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Fire modelling is used increasingly to enable fire-safety engineering solutions to meet performance-based regulatory requirements. There are many fire models, but perhaps the most useful are those based on computational fluid dynamics, or CFD (see also Digest DG 367 [1] ). Such tools in competent or expert hands are extremely powerful, but can be misused by those with limited knowledge of fire science and numerical modelling. Presentation of CFD results (often using video animation) can be very convincing, but the results must be assessed with some knowledge of the principles and awareness of any shortcomings of the model. Currently, CFD models employ either Reynolds- averaged Navier–Stokes (RANS) or large eddy simulation (LES) methodologies for application to practical fire problems. This Digest offers guidance on CFD models using the RANS methodology and on how to avoid some of the common pitfalls. No specific guidance is offered on LES models, but much of what is recommended here will also apply to them. INTRODUCTION The widespread application of computer fire models has grown as a result of the freedom to innovate offered by performance-based regulation [2] . Computer models enable designers to: test alternative fire-safety design solutions, quantify system performance specifications, and explore solutions to ‘what if?’ design questions. These processes are assisted by new standards, such as BS 7974:2001 [3] and BS ISO/TR 13387 [4] . Many computer fire models are available, ranging from simple engineering correlations and zone models to more advanced field (CFD) models. These models simulate the heat- and mass-transfer processes associated with a compartment fire, the heart of any systematic approach to safe design. The essential difference between zone and field models is in the way they treat the movement of the products of combustion within the building envelope and their respective reliance on experimental information. The two broad categories are illustrated in Figure 2, which shows the schematic representation of the same room fire-modelled by the two approaches. By solving the problem on a three-dimensional numerical grid (Figure 2b), not only are the predictions much more detailed, but an isosurface of the predicted temperature clearly shows that the fire plume becomes deflected by the air inflow at the doorway. This is important because it leads to higher entrainment rates of air into the fire and consequently higher smoke-production rates. The zone model does not account for this, unless it has been assumed a priori. DIGEST DG 511 FIRE MODELLING WITH COMPUTATIONAL FLUID DYNAMICS Suresh Kumar Figure 1: CFD modelling of fire inside a building illustrating smoke flows and thermal impact on a ceiling structural beam

Transcript of Bre Cfdchecklist Dg511

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Fire modelling is used increasingly to enable fire-safety engineering solutions to meet performance-based regulatory requirements. There are many fire models, but perhaps the most useful are those based on computational fluid dynamics, or CFD (see also Digest DG 367[1]). Such tools in competent or expert hands are extremely powerful, but can be misused by those with limited knowledge of fire science and numerical modelling. Presentation of CFD results (often using video animation) can be very convincing, but the results must be assessed with some knowledge of the principles and awareness of any shortcomings of the model. Currently, CFD models employ either Reynolds-averaged Navier–Stokes (RANS) or large eddy simulation (LES) methodologies for application to practical fire problems.

This Digest offers guidance on CFD models using the RANS methodology and on how to avoid some of the common pitfalls. No specific guidance is offered on LES models, but much of what is recommended here will also apply to them.

INTRODUCTIONThe widespread application of computer fire models has grown as a result of the freedom to innovate offered by performance-based regulation[2]. Computer models enable designers to:

test alternative fire-safety design solutions, quantify system performance specifications, andexplore solutions to ‘what if?’ design questions.

These processes are assisted by new standards, such as BS 7974:2001[3] and BS ISO/TR 13387[4].

Many computer fire models are available, ranging from simple engineering correlations and zone models to more

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advanced field (CFD) models. These models simulate the heat- and mass-transfer processes associated with a compartment fire, the heart of any systematic approach to safe design. The essential difference between zone and field models is in the way they treat the movement of the products of combustion within the building envelope and their respective reliance on experimental information.

The two broad categories are illustrated in Figure 2, which shows the schematic representation of the same room fire-modelled by the two approaches. By solving the problem on a three-dimensional numerical grid (Figure 2b), not only are the predictions much more detailed, but an isosurface of the predicted temperature clearly shows that the fire plume becomes deflected by the air inflow at the doorway. This is important because it leads to higher entrainment rates of air into the fire and consequently higher smoke-production rates. The zone model does not account for this, unless it has been assumed a priori.

DIGEST DG 511

FIRE MODELLING WITH COMPUTATIONAL FLUID DYNAMICS

Suresh Kumar

Figure 1: CFD modelling of fire inside a building illustrating smoke flows and thermal impact on a ceiling structural beam

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Zone models are closely related to well-established, traditional methods for the treatment of smoke movement, which were initiated before the widespread availability of the modern computer. They were first suggested in guidance on roof venting and still form the basis of much current advice on smoke control (see, for example, Digest DG 396[5]). These methods use simplifying assumptions about the physics of smoke movement suggested by experimental observation of fires in compartments.

In contrast, simulations using CFD are able to predict, without prior assumptions, the behaviour of smoke flow

from a known fire and enable smoke-control strategies to be assessed. Like their zonal counterparts, these models allow comparisons between the developing hazard and the time available for safe escape of the occupants.

CFD models are now being used extensively, particularly for complex designs where the zonal methodology may not be valid. As an illustration, Figure 3 shows an application of CFD to evaluate smoke-ventilation design for an underground train station, involving the solution of the underlying equations on a numerical grid comprising millions of grid cells.

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Figure 3: Simulation of smoke flow in smoke-ventilation design for an underground train station using the CFD program JASMINE

Figure 2: Schematic representation of zone and field models

a: Zone modelling b: Field (CFD) modelling

Ceiling layerOutflow or spill plume

Fire plume

Burning object

Outflow or spill plume

Ceiling layer

Fire plume

Burning object

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CFD MODELSThe development of CFD models continues apace following the inexorable growth in computer power. Three distinct CFD modelling methodologies have emerged:

Reynolds-averaged Navier–Stokes (RANS),large eddy simulation (LES), and direct numerical simulation (DNS).

The methodologies differ primarily in their treatments of the effects of turbulence on the heat- and mass-transfer processes and on the chemical kinetics.

Figure 4 illustrates the degree of resolution achieved by the three methodologies. The fluctuating gas velocity at a particular point in a growing fire is shown. It has a relatively slow underlying increase with time as the fire grows, but fluctuations of different wavelengths are present depending on the local turbulent eddies in the flow. The degree of resolution of the contributions made by the different wavelengths achievable by the different turbulent methodologies is illustrated. The DNS methodology resolves fluctuations of all wavelengths, and thus takes into account exactly their contribution to fire and smoke spread. The LES methodology simulates the fluctuations carrying large wavelengths and uses a (sub-grid) turbulence model for the fluctuations of smaller wavelengths. The RANS methodology uses a turbulence model for fluctuations of all the wavelengths. For example, in Figure 4, for the RANS methodology, the square root of the turbulent kinetic energy (√k) denotes the turbulence contribution of the fluctuating velocity and is represented here by the spread (in the form of dotted lines) around its mean value (ū).

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A detailed account of the three turbulence modelling methodologies is given by Luo[6]. Below is a summary of their main features.

RANS methodologyRANS is, at present, the most widely used methodology for practical application, both in fire-specific commercial software such as JASMINE[7] and SOFIE[8] and in general-purpose CFD programs such as PHOENICS, CFX, FLUENT and STAR-CD.

Essentially, the RANS methodology views the transient evolution of local gas temperature, velocity or chemical species as comprising a time-averaged component and a fluctuating component about that average. It solves only the statistically time-averaged equations that describe the principles of mass, momentum, energy and species conservation. These equations are supplemented by further transport equations that encompass the effect of turbulence influences and encapsulate the whole of the turbulence spectrum – from very large ‘room-scale’ turbulent eddy sizes (a few metres or more) down to the very smallest scales (order of a millimetre) – associated with the dissipation of energy by viscosity and the chemical reactions. The most commonly used turbulence model in RANS CFD programs for fire applications is the two-equation k–ε turbulence model, where k is the kinetic energy of turbulence and ε is its dissipation rate.

RANS-based CFD models predict the evolution over time of the statistically time-averaged properties of the fire at millions of locations throughout the enclosure of interest.

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Figure 4: An illustration of the resolution of velocity as a function of time using the RANS, LES and DNS methodologies

Time

Velo

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DNS

LES

RANS

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LES methodologyLES-based CFD models capture the fluctuating low-frequency, larger eddies, but need to model the smaller eddies using a ‘sub-grid’ model, in a similar way to the two-equation turbulence model used in the RANS methodology. In contrast to RANS, which uses time averaging, LES uses spatial averaging – also referred to as ‘filtering’– because it smoothes out the information contained in eddies smaller than grid cell size.

By adopting an averaging procedure used for smoothing out temporal fluctuations, LES-based CFD models can also provide predictions of time-averaged properties at each grid cell, for comparison with RANS predictions or with measurements (such as gas velocity and gas temperature). The fineness of the numerical mesh determines the size of those eddies that are resolvable and those that are not in the LES model. This needs to be chosen with great care since coarse meshes can give misleading results (see ‘Best-practice guidance’ below). LES models use finer numerical meshes than RANS models, so need far more computer power, which is now readily available.

LES is being increasingly adopted as computers become more powerful. One advantage is that it makes fewer assumptions about the role of turbulent mixing than the RANS approach. Another attraction of the LES methodology is the very visually appealing graphical animations that it generates. The FDS model, developed at the National Institute of Standards and Technology’s (NIST) Information Technology Laboratory in the US, is being used increasingly by fire safety practitioners[9].

Figure 5 illustrates a typical graphical output of the simulation of a hydrogen jet release in the atmosphere from the RANS and LES methodologies. It can be seen that the LES methodology reproduces only the large-scale structure but filters out small-scale flow details, whereas the RANS methodology reproduces the integrated flow behaviour by time-averaging fluctuations of all scales.

On the other hand, as explained in the next section, the DNS methodology reproduces the detailed flow field structure by exactly simulating the fluctuations of all turbulent properties (eg velocities, temperature, density, combustion species). However, since the DNS methodology is not yet ready to be exploited for practical application, its results are not shown here.

DNS methodologyThe DNS methodology has a much higher degree of resolution and is potentially more accurate than RANS and LES, but is even more demanding on computer power than the LES methodology. This is because it attempts to capture all eddy scales involved in the underlying physics and chemistry without resorting to turbulence modelling at all. DNS-based CFD models are still a long way from practical application to fire because computer power is still not adequate to allow rigorous simulation of all length scales for the domain sizes of practical interest to the fire engineer. There is active research using this approach, which is helping our understanding of the phenomena involved (eg Jiang and Luo[10]), but such models are unlikely to yield practical tools in the near future.

FIRE-SPECIFIC VERSUS COMMERCIAL SOFTWARECFD software tends to be divided between the fire-specific computer programs that have been developed by fire-research laboratories (eg JASMINE, SOFIE, FDS) and general-purpose commercial programs (eg PHOENICS, CFX, FLUENT, STAR-CD). The latter contain much of the same fundamental treatments for turbulence and thermal radiation, but often lack the fire-specific components in the specialist codes. All are alike in essence, although they do differ in detail, and each has its strengths and weaknesses. The commercial programs are usually more developed in their numerical efficiency and incorporate a broader range of treatments for some of the general physical aspects, but do not have the same breadth and depth of validation against fire experiments or fire-specific user interfaces as the fire-specific codes.

ENSURING CORRECT USE OF COMPUTER MODELSIssues and concernsIn 2001, the UK government sponsored a study into quality-assurance issues involved in using models in support of performance-based design[11].

Currently, there is no formal requirement for the practitioner to demonstrate competency with any computer fire models, particularly those using CFD. The fire practitioner may be expert in fire engineering but inexperienced in computer modelling and thus possess little or no understanding of the important underlying physics and numerical techniques. Conversely, the computer modeller may be expert in CFD and mathematical and numerical techniques but have no knowledge of fire science and therefore need to rely on a fire engineer for fire dynamics or fire engineering. There is a concern that many fire-engineering courses do not offer sufficient depth of teaching in computer modelling, particularly CFD.

The 2001 study highlighted a number of issues that strongly suggest that the application of CFD to fire-safety engineering has some way to go before it can be applied with confidence by the consulting engineering community. The issues included:

incorrect use of software without training,graphics used inappropriately,lack of sensitivity analysis, eg grid sensitivity in a CFD study and scenario sensitivity generally,

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Figure 5: CFD simulation of hydrogen release in the atmosphere from the RANS (top) and LES (bottom) methodologies

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lack of detailed understanding of CFD by authorities and enforcers,difficulty in finding people qualified to check/judge work,delays caused by third-party checking,inappropriate specification of a design fire, both in terms of its size and growth rate, inappropriate choices of initial and boundary conditions, anddifficulty in identifying ‘appropriate’ qualifications for the various professionals.

CoMPASThe Computer Model Performance Assessment Scheme (CoMPAS) was developed by BRE (in discussion with fire-safety practitioners) using critical success factors for ensuring proper use of computer models in support of performance-based fire-safety design. The critical success factors are here considered to be key elements of the scheme, which are necessary for CFD analysis for a fire-safety strategy to satisfy its objectives. CoMPAS is targeted at construction industry professionals who use computer models for performance-based fire-safety design. It is intended that the end-users of CoMPAS include fire-safety engineers, building-services engineers, system designers, building-control officers, approved inspectors, fire-safety officers, computer modellers, CFD vendors and educators.

CoMPAS offers a means of: addressing possible gaps in knowledge and experience of the computer modeller and fire practitioner, promoting proper use of computer fire models for (performance-based) fire-safety engineering design and assessment, streamlining the design and approval process by improving the dialogue between designers/engineers and enforcers, andoffering a consistent approach aligned with national and international standards.

CoMPAS evaluates the performance of computer model choice and fitness for purpose, the design team, and use of the model through various stages of the design and approval process. It does this by using the following five performance criteria:

Qualifications of the design teamThe design methodologyThe modelling methodologyQuality-control proceduresDocumentation and reporting

These criteria are evaluated in two stages:Validation of individual elements, to ensure the conformity or validity of each element in the overall fire-safety design and approval process. These are grouped into the following three categories:

Model validation – ensures that numerical errors are minimised and computer models have been verified against appropriate full-scale data. User validation – checks that the design team has appropriate training and experience in using the computer model.

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Use-of-model validation – ensures that computed results have been verified by an expert (in-house or third-party) and against simple, alternative methods.

Adherence to a checklist of critical success factors, to ensure that all essential aspects have been considered. These are grouped into the following three categories, which cover the five performance criteria mentioned above:

Choice of model – covers design methodology, modelling methodology, documentation and reporting.User of model – covers qualifications of the design team, quality-control procedures, documentation and reporting.Use of model – covers modelling methodology, quality-control procedures, documentation and reporting.

CoMPAS combines the above-mentioned two-stage evaluation criteria with best-practice guidance on the essential physical, chemical and numerical aspects of fire science and modelling for facilitating proper use of computer models for fire-safety design and hazard assessment.

Best-practice guidanceThe widespread availability of fire-modelling techniques provides enormous opportunity for designers to break free from the prescriptive rules of the past and to develop truly innovative designs. However, as with any design tool, there are serious risks that they can be misused. For example, users may fail to understand the assumptions implicit in the models or may not achieve sufficient numerical convergence in their simulations and produce misleading results. Detailed guidance is given by Cox and Kumar[12] and Gobeau[13]. The following sections also illustrate best-practice guidance with examples of the choice of important physical parameters for a successful CFD solution to a practical fire-safety engineering problem.

Non-dimensional heat-release-rate parameter Q*The performance of the CFD model depends on a proper description of the physical and chemical processes for the particular problem, combined with appropriate initial and boundary conditions. There are two essential components – the treatment of the ‘fire science’ and the establishment of a ‘good’ numerical solution.

An example of the possible misuse of the CFD model as a result of an incorrect prescription of the fire itself would be to characterise the fire source by a known or prescribed heat-release rate but then to associate that heat-release rate with an inappropriate fuel area. Close attention needs to be paid, for example, to the relative influences of momentum and buoyancy at the fire source. They are represented by the non-dimensional heat-release-rate parameter Q*, which is also referred to as the source Froude number.

Figure 6 illustrates the physical significance of Q*. For building fires, Q* ranges typically between 0.1 and 2.5[14]. A value of higher than around 2.5 is not representative of

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these temperatures over the numerical mesh spacing, it is unlikely that the model will predict temperatures as high as this. Anything above this temperature should be treated with great caution and anything above the adiabatic flame temperature must be incorrect. (The adiabatic flame temperature is a maximum theoretical flame temperature that assumes that there are no heat losses, and is in the region of 2000 °C for most hydrocarbon fuels in air and 2400 °C for acetylene in air.)

Volumetric heat source versus combustion modelToo small a volume of fire source will yield gas temperatures in the source that are much too high, and might result in unrealistically high peak gas temperature predictions above the adiabatic flame temperature – an absolute limit on gas temperature. Too large a volume of fire source will yield gas temperatures in the source that are much too low and might result in unrealistically low peak gas temperature predictions well below the minimum luminous flame temperatures, which are in the region of 1000 °C[14]. Ideally, a combustion model should always be used in preference to a volumetric heat source.

Clearly, such erroneous source descriptions grossly misrepresent buoyant acceleration, and indeed buoyant

buoyant building fires, but is more appropriate for higher-momentum jet fires. Thus, a higher value is perfectly reasonable if the hazard being modelled is a high-pressure gas leakage. On the other hand, a value in the region of 0.1 or smaller characterises a bush fire or forest fire with large floor area.

Heat-release rate per unit area of fuel surfaceHeat-release rate per unit area of the burning fuel is an important property of a fuel, and can be considered as an alternative to Q*. It is typically between 225 kW/m2 and 2000 kW/m2 for a wide range of building materials (including polymers and flammable liquids)[15]. Here, the lower value corresponds to solid wood (charring material) and clean-burning liquid fuels such as industrial methylated spirit, and the higher value to sooty fuels such as kerosene (liquid). Note that it is possible to specify accurately the burning area for liquid fuel but not for solid fuel, which tends to burn in depth as well as across the surface. Therefore, for solid fuels, the heat-release rate per unit area of fuel surace can only be used as a crude guide.

Fire plume temperaturesMeasured time-averaged gas temperatures in a fire seldom exceed around 1300 °C in the open or 1400 °C inside an enclosure. Since the CFD code spatially averages

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Figure 6: Characterising fire in terms of non-dimensional heat-release-rate parameter Q*

Q*~1 Q*~100Q*<0.1

Q*

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turbulent mixing, at the source. Such errors are easy to avoid with proper attention to the characteristics of buoyant fires, and by using a simple combustion model such as an eddy-break-up model.

A combustion model can also take into account local fluid dynamics in situations where, for example, fire plume is deflected by wind or by a jet of entrained air into the compartment from a doorway opening, thus providing realistic representation of the fire plume. In contrast to the volumetric heat source, the combustion model can thus take into account the enhanced air-entrainment rate due to the deflection of the plume. The entrainment rate controls smoke production, and thus has implications for the design of the smoke-control system. Figure 7 illustrates, for the volumetric heat source and combustion model representations of the fire, the differences in the shape and temperatures of a fire plume in a compartment with a doorway opening.

Even by taking realistic flame volume based on flame height (see orange cuboid in Figure 7a), the maximum centre-line gas temperature predicted by the volumetric heat source is very low (~500 °C) compared with that predicted by the combustion model (~1200 °C). Note that the centre-line gas temperatures in the plume are lower than these values. The entrainment rate and hot layer temperature predicted by the combustion model are in good agreement with the experimental data available for this scenario (see Wang et al[16] for a relative comparison of the volumetric heat source and combustion models).

Radiative exchange from fire plume to its surroundingsDepending on the fuel, a fire plume can lose up to 60% of its heat to its surroundings[17], which ensures that the plume remains in thermodynamic equilibrium with the surroundings and maintains its temperature at around 1000 °C. The fire plume loses heat by radiation of

non-luminous radiative gases (CO2 and water vapour) and luminous radiative soot (which gives the flame its orange or red colour). Figure 8 compares plume temperatures for a 250 kW methane fire by excluding and including radiative heat losses. Excluding radiation, the fire plume is much hotter (peak temperature ~1950 °C) and taller (flame height ~2.9 m) than when radiation is included (peak plume temperature ~1200 °C, flame height ~2.1 m). In Figure 8, the flame height (based on an isosurface of excess temperature of 370 °C) is indicated by the yellow marker in the plume region. Thus, including radiative heat losses, this leads to more realistic peak temperatures and flame height for the fire plume. For clean-burning fuel fires (eg industrial methylated spirit or ethyl alcohol) with flames greater than 1 m in diameter, the radiative losses could be in the range of 15% of the total heat-release rate, and for very smoky fuel fires (eg heptane, kerosene, polystyrene), radiative losses are in the range of 30–60%. The radiative heat losses for lower-hydrocarbon fuels such as methane and propane are between these two ranges[17]. Further details of the relative evaluation of the well-known radiative heat-transfer models are given by Wang et al[16].

Specification of free pressure boundaryTo numerically simulate a fluid flow, the boundary conditions along all or part of the boundary must be specified. It is important that the ‘free’ boundary conditions outside a compartment opening or surrounding an unbounded fire are far enough away so as not to influence the solution in the region of interest. At a ‘free’ boundary, pressure is defined to be ambient. An ambient pressure boundary condition across a doorway opening will not, for example, allow the proper inflow and outflow characteristics to be established. Free boundaries must be chosen carefully and, as shown in Figure 9 by green lines, should be far enough from any

FIRE MODELLING WITH COMPUTATIONAL FLUID DYNAMICS – DG 511

a: Volumetric heat source

Figure 7: Comparing volumetric heat source with combustion model characterisation of the fire source

b: Combustion source

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ventilation openings so as not to affect flows through them. Steep pressure gradients near the free pressure boundary should be avoided, and simulations should be reasonably insensitive to the boundary position.

Assessing the quality of the numerical solutionIt is comparatively easy to produce impressive images of fluid flow with modern software, but it is essential to demonstrate that the solution is reasonably well converged by checking for sensitivity to further numerical iteration and mesh refinement.

The first step is to check whether the normalised residual errors in the solution variables show a downward trend with numerical iterations and satisfy an agreed tolerance criterion (say below 1.E-02 or 1% ) when the

solution is terminated. The second step is to check the overall global balance of mass, heat and combustion parameters, such as the mixture fraction and mass fraction of the fuel. Typically, a mass balance of some 99% or heat balance of around 95% is acceptable for practical applications.

Figures 10–12 illustrate different levels of convergence. Figures 10 and 11 both show unconverged solutions. In Figure 10, the values of the solution variables are still changing with increasing iterations and normalised errors are significant, and the global balance is not within the agreed criterion (ie not better than 95% for heat). The concept of a traffic light system is used for a quick assessment of the convergence level, where any one red light on the left panel indicates non-convergence, whereas a combination of amber and green lights indicates partial convergence and a full complement of green lights indicates full convergence. A partially converged solution may be acceptable if the values in the residual column next to the amber lights are below 5.E-02 (ie 5%).

Note that, in Figure 11, the values of the solution variables are still changing with increasing iterations and normalised residual errors are significant, as shown by red traffic lights, even though the corresponding global balance given in Table 2 is well within the agreed criterion (ie better than 95% for heat and 99% for mass). The residual errors under the residual column for u and v velocities (indicated by red traffic lights) are more than 1.4E-01 (ie 14%), so the solution is still not fully converged.

Figure 12 and Table 3 show a fully converged solution, where the values of the solution variables are steady with increasing iterations, normalised residual errors are well below 1.E-02 (ie 1%) and the global balance is good (ie all balances better than 99%).

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a: Excluding radiative loss (unrealistically high plume temperatures and flame height)

Figure 8: Fire plume with and without radiative heat loss to its surroundings

b: Including radiative loss (realistic plume temperatures and flame height)

Figure 9: Physical domain extended for proper specification of free pressure boundary

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� FIRE MODELLING WITH COMPUTATIONAL FLUID DYNAMICS – DG 511

Mass [kg/s] 99.7%

Heat [J/s] 88.9%

Fmix […]*[kg/s] 84.6%

Mfu […]*[kg/s] 99.8%

Table 1: Global balance of an unconverged solution of Figure 10

Figure 10: Assessment of the convergence of the CFD numerical solution (unconverged)

Figure 11: Assessment of the convergence of the CFD numerical solution (unconverged)

Mass [kg/s] 99.9%

Heat [J/s] 99.9%

Fmix […]*[kg/s] 99.9%

Mfu […]*[kg/s] 99.9%

Table 2: Global balance of an unconverged solution of Figure 11

Figure 12: Assessment of the convergence of the CFD numerical solution (fully converged)

Mass [kg/s] 99.9%

Heat [J/s] 99.9%

Fmix […]*[kg/s] 99.9%

Mfu […]*[kg/s] 99.9%

Table 3: Global balance of a fully converged solution of Figure 1�

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Figure 13 shows the steady-state velocity vectors on a plane parallel to and close to the floor for the partially and fully converged solutions. It compares the relative performance of unconverged and converged solutions by plotting the results of velocity vectors. It shows the plan view of the velocity vector plot close to the floor for a fire situated near the back wall in the left corner of a compartment. The velocity vectors represent incoming air flow patterns induced by the fire. One would expect that the incoming air flow should be directed towards the fire, which is the case for the converged solution (Figure 13b), but not for the unconverged solution (Figure 13a).

Effect of grid refinementIt is worth emphasising that for a truly converged solution, the user must demonstrate that the CFD solution is not sensitive to the refinement of the numerical grid. Ideally, this can be done by progressive grid refinement, ie by increasing the number of grid cells by 50% or, if possible, doubling them in each direction, first vertically and then in both directions horizontally.

Figure 14 shows the velocity vectors in the steady state on a plane parallel to and close to the floor for coarse and fine grids. The vectors are evidently quite different for the two cases. Similar to Figure 13, the velocity vector plots

correctly show the cold air flow patterns being drawn into the fire for the fine solution (Figure 14b), whereas those for the coarse grid solution (Figure 14a) lack this feature and hence are incorrect. This demonstrates that the coarse grid solution is not grid independent, and clearly illustrates the importance of grid-sensitivity analysis.

Analysis of CFD predictions against the characteristics of fire componentsIn addition to the fire source itself, characteristic properties of other fire components such as the thermal plume above the flame tip, the resulting ceiling jet and the upper hot gas layer, together with wall and vent flows, need to be scrutinised closely when analysing a numerical solution. The characteristic properties of a fire plume, such as flame length, axial plume temperatures and velocities, and those of the ceiling jet, ceiling layer and spill plumes, are detailed in the published literature (see, for example, Cox[14]). Simple calculations can be performed to check that the converged solution reproduces important characteristics of the fire components.

Appendix A illustrates the step-by-step procedure for obtaining a converged numerical solution using the RANS CFD methodology. Appendices B and C provide checklists of some important considerations when setting up and examining a numerical solution.

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a: Unconverged – incorrect solution (global balance >99%, residual errors >20%)

Figure 13: Velocity vectors showing convective air flow into and around the fire source for unconverged and fully converged solutions

b: Fully converged – correct solution (global balance >99%, residual errors <1%)

a: 18 000 cells; flow rate through opening = 35 kg/s

Figure 14: Effect of grid refinement on fluid flow and air entrainment rate

b: 300 000 cells; flow rate through opening = 20.5 kg/s

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REFERENCES[1] Cox G. Fire modelling. Digest DG 367. Bracknell, IHS BRE Press, 2004.[�] Communities and Local Government. Approved Document B: Fire Safety. London, RIBA Bookshops, 2007, 2006 edition.[�] British Standards Institution. Application of fire safety engineering principles to the design of buildings – Code of practice. British Standard BS 7974:2001. London, BSI, 2001.[�] British Standards Institution. Fire safety engineering. British Standard BS ISO/TR 13387. London, BSI.[�] Morgan H. Smoke control in buildings: design principles. Digest DG 396. Bracknell, IHS BRE Press, 1994.[�] Luo K H. New opportunities and challenges in fire dynamics modelling. Proceedings of the 4th International Seminar on Fire and Explosion Hazards, Londonderry, 8–12 September 2004. (Eds D Bradley, D Drysdale and V Molkov.) Belfast, Universities Press, 2004. pp. 39–52.[�] Cox G and Kumar S. Field modelling of fire in forced ventilation enclosures. Combustion Science and Technology, 1987, 52 7.[�] Cox G. SOFIE – A model in the making. Building Services, 1994, (November) 31–33.[�] McGrattan K B, Rehm R G and Baum H R. Fire driven flows in enclosures. Journal of Computational Physics, 1994, 110 285.[10] Jiang X and Luo K H. Direct numerical simulation of the puffing phenomenon of an axisymmetric thermal plume. Theoretical Computational Fluid Dynamics, 2000, 14 55.[11] Shipp M. A process validation methodology for the use of fire safety engineering. Proceedings of Interflam 2004, 10th International Conference on Fire Science and Engineering, London, 5–7 July 2004. London, Interscience Communications Limited, 2004. p. 401. [1�] Cox G and Kumar S. Modelling enclosure fires using CFD. In SFPE handbook of fire protection engineering. Massachusetts, National Fire Protection Association, 2002, 3rd edition. pp. 3-194–3-218. [1�] Gobeau N. Guidance for HSE inspectors: smoke movement in complex enclosed spaces – Assessment of computational fluid dynamics. HSL/2002/29. Buxton, Health and Safety Laboratory, 2002. [1�] Cox G. Combustion fundamentals of fire. London, Academic Press, 1995. [1�] Drysdale D. An introduction to fire dynamics. Chichester, John Wiley & Sons, 2003, 2nd edition.[1�] Wang J, Hua J, Kumar K and Kumar S. Evaluation of CFD modelling methods for fire-induced air flow in a room. Journal of Fire Sciences, 2006, 24 (5) 393–411.[1�] Tewarson A. Generation of heat and gaseous, liquid and solid products in fires. In SFPE handbook of fire protection engineering. Massachusetts, National Fire Protection Association, 2008, 4th edition. p. 3-109 (see Tables 3-4.22 and 3-4.23).

APPENDIx A: STEP-BY-STEP PROCEDURE FOR OBTAINING A CONVERGED NUMERICAL SOLUTION USING THE RANS CFD METHODOLOGY

Review project objectives and architectural drawings. Follow the qualitative design review in discussion with the project team (fire engineer, system designer, enforcer).Input building geometry. Select only the geometrical features necessary for CFD simulation.

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Define the fire. Select the fuel type and fire growth rate, maximum size and location. Select physical sub-models, eg turbulence, combustion, radiation.Generate the numerical grid (finer near fire and other geometrical features, coarser elsewhere). Avoid cells with a large aspect ratio and maintain an expansion ratio between adjacent cells within 50%.Apply boundary conditions and fluid/solid properties to ventilation sources, wall properties and ambient conditions.Generate the solution. Check numerical convergence and the global balance. If the solution is converged, extract results.Analyse the results. Check that the solution reproduces the characteristics of fire components, eg fire plume, ceiling jet and layer, spill plume.

APPENDIx B: CONSIDERATIONS FOR SETTING UP A NUMERICAL SOLUTION

Resist the temptation to undertake two-dimensional simulations, which can provide physically misleading solutions. Choose the mesh to capture the main physical features of the flow, ensuring that the near-wall nodes are close to the surface. Select a mesh that is adequately fine for the fire source and at enclosure openings.When designing a grid, ensure that the aspect ratio of cells is not too large – typically not larger than 50. More importantly, ensure that the adjacent cells change in size (ie expand or contract) by no more than 50%. Analyse the accuracy of the mesh by a grid-refinement study, preferably using at least three different grid resolutions and ideally doubling the grid cells both vertically and horizontally. For these buoyant flows, special attention should be given to the vertical mesh spacing. If possible, use more detailed numerical differencing schemes (second or higher order) as convergence is approached. (It is likely that a first-order numerical differencing scheme will be used at least initially since it is stable.) Note that a CFD code uses a numerical scheme to convert differential equations into algebraic finite differential equations, which consequently introduces numerical discretisation errors. In Figures 10–12, these errors are represented in the form of total residuals (summed over all grid cells) that are normalised by the flux of the variable φ, flowing in the computational domain. Here, the variable φ characterises a set of physical quantities that are solved by finite-volume equations. The set of φ consists of: Fmix (mixture fraction); Mfu (mass fraction of fuel); H1 (enthalpy); KE (turbulent kinetic energy); EP (turbulent dissipation rate); U1 (velocity component in x-direction); v1 (velocity component in y-direction); and w1 (velocity component in z-direction). Note that the flux of φ has the units of mass flow rate times φ.Do not change too many numerical relaxation parameters at once, as it then becomes difficult to analyse which of the changes has influenced the solution.In transient simulations, be sure that the time-step is adapted to the choice of the grid and check the influence of the time-step on the results. For a rapidly developing fire, more iterations per time-step are generally needed.

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Normalised mass and momentum continuity errors, and residual errors for all the solved variables, should be less than about 1%, preferably less than 0.1%. In an ideal simulation, the residuals will decrease steadily. However, in practice some equations may oscillate for a while but the residuals should eventually decrease (in a damped-oscillatory manner). Examine convergence by following ‘monitor’ data, especially pressure, at critical locations (eg in the plume, in the hot gas layer and in ventilation openings). Monitor values should gradually settle down to their converged levels.The global mass and heat balance should be better than 95% in one or more of the analysis regions. One of these regions should encompass the entire enclosure or building. Generally, global mass balance is achieved relatively easily, regardless of the quality of the solution. Global heat balance is often more difficult and a good indicator of how well a solution is converged. Be careful when exploiting an assumed axis of symmetry. When a simulation is run on half a domain for economy, undertake the simulation on the full domain using the half-domain results as the initial condition.Explore difficulties in achieving a steady-state solution by utilising transient simulations. There may be no steady solution if physical oscillation is present.

APPENDIx C: CONSIDERATIONS FOR FIRE SCIENCE AND FIRE-SAFETY ENGINEERING

Identify the significant parts of the building and the level of detail to be included in the geometric model. Include material properties where heat transfer to enclosure walls is important.Use a combustion model to allow a proper coupling between local air flow and the distributed heat release.Check that Q* is representative of the fire of concern (for buoyant fires, Q*≤2.5).Incorporate radiative loss from the flaming region. The fire plume can lose up to 60% of its heat by radiation.Ensure that boundary heat losses are accounted for. These can cause ceiling layers to lose their buoyancy and cool wall currents to fall through a buoyant layer.

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Check ventilation conditions:What is the role of compartment leakage? (See, for example, Digest DG 396[5] for a discussion of this issue.)Have the heating, ventilation and air conditions (HVAC) been modelled if they are important?Are under-ventilated fire conditions likely, and if so have they been accounted for in the combustion modelling?

Check if modelling of fire-protection measures (eg detector, sprinkler) is required. Realistic reproduction of the ceiling jet characteristics and therefore a reasonably fine under-ceiling mesh resolution will be needed to predict the likelihood of detector or sprinkler activation. Impingement point details, if important, will not be accurately captured by the standard turbulence model. For smoke-movement problems, a six-flux radiation model is normally adequate. However, for boundary heat-transfer predictions, a more sophisticated model such as the discrete transfer method should be considered.Ensure that ‘free’ boundaries are chosen carefully. A free pressure boundary should be far enough from any ventilation openings so as not to affect flows through them. Avoid steep pressure gradients near the free pressure boundary and ensure that simulations are reasonably insensitive to the boundary position.Check that the predictions of the fire source make sense. Anything higher than 2500 °C must be incorrect due to an erroneous source specification, and anything higher than 1300 °C in the open or 1400 °C inside an enclosure should be examined closely. (Note that these numbers are not exact, and are included here for guidance purposes to check if the CFD solution is physically realistic.) Compare the characteristic properties of a fire (eg flame temperature, flame height, plume entrainment, upper layer temperature, ceiling jet properties) with semi-empirical correlations.

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