l.1. IntroductionEm pirical mod els are based on correlations obtained fiom analysis of experimental data. Themodels described below constitute a selection ofmethods commonly used in industry for riskassessm ent, etc. It does not purport to be an exhaustive selection.2.1.2. TNT Equivalency MethodThe TNT equivalency method is based on the assumption that gas explosions in somewayresemble those of high ch arge explosives, such as TNT. However, there are substantialdifferences between gas explosions and TNT. n the former the local pressure is much lessthan for TN T detona tions. Furthermore, the pressure decay from a TNT detonation ismuchmo re rapid than the acoustic wave from a vapour cloud explosion. Nevertheless the model hasbeen used extensively to predict peak pressures fiom gas explosions. The TNT equivalencymodel uses pressure-distance curves to yield the peak pressure. One mu st use a relation ship,see below, to find the mass of TNT equivalent to the mass ofhydrocarbon in the cloud.

Where WTNTs the mass of TNT, W,, is the actual mass of hydrocarbons in the cloud, and q isa yield factor (q= 0.03-0.05) based on experience. The factor 10represents the fact that m osthydrocarbo ns have ten times higher heat of combustion than TNT. n the original TNTequivalency model no consideration was aken of the geometry and therefore it isrecommended that this m odel should not be used, Bjerketvedt, Bakk e and van Wingerden(1997).A TNT equivalency model which does take geometry effects into account has been proposed,Harris and Wickens (1989). Results from experiments formed the basis forthe newformulation. The yield factor was increased to 0.2 and the mass of hydrocarbon instoichiomctric proportions was to correspond to the mass of gas in the severely congestedregion of the plant. For natural gas the mass of TNT can be arrived at using

where Vef= min (Y,,,,,c,o,,d)s the total volume of the congested region and y&d is the totalvolume of the g as cloud. The equation will hold for most hydrocarbons. It is recommendedthat the TNT quivalency model shouldno t be used.Weaknesses:Non-unique yield factor is needed

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Inform ation only of the positive phase durationNot suited for gas explosions, since the physical behaviour of gas explosions differssubstantially fiom that o f solid explosivesDifficult to define a sensible charge centre

2.f.3. TNOMethodTh e TNO method, W iekema (1980), resembles the multi-energy method described in Sect,2.1.4 below . The main difference between the two methods is that the TNO method assumesthat the w hole vapour cloud con tributes to the over-pressure, rather than ust the portionwhich happens to be in a confined an do r congested area. The TNO model and TNTequivalency model were used in the Dutch CPR14E handbook of methods for calculation ofphysical effects of the escape o f dangerous materials,CPR14E (1979). Themulti-energymethod has replaced the TN O model in the revised CPR14E handbook, Mercx and van denBerg (1997). The TNO method will not be discussed further, but see Sect. 2.1.4 for detailsand comments.2.1.4. Multl-Energy ConceptThe multi-energy concept, van den Berg (1985), can be used to estimate the blast from gasexplosions with variable s trength . The method assumes that only hat part of the gas cloudwhich is confined or obstructed will contribute to the blast. The rationale being thatunconfined vapour clouds give rise to only sm all over-pressures if ignited. The over-pressureincreases with increasing confinement.In essence, the method is based on numericalsimulations of a blast wave from a centrally ignited spherical cloud with constant ve locityflames.There are two parameters feed ing into the model. Firstly, a combustion-energy scaleddistance, R, , elated to the d istance to the explosion centre can be defined asR,, = R, (E/PJI/3, [m] (3)where Ro is the distance to the explosion centre, E is the total amount of combu stion energy,e.g. the combustionenergy per volume times V,,,,, where VcIorrds the volume of vapour cloudin the congested area, and PO s the atmosp heric-pressure. The total amount of nergy for astoichiometric hydrocarbon -air mixture does not vary significantly with the type ofhydrocarbon. Thus for a hydrocarbon-air mixture, the total combustion energy an beestimated fiom

Where Vclouds measured in m3. It is important to note that only the confined a d o r congestedareas contribute to the blast. Secondly, the strength of the explosion can be estimated by

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taking into account the layout of the explosion source. The charge strength is given a numberbetween one and 10,where 10 represents a detonation.The two parameters can then be used to read a non-dimensional maximum side-onover-pressure and a non-dimensional positive phase duration from diagrams, where the sourcestrength is represented by a set of curves.Strengths:

+ FastmethodConservative approximation can be made

Weaknesses:Setting a sensible value for the charge strength is difficult.Setting a sensible value for the total combustion energy, e.g. charge size is difficult.Not ideally suited to weak explosions, i.e. partly confined clouds.Difficult to accurately represent complicated geometriesNot clear how o deal with severa l congested regionsNot clear how to dea l with multiple blast waves

In light of the weaknesses isted above, the choice of charge size and strengthmust ideally bebased on other simulations, experimental data or by making a conservative assumption. Vanden Berg (1991) suggested that Velod hould be chosen to encompass the total volume of gas,that is both the confined and the unconfined part. Thiswill inmany cases lead to anoverestimationof the over-pressure caused by the blast.2.7.5. Baker-StrehlowMethodThe Baker-Strehlow method, Baker, Tang, Scheier and Silva (1994), was developed toprovide estimations of blast pressures from vapour cloud explosions. The model was furtherextended byBaker, D oolittle, Fitzgerald and Tang (1998). The methodology consists of anumber of steps, assessing flame speed, fuel reactivity, confinement, etc.

Walk through plant identifLing potential explosion sitesDecide on the dimensionality of the confined areas to work out flame speed

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Calculate burning velocity for fuel mixturesThe blast pressure and impulse are the read from a series of graphs. The revisions proposedby Baker et al. (1998) were the results of experience gained from plant walk throughs andhazard assessments.Strengths:

Easy to useFastTakes nto accoun some geometrical details, with regards to confinem entCan handle multi-ignition points

Weaknesses:Can be over conservative

2.7.8, ~ o n g e s t l o n ssessment MethodThe Con gestion Assessment Method (CAM) as developed at Shell Thornton ResearchCen tre, Cates and Sam ueIs (2991). The model hasbeen enhanced and further extended byPuttock, (1995, 1999).Cates and Samuels (1991) evised a decision tree procedure as guidance for estimating thesource pressure, taking into account the layout of the plant, e.g. degree of Confinement andcongestion and he type of fuel involved. The accuracyof the estimations was variable, butthe method was designed to yield conservative pressures.The m ethod com prises three steps:

1 ) An assessment of the congested region is carried out to assign a reference pressure,Pref which is an estimation of the maximum over-pressure generated by adeflagration of a vapour cloud of propane.

2) The type of fuel is taken into account through a fuel factor, which is thenmultipliedby the reference pressure worked out in step i) to determine the maximum sourcepressure.3) It is now possible to estimate the pressure experienced at various distances from heignition point. Cates and Samuels (1991) assumed a simple decay law inverselyproportionalto the distance. Puttock (1995) generated pressure d ecay curves by

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fitting polynomials to detailed computations, which in turn had been valida ted byexperimental data.Puttock (1 999,2000b) further improved the model when the results fiom the MERGE(Modelling and Experimental Research into Gas Explosions) project, which involved smallscale, medium scale and large scale experiments were published, Mercx (1993).Development of CA M 2, Puttock (1999,2000b) also addressed the problems of i)non-symmetric plants, ii) plants which are much longer in one spatial directionthan he othertwo, iii) making allowance for partial fill, e.g. where the gas cloud size is smaller than thecongested volume, and iv) how to deal with sharp-edged rather than rounded objects. Thecongestion assessment method is the most advanced empirical model reviewed in the presen treport. How ever, it is not known howwell the model would perform for a new scenario forwhich the model has not been calibmted.The user must assess the level of congestion and the level of confinement in the plant. This isnot a problem for sim ple geometries, but many plant installations are highly com plex innature. There are guidelines for how to assess the congestion and the confinement of theplant. Nevertheless, it is quite possible that two people could independently mak e suf ficientlydifferent assessments of the plant which could lead to potentially significantly differentpredicted exp losion generated over-pressures.Strengths:

Easy to useShort run imesCalibrated against a large number of experimentsApproaches sensiblemaximum over-pressure as severity index goes to inf inityCan deal w ith non-symmetrical congestion and long, narrow plant

Weaknesses:Allows only a relatively crude representation of the geometryNo uniqueness in the specificationof level of congestion and level of confinement

2.7.7. Sedgwick LossAssessment MethodThyer (1997) tested the vapour cloud explosion model developed by SedgwickEnergy Ltd.The Sedgwick model is based on Puttock's CAM model, see Sec tion 2.1.6, with somerefinements. Thyer (1997) noted that the degree of resemblance with the C A M method wasnot easy to assess, in part due to scarce amount of details in their promotional leaflets. The

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.-

packageallows the user to set up a simple computerrepresentationof the plant, using agraphical interface.

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2.2. PhenomenologicalModels2.2. f . IntmductionPhenomenologica l models are simplified physical models, which seek to represent only theessential physics of explosions. The greatest simplification made is with respect to themodelled geometry, Generally, no attempt is made to model the actual scenario geometry,which is instead represented by an idealisedsystem - e.g. a single vented chamber containinga number of turbulence generating grids. This is a reasonable approximation for certain typesof geometry (an offshore module for example), but may not be adequate for more complexsituations. The physics of the explosion process may be described either empirically ortheoretically. Phenomenological models fall somewhere between empirical correlationsandCFD models, in terms of complexity. CFD models may in fact share some of the embeddedphysics with phenomenological models, but of course are in principle better able to modelcomplex, arbitrary geometries. The run times for phenomenological models are short, of theorder of a few seconds. This type of model iswell suited to running through large number ofdifferent scenarios and can be used to pick out particular situations which can then b einvestigated using a CFD code to obtain further details.2.2.2. SCOPEThe SCO PE (Shell Code for Over-pressure Prediction in gas Explosions) model is undercontinu ing developm ent at Shell's Thornton Research Centre. The SCOPEmodel wasinitially designed for modelling explosions in offshore modules. However, the model may beapplied to any geometry where a single flame path may be identified. SCOPE was eleasedin March 1994. It is based on the original version of SCOPE described by Cates and Samuels(1991). The presen t incarnation of SCOPE s SCOPE 3 which went live in early 1997,Puttock, Yardley and Cresswell (2000). This section will describe the SCOPE code andthen highlight the revisions which have been incorporated in SCOPE 3. Appendix B containsthe differential equations solved in SCOPE.SCOPE 2The SCOPE ode seeks to model gas explosions by representing the essential physics in asimplified form. Models of this type a re to be distinguished from empirical models that arenothing more than 'fits' to existing experimental data and are of limited applicability. Themodel is one-dimensional and s based on the idealised geomehy of a vented vesselcontaining a series of obstacle grids. The flow through each of these grids determinestheturbulence and hence tlie rate of turbulent combustion downstream from the grid.The flowsfrom the vents are modelled using standard compressible vent flow elations. Ventopening may also be modelled using SCOPE 2. The vent area is taken to be zero until thevent opening pressure is reached, at which point the vent area is increased linearly with timeuntil the vent is fully open at a pre-set value of the vent opening time.The external explosion, generated by combustion in the unburnt gas pushed from the box,may exert a large nfluence on the internal pressure felt by the box. The vented gas formsa

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mushroom-shaped jet and thehighest external pressure is generated when the flame burns nthe vortex at the mushroom head. The last of the gas to be vented from the box forms thestem of the mushroom. Therefore, the gas vented in the last stages of the explosion eventcontributes little to the external over-pressure. The external over-pressure calculated by hemodel is related to the vent flow (which in turn is related to the box internal pressure) whenthe flame has traversed 70% of the box Iength. The ratio of the external pressure to theinternal pressure also dependson the vent area, this ratio is taken as

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Strengths:Can handle venting and external expIosionsImposed limits to flame self-acceleration yield sens ible flame speedsValidated against a large number of small-, medium- to large-scale experimentsinvolving different gases and various degrees of congestionCon tains less geometrical detail than CFD modelsA fast tool for eva luating different scenarios during plant design phase

Weaknesses:Roes not provide the samewealth of information about theflow field as do CFDmodelsContains less geometrical detail than CFD modelsCan deal with single enclosuresonly

2.2.3, CLICHEThe CLICHE (Confined LInked CHamberExplosion) code has been developed byAdvantica Technologies Ltd. The status of its present development is unknown. CLICHEwas developed to study confined explos ions in buildings but its use has been extended tomodelling explosions in off- and on-shore plant. The basis of CLICHE swell established inapplications to vented vessels explosions, Fairweather and Vasey (1982) and Chippett (1984),however, the CLICHE cod e represents a generalisation of this concept to a sequence ofinterlinked explosion chambers. Typically process plant consist of semi-confined areascongested with pipework and process vessels. The expansion induced flow in an explosionwill be subject to a largepressure gradient caused by the drag from these obstacles. Region sare represented in the CLICHE code by a series of linked chambers, the pressure gradients aremodelled by applying appropriate resistance terms at the inter-chamber vents. The necessaryparameters to model the drag and flame / obstacle interaction are determined from anum erical database containing a detailed descriptionof the plant geometry. A combustionsub-model based on the local flow properties is used to determine both lam inar and turbulentburning velocities. A n y external burning, caused by vented gases, is treated by a separateexternal combu stion model.The ex plosion model formulation used in CLICHE was developed by applying theconservation law s to the unburnt and burnt gas volumes in each chamber, assuming that th eproperties within each chamber are uniform and that any momentum changes occur only a t

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the perimeter of these volumes. This fatter assumption does not allow the prediction of theflow distribution within he volume, and hence the flame distortion. Consequently a flameshape is empirically prescribed, based on the geometry and the volum e of burnt gas. Theequation set describing the series of chambers forms a system of coupled ordinary differentialequations which are solved numerically. Equilibrium properties are assumed for the burnt gasand these properties are calculated during the CLICHE simulation, taking in to account thepressure and tem perature dependence. CLICHE uses a numerically generated flame area,which enables the model to simulate ignition from any position, with the initiaI flameassuming a spherical shape. Flame distortion effects are treated by empirical correlations.When the flame interacts with obstacles it develops 'folds' or 'fingers', which grow as theflame passes the obstacles and within which the burning rates are locally higher due to theturbulence generated in the obstacle wakes. CLICHE alculates the rate of growth of flamefolds from the mean velocity of unburnt gas past the obstacles.The burn ing velocity is assigned the value of the maximum of the laminar and turbulentburning velocities, calculated from the known flm e adius, root mean square turbulencevelocity and turbulence integral length scale. Ignition in an initially quiescent medium resultsin laminar flame propagation, until the flame intersects an obstacle at which point the flamedownstream of the obstacle becomes turbulent. Turbulence parameters are based upon themean flow velocities and the characteristicsof the wake turbulence shed by the obstacles.The model also allows an initial non-zero turbulence field to be present.The laminar burning velocity isbased upon empirical correlations of the flame speed as afunction of lame radius. The turbulentburning velocity is based upon a Kolmogorov,Petrovsky and Piskounov analysis of the combustion model of Bray (1987)which has beencalibrated agains t measurements made by Abdel-Gayed, Bradley and Lawes ( I 987). Themodel is based upon the assumption that the turbulent flame is an ensemble of laminarflamelets and takes account of the quenching of the flamelets by the turbulence strain field.Com bustion in the semi-confined region causes unburnt gas ahead of the flame to be expelledthrough perimeter vents. When the flame propagates through a vent an external explosion istriggered, which as well as providing an external source of pressure generation may increasethe pressure inside the semi-confined region by impeding the escape of further gas. Theexternal explosion and the propagation of the pressure wave towards the vent are described byan acoustic model, S trehlow, Luckritz, Adamczyk and Shimpi (1 979) and Catlin (1985) forpeak over-pressures below 300 mbar. This assumes a sphericalflame and an empiricallyderived peak over-pressure and flame speed.Strengths:

Allow s ign ition location anywhere within a cuboidal volumeSimple combustion model, based on a mixture of some fundamental physics andempirical correlationsFlam e distortion effects due to vents, etc., are included

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Can handle external explosionsCan generate its own input parameters from an obstacle databaseShort run times

Weaknesses:Simplified representationof the geometry, through a series of inter-linked chambersDoes not provide the same wealth of information about the flow field as do CFDmodels

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2.3. CFD Models2.3. a introductionComputational Fluid Dynamics (CFD) m odels find numerical solutions to the partialdifferential equa tions governing the explosion process. Appendix A describes theNavier-Stokes equations, which govern the fluidflow, nd the sub-models used to representthe term s which are not modelled exactly. The numerical solutions are generated bydiscretizing the solution domain (in both space and time). The conservation equations areapplied to eachof the sub-domains formed by the discretization process, genera ting a numberof coupled a lgebraic equations that are normally solved by an terative procedure.Solutions obtained with CFD codes contain a great wealth of information about the flow field,i.e. velocities, pressure, density, species concentrations, etc. Surface pressure data can beused for structural analysis. CFD is widely applicable and can be used in many differentdisciplines - from designing aeroplanes, cars or artificial heart valves, to w eather foreca stingand environm ental modelling. CFD simulations can offer insight into the flow behaviour insituations w here it is impractical or impossible to carry out experiments. In principle, it ispossible to try out many different scenarios, with little extra effort. CFD nd experimentsshould be viewed as complementarymeansof investigating flow situations. It is vitallyimportant that the sub-models used are properly validated against well-controlled,well-defined and repeatable experiments. If the models have not been validated, confidencein the results obtained from calculations with CFD codes must be low, and the results usedwith prudence, if at all. The importance of solving the right problem, i.e. using the correctgeometry, correc t initial and boundary conditions, can not be over emphasised. CFD codesare im mensely powerfid and useful tools, if applied correctly.Themain drawbacks associated with the use of CFD re caused by the limitations imposed bythe available computing hardware, for example it is currently impractical (if not impossible)to simulate exactly a turbulent combusting flow. Hence, sub-models of combustion andturbulent transport have been developed that simplify the calculation process. Small-scale(relative to the explosion domain) objects may cause significant over-pressure generation in agas explosion, du e to the turbulence generated. Explicit representationof small-scale featuresis demanding in terms of computer memory and computing speed, hence an alternativemethod of modelling turbulence generation caused by small-scale objectshas been developed,the so-called PorosityDistributed Resistance, or PDR, ethod. The CFDmodels presented inthis section rely heavily on sub-models for the representation of small-scale objects, coup ledwith relatively simple numerical schemes for the solution of the governing flow equations.,The rate of progress in model development in the field has been relatively slow. Turbu lenceremains a highly active topic of research. The mathematical understanding of the subject isimproving, but there are still a number of issues which have not been fu lly resolved, i.e.transition from laminar to turbulentflow.Furthermore, the process of incorporating the newfindings into the existing turbulence models has been slow. This is to some extent due to thefact that most of these models are relatively crude approximations of reality and can there forenot easily accommodate the mechanisms involved. The first papers discussing secondmoment closu re modelling appeared in the early 1970's. In principle, second moment

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closures shou ld be more general that the simpler turbulence models, Mo dels of thatcomplexity should able to better rqre sen t many different types of flows. Bu t thirty years on,Reynolds stress transport models are still not applied routinely. The implementations ofReynolds stress models in the currently available commercial CFD odes lack oneof the mostimportant proper ties to industry, nameIy robustness,In fairness, some of the outstanding issues are to dowith numerical aspects, i.e. discretisationof th e transport equations, etc., rather than to dowith the numerical modelling. It seem sunlikely that fully simulating a turbulent combusling flow in a real plant - with all itsassociated time and length scales, and involving a great number of obstacles and otherconfigu rational complexities, will be possible for several decades, judging by the current rateof progress. However the rapid development of faster processors with more random accessmemory, and pardlel processing - but which might require rewriting of parts of the CFDcodes to take Eull advantage of massively parallel architecture, may go some way to alleviatematters.2.3.2. EXSlMThe EXSIM code is under continuing development at the Telernark TechnologicalR&DCentre (Tel-Tek) in Norway and She11 Global So lutions in United Kingdom . The currentversion of the EXSIM code is version 3.3. EXSIM is a structured Cartesian grid,semi-implicit, finite volume code that relies on the Porosity / Distributed Resistance methodfor the representation of small-scale objects. The main effect of these obstacles is to obstructthe flow and generate additional turbulence. Using the PDR approach, small scale ob jects arerepresented by a volume porosity, an area porosity, and a drag coefficient. The draggenerated by the obstacles feeds into the k-E turbulence model, via a modified generation rateof turbulence term, and subsequently into the Navier-Stokes equations. Sect. C1 of AppendixC describes how the PDR method is implemented in the code and gives details on theimplemented combustion model. EXSIM, ersion 3.3, is using AUTOCAD 14 aspre-processor with an additional LISP program called EXCAD.The scalar variables are stored at positions within the control volumes, whereas the velocitycomponents and the a rea porosities are stored at the control volume boundaries. First orsecond o rder accurate upwind differencing schemes may be used to generate the numericalapproximations to the governing equations. The second order upwind scheme isboundedbythe van Leer limiter. Time integration is performed using the implicit Euler scheme,which isfirst order accurate. The resulting system of non-linear algebraic equations is solved byapplying the tri-diagonal matrix algorithm in the three co-ordinate directions. A version ofthe SIMPLE, (Patankar and Spalding (1972), algorithm, modified for compressible flows,Hjertager (1982), is used to solve the pressure/velocity/densitycoupling of the momentumequations and the mass balance. The method introduces a pressure correction, which makesthe necessary corrections to the velocity components, pressure and density to ensure that massis conserved at the new time step.Th e pre-processor in oider versions, pre 3.3, of EXSIM only allowed geometry specificationwith standard obstacles. A box shaped domain is specified, the subsequent geometry beingbuilt up by the addition of variations of eight basic objects. These objects are:

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1) Large box, resolved by he grid.2) Cylinder aligned with one of the co-ordinate directions,3) Pipe bundle in the form of a box.4) General porous box.5 ) Low ered wall6) Box beam or box that is not resolved by the grid.7) Sharp edged beam.8) Grating.

The pre-processor in version 3.3 of EXSIM makes it possible to convert data from a numberof different CAD formats, extracted from CAD databases, to E X S N ormat which allows fora quicker setting up of he geom etry, Chynoweth (2000).Version 3.3 ofExsim, Chynoweth and Ungut (2000) has been extensive ly validated aga instthe experimental data from Phase 2 of the Flast and Fire Engineering for Topside Structures,experiments carried out by DNV, Shell Solvex full and V6-t.h scale tests, tests carried out byCM R on their M24 and M25 modules, further ests carried out by Shell at their Buxton site,etc. The code can also be applied to congested configurations with varying degrees ofconfinement, including a completely unconfined geometry.Current developments include implementation of an adaptive mesh algorithm to improve theresolution of areas of interest, i.e. flame ronts, and inclusion of a gas dispersion model so thatthe shape of a vapour cloud and the gas concentration, i.e.from a pipe rupture, can beestimated.Strengths:

Allows the user to specify (arbitrary?) spatial resolution of obstaclesHas been compared against small-scale, medium-scale and large-scale experimen tsCanbe applied to congested but unconfined geometriesCan be applied to external explosionsCan read in CAD data

Weaknesses:

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. Using standard k-E modelDoes no t have a local grid refinement / de-refinement facility yet

2.3.3. FLACSThe FLACS (FL am e Acceleration Simulator) code has been developed at the ChristianMich elsen Research Institute in Norway, now CM R-GEXCON. FLACS is a finitevolumecode based on a structured Cartesian grid. The Porosity / Distributed Resistance approach isused to model sub-grid scale obstacles. Transport of scalars and momentum hrough turbulentprocesses is modelled using thek-E turbulence model. The discretisation of the governingequations follows a w eighted upwind / central differencing scheme, which is first orderaccurate. However, for the reaction progress variable the second order accu rate van Leerscheme is used - van Leer (1974) - to prevent artificial flame thickening, caused by numericaldiffusion.The comb ustion model originally employed in FLACS was a version of the eddy break-upmodel. This has recently been replaced by a model, called D flamemodel, based oncorre lations of turbulent burning veloc ities with turbulence parameters - Arntzen (1995,1998).The #? flamemodel assumes that the flamepropagates at a constant burning velocity and has aspec ified constant flam e thickness, e.g. three grid cells, Arntzen (1998). Furthermore, theflame model uses correction functions to account for flame thickness, due to numericaldiffus ion, flame curvature and burning towards walls, Arntzen (1 998). The reaction rate andthe turbulent viscosity are set in the transport equation for the reaction progress variable so asto ensure that the burning velocity matches that given by a correlation - this is sim ilar to themethod employed in C O B A .An advanced user interface to FLACS has been developed. This consists of Com puter AidedScenario Design (CASD) and Flowvis. CASD is used to generate the scenario definition forFLACS and Flowvis presents the results from the FLACS simulations. Thescenario isdefined by simplifying the geometry - for example pipes are represented by long cylinders,beams which are not vertical or horizontal are represented by horizontal or vertical beam swith a blockage similar to the original beams. Ingeneral all objects with a dimension greaterthan 0.03 m are included, although areas which contain a high density of smaller obstacleswill have to be represented as well. Obstacles which are not resolved by this grid arerepresented as an area blockage and a volume blockage. Walls and decks may be modelled infour different ways: solid unyielding surface, porous surface, blow out / explosion reliefpanel, or open.Earlierversions of FLACS - up to 1993, required that the geometry be meshed with a gridofcells of 1 m3 volume (1 rn sides), as the code was calibrated for cells of this size. This iscontrary to generally accepted CFD practice, in which it should - at least in principle, bepossible to perform a grid dependency study to ensure that the solution does not contain grossnumerical errors due to grid coarseness. In FLACS-93 and later versions the grid resolution isbased on a certainnumber of cells across he gas cloud. This means that the cells can besmaller than 1 m cube, see Appendix E. However for a typicaloffshore module a cell size

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of 1 rn would still be used, with 2 rn x 2 m x 2 rn cells employed for large offshore modulesand onshore plants, see Appendix E.FLA CS does not have adaptive meshing capabilities. However, the user can, a priori, refinethe grid in the region where it is deemed to be needed, i.e. the grid cells could be of he orderof 2 to 5 cm near a je t leak, Hansen (2001) - Appendix E. FLACS does not have multi-gridcapability per se. However, for blast waves in the far field FLAC S has a multi-block concept,allowing turbulence and com bustion equations to be solved in the explosion block and heEuler equations in the blocks where the flow is essentially inviscid, Hansen (2001) -Appendix E.CMR state that FLA CS has been validated against a wide range of experiments.Unfortunately many of these results are confidential. However, comparisons of FLACSpredictions with measurements were undertaken and pubIished as part of the MERGE,Mercx(1993), EMERGE nd BFETS, Selby and Burgan (1998), projects.CMR tate that they are content if the accuracy with which the code predicts explosionover-pressures is of the order off 30%, see Section E3 of Appendix E. They also note thatin some cases the discrepancy can be a factor of two. Hansen (2001), n Section E3 ofAppendix E, states that, since average over-pressure measurements can vary by a factor oftwo between tests which are essentially identical, it is difficult to see how accuracies can besubstantially improved. The need for accurate measurements and high repeatability has beendiscussed elsewhere, see Section 3.6, in the present report.There have apparently been further developments in the FLACS code, van Wingerden (2001),i.e. to the laminar and turbulent combustion modelling, to the modelling of turbulencegeneration at walls and implementation of a subgrid model describing turbulence length scaleas a function of obstacle size. Unfortunately, these developments are not published in theopen literature - being kept confidential to clients and sponsors. It is therefore not possib le tocomment on the impact of these developments.Strengths:

Have been compared against a range of small-scale, medium -scale and large-scaleexperimentsUses second order accurate discretisation scheme, a van Leer Upwind scheme, butfor the reaction progress variable onlyCan be applied to congested, but unconfined geometriesCanb e applied to external explosionsCan read in CAD dataIncorporates a water deluge model

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WeaknessesUses k-Emode1;but with modifications to deal with near-wail flows, etc.Uses a first-order accurate, weighted upwindcentral differencing scheme for allvariables except for the reaction progress variableVersions of the code up to 1993 were calibrated for 1 m cube grid cell size - thusnot allowing grid dependency to be examined.Recent developments not in the open literature, hence not possib le to comment onpresent theoretical basis.

2.3.4. AutoReaGasAutoReaGas is the result of a joint ven ture, between Century Dynamics Ltd. and TNO, thatbegan in 1993. The code integrates features of the WAGAS and BLAST odes developed byTNO and have been incorporated into an nteractive environment based o n theAUTODYN-3D code developed by Century Dynamics Ltd. REAGA S is a gas explosionsimulator whereas BLAST imulates the propagation of blast waves. The REAGAS andBLAST software w ere implemented in AutoReaGas as the gas explosion solver and blastsolver, respectively. AutoReaGas can be used on most computer platforms running un dereither UNIX, Windows 95 or later versions or W indows NT operating system s.The gas explosion solver is a three dimensional finite volume CFD ode based on astructured, Cartesian grid. Discretization is achieved by use of the first order accurate Pow erLaw sch eme, with the SIMPLE algorithm implemented for pressure correction. Turbulenttransport is modelled by use of the standard two equation k-Emodel. Large objects may beresolved by the grid, but sub-grid scale obstacles are modelled as a source of turbulence anddrag (a Porosity / Distributed Resistance approach). The code also allows blow-out panels tobe included in a simulation. The combustion model assumes that the combustion reactiontakes place as a sing le step process. Transport equations are solved for the fuel mass fractionand the m ixture fraction, which is a conserved quantity (i.e. a quantity that is unaffected bychem ical reactions). The add ition of the mixture fraction transport equation allows themodelling of explosions in non-uniform gas mixtures. The reaction rate is determined fxoman empirical correlation for flame speed (Bray (1990) and see also section 2.2.3),where thetransition from l am in a to turbulent combustion is based upon the local flow conditions.The blast solver solves the three dimensionalEuler equationsfor blast wave propagationusing the Flux C orrected Transport technique. An automatic 'remapping' facility is availableto take the output from a gas explosion simulation into a larger domain for a study of thefar-field blast effects.Scen ario geometry may be supplied to the code by defining a combination of objectprimitives, such as boxes, cy linders and planes (cf EXSIM, ection 2.3.2), or alternativelymay be imported from a CAD package.

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Present developm ent work is concerned with improving important aspects of the solver; inparticular a higher order numerical discretization scheme will be implemented in the nearfuture. A new im proved combustion model will also be implemented. In addition, a wd 1friction model will be incorporated for modelling gas expIosions in geometries with nosub-grid scale obstacles. In the longer term a number of developments areplanned; theseinclude:

A dynamic structural response capability coupled with the explosion and blastprocessorGas dispersion modellingMulti-block mesh, which allows a more efficient grid structure to b e used

The latest release, version 3-0,contain a number of new features: the pre- and post-processinghas been improved and a new flow solution and geometry visualizer has been implemented.The objects database uses dynamicmemory allocation,e.g. there isno restriction on thenumber of objects. Furthermore, object modelling has been enhanced, .e. non-orthogonalobjects can now be used. Pressure surfaces (when specifying blow out panels), cold frontquenching and a water deluge model have been implemented.Considerable effort has gone and continues to go into model validation against themedium-scale and arge-scale experiments carried out within the MERGEIEMERGE projectsand the Joint Industry Project Blast and Fire Engineering for Topside Structures (phases 2 and3), respectively.Significantly, a validation manual is supplied with the latest release of AutoReaG as, version3.0.Strengths:

Has been compared against small-scale, medium-scale and large-scale experimentsIncorporatesa water deluge modelCan ead in CA D dataCan accept a large number ofobjects through dynamic memory allocation of th eobjects database

Weaknesses:Currently uses a first-order accurate discretization scheme for dl variablesUses standard k-E turbulence model

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2.4. Advanced CFD Models2.4.7. /ntroductionThe CFD mod els presented in this section attempt a more com plete description of theexplosion process. The differences between these models and those presented in the prev ioussection mainly lie with the representation of the geometry and the accuracy of the numericalschem es used. The CFD codes presented in this section (with the exception of th e COBRAcode) allow an exact geometric representation of the explosion scenario, limited by theavailable computer memory. The mem ory limitations can limit the app licability o f the codeto less com plex configurations or might force the user to omit objects to stay within theavailable mem ory. All of the codes detailed in this section use numerical schemes ofincreased accuracy, when compared with the CFD odes described in the previous section.

CFX-4 s a general purpose, comm ercially available CFD ode, under development atAEATech nology Engineering Software at Harwell. An explosion module has been developed forthis code by the code vendors, funded by the HSE. Thismodule was initially available to theHSE, ut has now been released commercially in release 3, December 1999. CFX-4 s afinite-volume, structured grid code. To facilitate the modelling of complex geom etries thecode allows multi-block, non-orthogonal grids. A variety of equation solvers may be usedalong w ith a w ide selection of first order and bounded second order accurate differ6ncingschemes. A s well as the comm only used k-e urbulence model, the code also includes a fullReyno lds stress turbu lence model, which has not been tested for explosion modelling. Fur therinformation on the basic code may be obtained from the solver manual. A CFD code usingunstructured grids, called CFX-5, is also under development at AEA Technology Enginee ringSoftw are. How ever, at present CFX-5 oes not contain the physical models necessary tomodel an explosion.Before release 3, the standard CFXi4 software included many options for sp atial differencing,but only two for temporal differencing. These are the first order accurate implicit Euler andthe second order C rank-Nicolson schemes. The C rank-Nicolson scheme is not bounded forpositive definite variables and therefore very small time steps must be used when a turbulencemodel is included (turbulence kinetic energy and its dissipation rate are strictly positivequantities). Therefore, a new higher order backward differencing scheme has been includedin release 3, that guarantees positivity. The temporal differencing scheme is also adaptive,failure to m eet th e convergence criteria at a particular time step results in the time step beingreduced for another attempt at convergence. Successful convergence at five successive timesteps results in the time step being increased.Mesh generation for CFX-4 may be accomplished by using.eitherof two codes w ritten for thispurpose, CFX-MESHBUILD and CFX-BUILD. To allow fu rther flexibility theCFX-BUILDcode allows the user to import geometry files from a wide range of CAD ackages.The code has been used for prediction of explosion over-pressure in a ser ies of small-scalebaffled and vented enclosures - Pritchard, Freeman and Guilbert (1996). The agreement

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reported by Pritchard et al. (1996), between the CFD predictions and the experimentallydetermined over-pressures for these enclosures, is very good. Pritchard, Lewis, Hedley andLea (1999) stressed that great care must be taken when applying models to other gases thanthe one for which the model has been "tuned", or calibrated. Pritchard et al. (1999) found thatthe agreement between calculations and experiments was poor when changing gas fiommethane, the gas for which the model was calibrated, to propane. A recent paper, Rehm andJahn (2000), presented good agreement between over-pressures calculated by CFX-4 ndmeasured over-pressures in hydrogen explosion experiments.Pritchard et al. (1999) contains a detailed discussion on the deficiencies with the ignitionmodel and the thin flame model implemented in CFX-4. he ignition model g ives physicallyimplausible results. One would expect the gas velocity ahead of the approaching flame toincrease with tim e until the flame eaches the observer. The ignition model implemented inCFX-4 redicts that the gas velocity reaches a peak and then decreases before flame arrival.Moreover the flame is not f il ly developed by the end of the ignition period. Thus the modeldoes not provide a suitable precursor to the thin flamemodel. There is also an exponentialgrowth in numerical error in all conservation equations due to the steep gradient in volum eexpansion at the boundary of the ignition region. The thin flame model will give rise tounwanted oscillations which are caused by the abrupt initiation of reaction in each new cellentering the reaction zone, Furthermore, the steep gradient involume expansion betweenneighbouring reacting and non-reacting cells at the cold fiont is a source of exponentialgrowth in numerical error.Strengths:

Offers multi-block capability for greater control over the meshingWide selectionof discretization schemesA number of turbulence models, including Reynolds stress transport models, areimplementedCan ead in CAD dataHas an integrated geometry building front-endPerforms adequately forCH, nd Hz eflagrations

Weaknesses:Yields poor agreement with experiments for gases other than methane and hydrogen,to which the model appears to have been tuned.Uses a thin flame model which is not well suited to explosion modellingUses an gnition model w ith deficiencies

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The explosion model and ignition model are not thoroughly validated2.4.3. COBRAThe COBRA CFD code has been developed by Mantis Numerics Ltd. in conjunction withAdvantica Technologies Ltd. It appears that there has been no development of the code since1997, although its Advantica Technologies Ltd application continues.COBRA ses an explicit or implicit, second order accurate (spatial and temporal),finite-volume integration scheme coupled to an adaptive grid algorithm. The grid iseffectively unstructured and may be refined and de-refined autom atically locally w ithin theflow, in principle allowing features such as flame fronts and shear layers to be resolvedaccurately. The grid isupdated after each time-marching cycle, ensuring that a fine gridresolution follows moving flow features, Catlin, Fairweather and Ibrah im (1995). Despitethis adaptive grid capability COBRA employs the PDR pproach for modelling sub-grid scaleobstacles - see the discussion of EXSIM (section 2.3.2) for a description of this approach.The PDR approach has its deficiencies, but if there is a need for practical simula tions for realcomplex geometries, then PDR is, in many cases, the only viable approach. The turbulentreaction rate is prescribed using burning velocity correlations.In addition to the conventional ensemble averaged, density-weighted equations for continuityand momentum, COBRA also solves transport equations for a reaction progress variable andthe total mixture energy. Closure of this equation set in the turbulent flow is achievedthrough use of the k-E urbulence model, which is modified to include com pressibility effects,Jones (1980), or a Reynolds stress transport model.COBRA s a finite volume code, with the cell average values of the dependent variablesstored in the computational cells. To second order, these cell averages correspond to values atthe centroids of computational cells. Diffusion and source terms are approximated usingcentral differencing and the convective and pressure fluxes are obtained using a second orderaccurate variant of Godunovs method - Godunov (1959) - derived from a conventional firstorder Godunov scheme by introducing gradients within the computational cells. The meshemployed within COBRA s Cartesian, cylindricalpolar or curvilinear and may be refined,where necessary, by successively overlaying layers of refined mesh. Each layer is generatedfrom the previous layer by doubling the number of cells in each co-ordinate direction. Th emesh can also be de-refined, but only to its original fineness.Mantis Numerics has supplied a simple visualisation program calledMUVI,which iscommand line driven. It is possible to dump out data from the solution by means of adding alines of code to a user subroutine.Results with th e COBRA code ha s been compared to experimental data from Phase I1 of theBFETS project, Popat et al. (1996), to experiments carried out by Advantica in 1m long tubesof lm length, and to experiments carried out by CMR n a 10m long tube, Catlin, Fairweatherand Ibrahim (1995), Fairweather, Ibrahim, Jaggers and Walker (1996), and Fairweather,Hargrave, Ibrahim and Walker (1999). Catlin, Fairweather and Ibrahim (1995) show ed goodagreement, to within 50%, between the calculations and the experiments for the over-pressure

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at two different locations in the explosion tube; however, at two other locations the calcu latedmaximum over-pressure was twice the measured over-pressure. The calculationsunderpredicted time of arrival of the pressure wave, at the four pressure transducers, by about20 ms, equivalent to an error of the order of 20 %. Moreover, the pressure decay was muchmore rapid in the experiments than n the COBRA alculations.Strengths:

Second order accurate spatial and temporal discretizationCartesian mesh, which makes meshing particularly easy, but can also handlecylindrical polar or arbitrary hexahedral meshesAdvanced grid refinemendde-refinement facility enabling flame fkont tracking andshock w ave capturing.Can read in CAD generated geometries

Weaknesses:Uses the standard k-Emodel, but offasWolfshtein's two-layer k-E urbulence model,which uses an algebraic expression for the energy dissipation rate, E, in the near-wallregion and the standard k-E model elsewhere

4 Setting up complex geometries can be time-consuming and difficultDoes not have a model for transition from lam in a to turbulent flow, which mightaffect the initial growth of the flameVisualisation of flow fields with the MUVI program is slow and aborious, beingcommand line driven, compared to commercially available visualisation tools, i.e.EnSight and Fieldview

The underlying numerical methods available within COBRA have recently been updated toimprove computer mn times, particularly for complex three-dimensional geometries, byMantis Num erics Ltd. This new code, called PICA, is currently being developed asanexplosion model by Mantis Numerics Ltd. and the University ofLeeds independently ofAdvantica Technologies Ltd.'2.4.4. #EWTNEWT is an unstructured adaptive mesh, three dimensional, finite volume (tetrahedralvolumes), computational fluid dynamics code. The unstructured mesh makes it amenable tothe modelling of very complex geometries. NEWT was originally developed fornon-combusting, turbomachinery applications but is now being adapted for explosion

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prediction at the Engineering Departmentof Cambridge University, the work beingpart-funded by the Offshore Safety Division of the Health & Safety Executive,Due to its adaptive grid capabilities, the NEWT code should allow explosion prediction invery congested env ironments containing, of the order, one hundred obstacles, Currentobjectives of the work on NEWT re to refine the code and also to use the model to helprefine currentPDRmethods. The first phase of the OSD, HSE ponsored work hasconcentrated on im plementing into NEWT models developed for the CFX-4 ode by AEATechnology Engineering Software, Harwell in collaboration with the Health & SafetyLaboratory, Buxton.A second-order accurate discretisation scheme is used for the convective fluxes. Artificialdissipation - a combination of second-order and fourth-order derivatives - is added to controlshock capture and solution decoupling. The fourth-order smoothing takes place throughoutthe dom ain, while the second-order smoothing is only used in regions of large pressuregradients. A fourth-stage Runge-Kutta time integration approach is used for the timedependen t calculations. Maximum local time steps can be used in order to enhanceconvergence, when a steady state soht ion is sought.The NEWT ode uses a modified Lam and Bremhorst variant of the k-e turbulence m odelwhere the near wall damping function is dependent on the turbulence Reynolds number andnot th e wall norm al distance, Watterson, Connelt, Savill and Dawes (1998).The com bustion is modelled using the eddy break-up model or a laminar flamelet model,Bray et a2. (1985). The eddy break-up model can give rise to spurious ignition ahead of theflame. This is countered by suppressing the flame leading edge at each time step, Wa ttaso nef al. (1 998). Ignition of the gas mixture is achieved through a ramping of he reactionprogress variable, from zero to unity, in the specified ignition region during the specifiedignition period. The laminar flamelet model does not requires fixes, like the leading edgesuppression described above, and yields better agreement between the predicted andexperimentally observed flame shapes for bam ed channel test cases, Birkby, Cant and Sav ill(1997), while incurring slightly higher com putational overheads than the EBU model.Special treatment was needed for low Mach number flows (Ma .3), du e to convergenceproblems with density based flow solvers. This was a particular problem fo r the laminarflame propagation phase, W atterson etal. (1998).Also currently in progress a t Cam bridge University is a research project that will lead to thedevelopment of a CA D interface to NEWT. This interface will automatically mesh the CADgenerated geometry, allowing the modelling of more complex scenarios. The firstimplementation of the adaptive grid only allowed a single level of refinemen t (andde-refinement), whereby one parent cell may split into up to eight child cells. How ever, toincrease the accuracy of the code, and o reduce the memory requirem ents, a multi-levelrefinemen t algorithm has been implemented, Watterson et al . (1998).Watterson et al. (1998) presented calcu lations where they claimed to achieved qualitativeagreement in terms of flame brush propagation and lame brush shape with small-scale

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experiments in the HSE affled channel, Freeman (1994), and with large-scale experim ents inShell SOLVEX box, Pu ttock, Cresswell,Marks, amules and Prothero (1996). However, thecalcu lated maxim um over-p ressure was overpredicted by between 2 and 15 times. Themaximum flames speed was also overpredicted, by about 50 % or more, while time tomaximum overpressure in the SOLVEX est case was substantially underpred icted by NEWT.These discrepancies can perhaps be e

Documents

C.J. Lea and H.S. Ledin- A Review of the State-of-the-Art in Gas Explosion Modelling