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

1. ComputationalModelsfor Prediction of Fire Behaviour Dr. Andrej Horvat Intelligent Fluid Solutions Ltd. Ljubljana, Slovenia 17 January, 2008

2. 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

3. 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

4. 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)

5. Personal information As well as CFD, experiences also in: • Experimental methods • QA procedures • Standardisation and technical regulations • Commercialisation of technical expertise and software products

6. 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

7. 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

8. 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)

9. Overview of fluid dynamics transport equations

10. 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

11. 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

12. Transport equations • Transport of mass and composition • Transport of momentum • Transport of energy

13. 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

14. Transport equations Droplets trajectoriesfrom sprinklers (left), gas temperature field during fire suppression (right)

15. 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

16. 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

17. Eulerian formulation of momentum equation Transport equations viscous force (diffusion) change of momentum in a control vol. volumetric force pressure force flux difference (convection)

18. Eulerian formulation of energy transport equation Transport equations change of internal energy in a control vol. flux difference (convection) deformation work diffusive heat flow

19. 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

20. Transport equations • Transport of mass and composition • Transport of momentum • Transport of energy

21. 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

22. - 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

23. Thermal radiation Transport equations s I(s) I(s+ds) dA Ie Is change of radiation intensity absorption and out-scattering emission in-scattering

24. 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

25. Averaging and simplification of transport equations

26. 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

27. 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 ,

28. 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

29. 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

30. 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

31. 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

32. 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

33. Averaging and simplification of transport equations Buoyancy induced flow over a heat source (Gr=10e10); inert model of a fire

34. Averaging and simplification of transport equations (a) LES model; instantaneous temperature field (b)

35. Averaging and simplification of transport equations a) b) Temperature field comparison: a) steady-state RANS model, b) averaged LES model results (a) (b)

36. 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)

37. 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

38. Zone models

39. 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

40. 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

41. 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)

42. 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

43. Field models

44. 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

45. 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

46. 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

47. 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)

48. 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

49. 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

50. 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