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Dr. Andrej HorvatIntelligent Fluid Solutions Ltd.
Ljubljana, Slovenia
17 January, 2008
Computational Models for
Prediction of Fire Behaviour Computational Models for
Prediction of Fire Behaviour
2
IFSIFS 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: [email protected]
Web: www.intelligentfluidsolutions.co.uk
Contact information
3
IFSIFS 1995, Dipl. -Ing. Mech. Eng. (Process Tech.)
University of Maribor
1998, M.Sc. Nuclear Eng.
University of Ljubljana
2001, Ph.D. Nuclear Eng. University of Ljubljana
2002, M.Sc. Mech. Eng. (Fluid Mechanics & Heat Transfer) University of California, Los Angeles
Personal information
4
IFSIFSMore 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
5
IFSIFSAs well as CFD, experiences also in:
Experimental methods
QA procedures
Standardisation and technical regulations
Commercialisation of technical expertise and software products
Personal information
6
IFSIFS 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
7
IFSIFS 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
Contents
8
IFSIFS 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 cost and 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)
Some basic thoughts …
9
IFSIFS
Overview of fluid dynamics
transport equations
10
IFSIFS Transport equations
The continuum assumption
- A control volume has to contain a large number of particles (atoms or molecules): Knudsen number << 1.0
- At equal distribution of particles (atoms or molecules) flow quantities remain unchanged despite of changes in location and size of a control volume
11
IFSIFS Transport equations
Eulerian and Lagrangian description
Eulerian description – transport equations for mass, momentum and energy are written for a (stationary) control volume
Lagrangian description – transport equations for mass, momentum and energy are written for a moving material particle
12
IFSIFS Transport of mass and composition
Transport of momentum
Transport of energy
Transport equations
13
IFSIFS Transport equations
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
Lagrangian formulation is basis for modelling of particle dynamics: bubbles, droplets (sprinklers), solid particles (dust) etc.
14
IFSIFS Transport equations
Droplets trajectories from sprinklers (left), gas temperature field during fire suppression (right)
15
IFSIFS Transport equations
Eulerian formulation of mass transport equation
integral form differential (weak) form
The equation also appears in the following forms
non-conservative form
change of mass in a control vol.
flux difference(convection)
~ 0
in incompressible fluid flow
16
IFSIFS Eulerian formulation of mass fraction transport equation
(general form)
Transport equations
change of mass of a component in a control vol.
flux difference
(convection)
diffusive mass flow
17
IFSIFS Transport equations
Eulerian formulation of momentum equation
change of momentum in a control vol. flux difference
(convection)
volumetric force
pressure force
viscous force
(diffusion)
18
IFSIFSTransport equations
Eulerian formulation of energy transport equation
change of internal energy in a control vol.
flux difference
(convection)
deformation work
diffusive heat flow
19
IFSIFS The following physical laws and terms also need to be
included
- Newton's viscosity law - Fourier's law of heat conduction- Fick's law of mass transfer
- Sources and sinks due to thermal radiation, chemical reactions etc.
Transport equations
diffusive terms -flux is a linear function of a gradient
20
IFSIFS Transport of mass and composition
Transport of momentum
Transport of energy
Transport equations
21
IFSIFS Transport equations
Lagrangian formulation is simpler
- equation of the particle location
- mass conservation eq. for a particle
- momentum conservation eq. for a particle
volumetric forces
drag lift
22
IFSIFS Transport equations
- thermal energy conservation eq. for a particle
Conservation equations of Lagrangian model need to be solved for each representative particle
thermal radiation
convection latent heat
23
IFSIFSThermal radiation
s
I(s) I(s+ds)
dA
Ie Is
Transport equations
in-scatteringchange of radiationintensity
absorption and
out-scattering
emission
24
IFSIFS 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-scatteringchange of radiationintensity
absorption and
out-scattering
emission
25
IFSIFS
Averaging and simplification
of transport equations
26
IFSIFSAveraging 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 on density of the numerical grid, and in transient cases, also on the size of the integration time-step
Averaging and simplification 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
27
IFSIFSAveraging 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
IFSIFS
Kolmogorov scale is (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
t,xht,xht,xhd,xhtGt,xh
t,x'h t,xht,xh d t,h xGt,xh
Averaging and simplification of transport equations
29
IFSIFS
Transport equation variables can be decomposed onto a filtered (averaged) part and a residual (fluctuation)
Filtered (averaged) transport equations
sources and sinks represent a separate problem and require additional models
- turbulent stresses- Reynolds stresses- subgrid stressesturbulent heat fluxes
turbulent mass fluxes
Averaging and simplification of transport equations
30
IFSIFS
Turbulent stresses
Transport equation
- the equation is not solvable due to the higher order product
- all turbulence models include at least some of the terms of this equation (at least the generation and the dissipation term)
turbulence generation
turbulence dissipation
higher order product
Averaging and simplification of transport equations
31
IFSIFS
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
generation
dissipation
higher order product
Averaging and simplification of transport equations
32
IFSIFS
Turbulent heat fluxes due 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
33
IFSIFS
Buoyancy induced flow over a heat source (Gr=10e10); inert model of a fire
Averaging and simplification of transport equations
34
IFSIFS
LES model; instantaneous temperature field
(a)
Averaging and simplification of transport equations
35
IFSIFS
(a) a) b)
Temperature field comparison: a) steady-state RANS model, b) averaged LES model results
Averaging and simplification of transport equations
36
IFSIFS
(a) a) b)
Comparison of instantaneous mass fraction in a gravity current : a) transient RANS model, b) LES model
Averaging and simplification of transport equations
37
IFSIFS
Additional simplifications
- flow can be modelled as a steady-state case the solution is a result of force, energy and mass flow balance taking 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 transfer is modelled as a simple sink of thermal energy FDS takes 35% of thermal energy
- control volumes can be so large that continuity of flow properties is not preserved zone models
Averaging and simplification of transport equations
38
IFSIFS
Zone models
39
IFSIFS 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 models take 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
IFSIFS 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)
Qin (konv)Qout (konv+rad)
mout minmf , Hf
pg , Tg , mg , vg
41
IFSIFS One-zone and two-zone models
- two-zone models can be used for evaluation of a localised fire before flashover
- a room is separated onto different zone, most often onto an upper and lower zone, a fire and buoyant flow of gases above the fire
- conditions are uniform and constant in each zone
Zone models
Qw (konv+rad)
Qin (konv)
QU,out (konv+rad)
mU,out
mL,out
mf , Hf
spodnja conapL,g , TL,g , mL,g , vL,g
zgornja conapU,g , TU,g , mU,g , vU,g
mL,in
QL,out (konv+rad)
42
IFSIFS 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
IFSIFS
Field models
44
IFSIFS Numerical grid and discretisation of transport equations
- analytical solutions of transport equations are known only for few very simple cases
- for most real world cases, one needs to use numerical methods and 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 called discretisation. The following methods are used: finite difference method, finite volume method, finite element method and boundary element method (and different hybrid methods)
Field models
45
IFSIFSNumerical grid and discretisation of transport equations
- simple example of discretisation
- many different discretisation schemes exist; they can be divided onto conservative and non-conservative schemes (linked to the discrete form of the convection term)
Field models
46
IFSIFS Numerical grid and discretisation of transport equations
- non-conservative schemes represent a linear form and therefore they are more stable and numerically better manageable
- non-conservative schemes do 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
IFSIFS Numerical grid and discretisation of transport equations
- quality of numerical discretisation is defined with discrepancy between a numerical approximation and an analytical solution
- error is closely link to the order of discretisation
Field models
1st order truncation (~x)
48
IFSIFS 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: dissipation and dispersion
Field models
49
IFSIFS 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 also higher order schemes (ENO, WENO etc.) but their use is limited on structured numerical meshes
Field models
50
IFSIFS Numerical grid and discretisation of transport equations
- connection matrix and location of neighbouring grid nodes defines two types of numerical grid: structured and unstructured numerical grid
structured grid unstructured grid
Field models
k k+3 k+9
k+1k+2
k+7 k+5
i, j
i+1, j i-1, j
i, j+1 i-1, j+1
i-1, j-1 i, j-1 i+1, j-1
i+1, j+1
k+4
k+6
51
IFSIFS Numerical grid and discretisation of transport equations
- unstructured grids raise a possibility of arbitrary orientation and form of control volumes and therefore offer larger geometrical flexibility
- all modern simulation packages (CFX, Fluent, Star-CD) are based on the unstructured grid arrangement
Field models
52
IFSIFS Numerical grid and discretisation of transport equations
Field models
- flame above a burner
- automatic refinement of unstructured numerical grid
- start with 44,800 control volumes; 3 stages of refinement which leads to 150,000 cont. volumes
- refinement criteria - velocity and temperature gradients
53
IFSIFS
Turbulence
models
54
IFSIFS
Turbulence models
laminar flow
transitional flow
turbulent flow
van Dyke, 1965
55
IFSIFSTurbulence models introduce additional (physically related)
diffusion to a numerical simulation
This enables :
- RANS models to use a larger time step (Δt >> Kolmogorov time scale) or even steady-state simulation
- LES models to use less dense (smaller) numerical grid (Δx > Kolmogorov length scale)
The selection of the turbulence model influences the distribution of the simulated flow fundamentally and hence that of the flow variables (velocity, temperature, heat flow, composition etc)
Turbulence models
56
IFSIFS In general 2 kinds of averaging (filtering) exist, which
leads to 2 families of turbulence models:
- filtering over a spatial interval Large Eddy Simulation (LES) models
- filtering over a time interval Reynolds Averaged Navier-Stokes (RANS) models: k-epsilon model, SST model, Reynolds Stress models etc
For RANS models, size of the averaging time interval is not known or given (statistical average of experimental data)
For LES models, size of the filter or the spatial averaging interval is a basic input parameter (in most case it is equal to grid spacing)
Turbulence models
57
IFSIFSTurbulence models
Reynolds Averaged Navier-Stokes (RANS) models
For two-equation models (e.g. k-epsilon, k-omega or SST), 2 additional transport equations need to be solved:
- for kinetic energy of turbulent fluctuations
- for dissipation of turbulent fluctuations
or
- for frequency of turbulent fluctuations
58
IFSIFS Reynolds Averaged Navier-Stokes (RANS) models
k-epsilon model
production (source) term
Turbulence models
convection production (source) term diffusion destruction (sink) term
59
IFSIFS Reynolds Averaged Navier-Stokes (RANS) models
- model parameters are usually defined from experimental data e.g. dissipation of grid generated turbulence or flow in a channel
- from the calculated values of k in , eddy viscosity is defined as
- from eddy viscosity, Reynolds stresses, turbulent heat and mass fluxes are obtained
Turbulence models
C C1 C2 C3 k Prt
0.09 1.44 1.92 1.0 1.0 1.3 0.9
60
IFSIFSTurbulence models
Reynolds Averaged Navier-Stokes (RANS) models
- transport equation for k is derived directly from the transport equations for Reynolds stresses
- transport equation for is empirical
- these equations have a common form: source and sink term, convection and diffusion term
- the rest of the terms are model specific and they can be numerically and computationally very demanding
- definition and implementation of boundary conditions is different even for the same turbulence model between different software vendors
61
IFSIFSTurbulence models
Reynolds Averaged Navier-Stokes (RANS) models
For Reynolds Stress (RS) model, 7 additional transport equations need to be solved:
- for 6 components of Reynolds stress tensor
- for dissipation of turbulent fluctuations
or
- for frequency of turbulent fluctuations
62
IFSIFS Reynolds Averaged Navier-Stokes (RANS) models
Reynolds stress model
generation (source) term
Turbulence models
convection generation (source) term
diffusion term destruction (sink) term
pressure-velocity fluctuation term
63
IFSIFS Reynolds Averaged Navier-Stokes (RANS) models
- Reynolds stress models calculate turbulent stresses directly introduction of eddy viscosity is not needed
- includes the pressure-velocity fluctuation term
- describes anisotropic turbulent behaviour
- computationally more demanding than the two-equation models
- due to higher order terms (linear and non-linear), RS models are numerically more complex (convergence)
Turbulence models
64
IFSIFS Turbulence models
Large Eddy Simulation (LES) models
- Large Eddy Simulation (LES) models are based on spatial filtering (averaging)
- many different forms of the filter exist, but most common is "top hat" filter (simple geometrical averaging)
- the size of the filter is based on grid node spacing
Basic assumption of LES methodology:
Size of the used filter is so small that the averaged flow structures do no influence large structures, which contain most of the energy.
These small structures are being deformed, disintegrated onto even smaller structures until they do not dissipate due to viscosity (kinetic energy thermal energy).
65
IFSIFS Turbulence models
Large Eddy Simulation (LES) models
- required size of flow structures for LES modelling
- these structures are in the turbulence inertial subrange and they are isotropic
- on this level, turbulence production is of the same size as turbulence dissipation
66
IFSIFS Turbulence models
Large Eddy Simulation (LES) models
- eddy (turbulent) viscosity is defined as
where
- using the definition of turbulent (subgrid) stresses
and turbulent fluxes
the expression for turbulent viscosity can be written as
where the contribution due to buoyancy is
grid spacing
67
IFSIFS Turbulence models
Large Eddy Simulation (LES) models
- presented Smagorinsky model is the simplest from LES models
- it requires knowledge of empirical parameter Cs, which is not constant for all flow conditions
- newer, dynamic LES models calculates Cs locally - the procedure demands introduction of the secondary filter
- LES models demand much denser (larger) numerical grid
- they are used for transient simulations
- to obtain average flow characteristics, we need to perform statistical averaging over the simulated time interval
68
IFSIFS Turbulence models
Comparison of turbulence models
25 50 75 100
z/R
1
2
3
4
5
678
wc(
R/F
0)1
/3
k-e (Gr = 10 10)k-e N&B (Gr = 10 10)RNG k-e (Gr = 10 10)S S T (Gr = 10 10)S S G (Gr = 10 10)LES (Gr = 10 10)Rous e e t al. (1952)S habbir and Ge orge (1994)
25 50 75 100
z/R
10 -2
10 -1
bc(
R5/F
02)1
/3
k-e (Gr = 10 10)k-e N&B (Gr = 10 10)RNG k-e (Gr = 10 10)S S T (Gr = 10 10)S S G (Gr = 10 10)LES (Gr = 10 10)Rous e e t al. (1952)S habbir and Ge orge (1994)
a) b)
Buoyant flow over a heat source: a) velocity, b) temperature*
69
IFSIFS
Combustion
models
70
IFSIFSCombustion models
Chen et al., 1988
Grinstein,Kailasanath, 1992
71
IFSIFS Combustion can be modelled with heat sources - information on chemical composition is lost - thermal loading is usually under-estimated
Combustion modelling contains
- solving transport equations for composition
- chemical balance equation
- reaction rate model
Modelling approach dictates the number of additional transport equations required
Combustion models
72
IFSIFS Modelling of composition requires solving n-1 transport
equations for mixture components – mass or molar (volume) fractions
Chemical balance equation can be written as
or
Combustion models
73
IFSIFS Reaction source term is defined as
or for multiple reactions
where R or Rk is a reaction rate
Reaction rate is determined using different models
- Constant burning (reaction) velocity - Eddy break-up model and Eddy dissipation model - Finite rate chemistry model - Flamelet model - Burning velocity model
Combustion models
74
IFSIFS Constant burning velocity sL
speed of flame front propagation is larger due to expansion
- values are experimentally determined for ideal conditions - limits due reaction kinetics and fluid mechanics are not
taken into account
- source/sink in mass fraction transport equation
- source/sink in energy transport equation - expressions for sL usually include additional models
Combustion models
75
IFSIFS Eddy break-up model and Eddy dissipation model
- is a well established model - based on the assumption that the reaction is much faster
than the transport processes in flow - reaction rate depends on mixing rate of reactants in
turbulent flow
- Eddy break-up model reaction rate
- Eddy dissipation model reaction rate
Combustion models
76
IFSIFS Eddy break-up model and Eddy dissipation model
- typical values of model coefficients CA = 4 in CB = 0.5
- the model can be used for simple reactions (one- and two-step combustion)
- in general, it cannot be used for prediction of products of complex chemical processes (NO, CO, SOx, etc)
- the use can be extended by adding different reaction rate limiters → extinction due to turbulence, low temperature, chemical time scale etc.
Combustion models
77
IFSIFS Backdraft simulation
Combustion models
78
IFSIFS Finite rate chemistry model
- it is applicable when a chemical reaction rate is slow or comparable with turbulent mixing
- reaction kinetics must be known
- for each additional component, the component molar concentration I needs to be multiplied with the product
- for each additional reaction the same expression is added
Combustion models
79
IFSIFS Finite rate chemistry model
- the model is numerically demanding due to exponential terms
- often the model is used in combination with the Eddy dissipation model
Combustion models
80
IFSIFS Flamelet model
- describes interaction of reaction kinetics with turbulent structures for a fast reaction (high Damköhler number)
- basic assumption is that combustion is taking place in thin sheets - flamelets
- turbulent flame is an ensemble of laminar flamelets
- the model gives a detailed picture of chemical composition - resolution of small length and time scales of the flow is not needed
- the model is also known as "Mixed-is-burnt" - large difference between various implementations of the model
Combustion models
81
IFSIFS Flamelet model
- the model is only applicable for two-feed systems (fuel and oxidiser)
- it is based on definition of a mixture fraction
or
Combustion models
Z kg/s fuel
mešalni proces
1 kg/s mixture
1-Z kg/s oxidiser
Z is 1 in a fuel stream, 0 in an oxidiser stream
A
BM
82
IFSIFS
- conserved property often used in the mixture fraction definition
- for a simple chemical reaction
the stoihiometric ratio is
Combustion models
Flamelet model
83
IFSIFS Flamelet model
- Shvab-Zel'dovich variable
- the conditions in vicinity of flamelets are described with the respect to Z; Z=Zst is a surface with the stoihiometric conditions
- transport equations are rewritten with Z dependencies; conditions are one-dimensional ξ(Z) , T(Z) etc. - for limited cases, the simplified equations can be solve
analytically
Combustion models
84
IFSIFS Flamelet model
- numerical implementations of the model differ significantly
- for turbulent flow, we need to solve an additional transport equation for mixture fraction Z
- and a transport equation for variation of mixture fraction Z"
Combustion models
85
IFSIFS Flamelet model
- composition is calculated from preloaded libraries
- is the scalar dissipation rate - it increases with stresses (stretching of a flame front) and decreases with diffusion. - at critical value of flame extinguishes
Combustion models
dZZPDFZ~jj
1
0
ddZPDFZPDF,Z~jj
1
0 0
these PDFs are tabulated for different fuel, oxidiser, pressure and temperature
86
IFSIFSCombustion models
Ferreira, Schlatter, 1995
Flamelet model
87
IFSIFS Burning velocity model
- it is used for pre-mixed or partially pre-mixed combustion
- contains: a) model of the reaction progress: Burning Velocity Model (BVM) or Turbulent Flame Closure (TFC)
b) model for composition of the reacting mixture: Flamelet model
- definition of the reaction progress variable c, where c = 0 corresponds to the fresh mixture, and c = 1 to combustion products
Combustion models
88
IFSIFSBurning velocity model
Combustion models
Oxidiser
Fuel
Products
Temperature
x
T, j
Flame location
Preheating Oxidation layer
Reaction layer O()
mm5010 .....lF mm01.0l
89
IFSIFS Burning velocity model
- additional transport equation for the reaction progress variable
- source/sink due to combustion is defined as
- better results by solving the transport equation for weighted reaction progress variable
Combustion models
source term
modelling of the turbulent burning velocity
90
IFSIFS Burning velocity model
- it is suitable for a single step reaction
- applicable for fast chemistry conditions (Da >> 1)
- a thin reaction zone assumption
- fresh gases and products need to be separated
Combustion models
91
IFSIFS
Thermal radiation
models
92
IFSIFS It is a very important heat transfer mechanism during
fire In fire simulations, thermal radiation should not be
neglectedThe simplest approach is to reduce the heat release
rate of a fire (35% reduction in FDS)Modelling of thermal radiation - solving transport
equation for radiation intensity
Thermal radiation
in-scatteringchange of intensity
absorption and scattering
emission
93
IFSIFSRadiation intensity is used for definition of a source/sink
in the energy transport equation and radiation wall heat fluxes
Energy spectrum of blackbody radiation
- frequency c - speed of light n - refraction index h - Planck's constant kB - Boltzmann's constant
integration over the whole spectrum
Thermal radiation
94
IFSIFS Models
- Rosseland (primitive model, for optical thick systems, additional
diffusion term in the energy transport equation)
- P1 (strongly simplified radiation transport equation - solution of an additional Laplace equation is required)
- Discrete Transfer (modern deterministic model, assumes isotropic scattering, reasonably homogeneous properties)
- Monte Carlo (modern statistical model, computationally
demanding)
Thermal radiation
95
IFSIFS Discrete Transfer
- modern deterministic model - assumes isotropic scattering, homogeneous gas properties - each wall cell works as a radiating surface that emits rays through the surrounding space (separated onto multiple solid
angles)- radiation intensity is integrated along each ray between the walls of the simulation domain
- source/sink in the energy transport equation
Thermal radiation
96
IFSIFS Monte Carlo
- it assumes that the radiation intensity is proportional to (differential angular) flux of photons
- radiation field can be modelled as a "photon gas"
- absorption constant Ka is the probability per unit length of photon absorption at a given frequency
- average radiation intensity I is proportional to the photon travelling distance in a unit volume and time
- radiation heat flux qrad is proportional to the number of photon incidents on the surface in a unit time
- accuracy of the numerical simulation depends on the number of used "photons"
Thermal radiation
97
IFSIFS These radiation methods can be used:
- for averaged radiation spectrum - grey gas
- for gas mixture, which can be separated onto multiple grey gases (such grey gas is just a modelling concept)
- for individual frequency bands; physical parameters are very different for each band
Thermal radiation
98
IFSIFS Flashover simulation
Thermal radiation
99
IFSIFS
Conclusions
100
IFSIFS The seminar gave a short (but demanding) overview of
fluid mechanics and heat transfer theory that is relevant for fire simulations
All current commercial CFD software packages (ANSYS-CFX, ANSYS-Fluent, Star-CD, Flow3D, CFDRC, AVL Fire) contain most of the shown models and methods:
- they are based on the finite volume or the finite element method and they use transport equations in their conservative form
- numerical grid is unstructured for greater geometrical flexibility
- open-source computational packages exist and are freely accessible (FDS, OpenFoam, SmartFire, Sophie)
Conclusions
101
IFSIFS I would like to remind you to the project "Methodology for
selection and use of fire models in preparation of fire safety studies, and for intervention groups", sponsored by Ministry of Defence, R. of Slovenia, which contains an overview of functionalities that are offered in commercial software products
Conclusions
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IFSIFSAcknowledgement
I would like to thank to our hosts and especially to Aleš Jug
I would like to thank to ANSYS Europe Ltd. (UK) who permitted access to some of the graphical material