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D r. Andrej Horvat Intelligent Fluid Solutions Ltd. Ljubljana , Slovenia 17 January, 200 8

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## D r. Andrej Horvat Intelligent Fluid Solutions Ltd. Ljubljana , Slovenia 17 January, 200 8

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**ComputationalModelsfor Prediction of Fire Behaviour**Dr. Andrej Horvat Intelligent Fluid Solutions Ltd. Ljubljana, Slovenia 17 January, 2008**Contact information**Andrej Horvat Intelligent Fluid Solution Ltd. 127 Crookston Road, London, SE9 1YF, United Kingdom Tel./Fax: +44 (0)1235 819 729 Mobile: +44 (0)78 33 55 63 73 E-mail: andrej.horvat@intelligentfluidsolutions.co.uk Web: www.intelligentfluidsolutions.co.uk**Personal information**• 1995, Dipl. -Ing. Mech. Eng. (Process Tech.) Universityof Maribor • 1998, M.Sc. Nuclear Eng. Universityof Ljubljana • 2001, Ph.D. Nuclear Eng. Universityof Ljubljana • 2002, M.Sc. Mech. Eng. (Fluid Mechanics & Heat Transfer) University of California, Los Angeles**Personal information**More than 10 years of intensive CFD related experience: • R&D of numerical methods and their implementation (convection schemes, LES methods, semi-analytical methods, Reynolds Stress models) • Design analysis (large heat exchangers, small heat sinks, burners, drilling equip., flash furnaces, submersibles) • Fire prediction and suppression (backdraft, flashover, marine environment, gas releases, determination of evacuation criteria) • Safety calculations for nuclear and oil industry (water hammer, PSA methods, severe accidents scenarios, pollution dispersion)**Personal information**As well as CFD, experiences also in: • Experimental methods • QA procedures • Standardisation and technical regulations • Commercialisation of technical expertise and software products**Contents**• Overview of fluid dynamics transport equations - transport of mass, momentum, energy and composition - influence of convection, diffusion, volumetric (buoyancy) force - transport equation for thermal radiation • Averaging and simplification of transport equations - spatial averaging - time averaging - influence of averaging on zone and field models • Zone models - basics of zone models (1 and 2 zone models) - advantages and disadvantages**Contents**• Field models - numerical mesh and discretisation of transport equations - turbulence models (k-epsilon, k-omega, Reynolds stress, LES) - combustion models (mixture fraction, eddy dissipation, flamelet) - thermal radiation models (discrete transfer, Monte Carlo) - examples of use • Conclusions - software packages • Examples - diffusion flame - fire in an enclosure - fire in a tunnel**Some basic thoughts …**• Today, CFD methods are well established tools that help in design, prototyping, testing and analysis • The motivation for development of modelling methods (not only CFD) is to reduce costand time of product development, and to improve efficiency and safety of existing products and installations • Verification and validation of modelling approaches by comparing computed results with experimental data are necessary • Nevertheless, in some cases CFD is the only viable research and design tool (e.g. hypersonic flows in rarefied atmosphere)**Overview of fluid dynamics**transport equations**The continuum assumption**Transport equations - A control volume has to contain a largenumber of particles(atoms or molecules): Knudsen number << 1.0 - At equal distribution of particles (atoms or molecules) flow quantitiesremain unchangeddespite of changes in location and size of a control volume**Eulerian andLagrangian description**Transport equations • Eulerian description– transport equations formass, momentumand energy are written fora (stationary) control volume • Lagrangian description– transport equations for mass, momentum and energy are written for a moving material particle**Transport equations**• Transport of mass and composition • Transport of momentum • Transport of energy**Majority of the numerical modelling in fluid mechanics is**based on Eulerian formulation of transport equations • Using the Eulerian formulation, each physical quantity is described as a mathematical field. Therefore, these models are also named field models • Lagrangianformulationis basis for modelling of particle dynamics: bubbles, droplets (sprinklers), solid particles (dust) etc. Transport equations**Transport equations**Droplets trajectoriesfrom sprinklers (left), gas temperature field during fire suppression (right)**Eulerian formulation of mass transport equation**• integral form differential (weak) form • The equation also appears in the following forms • non-conservative form Transport equations flux difference (convection) change of massin a control vol. ~ 0 in incompressible fluid flow**Transport equations**• Eulerian formulation of mass fraction transport equation (general form) change of mass of a component in a control vol. flux difference (convection) diffusive mass flow**Eulerian formulation of momentum equation**Transport equations viscous force (diffusion) change of momentum in a control vol. volumetric force pressure force flux difference (convection)**Eulerian formulation of energy transport equation**Transport equations change of internal energy in a control vol. flux difference (convection) deformation work diffusive heat flow**Transport equations**• The following physical laws and terms also need to be included - Newton's viscosity law • Fourier'slaw of heat conduction • Fick's law of mass transfer • Sources and sinksdue to thermal radiation, chemical reactions etc. diffusive terms - flux is a linear function of a gradient**Transport equations**• Transport of mass and composition • Transport of momentum • Transport of energy**Lagrangianformulationis simpler**- equation of the particle location - mass conservation eq. for a particle - momentum conservation eq. for a particle Transport equations drag lift volumetric forces**- thermal energy conservation eq. for a particle**Conservation equations of Lagrangian model need to be solved for each representative particle Transport equations convection latent heat thermal radiation**Thermal radiation**Transport equations s I(s) I(s+ds) dA Ie Is change of radiation intensity absorption and out-scattering emission in-scattering**Thermal radiation**Equations describing thermal radiation are much more complicated - spectral dependency of material properties - angular (directional) dependence of the radiation transport Transport equations in-scattering change of radiation intensity absorption and out-scattering emission**Averaging and simplification**of transport equations**The presented set of transport equations is analytically**unsolvable for the majority of cases • Success of a numerical solving procedure is based ondensity of the numerical grid, and in transient cases, also on the size of the integration time-step • Averagingandsimplification of transport equations help (and improve) solving the system of equations: • - derivation of averaged transport equations for turbulent flow simulation • -derivation of integral (zone) models Averaging and simplification of transport equations**Averaging and simplification of transport equations**• Averaging and filtering The largest flow structures can occupy the whole flow field, whereas the smallest vortices have the size of Kolmogorov scale ,vi , p, h w ,**Averaging and simplification of transport equations**• Kolmogorov scaleis (for most cases) too small to be captured with a numerical grid • Therefore, the transport equations have to be filtered (averaged) over: - spatial interval Large Eddy Simulation (LES) methods • - time interval k-epsilon model, SST model, • Reynolds stress models**Averaging and simplification of transport equations**• Transport equation variables can be decomposed onto a filtered (averaged) partanda residual (fluctuation) • Filtered (averaged) transport equations turbulent mass fluxes sources and sinks represent a separate problem and require additional models - turbulent stresses - Reynolds stresses - subgrid stresses turbulent heat fluxes**Averaging and simplification of transport equations**• Turbulent stresses • Transport equation - the equation is not solvable due to the higher order product - all turbulence models include at least some of the termsof this equation (at least the generation and the dissipation term) higher order product turbulence generation turbulence dissipation**Averaging and simplification of transport equations**• Turbulent heat and mass fluxes • Transport equation - the equation is not solvable due to the higher order product - most of the turbulence models do not take into account the equation higher order product generation dissipation**Averaging and simplification of transport equations**• Turbulent heat fluxesdue to thermal radiation - little is known and published on the subject - majority of models do not include this contribution - radiation heat flow due to turbulence**Averaging and simplification of transport equations**Buoyancy induced flow over a heat source (Gr=10e10); inert model of a fire**Averaging and simplification of transport equations**(a) LES model; instantaneous temperature field (b)**Averaging and simplification of transport equations**a) b) Temperature field comparison: a) steady-state RANS model, b) averaged LES model results (a) (b)**Averaging and simplification of transport equations**a) b) Comparison of instantaneousmass fraction in a gravity current : a) transient RANS model, b) LES model (a) (b)**Averaging and simplification of transport equations**• Additional simplifications - flow can be modelled as a steady-state case the solution is a result of force, energy and mass flow balancetaking into consideration sources and sinks - fire can be modelled as a simple heat source inert models; do not need to solve transport equations for composition - thermal radiation heat transferis modelled as asimple sinkof thermal energy FDStakes 35% of thermal energy - control volumescan be solarge that continuity of flow properties is not preserved zone models**Basics**- theoretical base of zone model is conservation of mass and energy in a space separated onto zones - thermodynamic conditions in a zone are constant; in fields models the conditions are constant in a control volume - zone modelstake into account released heat due to combustion of flammable materials, buoyant flows as a consequence of fire, mass flow, smoke dynamics and gas temperature - zone models are based on certain empirical assumptions - in general, they can be divided onto one- and two-zone models Zone models**One-zone and two-zone models**- one-zone models can be used only for assessment of a fully developed fire after flashover - in such conditions, a valid approximation is that the gas temperature, density, internal energy and pressure are (more or less)constant across the room Zone models Qw (konv+rad) Qout (konv+rad) Qin (konv) pg , Tg , mg , vg mout min mf , Hf**One-zone and two-zone models**- two-zone modelscan be used for evaluation of a localised fire before flashover - a room is separated onto different zone, most often onto an upperandlower zone, afireandbuoyant flowof gases above the fire - conditions are uniform and constant in each zone Zone models QU,out (konv+rad) Qw (konv+rad) zgornja cona pU,g , TU,g , mU,g , vU,g mU,out spodnja cona pL,g , TL,g , mL,g , vL,g mL,out mL,in mf , Hf QL,out (konv+rad) Qin (konv)**Advantages and disadvantages of zone models**- in zone models, ordinary differential equations describe the conditions more easily solvable equations - because of small number of zones, the models are fast - simple setup of different arrangement of spaces as well as of size and location of openings - these models can be used only in the frame of theoretical assumptions that they are based on - they cannot be used to obtain a detailed picture of flow and thermal conditions - these models are limited to the geometrical arrangements that they can describe Zone models**Numerical grid and discretisation of transport equations**- analytical solutionsof transport equations are known only for few very simple cases - for most real world cases,one needs to use numerical methodsand algorithms, which transform partial differential equations to a series of algebraic equations - each discrete point in time and space corresponds to an equation, which connects a grid point with its neighbours - The process is calleddiscretisation.The following methods areused: finite difference method, finite volume method, finite element methodandboundary element method (and different hybrid methods) Field models**Numerical grid and discretisation of transport equations**- simple example of discretisation - many different discretisation schemes exist; they can be divided ontoconservativeandnon-conservative schemes (linked to the discrete form of the convection term) Field models**Numerical grid and discretisation of transport equations**- non-conservative schemesrepresent a linear form and therefore they are more stable and numericallybetter manageable - non-conservative schemesdo not conserve transported quantities, which can lead to time-shift of a numerical solution Field models time-shift due to a non-conservative scheme**Numerical grid and discretisation of transport equations**- qualityof numerical discretisation is defined with discrepancy between a numerical approximation and an analytical solution - error is closely link to the orderof discretisation Field models 1st order truncation (~x)**Numerical grid and discretisation of transport equations**- higher order methods lead to lower truncation errors, but more neighbouring nodes are needed to define a derivative for a discretised transport equation - two types of numerical error: dissipationanddispersion Field models**Numerical grid and discretisation of transport equations**- during the discretisation process most of the attention goes to the convection terms - the 1st order methods have dissipative truncation error, whereas the 2nd order methods introduce numerical dispersion - today's hybrid methods are a combination of 1st and 2nd order accurate schemes. These methods switch automatically from a 2nd order to a 1st order scheme near discontinuities to damp oscillations (TVD schemes) - there are alsohigher order schemes (ENO, WENO etc.) but their use is limited on structured numerical meshes Field models**i-1, j+1**i, j+1 i+1, j+1 i, j i-1, j i+1, j i, j-1 i+1, j-1 i-1, j-1 • Numerical grid and discretisation of transport equations - connection matrix and location of neighbouring grid nodes defines two types of numerical grid: structured and unstructurednumerical grid structured grid unstructuredgrid Field models k+2 k+1 k+6 k k+9 k+3 k+5 k+7 k+4