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Fire Dynamics Simulator (Version 5) User's Guide

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1. 4 T r r 4 3 5 surf mass vent char cart fuel 35 surf mass vent char cart gas a 2 51 Me g 21 onm 4 E rra N e 15r At J P od lr lr p Expected of 0 5 Gaseous J 0 54 2 Expected nid solid aa Gaseous Fuel PL 0 L L n 0 lr L L 0 50 100 150 200 0 50 100 Time s Time s 2 _ surf mass vent char cyl fuel 2r surf mass vent char cyl gas E E E Eig E s 1 s 1 e A E eer PAPA 0 5r Pd Expected 0 5 ot Gaseous Expected reina olid Pd 7 Gaseous 0 Gaseous Fuel Pd 0 20 40 60 80 100 0 20 40 60 80 100 Time s Time s 1 5 T T T T 1 5 surf mass vent char spher fuel surf mass vent char spher gas 1 po ew fe E Me amp Elm 0 5r 7 0 5r d 4 P Expected Pid Gaseous d Expected az Exe Solid i rd Gaseous pes ns Sg oli 0 V4 Gaseous Fue ole Solid 0 20 40 60 80 100 0 20 40 60 80 Time s Time s Figure 7 1 Comparison of analytical mass change and simulated mass changes for charring surfaces asso ciated with vents 55 5 4 r r 5 surf mass vent nonchar cart fuel surf mass vent nonchar cart gas 4r 4r 7 aL Ej 3 ran c 3 2 Expected Gaseous m Bp P DL Solid 2 jf p Ganons E 2 Gaseo
2. FDS Back 0 n n i 1 n 0 1 n L F 1 0 5 10 15 20 25 30 0 50 100 150 200 250 300 Time min Time min 150 r r r r r 150 Slab Temperature heat conduction c Slab Temperature heat conduction d o O eo 1007 s 1007 Analytical Front g g Analytical 4 cm E E Analytical Back E 5 Sun a F sol Analytical Front S 50 E e FDS E amp Analytical 4 cm Analytical Back FDS Front FDS 4 cm FDS Back 0 n 1 n 1 1 0 n n 1 0 100 200 300 400 500 600 0 200 400 600 800 Time min Time min Figure 6 1 Comparison of heat conduction calculations with analytical solutions 50 6 2 Temperature Dependent Thermal Properties heat conduction kc This example demonstrates the 1 D heat conduction in cartesian cylindrical and spherical geometries with temperature dependent thermal properties The cartesian solution was computed using HEATING ver sion 7 3 a multi dimensional finite difference general purpose heat transfer model 66 The cylindrical and spherical solutions were computed using a commercial finite element solver ABAQUS The sample of homogenous material is initially at O C and at gt 0 exposed to a gas at 700 C A fixed heat transfer coefficient of 10 W m K is assumed The density of the material is 10000 kg m The conductivity and specific heat are functions of temperature with the following values k 0 0 10 W m K
3. 1 1 de dh os pa 5 dh vap pdv 8 3 Multiplying by mass and noting that the volume V is constant yields dE dH V dp 8 4 The enthalpy decrease of the liquid water droplets is equal to the enthalpy gain of the gas both expressed in kJ minus the pressure increase times the volume in units of kPa and m respectively Finally note that in this example that a water droplet will evaporate until the vapor pressure at the droplet surface is in equilibrium with the vapor pressure in the surrounding air Thus the relative humidity should be equal to 100 46 but since FDS does not currently compute condensation a slight overshoot is not unexpected 69 500 Enthalpy water_evaporation d eee EE d 300 Analytical h gas gt Analytical h_water E FDS h gas 200r FDS h water E 100r ds a Qu SEN EIN Sm 0 1 2 3 4 5 Time s 1 25 Density water_evaporation 1 24 8 1 23 i oD S Ql 222 2 2 caca B 1 22 7 5 i D A 1 21 1 2 Analytical dens FDS dens 1 19 amp 1 T 1 2 3 4 5 Time s 10 Over Pressure water_evaporation 8 E T Es Bopeeu mugs AS SI 4 A 2 Analytical pres FDS pres 0 L L T T 0 1 2 3 4 5 Time s 120 Relative Humidity water_evaporation 100r A MMC a a d 7 e e d S 80
4. FDS density_2 es FDS pressure 2 1 1 n 1 n 1 1 0 1 1 1 1 1 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Time s Time s 40 450 r Temperature isentropic Enthalpy isentropic 35 NCC CC o o H ood adm aie e 1 P d 2 P P d g 30r git iu 1 d E 1 a amp m E i Lc E 400F 2 1 a E 1 2 a 25r 4 a 1 pd 3 1 D d m 1 a di fae 1 d 204 Analytical Temperature k p E Analytical Enthalpy FDS temperature_1 LR FDS enthalpy 1 FDS temperature 2 uo FDS enthalpy 2 15 1 n 1 1 1 350 n n 1 1 1 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Time s Time s Figure 3 15 Density pressure temperature and enthalpy rise due to the injection of nitrogen into a sealed compartment 3 7 3 Gas Injection via a Non Isentropic Process isentropic2 This example checks that if nitrogen is added via an external vent to a sealed compartment with adiabatic i e no heat loss walls that the density pressure and temperature ought to rise to the same values regardless of the time of injection In the two cases 0 2 kg of N are added to a compartment that is 1 m in volume In the first case the injection occurs in 10 s in the second case in 50 s The temperature of the gas in both cases is 500 C It is expected that the pressure p should rise at the rate dp YypuA pa 3 43 dt V 33 where u is the injection velocity and A is the area of the vent The vent area is 0 04 m The density of t
5. Figure 3 9 LES of square channel flow with smooth walls and periodic streamwise boundaries using dynamic Smagorinsky and the Werner Wengle wall model For this image N 32 and the mean pressure drop is dp dx 1 Pa m resulting in Rey 7 5 x 10 and a friction factor of f 0 0128 23 1 0 01 1 0 001 E N 0 0001 10 O oS A N O N gt N 10 10 Figure 3 10 The FDS Moody Chart friction factor f versus Reynolds number Re The solid line for Re lt 2000 is the analytical result for 2D Poiseuille flow f 24 Re The solid lines for Re gt 2000 from the Colebrook equation 3 10 are for turbulent flow at various levels of relative roughness zo H shown on the right axis Stars are DNS results from FDS ata single grid resolution N 64 Symbols are FDS results for 3D LES with dynamic Smagorinsky Black symbols show results for the Werner Wengle wall model at three grid resolutions N 8 16 32 Colored symbols are FDS results for the rough wall cases at different grid resolutions and relative roughnesses as differentiated by the symbol shapes 24 3 5 Analytical Solutions to the Continuity Equation Analytical solutions for primitive flow variables density velocity pressure etc are useful in the develop ment and testing of numerical schemes for computational fluid dynamics CFD For example an analytical solution to the 2D incompressible Navier Stokes NS equations
6. The specification of the fuel mass flux is probably the most commonly used boundary condition for speci fying a fire When the user specifies the HRRPUA heat release rate per unit area FDS divides this input by the heat of combustion for the specified fuel propane by default and uses this values as the specified mass flux m at the VENT This seems simple enough But the problem is complicated by the fact that the total species flux is the sum of the advective and diffusive fluxes oY ri PY qn PD 5 1 where u is the face normal mass average velocity and 0 dn is the gradient normal to the face The velocity is determined from the total mass flux and the density at the face 5 2 Uy The density is computed using old values of the face mass fractions and the face temperature which may be specified or computed depending on choices made by the user The new face mass fraction is then set to satisfy 5 1 The test case below is designed to exercise contributions from both the advective and diffusive terms in this boundary condition In the test case we inject propane into a cube with 1 m vents on all six faces We specify the MASS_FLUX of propane to be 0 0001 kg m s and the temperature of the face of the VENT TMP_FRONT is specified to be 500 C The box is initially filled with air at standard conditions We DUMP a MASS FILE and compare the accumulation of propane with the specified rate The results are shown in Figu
7. plate view factor so ec gow gy ae Rs eR meo re Be b Rowe BE Reo o 4 2 Radiation inside a box radiation in a box 4 3 Radiation from a plane layer radiation plane layer 4 4 Wall Internal Radiation wall internal radiation 4 5 Radiation Emitted by Hot Spheres hot spheres o o 4 6 Radiation Absorbed by Liquid Droplets droplet absorption 5 Species and Combustion 3 Boundary Conditions 152a oe om a DA we a teo aoe ee ed 5 1 1 Specified Mass Flux low_flux_hot_gas_filling 5 2 Fractional Effective Dose FED Device 6 Heat Conduction 6 1 Simple Heat Conduction Through a Solid Slab heat conduction 6 2 Temperature Dependent Thermal Properties heat conduction kc 6 3 Simple Thermocouple Model thermocouples 7 Pyrolysis 7 Mass conservation of pyrolyzed mass surf mass conservation Tl Pyrolysis ta Sold Surface 2 oon S x yog ok a ae 7 1 2 Pyrolysis of Discrete Particles os nce ecs e osos RR 7 2 Development of surface emissivity emissivity 7 3 Enthalpy of solid materials enthalpy lens 7 4 A Simple Two Step Pyrolysis Example two step solid reaction 7 5 Interpreting Bench Scale Measurements 7 5 1 General Theory 4 o 8dR a EIER a Se RM doe d 7 5 2 Using Micro Calorimetry Data cable_11_mece 7 5 3 Using TGA Data
8. 100 200 300 400 500 600 100 200 300 400 500 600 Time s Time s Figure 3 14 The Energy Budget for two simple compartment fire simulations 3 7 2 Gas Injection via an Isentropic Process isentropic This example checks that if nitrogen is added to a sealed compartment with adiabatic i e no heat loss walls that the density pressure and temperature ought to rise according to the ideal gas law for an isentropic process Y Y RS pP o Try qt p 2 7 TM 32 The subscripts 2 and 1 refer to the final and initial state respectively Nitrogen is a diatomic gas for which y 1 4 As an additional check the nitrogen is injected at two different rates such that in case A the injection occurs in 10 s and in case B the injection occurs in 50 s The nitrogen is introduced into the domain via small spheres that do not generate or absorb heat They do not occupy volume either They just inject the nitrogen at a specified rate into the particular grid cell that each occupies 4 x 10 2 5 Density isentropic Pressure isentropic 1 35F J 2 pn ee A A E undici el 1 31 E e e i E E di Gist of P c et o 1 a z 125r s 3 1 P z 1 p Z 1 1 ae 3 1 2 d a a 2 ad E 1 a 12 7 1 y D d 1 15 Analytical Density 05r Pd Analytical Pressure FDS density_1 po 47 FDS pressure 1
9. PsCs at r or AY x ds PsCs ot r2 dr r S dr ds FDS offers the user these options with the assumption that the obstruction is not actually recti linear but rather cylindrical or spherical in shape This option is useful in describing the behavior of small complicated targets like cables or heat detection devices 49 6 1 Simple Heat Conduction Through a Solid Slab heat_conduction Analytical solutions of transient one dimensional heat conduction through a slab can be found in Refs 64 and 65 Four cases are examined here In each a slab of thickness L 0 1 m is exposed on one face to an air temperature of T 120 C The other face is insulated adiabatic The convective heat transfer from the gas to the slab is q h T T where h is constant and T is the slab face temperature No thermal radiation is included Case k p c h Bi W m K kg m kJ kg K W m K hL k A 0 1 100 1 100 100 B 0 1 100 1 10 10 C 1 0 1000 1 10 1 D 10 0 10000 1 10 0 1 150 150 Slab Temperature heat conduction a Slab Temperature heat conduction b eo 100 Analytical Front e 100 g Analytical 4 cm g E Analytical Back E 8 FDS Front 8 Ed FDS 4 cm Ed 2 5 FDS fm 2 5 Analytical Front E 0 E 0 Analytical 4 cm Analytical Back FDS Front FDS 4 em
10. clearly showing convergence of the FDS numerical solution open circles to the analytical solution solid line The case is run with constant properties p 1 kg m and u 0 1 kg m s and a CFL of 0 25 13 10 E 107 Tag amp E H H o 2 E E E El a n 10 107 as m O 62 O 62 O x O x FDS rms error s FDS rms error 3 3 19 19 LL 10 10 Grid Spacing dx m Grid Spacing dx m Figure 3 3 Left Convergence rate for the u component of velocity with v 0 showing that the advective terms in the FDS code are second order accurate The triangles represent the rms error in the u component for grid spacings of 6x L N where L 2x m and N 8 16 32 64 The solid line represents first order accuracy and the dashed line represents second order accuracy The simulation is run to a time of t 27 s with a CFL of 0 25 The u component at the center of the domain is compared with the analytical solution at the same location Right Same case except v 0 1 showing that the viscous terms in the FDS code are second order accurate 14 3 2 Decaying Isotropic Turbulence In this section we present a canonical flow for LES which tests whether the subgrid stress model has been coded properly In some cases the difference between verification and validation is not so clear Once a model is well established and validated it may actually be us
11. is explained in Ref 61 When the intensities corresponding to the bands are known the total intensity is calculated by summing over all the bands Mz I x s Y I x s 4 5 n 1 There are numerous examples in the heat transfer literature of exact solutions for simple configurations of hot and cold objects of the radiation transport equation 37 4 1 Radiation from parallel plate in different co ordinate systems plate view factor This verification case tests the computation of radiative heat flux from hot surface to a differential parallel surface at 1 m distance in different co ordinate systems The radiating surface is at 1000 C temperature and has emissivity of 1 0 The exact values are calculated using the analycal expressions for the view factors Co ordinates Radiation source Heat flux kW m 2D cartesian Infinite plate of width 2 m 105 3 3D cartesian Square plate of width 2 m 81 8 2D cylindrical Circular disk of diameter 2 m 74 1 A comparison of exact values and FDS predictions at three diffferent angular resolutions is shown below Radiative heat flux plate view factor 120 cC 110 E 100r cA a x 90r TE a na um __ _ 9 80 q E __ o 70r m g 2 2 Lad Exact 2D eot gu O FDS 2D d c Exact cart S FDS cart e sor Exactcyl FDS cyl 40 1 1 1 1 1 7 7 20 30 40 50 60 70 80 90
12. k 200 0 20 W m K c 0 1 0 kJ kg K c 100 1 2 kJ kg K c 200 1 0 kJ kg K The thickness radius of the sample is 0 01 m In the cartesian case the back surface of the material is exposed to a gas at 0 C In the figure below the light colored solid lines are FDS results and the dark lines are the HEATING results An example input with cylindrical geometry looks like amp MATL ID MAT_1 EMISSIVITY 0 0 CONDUCTIVITY RAMP K RAMP SPECIFIC HEAT RAMP C_RAMP DENSITY 10000 amp RAMP ID K RAMP T 0 F 0 10 amp RAMP ID K RAMP T 100 F 0 15 amp RAMP ID K RAMP T 200 F 0 20 amp RAMP ID C RAMP T 0 F 1 00 amp RAMP ID C RAMP T 100 F 1 20 amp RAMP ID C RAMP T 200 F 1 00 amp SURF ID SLAB STRETCH FACTOR 1 0 GEOMETRY CYLINDRICAL MATL ID MAT 1 THICKNESS 0 01 250 50 Surface Temperature heat conduction kc Back Inner Temperature heat conduction kc 200r 40r o o e 2 HEATING cart_back g 150r y 30r ABAQUS cyl back ic E ABAQUS sph back 8 S FDS cart_back amp L 1 amp 20H FDS cyl back E 100 HEATING cart surf a 2 FDS EL E ABAQUS cyl surf ABAQUS sph surf 50r FDS cart_front 7 10r FDS cyl front FDS sph front 0 1 1 1 0 n 0 s 10 15 0 5 10 15 Time min Time min Figure 6 2 Comparison of heat conduction calculat
13. 30 0 26 0 26 0 22 0 22 0 18 0 18 0 14 0 14 0 10 0 10 0 06 0 06 Frame 0 Frame 85 Time 0 000 Time 0 689 DDI Figure 3 4 Initial and final states of the isotropic turbulence field here equivalent to the grid spacing is decreased To the right of each decay curve plot in Figure 3 5 is the corresponding spectral data comparison The three black solid lines are the CBC spectral data for the points in time corresponding to dimensional times of t 0 00 0 28 and 0 66 seconds in our simulations As described above the initial FDS velocity field represented by the black dots is specified to match the CBC data up to the grid Nyquist limit From there the spectral energy decays rapidly as discussed in 40 For each of the spectral plots on the right the results of interest are the values of the red and blue dots and how well these match up with the corresponding CBC data For the 32 case top right the results are remarkably good Interestingly the results for the more highly resolved 64 case are not as good This is because the viscous scales are rather well resolved at the later times in the experiment and as mentioned it is well known that the constant coefficient Smagorinsky model is too dissipative under such conditions Overall the agreement between the FDS simulations and the CBC data is satisfactory and any discrep ancies can be explained by limitations of the model Therefore as a verification the results here a
14. 500 600 Temperature C Temperature C Figure 7 8 Results of a micro calorimetry analysis of a sample of cable insulation left and jacket material right obtained directly from the figures The value of r Yo for the ith reaction can be found from rea Babs aw f q T dT 7 16 where p i is the value of the ith heat release rate peak The values Yo can be estimated from the relative area under the curve Their sum ought to be 1 It is important to check the units of all of these quantities because the results of these experiments are often presented in different ways depending on the particular application A mistake in units can result in values of A and or E that will invariably cause spurious results The dashed curves in Fig 7 8 are the results of numerically integrating Eq 7 6 within FDS for each material component A typical input line for FDS that describes a single material component undergoing a single reaction is given by amp MATL ID Cable 11 Jacket Component A EMISSIVITY DENSITY E CONDUCTIVITY SPECIFIC_HEAT REACTIONS EE REFERENCE TEMPERATURE 300 REFERENCE RATE 0 0064 HEATING RATE 60 NU RESIDUE 0 49 RESIDUE char U FUEL 0 51 HEAT OF REACTION Only the relevant parameters are shown The other parameters are not relevant in thi
15. C in a mixture consisting of 20 O and 80 96 No The resulting curve shows the heat release rate of the sample as it was heated normalized by the mass of the original sample There are usually one two or three noticeable peaks in the curve corresponding to temperatures where a significant decomposition reaction occurs Each peak can be characterized by the maximum value of the heat release rate p i the temperature T and the relative fraction of the original sample mass that undergoes this particular reaction Yo The area under the curve f nar BAH 7 14 0 is the sample heating rate PB times the energy released per unit mass of the original sample AH This latter quantity is related to the more conventional heat of combustion via the relation AH AH 7 15 1 v where v is the fraction of the original mass that remains as residue Sometimes this is referred to as the char yield Note that it is assumed to be the same for all reactions The MCC measurement is similar to TGA in that it is possible to derive the kinetic parameters A and Ej for the various reactions from the heat release rate curve As an example of how to work with MCC data consider the two plots shown in Fig 7 8 The solid curves in the figures display the results of micro calorimetry measurements for the insulation and jacket material of a multi conductor control cable the number 11 has no particular meaning other than to distinguish
16. Finite Difference Calculations of Buoyant Convection in an Enclosure Part I The Basic Algorithm SIAM Journal of Scientific and Statistical Computing 4 1 117 135 March 1983 3 H R Baum and R G Rehm Finite Difference Solutions for Internal Waves in Enclosures SIAM Journal of Scientific and Statistical Computing 5 4 958 977 December 1984 3 H R Baum and R G Rehm Calculations of Three Dimensional Buoyant Plumes in Enclosures Com bustion Science and Technology 40 55 77 1984 3 R G Rehm P D Barnett H R Baum and D M Corley Finite Difference Calculations of Buoyant Convection in an Enclosure Verification of the Nonlinear Algorithm Applied Numerical Mathematics 1 515 529 1985 3 K B McGrattan T Kashiwagi H R Baum and S L Olson Effects of Ignition and Wind on the Transition to Flame Spread in a Microgravity Environment Combustion and Flame 106 377 391 1996 4 T Kashiwagi K B McGrattan S L Olson O Fujita M Kikuchi and K Ito Effects of Slow Wind on Localized Radiative Ignition and Transition to Flame Spread in Microgravity In Twenty Sixth Symposium International on Combustion pages 1345 1352 Combustion Institute Pittsburgh Penn sylvania 1996 4 W Mell and T Kashiwagi Dimensional Effects on the Transition from Ignition to Flame Spread in Microgravity In Twenty Seventh Symposium International on Combustion pages 2635 2641 Combustion Institute Pittsburgh Pennsylvania 1998 4 7
17. Heat Release Kinetics Fire and Materials 24 179 186 2000 63 R E Lyon and R N Walters Pyrolysis Combustion Flow Calorimetry Journal of Analytical and Applied Pyrolysis 71 1 27 46 March 2004 64 American Society for Testing and Materials West Conshohocken Pennsylvania ASTM D 7309 07 Standard Test Method for Determining the Flammability Characteristics of Plastics and Other Solid Materials Using Microscale Combustion Calorimetery 2007 64 75
18. Reynolds number based on H To provide a qualitative picture of the flow field Figure 3 9 shows contours of stream wise velocity for the case dp dx 1 Pa m and N 32 Rough Walls With the same grid set up as described above the smooth walls a series of cases labeled as z0x in the repository were run at various roughness heights grid resolutions and Reynolds numbers The results are presented together with the smooth wall cases in Fig 3 10 The laminar cases provide accurate results for two different Reynolds numbers As can bee seen both the smooth wall and rough wall treatments behave well over the range tested 3 4 5 Conclusions In this work the FDS wall model has been verified for both laminar and turbulent flow through straight channels with smooth or rough walls It is shown that for the laminar DNS case FDS is second order accurate It is suggested elsewhere that as a rule of thumb 10 96 accuracy is the best that can be expected from friction factor calculations of turbulent flow 60 The Werner and Wengle wall model is adapted to variable density flows though only constant density flows are tested here for smooth walls and it is shown that FDS is capable of reproducing friction factors for a broad range of Reynolds numbers to within 6 0 96 relative accuracy A log law for rough walls is adopted to FDS with similar results 22 Slice U VEL mis 15 0 13 5 12 0 10 5 9 00 7 50 6 00 4 50 3 00 1 50 0 00 8 0
19. Solid Fuels Code Checking u 4 28 hace a 3e xp a Roe uos Ro nih Se ADU We NR de 3 The Basic Flow Solver 3 1 3 2 3 3 3 4 35 3 6 3T 3 8 2D Analytical Solution to Navier Stokes o o e e Decaying Isotropic Turbulenc s seoa sog a ok ve CR RE ow vos 9 xD Eee ss The Dynamic Smagorinsky Model een FDS Wall Flows Part I Straight Channels lees 34 1 FPornnmulatiol kk Pewee RU EUR Re xo Rem xo REOR AUR RUE eda 34 REUS o 52 sss la ae ad tle a dialed A Pea a e s dos SAS CORClUSIODS e cote o eR tme Ke ee hs Ws eve EC IP S ve dies Analytical Solutions to the Continuity Equation o o o 3 23 Pulsaime 1D solution s s 2 Rao xe dera a A aia 32542 Pulsating 2D solution i s a sa ana ge wee aioe ala e Aa Gal AR a 3 5 3 Stationary compression wave in ID 2 6 ee ee a RR 3 5 4 Stationary compression wavein2D 0 0002 Scalar Transport move slug lt acs e ooo tm A A A Energy Conservation energy_budget 0 02002 eee eee 3 7 1 The Heat from a Fire energy_budget llle 3 7 2 Gas Injection via an Isentropic Process isemtropic 3 7 3 Gas Injection via a Non Isentropic Process isentropic2 Checking for Coding Errors Symmetry_test o o e vil iii 4 Thermal Radiation 4 1 Radiation from parallel plate in different co ordinate systems
20. a cube in a plate channel In 8th Symposium on Turbulent Shear Flows pages 155 168 1991 20 57 NIST Web Site http www fire nist gov wui 20 58 L F Moody Friction factors for pipe flow Transactions of the ASME 66 1944 20 59 H Tennekes and J L Lumley A First Course in Turbulence MIT Press 1972 20 60 Bruce R Munson Donald F Young and Theodore H Okiishi Fundamentals of Fluid Mechanics John Wiley and Sons 1990 22 74 61 62 63 64 65 66 67 68 69 R Siegel and J R Howell Thermal Radiation Heat Transfer Taylor amp Francis New York 4th edition 2002 37 39 Y B Zel dovich and Y P Raizer Physics of shock waves and high temperature hydrodynamic phenom ena Dover Publications New York 2002 Translated from the Russian and then edited by W D Hayes and R F Probstein 40 41 D A Purser SFPE Handbook of Fire Protection Engineering chapter Toxicity Assessment of Com bustion Products National Fire Protection Association Quincy Massachusetts 3rd edition 2002 46 D Drysdale An Introduction to Fire Dynamics John Wiley and Sons New York 2nd edition 2002 50 H S Carslaw and J C Jaegar Conduction of Heat in Solids Oxford University Press 2nd edition 1959 50 K W Childs HEATING 7 Multidimensional Finite Difference Heat Conduction Analysis Code System Technical Report PSR 199 Oak Ridge National Laboratory Oak Ridge TN 1998 51 R E Lyon
21. algorithms have been used at a grid resolution of roughly 1 mm to look at flames spreading over paper in a microgravity environment 9 10 11 12 13 14 as well as g jitter effects aboard spacecraft 15 Simulations have been compared to experiments performed aboard the US Space Shuttle The flames are laminar and relatively simple in structure and the comparisons are a qualitative assessment of the model solution Similar studies have been performed comparing DNS simulations of a simple burner flame to laboratory experiments 16 Another study compared FDS simulations of a counterflow diffusion flames to experimental measurements and the results of a one dimensional multi step kinetics model 17 Early work with the hydrodynamic solver compared two dimensional simulations of gravity currents with salt water experiments 18 In these tests the numerical grid was systematically refined until almost perfect agreement with experiment was obtained Such convergence would not be possible if there were a fundamental flaw in the hydrodynamic solver 2 3 Sensitivity Analysis A sensitivity analysis considers the extent to which uncertainty in model inputs influences model output Model parameters can be the physical properties of solids and gases boundary conditions initial conditions etc The parameters can also be purely numerical like the size of the numerical grid FDS typically requires the user to provide several dozen different types of in
22. and immersed boundary methods Kevin McGrattan is a mathematician in the Building and Fire Research Laboratory BFRL of NIST He received a bachelors of science degree from the School of Engineering and Applied Science of Columbia University in 1987 and a doctorate at the Courant Institute of New York University in 1991 He joined the NIST staff in 1992 and has since worked on the development of fire models most notably the Fire Dynamics Simulator Simo Hostikka is a Senior Research Scientist at VTT Technical Research Centre of Finland He received a master of science technology degree in 1997 and a doctorate in 2008 from the Department of Engineering Physics and Mathematics of the Helsinki University of Technology He is the principal developer of the radiation and solid phase sub models within FDS Jason Floyd is a Senior Engineer at Hughes Associates Inc in Baltimore Maryland He received a bach elors of science and Ph D in the Nuclear Engineering Program of the University of Maryland After graduating he won a National Research Council Post Doctoral Fellowship at the Building and Fire Research Laboratory of NIST where he developed the combustion algorithm within FDS He is cur rently funded by NIST under grant 7ONANB8H8161 from the Fire Research Grants Program 15 USC 278f He is the principal developer of the multi parameter mixture fraction combustion model and control logic within FDS 111 iv Acknowledgments FDS is supp
23. ar St Bcos x cos t 0 3 21 x 2 Bsin y cos or x Bcos y cos t 0 3 22 Thus utilizing 3 15 and 3 16 and replacing q xo x 1 0 q2 yol 1 0 with go x y t we find that the solution to 3 20 is q x y t qo x y t 1 a xo x 1 exp 22 sin or i nf LraQo sr and Le 400b exp sin or 1 a yoly t 78 sn or 3 23 0 where a z tan 5 y 3 24 and the initial positions are given by xo x of 2arctan an 5 exp 2 sn on 3 25 yo y t 2arctan tan 5 exp 2 sn on 3 26 Note that the initial condition qo x y t is restricted to cases where Agi is independent of y and a is inde pendent of x That is the function qo must be additively separable An example of the solution to 3 23 is shown in Figure 3 11 The initial condition for the density is specified as p x 0 1 and the amplitude and frequency are set to unity B 1 and 1 FDS is run with three scalar transport schemes central differencing Superbee and the CHARM flux limiter The solution at x y 31 2 3n 2 for successively finer grid resolutions is plotted as a time series on the left and may be compared with the analytical solution black line On the right we confirm second order convergence for the FDS implementation Central differencing and the CHARM limiter outperform Superbee for this problem because the solution is relatively smooth 26 10 FDS Centra
24. it from other cables being studied The insulation material exhibits two fairly well defined peaks whereas the jacket material exhibits three Thus the insulation material is modeled using two solid components each undergoing a single step reaction that produces fuel gas and a solid residue The jacket material is modeled using three solid components The residue yield for the insulation material is 6 for the jacket 49 96 obtained simply by weighing the sample before and after the micro calorimetry measurement It is not known which reaction produces what fraction of the residue Rather it is assumed that each reaction yields the same residue in the same relative amount The dashed curves in Fig 7 8 are the results of FDS simulations of the MCC measurements To mimic the sample heating a very thin sheet comprised of a mixture of the solid components with an insulated backing is heated at the rate specified in the experiment 1 K s or 60 K min the units needed in FDS For each reaction the kinetic parameters are calculated using the formulae 7 12 and 7 13 The values of 7 are 64 800 T r 800 r r 2001 Heat Release Rate cable 11 insulation mcc 700l Heat Release Rate cable 11 jacket mcc 600 1 600r 8 500 amp 500 E Exp HRR E Exp HRR e w0 FDS hrrpum E 4001 FDS hrrpum E 300 amp 300 200r 200r 100r 100r 0 0 n 0 100 200 300 400 500 600 0 100 200 300 400
25. no closed form mathematical solutions for the fully turbulent time dependent Navier Stokes equations CFD provides an approximate solution for the non linear partial differential equations by replacing them with discretized algebraic equations that can be solved using a powerful computer While there is no general analytical solution for fully turbulent flows certain sub models address phenomenon that do have analytical solutions for example one dimensional heat conduction through a solid These analytical solutions can be used to test sub models within a complex code such as FDS The developers of FDS routinely use such practices to verify the correctness of the coding of the model 3 4 Such verification efforts are relatively simple and routine and the results may not always be published nor included in the documentation Examples of routine analytical testing include The radiation solver has been verified with scenarios where simple objects like cubes or flat plates are positioned in simple sealed compartments All convective motion is turned off the object is given a fixed surface temperature and emissivity of one making it a black body radiator The heat flux to the cold surrounding walls is recorded and compared to analytical solutions These studies help determine the appropriate number of solid angles to be set as the default Solid objects are heated with a fixed heat flux and the interior and surface temperatures as a function
26. predictions of varying grid sizes were compared to two separate fire experiments The University of Canter bury McLeans Island Tests and the US Navy Hangar Tests in Hawaii The first set of tests utilized a room with approximate dimensions of 2 4 m by 3 6 m by 2 4 m and fire sizes of 55 kW and 110 kW The Navy Hangar tests were performed in a hangar measuring 98 m by 74 m by 15 m in height and had fires in the range of 5 5 MW to 6 6 MW The results of this study indicate that FDS simulations with grids of 0 15 m had temperature predictions as accurate as models with grids as small as 0 10 m Each of these grid sizes produced results within 15 of the University of Canterbury temperature measurements The 0 30 m grid produced less accurate results For the comparison of the Navy Hangar tests grid sizes ranging from 0 60 m to 1 80 m yielded results of comparable accuracy Musser et al 27 investigated the use of FDS for course grid modeling of non fire and fire scenarios Determining the appropriate grid size was found to be especially important with respect to heat transfer at heated surfaces The convective heat transfer from the heated surfaces was most accurate when the near surface grid cells were smaller than the depth of the thermal boundary layer However a finer grid size produced better results at the expense of computational time Accurate contaminant dispersal modeling re quired a significantly finer grid The results of her study indicate t
27. 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 W Mell S L Olson and T Kashiwagi Flame Spread Along Free Edges of Thermally Thin Sam ples in Microgravity In Twenty Eighth Symposium International on Combustion pages 2843 2849 Combustion Institute Pittsburgh Pennsylvania 2000 4 K Prasad Y Nakamura S L Olson O Fujita K Nishizawa K Ito and T Kashiwagi Effect of Wind Velocity on Flame Spread in Microgravity In Twenty Ninth Symposium International on Combus tion pages 2553 2560 Combustion Institute Pittsburgh Pennsylvania 2002 4 Y Nakamura T Kashiwagi K B McGrattan and H R Baum Enclosure Effects on Flame Spread over Solid Fuels in Microgravity Combustion and Flame 130 307 321 2002 4 W E Mell K B McGrattan and H R Baum g Jitter Effects on Spherical Diffusion Flames Micro gravity Science and Technology 15 4 12 30 2004 4 A Mukhopadhyay and I K Puri An Assessment of Stretch Effects on Flame Tip Using the Thin Flame and Thick Formulations Combustion and Flame 133 499 502 2003 4 A Hamins M Bundy LK Puri K B McGrattan and W C Park Suppression of Low Strain Rate Non Premixed Flames by an Agent In Proceedings of the 6th International Microgravity Combustion Workshop NASA CP 2001 210826 pages 101 104 National Aeronautics and Space Administration Lewis Research Center Cleveland Ohio May 2001 4 K B Mc
28. 100 0 Number radiation angles 38 4 2 Radiation inside a box radiation in a box This verification case tests the computation of three dimensional configuration factor inside a cube box with one hot wall and five cold 0 K walls An overview of the test geometry is shown here The configuration factors are calculated at the diagonal of the cold wall opposite to the hot wall The exact values of the configuration factor from plane element dA to parallel rectangle H are calculated using the analytical solution 61 yz Praa yz Qua 0 025 0 1457 0 275 0 2135 0 075 0 1603 0 325 0 2233 0 125 0 1748 0 375 02311 0 175 0 1888 0 425 0 2364 0 225 0 2018 0 475 0 2391 Different variations of the case include the mesh resolution 20 and 100 cells and the number of radiation angles 50 100 300 1000 2000 The exact and FDS results are shown here Incident Heat Flux radiation box Incident Heat Flux radiation box 0 3r 0 3 8 0 25 8 025 gt gt E 0 2 E 0 2r INIA ois 0 ae 0 d E Snr Analytical Phi HdA tens E Te 1 Analytical Phi HdA oil FDS Flux_20_50 8 ol iom FDS Flux 100 50 m FDS Flux 20 100 hs 7 FDS Flux 100 100 s FDS Flux 20 300 FDS Flux 100 300 0 05 FDS Flux 20 1000 1 0 05 FDS Flux 100 1000
29. 2 3 4 Sensitivity of Thermophysical Properties of Solid Fuels An extensive amount of verification and validation work with FDS version 4 has been performed by Hi etaniemi Hostikka and Vaari at VTT Finland 34 The case studies are comprised of fire experiments ranging in scale from the cone calorimeter ISO 5660 1 to full scale fire tests such as the room corner test ISO 9705 Comparisons are also made between FDS results and data obtained in the SBI Single Burning Item Euro classification test apparatus EN 13823 as well as data obtained in two ad hoc experimental configurations one is similar to the room corner test but has only partial linings and the other is a space to study fires in building cavities All of the case studies involve real materials whose properties must be prescribed so as to conform to the assumption in FDS that solids are of uniform composition backed by a material that is either cold or totally insulating Sensitivity of the various physical properties and the boundary conditions were tested Some of the findings were The measured burning rates of various materials often fell between two FDS predictions in which cold or insulated backings were assumed for the solid surfaces FDS lacks a multi layer solid model The ignition time of upholstery is sensitive to the thermal properties of the fabric covering but the steady burning rate is sensitive to the properties of the underlying foam Moisture content of wo
30. 23 There are also refinements of the original Smagorinsky model 31 32 33 that do not require the user to prescribe the constants but rather generate them automatically as part of the numerical scheme 2 3 3 Sensitivity of Radiation Parameters Radiative heat transfer is included in FDS via the solution of the radiation transport equation for a non scattering gray gas and in some limited cases using a wide band model The equation is solved using a technique similar to finite volume methods for convective transport thus the name given to it is the Finite Volume Method FVM There are several limitations of the model First the absorption coefficient for the smoke laden gas is a complex function of its composition and temperature Because of the simplified combustion model the chemical composition of the smokey gases especially the soot content can effect both the absorption and emission of thermal radiation Second the radiation transport is discretized via approximately 100 solid angles For targets far away from a localized source of radiation like a growing fire the discretization can lead to a non uniform distribution of the radiant energy This can be seen in the visualization of surface temperatures where hot spots show the effect of the finite number of solid angles The problem can be lessened by the inclusion of more solid angles but at a price of longer computing times In most cases the radiative flux to far field targets
31. 3 25 7191 0 5 82 9457 83 1353 82 8224 84 3719 84 0542 84 0311 1 0 116 2891 115 4055 114 9710 117 8011 117 3576 116 7755 10 148 9698 148 9619 148 4011 148 9677 148 4069 148 9695 oo 148 9709 147 7533 147 1970 147 9426 147 3856 147 9419 40 4 4 Wall Internal Radiation wall_internal_radiation In depth absorption of thermal radiation in a solid is computed using a two flux model In this example the accuracy of the two flux model is tested in the computation of the emissive flux from a homogenous layer of material thickness L 0 1 m at 1273 15 K temperature surrounded by an ambient temperature of 10 K The absorption coefficient K is varied to cover a range 0 01 10 of optical depth t KL The exact solutions for radiative flux are the analytical solutions of plane layer emission 62 S t Sp 1 2E3 1 4 7 where Sj oT is the black body heat flux from the radiating plane and E3 t is the exponential integral function order 3 of optical depth t The exact solutions and FDS results are shown in the table below T S t FDS kW m kW m 0 01 2 897 2 950 0 1 24 94 26 98 0 5 82 95 93 90 1 0 116 3 128 4 10 149 0 149 0 41 4 5 Radiation Emitted by Hot Spheres hot spheres This case tests the calculation of the radiation heat flux from a collection of hot objects Within two com pletely open volumes that are 1 m on a side hot s
32. 34 27 The continuity equation can be written as lo lo lo X ei sin x a er sin y 5 cos x cos y 0 3 35 A solution to 3 35 is q x y t qo x y t F I x t M x t bot DB 3 36 where L zt In c7 cos bjt 2 arctan y z t bisin bjt 2arctan y z t 3 37 Plot In c cos 2 arctan y z t b sin 2arctan y z t 3 38 and bi 4 1 c gt 0 3 39 1 c tan 234 Yi z 1 5 3 40 i 1 i 2 it 1 zo z t 2arctan Pi eoi arctan uL 2 3 41 Ci b 2 Ci Note that zo xo for i 1 and zo yo for i 2 To be clear no summation is implied over repeated indices Also note that the same restrictions apply to the initial condition as did in Section 3 5 2 Namely that Ao is independent of y and en is independent of x An example of the solution to 3 36 is shown in Figure 3 12 In this case we set c 2 and cz 3 to create an asymmetry in the flow The periodicity in time depends on the choices of c and c it is possible that no periodicity exists We have not found a case that generates a singularity The analytical time series of the density at the position x y 31 2 31 2 is shown as the solid black line FDS is run with the CHARM flux limiter scheme as this is a DNS flow field The solution at successively finer grid resolutions is plotted and compared with the analytical solution demonstrating convergence of the scheme On the right side of the f
33. FDS Flux 20 2000 FDS Flux 100 2000 0 L L L 1 0 i T T 1 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1 Position m Position m 39 4 3 Radiation from a plane layer radiation plane layer This case tests the computation of three dimensional radiation from a homogenous infinitely wide layer of hot gases The temperature of the layer is 1273 15 K and the absorption coefficient K is varied The thickness of the layer is fixed at 1 m and the optical depth is t 1x m Wall temperatures are set to 0 K The results are compared against the exact solution S T presented in 62 S t Sp 1 2E3 1 4 6 where Sp OT is the black body heat flux from the radiating plane and E3 t is the exponential integral function order 3 of the optical depth 7 The FDS results are computed at two mesh resolutions in the x direction I 20 and I 150 For I 20 both one band and six band versions are included to test the correct integration of heat fluxes over multiple bands For I 20 2 D versions are also computed J 1 The limiting case t co using a solid wall of temperature 1273 15 K is computed to test the wall heat flux computation The exact values and FDS predictions of the wall heat fluxes are given in the table below T S t FDS 1220 J 20 FDS 1220 J 1 FDS I 150 m7 kW m 1 band 6 bands 1 band 6 bands 1 band 0 01 2 8970 2 9214 2 9104 2 8364 2 8257 2 9285 0 1 24 9403 25 5668 25 4705 25 1078 25 013
34. Grattan R G Rehm and H R Baum Fire Driven Flows in Enclosures Journal of Computa tional Physics 110 2 285 291 1994 4 P Friday and F W Mowrer Comparison of FDS Model Predictions with FM SNL Fire Test Data NIST GCR 01 810 National Institute of Standards and Technology Gaithersburg Maryland April 2001 6 A Bounagui N Benichou C McCartney and A Kashef Optimizing the Grid Size Used in CFD Simulations to Evaluate Fire Safety in Houses In 3rd NRC Symposium on Computational Fluid Dynamics High Performance Computing and Virtual Reality pages 1 8 Ottawa Ontario Canada December 2003 National Research Council Canada 6 R L Alpert SFPE Handbook of Fire Protection Engineering chapter Ceiling Jet Flows National Fire Protection Association Quincy Massachusetts 3rd edition 2003 6 A Bounagui A Kashef and N Benichou Simulation of the Dynamics of the Fire for a Section of the L H La Fontaine Tunnel IRC RR 140 National Research Council Canada Ottawa Canada K1AO0R September 2003 6 Y Xin Assessment of Fire Dynamics Simulation for Engineering Applications Grid and Domain Size Effects In Proceedings of the Fire Suppression and Detection Research Application Symposium Orlando Florida National Fire Protection Association Quincy Massachusetts 2004 6 J A Ierardi and J R Barnett A Quantititive Method for Calibrating CFD Model Calculations In Pro ceedings of the CIB CTBUH International Conference
35. NIST Special Publication 1018 5 Fire Dynamics Simulator Version 5 Technical Reference Guide Volume 2 Verification Randall McDermott Kevin McGrattan Simo Hostikka Jason Floyd NIST National Institute of Standards and Technology U S Department of Commerce NIST Special Publication 1018 5 Fire Dynamics Simulator Version 5 Technical Reference Guide Volume 2 Verification Randall McDermott Kevin McGrattan Fire Research Division Building and Fire Research Laboratory Simo Hostikka VTT Technical Research Centre of Finland Espoo Finland Jason Floyd Hughes Associates Inc Baltimore Maryland October 29 2010 FDS Version 5 5 SVN Repository Revision 6843 TOF C NM Co iz n De yy 2 e o r CA a STATES of is U S Department of Commerce Gary Locke Secretary National Institute of Standards and Technology Patrick Gallagher Director Preface This is Volume 2 of the FDS Technical Reference Guide Volume 1 describes the mathematical model and numerical method Volume 3 documents past and present experimental validation work Instructions for using FDS are contained in a separate User s Guide 1 The three volumes of the FDS Technical Reference Guide are based in part on the Standard Guide for Evaluating the Predictive Capability of Deterministic Fire Models ASTM E 1355 2 ASTM E 1355 defines model evaluation as the process of quantifying the accuracy of chosen re
36. T T 80 M T T 2 4 6 8 10 0 2 4 6 8 10 Time s Time s 25 T T T 100 r r r Incident Heat Flux hot spheres Integrated Intensity hot spheres _ 20r qe emm IUE eS arta 80r AA OS pecie areas ut il R i ES 1 El r z r r E M i E 60 E ie E 101 A 40t a E E i i 4 st ug o 1 Exact Rad Flux e Exact Intensity d FDS rad flux E FDS UII 0 1 1 n I 0 7 L fi n n 0 2 4 6 8 10 0 2 4 6 8 10 Time s Time s Figure 4 1 The total heat losses radiative heat flux and integrated intensity of a collection of loosely and densely packed radiating spheres 42 4 6 Radiation Absorbed by Liquid Droplets droplet absorption This case tests the conservation of energy that is absorbed by liquid droplets We want to make sure that the energy that is taken away from the thermal radiation field is accuratelly converted into increased temperature of the droplets Considering the total mass of absorbing droplets the average droplet temperature T is increased by the absorbed radiation Q according to the following ODE d a 4 8 MCp a Q 4 8 where m and c are the total mass and specific heat of the droplets respectively Here we have assumed that the convective heat transfer between the gas and droplets is small This is implemented by increasing the gas phase Prandtl number into a artificially high value If the absorbed power remains constant during the time step the average droplet temperature in the e
37. ant verification test is to run this peri odic isotropic turbulence simulation in the absence of both molecular and turbulent viscosity For so called energy conserving explicit numerics the integrated energy will remain nearly constant in time This is demonstrated by the blue line in the top left plot in Figure 3 5 The deviations from identical energy conser vation to machine precision are due solely to the time discretization the spatial terms are conservative as discussed in 41 and converge to zero as the time step goes to the zero Note that strict energy conserva tion requires implicit time integration 42 43 and as shown by the red curve on the same plot where only molecular viscosity is present in the simulation this cost is unwarranted given that the molecular dissipation rate clearly overshadows the relatively insignificant amount of numerical dissipation caused by the explicit method The FDS result using the Smagorinsky eddy viscosity the black solid line matches the CBC data red open circles well for the 32 case top left However the FDS results are slightly too dissipative in the 64 case bottom left This is due to a well known limitation of the constant coefficient Smagorinsky model namely that the eddy viscosity does not converge to zero at the appropriate rate as the filter width 15 Smokeview 5 2 2 Jul 18 2008 Slice Smokeview 5 2 2 Jul 18 2008 Slice l ve d i8 d i8 0 42 0 42 0 38 0 38 0 34 0 34 0 30 0
38. ass loss per unit area is 360 1 0 5 x r 2 0 9 kg m for charring and 1 8 kg m for non charring materials For spherical surfaces the volume per unit surface area is r 3 and thus the mass loss per unit area is 360 1 0 5 x r 3 0 6 kg m for charring and 1 2 kg m for non charring materials On the figures found on the following pages the computed results are labeled as follows Expected indicates the total mass that has pyrolyzed by the end of the simulation Gaseous indicates the instantaneous concentration of pyrolyzed mass integrated over the volume of the computational domain It should gradually increase from zero to the Expected value 53 Solid indicates the instantaneous value of the solid surface density integrated over the entire surface area For charring materials it should decrease from its initial value twice the final value to the final Expected value For non charring materials it should decrease from the Expected value to zero Fuel Gas is the total burning rate integrated over time It should increase from zero to the Expected value 7 1 1 Pyrolysis at a Solid Surface The analytical mass losses are calculated by multiplying the mass per unit area by the VENT area which in all cases is 1 m The expected and computed results for charring material are compared in 7 1 The expected and computed results for non charring material are compared in 7 2 54
39. based on the relative area underneath each peak The values of Yo should sum to 1 63 7 5 2 Using Micro Calorimetry Data cable 11 mcc This section describes a method for interpreting micro combustion calorimeter MCC measurements The pyrolysis combustion flow calorimeter PCFC developed by Lyon and Walters 68 at the U S Federal Avi ation Administration FAA is a device used to measure the heat generated from the combustion of small 4 mg to 6 mg material samples by oxygen depletion calorimetry Samples are pyrolyzed at a specified heat ing rate in an anerobic atmosphere typically N2 and the resulting gases are mixed with excess oxygen and combusted in a separate chamber The heat release rate from the specimen is obtained from measurements of the concentration of oxygen in the effluent exiting the combustor as a function of time The methodology is the basis for the standard test ASTM D 7309 69 The results of PCFC measurements for several multi conductor control cables are shown in Fig 7 8 For each cable the insulation and jacket material were tested separately and at least three replicates were performed for each only one replicate is shown for each sample The samples weighing approximately 5 mg were cut from the cable jackets and conductor insulation material of each of the cables These samples were pyrolyzed in the PCFC at a rate of 1 K s from 100 C to 600 C in a nitrogen atmosphere and the effluent combusted at 900
40. be seen from the energy spectra lower right the energy near the grid Nyquist limit is more accurately retained by the dynamic model This equates to better flow structure with fewer grid cells Thus for practical calculations of engineering interest the small computational overhead of computing the coefficient may be recuperated by a reduction is cell count 19 3 4 FDS Wall Flows Part I Straight Channels Wall flows are notoriously challenging for large eddy simulation LES 52 53 54 50 55 In spite of their promise and sophistication practical LES codes are resigned to model the wall shear stress as opposed to resolving the dynamically important length scales near the wall In this work we introduce the Werner and Wengle WW wall model 56 and the rough wall log law from Pope 50 into the NIST Fire Dynamics Simulator FDS as a practical first step in developing models for turbulent flow around complex geometry and over complex terrain Such models are required in order for FDS to accurately model for example tunnel fires smoke transport in complex architectures and wildland urban interface WUD fires 57 As a minimum requirement a wall model should accurately reproduce the mean wall stress for flow in a straight channel We verify that this is true for FDS by reproducing the Moody chart a plot of friction factor versus Reynolds number for pipe flow 58 The remainder of this section is organized as follows In Section 3 4 1
41. birch tga e 8 Lagrangian Particles 8 1 Momentum Transfer particdle drag lens 8 2 Water Droplet Evaporation water evaporation Bibliography viii 49 50 51 52 53 53 54 57 60 61 62 63 63 64 66 67 67 69 71 Chapter 1 What is Verification The terms verification and validation are often used interchangeably to mean the process of checking the accuracy of a numerical model For many this entails comparing model predictions with experimental measurements However there is now a fairly broad based consensus that comparing model and experiment is largely what is considered validation So what is verification ASTM E 1355 2 Standard Guide for Evaluating the Predictive Capability of Deterministic Fire Models defines verification as The process of determining that the implementation of a calculation method accurately repre sents the developer s conceptual description of the calculation method and the solution to the calculation method and it defines validation as The process of determining the degree to which a calculation method is an accurate representa tion of the real world from the perspective of the intended uses of the calculation method Simply put verification is a check of the math validation is a check of the physics If the model predictions closely match the results of experiments using whatever metric is appropria
42. cessarily translate into a comparable decrease in the error of a given FDS output quantity To find out what effect a finer grid has on the solution model users usually perform some form of grid sensitivity study in which the numerical grid is systematically refined until the output quantities do not change appreciably with each refinement Of course with each halving of the grid cell size the time required for the simulation increases by a factor of 2 16 a factor of two for each spatial coordinate plus time In the end a compromise is struck between model accuracy and computer capacity Some grid sensitivity studies have been documented and published Since FDS was first publicly re leased in 2000 significant changes in the combustion and radiation routines have been incorporated into the model However the basic transport algorithm is the same as is the critical importance of grid sensitivity In compiling sensitivity studies only those that examined the sensitivity of routines no longer used have been 5 excluded As part of a project to evaluate the use of FDS version 1 for large scale mechanically ventilated enclo sures Friday 19 performed a sensitivity analysis to find the approximate calculation time based on varying grid sizes A propylene fire with a nominal heat release rate was modeled in FDS There was no mechanical ventilation and the fire was assumed to grow as a function of the time from ignition squared The compart m
43. city m s 0 10 20 30 40 50 Time s Figure 3 17 Flow field left and velocity component plot right for the symmetry_test case 36 Chapter 4 Thermal Radiation The Radiative Transport Equation RTE for an absorbing emitting and scattering medium is Y Os x s V x s K x A 0s x 2 b x s B x A EC m P s s I x s ds 4 1 4n where 1 x s is the radiation intensity at wavelength A s is the direction vector of the intensity k x A and 0 x are the local absorption and scattering coefficients respectively and B x is the emission source term The integral on the right hand side describes the in scattering from other directions In the case of a non scattering gas the RTE becomes s Vl x s k x A n b x s 4 2 where x is the source term given by the Planck function see below In practical simulations the spectral A dependence cannot be solved accurately Instead the radiation spectrum is divided into a relatively small number of bands and a separate RTE is derived for each band The band specific RTE is s VI x s K x lp n x In x s n 1 N 4 3 where J is the intensity integrated over the band n and K is the appropriate mean absorption coefficient inside the band The source term can be written as a fraction of the blackbody radiation Ton Fallas Amax o T n 4 4 where o is the Stefan Boltzmann constant The calculation of factors F
44. contain the core of the algorithm The external researchers provide feedback on the organization of the code and its internal documentation that is comments within the source code itself Plus they must compile the code on their own computers adding to its portability 10 Chapter 3 The Basic Flow Solver In this chapter we present test cases aimed at exercising the advective pressure and viscous terms as well as the time integration for non reacting flows 3 1 2D Analytical Solution to Navier Stokes In this section we present an analytical solution that is useful for confirming the convergence rates of the truncation errors in the discretization of the terms in the governing equations Consider the 2D incompress ible Navier Stokes equations d 5 u Vu Vp vV u 3 1 where the velocity is given by u u v and the kinematic viscosity and pressure are denoted v and p respectively An analytical solution of these equations is given by 37 u x y t 1 Acos x t sin y t e 3 2 v x y f l Asin x 1 cos y t e 2 3 3 A p x y 1 eos 2 x 1 c eosQ 0 e 7 3 4 Here A represents an arbitrary amplitude and is assumed to take a value of 2 in this example Note that this solution satisfies continuity for all time V u 0 3 5 is spatially periodic on an interval 27 in each direction and is temporally periodic on 27 if v 0 otherwise the solution decays exponentially Below we present
45. cribed In such cases minor changes in the properties of bounding surfaces do not have a significant impact on the results However when the HRR is not prescribed but rather predicted by the model using the thermophysical properties of the fuels the model output is sensitive to even minor changes in these properties The sensitivity analyses described in this chapter are all performed in basically the same way For a given scenario best estimates of all the relevant physical and numerical parameters are made and a baseline simulation is performed Then one by one parameters are varied by a given percentage and the changes in predicted results are recorded This is the simplest form of sensitivity analysis More sophisticated techniques that involve the simultaneous variation of several parameters are impractical with a CFD model because the computation time is too long and the number of parameters too large to perform the necessary number of calculations to generate decent statistics 2 3 1 Grid Sensitivity The most important decision made by a model user is the size of the numerical grid In general the finer the numerical grid the better the numerical solution of the equations FDS is second order accurate in space and time meaning that halving the grid cell size will decrease the discretization error in the governing equations by a factor of 4 Because of the non linearity of the equations the decrease in discretization error does not ne
46. d converge to a DNS if the flow field is sufficiently resolved 44 The dynamic procedure for calculating the model coefficient invoked by setting DYNSMAG TRUE on the MISC line alleviates this problem The basis of the model is that the coefficient should be the same for two different filter scales within the inertial subrange Details of the procedure are explained in the following references 45 46 47 48 49 Here we present results for the implementation of the dynamic model in FDS In Figure 3 6 we show contours of the Smagorinsky coefficient C x t at a time midway through a 64 simulation of the CBC experiment Notice that the coefficient ranges from 0 00 to roughly 0 30 within the domain with the average value falling around 0 17 Next in Figure 3 7 we show results for the dynamic model analogous to Figure 3 5 For the 32 case the result is not dramatically different than the constant coefficient model In fact one might argue that the 32 constant coefficient results are slightly better But there are several reasons why we should not stop here and conclude that the constant coefficient model is superior First as pointed out in Pope Exercise 13 34 50 38 is required to resolve 8096 of the total kinetic energy for this flow and thus put the cutoff wavenumber within the inertial subrange of turbulent length scales Pope recommends that simulations which are under resolved by this criterion should be termed very large eddy simula
47. ductivity of both materials are 30 kg m and 10 W m K respectively The emissivity of front and back is 1 The specific heat of material A changes from 1 0 kJ kg K to 0 1 kJ kg K above 80 C while the specific heat of material B is constant at 1 0 kJ kg K The slab is 1 mm thick 200 Surface Temperature enthalpy EN cA o 100 Temperature C 50r Analytical T_slab FDS T slab 0 1 1 1 0 1 2 3 4 Time s Figure 7 6 Testing the enthalpy of solid materials Note that the analytical solution is actually a simple numerical integration of the equations above with a small time step to ensure accuracy This example tests a number of features including the reaction rate mass weighted specific heats and radiation boundary conditions Note that the convective heat transfer has been turned off and the correct steady state temperature is calculated by FDS 61 7 4 A Simple Two Step Pyrolysis Example two step solid reaction Before considering actual experimental measurements it is necessary to check the accuracy of the ordi nary differential equation solver within FDS Consider the simplified set of ordinary differential equations describing the mass fraction of three components of a solid material undergoing thermal degradation dY dt m KupYa dY de KabYa KocYp 7 3 dY a KbcYa where the mass fraction of component ais 1 initially The analytica
48. e scalar bounds set to 0 1 these slugs demonstrate both the boundedness and TVD total variation diminishing behavior of the transport scheme This case also tests two different types of boundary conditions applied in FDS First the domain is periodic and the simulation runs for one flow through time The scalar slugs therefore ideally arrive back to their original locations with as little diffusion as possible Also the domain is broken into four equally sized meshes each with 40 x 40 uniform cells To increase temporal accuracy and focus on the potential spacial error we run the case with a CFL of 0 25 In FDS we refer to the mesh interface as an interpolated boundary The results of the test are shown visually in Figure 3 13 The upper left image shows the initial condi tion The black lines indicate the mesh interfaces To the right of the initial condition we show the first slug crossing the mesh interfaces without incurring spurious noise The lower left image shows the final result for the Superbee limiter By comparison with a first order scheme lower right this test case confirms that relatively low levels of diffusion are incurred at both periodic and interpolated boundaries in FDS 30 Dd Ej o lo Figure 3 13 Upper left Initial condition Upper right Superbee solution after 0 175 seconds showing the scalar slug cleanly passing through the mesh interface Lower left Final result for Superbee after one flow through ti
49. e walls are perfect insulators To simplify the case even further the radiation transport algorithm is turned off It is expected that in this case 1200 kW ought to flow out of the compartment either via the door or ceiling vent The plot to the left side of Fig 3 14 shows both the HRR and enthalpy flow out of the compartment converging to 1200 kW During the warm up phase the enthalpy flow is less than the HRR because energy is consumed heating up the air within the room Next the same compartment with the same fire is now assumed to have cold 20 C walls and the radiation is switched back on After a few minutes of simulation the net enthalpy outflow is approximately 470 kW and the heat losses to the wall both radiative and convective are approximately 730 kW The plot is shown on the right hand side of Fig 3 14 1400 r r r r r 1400 r r r Energy Budget adiabatic walls Energy Budget cold walls 1200 a um mL PECES 1200 1 See es cee eee _ v t gu 1 1 10005 E 1000 ee 2 800 g 800 3 q UU E EA c 1 E ENT ce gt 600 ps 600 B I Expected HRR B Ea ce Expected HRR a Expected Enthalpy Outflow g ne Expected Enthalpy Outflow gm 4001 F ntaa py gm 400m F PAE DY I Expected Wall Loss Expected Wall Loss FDS HRR FDS HRR 200 FDS CONV LOSS 7 200 FDS CONV LOSS FDS COND LOSS FDS COND LOSS
50. ed as a form of verification Granted such a test is not as strong a verification as the convergence study shown in Section 3 1 Nevertheless these tests are often quite useful in discovering problems within the code The case we examine in this section decaying isotropic turbulence is highly sensitive to errors in the advective and diffusive terms because the underlying physics is inherently three dimensional and getting the problem right depends strongly on a delicate balance between vorticity dynamics and dissipation An even more subtle yet extremely powerful verification test is also presented in this section when we set both the molecular and turbulent viscosities to zero and confirm that the integrated kinetic energy within the domain remains constant In the absence of any form of viscosity experience has shown that the slightest error in the advective terms or the pressure projection will cause the code to go unstable This verification is therefore stronger than one might initially expect In this section we test the FDS model against the low Reynolds number Re data of Comte Bellot and Corrsin CBC 38 Viscous effects are important in this data set for a well resolved LES testing the model s Re dependence Following 39 we use a periodic box of side L 9 x 2x centimeters 0 566 m and v 1 5 x 10 m s for the kinematic viscosity The non dimensional times for this data set are x M 42 initial condition 98 and 171 where M i
51. either manually or automatically with profiling programs to detect irregularities and inconsistencies 2 At NIST and elsewhere FDS has been compiled and run on computers manufactured by IBM Hewlett Packard Sun Microsystems Digital Equipment Corporation Apple Silicon Graphics Dell Compaq and various other personal computer vendors The operating systems on these platforms include Unix Linux Microsoft Windows and Mac OSX Compilers used include Lahey Fortran Digital Visual Fortran Intel Fortran IBM XL Fortran HPUX Fortran Forte Fortran for SunOS the Portland Group Fortran and several others Each combination of hardware operating system and compiler involves a slightly different set of compiler and run time options and a rigorous evaluation of the source code to test its compliance with the Fortran 90 ISO ANSI standard 36 Through this process out dated and potentially harmful code is updated or eliminated and often the code is streamlined to improve its optimization on the various machines However simply because the FDS source code can be compiled and run on a wide variety of platforms does not guarantee that the numerics are correct It is only the starting point in the process because it at least rules out the possibility that erratic or spurious results are due to the platform on which the code is running Beyond hardware issues there are several useful techniques for checking the FDS source code that have been developed over t
52. ent was a 3 m by 3 m by 6 1 m space Temperatures were sampled 12 cm below the ceiling Four grid sizes were chosen for the analysis 30 cm 15 cm 10 cm 7 5 cm Temperature estimates were not found to change dramatically with different grid dimensions Using FDS version 1 Bounagui et al 20 studied the effect of grid size on simulation results to de termine the nominal grid size for future work A propane burner 0 1 m by 0 1 m was modeled with a heat release rate of 1500 kW A similar analysis was performed using Alpert s ceiling jet correlation 21 that also showed better predictions with smaller grid sizes In a related study Bounagui et al 22 used FDS to evaluate the emergency ventilation strategies in the Louis Hippolyte La Fontaine Tunnel in Montreal Canada Xin 23 used FDS to model a methane fueled square burner 1 m by 1 m in the open Engineering correlations for plume centerline temperature and velocity profiles were compared with model predictions to assess the influence of the numerical grid and the size of the computational domain The results showed that FDS is sensitive to grid size effects especially in the region near the fuel surface and domain size effects when the domain width is less than twice the plume width FDS uses a constant pressure assumption at open boundaries This assumption will affect the plume behavior if the boundary of the computational domain is too close to the plume Ierardi and Barnett 24 used FDS v
53. ents Each material component may undergo several competing reactions and each of these reactions may produce some other solid component residue gaseous fuel and or water vapor 7 1 Mass conservation of pyrolyzed mass surf mass conservation The calculations described in this section check the conservation of mass produced by the pyrolysis algo rithm Parameters describing the geometric configuration of the solid are input via a SURF line and the reacting materials are described on respective MATL lines In the tests four independent modeling options are varied 1 The SURF line can be associated with either a solid surface as designated by a VENT line or by solid particles as described by a PART line 2 The SURF geometry can be either CARTESIAN CYLINDRICAL or SPHERICAL 3 The MATL can be either charring non zero NU_RESIDUE or non charring 4 The pyrolysis product can be either the fuel gas defined by the mixture fraction model or an additional gas species defined by a SPEC line In all cases the wall thickness or radius for cylindrical and spherical geometries is 0 01 m The material density is 360 kg m and the yield of gaseous products for the charring cases is 0 5 i e half of the original mass For cartesian surfaces the mass loss per unit area is 1 8 kg m for charring and 3 6 kg m for non charring materials For cylindrical surfaces the volume per unit surface area is r 2 and thus the m
54. ere is also a reaction in the simulation that does nothing more than evaporate the small amount of moisture in the wood This evaporation is evident in Fig 7 9 near the temperature of 100 C Exp 2 K min Exp 20 K min FDS 2 K min FDS 20 K min Mass Fraction 0 100 200 300 400 500 600 700 800 Temperature C Figure 7 9 Comparison of a solid phase model of birch wood with TGA data 66 Chapter 8 Lagrangian Particles This chapter contains verification cases that test all aspects of particles droplets sprays and so on Note that in FDS lagrangian particles are used for a variety of purposes not just water droplets 8 1 Momentum Transfer particle drag The particle drag test cases consider a 1 m by 1 m by 1 m channel with periodic boundary conditions on the x faces and FREE SLIP walls on y and z faces Static droplets are placed in the center of the channel one particle per computational cell so that they form a surface perpendicular to the flow direction Gravity is set to zero Due to the symmetry of the problem the flow is one dimensional Assuming that the droplets are of uniform diameter and the drag coefficient and gas density are constant the velocity in the channel decays according to uo i u 1YyCpnr a ee gt 2 y In the above V is the volume of the channel r is the droplet radius Cp is the droplet drag coefficient and u is the gas veloci
55. ersion 3 to model a 0 3 m square methane diffusion burner with heat release rate values in the range of 14 4 kW to 57 5 kW The physical domain used was 0 6 m by 0 6 m with uniform grid spacings of 15 10 7 5 5 3 1 5 cm for all three coordinate directions For both fire sizes a grid spacing of 1 5 cm was found to provide the best agreement when compared to McCaffrey s centerline plume temperature and velocity correlations 25 Two similar scenarios that form the basis for Alpert s ceiling jet correlation were also modeled with FDS The first scenario was a 1 m by 1 m 670 kW ethanol fire under a 7 m high unconfined ceiling The planar dimensions of the computational domain were 14 m by 14 m Four uniform grid spacings of 50 33 3 25 and 20 cm were used in the modeling The best agreement for maximum ceiling jet temperature was with the 33 3 cm grid spacing The best agreement for maximum ceiling jet velocity was for the 50 cm grid spacing The second scenario was a 0 6 m by 0 6 m 1000 kW ethanol fire under a 7 2 m high unconfined ceiling The planar dimensions of the computational domain were 14 4 m by 14 4 m Three uniform grid spacings of 60 30 and 20 cm were used in the modeling The results show that the 60 cm grid spacing exhibits the best agreement with the correlations for both maximum ceiling jet temperature and velocity on a qualitative basis Petterson 26 also completed work assessing the optimal grid size for FDS version 2 The FDS model
56. etween the 21 Table 3 1 Case matrix and friction factor results for turbulent channel flow with smooth walls The height of the first grid cell 5z is given in viscous units z for each case Additionally the table gives the nominal Reynolds number Reg and the FDS friction factor results compared to the Colebrook equation 3 10 dp dx Ze Rey f FDS f Colebrook rel error Pam N 28 N 16 N _ 32 N 32 Eq 3 10 0 01 190 95 47 5 9 x 107 0 0212 0 0202 4 8 ET 1 9 x10 950 470 7 5 x10 0 0128 0 0122 4 6 100 1 9x10 9 5x 10 47 x 105 9 8x 10 0 0077 0 0081 6 0 streamwise pressure drop and the integrated wall stress from the WW model FDS outputs the planar average velocity in the streamwise direction and once a steady state is reached this value is used to compute the Reynolds number and the friction factor Table 3 1 provides a case matrix nine cases for three values of specified pressure drop and three grid resolutions The nominal Reynolds number obtained post run is listed along with the friction factor from the most refined FDS case and the friction factor computed iteratively from the Colebrook equation 1 H 251 AE 3 10 Vf 3 7 T Reg yf which is a fit to the turbulent range of the Moody chart for example see Ref 60 The parameter zo H is the relative roughness where H is the hydraulic diameter of the pipe or channel and Reg is the
57. hat non fire simulations can be completed more quickly than fire simulations because the time step is not limited by the large flow speeds in a fire plume 2 3 2 Sensitivity of Large Eddy Simulation Parameters FDS uses the Smagorinsky form of the Large Eddy Simulation LES technique This means that instead of using the actual fluid viscosity the model uses a viscosity of the form Mes P C A S 2 1 where C is an empirical constant A is a length on the order of the size of a grid cell and the deformation term S is related to the Dissipation Function see FDS Technical Reference Guide 28 for details Related to the turbulent viscosity are comparable expressions for the thermal conductivity and material diffusivity Huss Sc _ Muss Cp LBS C Pr PD ies 2 2 where Pr and Sc are the turbulent Prandtl and Schmidt numbers respectively Thus Cs Pr and Sc are a set of empirical constants Most FDS users simply use the default values of 0 2 0 5 0 5 but some have explored their effect on the solution of the equations In an effort to validate FDS with some simple room temperature data Zhang et al 29 tried different combinations of the Smagorinsky parameters and suggested the current default values Of the three pa rameters the Smagorinsky constant C is the most sensitive Smagorinsky 30 originally proposed a value of 0 23 but researchers over the past three decades have used values ranging from 0 1 to 0
58. he incoming Na is found from the Equation of State Wp p e RT The injection velocity is the mass flux divided by the density u m p in which case the pressure rise can be written 3 44 MI ee La ALA 3 45 dt WV Note that the pressure rise is constant In both the fast and slow injection cases the pressure is expected to rise 64282 Pa above ambient The density and temperature rise are also linear The density increases from 1 164 kg m to 1 364 kg m The temperature increases from 20 C to 135 7 C The change in the internal energy of the system based on the mass and temperature of the added Na is AE 0 2 kg x 1 039 kJ kg K x 773 15 K 160 7 kJ 3 46 Adding in the work due to the pressure yields the change in total enthalpy AH AE V AP 160 7 kJ 1 m x 64 3 kJ m 225 kJ 3 47 34 4 10 L5 87 l j s Density isentropic2 at Pressure isentropic2 1 4 6r dc NON a 6 gt 1 p B 135 P m F 5 a E pee x a a 2 g l A i Pr adl oi Pd 8125 d 23t a Lf A P d ou 1 1 2 di J 2 K d Lo Analytical Density 1 yz Analytical Pressure 1 157 FDS density_1 Lpd e FDS pressure 1 FDS density_2 u d FDS pressure 2 1 1 j 0 i 10 20 30 40 50 60 0 10 20 30 40 50 60 Time s Time s 160 r r r r r 650 r r r
59. he channel is L 8 m The number of grid cells in the streamwise direction x is N 8 The number of cells in the wall normal direction z is varied N 8 16 32 64 The fluid density is p 1 2 kg m and the viscosity is 0 025 kg m s The mean pressure drop is prescribed to be dp dx 1 Pa m resulting in Reg 160 The Moody friction factor f which satisfies L1 Ap fg xpi 3 9 is determined from the steady state mean velocity 4 which is output by FDS for the specified pressure drop The exact friction factor for this flow is fevact 24 Reg The friction factor error f fexact is plotted for a range of grid spacings 6z H N in Figure 3 8 demonstrating second order convergence of the laminar velocity field Turbulent Smooth Walls To verify the WW wall model for turbulent flow we perform 3D LES of a square channel with periodic boundaries in the streamwise direction and a constant and uniform mean pressure gradient driving the flow The problem set up is nearly identical to the laminar cases of the previous section except here we perform 3D calculations and maintain cubic cells as we refine the grid we hold the ratio 8 1 1 between N Ny N for all cases The cases shown below are identified by their grid resolution in the z direction The velocity field is initially at rest and develops in time to a mean steady state driven by the specified mean pressure gradient The presence of a steady state is the result of a balance b
60. he key quantitative result of this verification test In this figure we plot the rms error Erms in the u component of velocity against the grid spacing The error is defined by 2 Erms 15 UE u x Y tx 3 6 rms ME ij i js where M is the number of time steps and k is the time step index The spatial indices are i N 2 j N 2 and Uf represents the FDS value for the u component of velocity at the staggered storage location for cell i j at time step k u x J tx is the analytical solution for the u component at the corresponding location in space and time The figure confirms that the advective terms the viscous terms and the time integration in the FDS code are convergent and second order accurate 12 Analytical uve ns2d 16 nuptl Analytical u vel FDS UVEL FDS UVEL ns2d 8 nuptl Velocity m s Velocity m s ns2d 32 muptl Analytical vel ns2d 64 nupt Analytical u vel FDS UVEL FDS UVEL 2 7 2F T 15 15 E B 3 9 E E I J Sol 0 57 7 0 5 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 Time s Time s Figure 3 2 Time history of the u component of velocity half a grid cell below the center of the domain for a range of grid resolutions The domain is a square of side L 21 m The N x N grid is uniform Progressing from left to right and top to bottom we have resolutions N 8 16 32 64
61. he years One of the best ways is to exploit symmetry FDS is filled with thousands of lines of code in which the partial derivatives in the conservation equations are approximated as finite differences It is very easy in this process to make a mistake Consider for example the finite difference approximation of the thermal diffusion term in the ijkth cell of the three dimensional grid 1 Ti 1 jk Tijk Tijk Ti 1 jk VEAS RE ay issn a BBC w D 1 k p UNE a DERE de By Mit MA y 1 Tijk 1 Tijk k Ti jk Tijk 1 z 4 z ij4 3 z which is written as follows in the Fortran source code DTDX TMP I 1 J K TMP I J K RDXN I KDTDX I J K 5 KP 1 1 J K KP I J K DTDX DTDY TMP I J 1 K TMP I J K RDYN J KDTDY I J K 5 KP I J 1 K KP I J K x DTDY DTDZ TMP I J K 1 TMP I J K RDZN K KDTDZ I J K 5 KP I J K 1 KP I J K DTDZ DELKDELT KDTDX I J K KDIDX I 1 J K RDX I KDTDY I J K KDIDY I J 1 K RDY J KDTDZ I J K KDTDZ I J K 1 RDZ K This is one of the simpler constructs because the pattern that emerges within the lines of code make it fairly easy to check However a mis typing of an 1 or a J a plus or a minus sign or any of a hundred different mistakes can cause the code to fail or worse produce the wrong answer A simple way to eliminate many of these mistakes is to run simple scenarios that have perfectly symmet
62. i and G Candler Subgrid scale models for compressible large eddy simulation Theoret Comput Fluid Dynamics 13 361 376 2000 18 47 P Moin K Squires W Cabot and S Lee A dynamic subgrid scale model for compressible turbulence and scalar transport Phys Fluids A 3 11 2746 2757 1991 18 48 T S Lund On the use of discrete filters for large eddy simulation Center for Turbulence Research Annual Research Briefs 1997 18 49 R McDermott Variable density formulation of the dynamic smagorinsky model Unpublished notes http randy mcdermott googlepages com dynsmag_comp pdf 2004 18 50 Stephen B Pope Turbulent Flows Cambridge 2000 18 20 51 S B Pope Ten questions concerning the large eddy simulation of turbulent flows New Journal of Physics 6 1 24 2004 19 52 J S Baggett Some modeling requirements for wall models in large eddy simulation Stanford Center for Turbulence Research Annual Research Briefs 1997 20 53 J S Baggett On the feasibility of merging LES with RANS for the near wall region of attached turbulent flows Stanford Center for Turbulence Research Annual Research Briefs 1998 20 54 W Cabot Large eddy simulations with wall models Stanford Center for Turbulence Research Annual Research Briefs 1995 20 55 Pierre Sagaut Large Eddy Simulation for Incompressible Flows Springer 2001 20 56 H Werner and H Wengle Large eddy simulation of turbulent flow over and around
63. igure we demonstrate second order convergence of the central Superbee and CHARM limiter schemes in FDS 28 8 10 FDS Central 7r e FDS Superbee 5 FDS CHARM 7 6 O 9x 22 O z B E 10 F x St gt E c E E 23 E E 3 a 10 2l 3 1 0 1 107 A 0 2 4 6 8 10 12 10 107 10 Time s Grid Spacing dx m Figure 3 12 Left Time series of p at the position x y 31 2 3n 2 for several grid resolutions using the CHARM flux limiter Right Convergence plot for three different scalar transport schemes in FDS central Superbee and CHARM All schemes are second order accurate In addition notice that Superbee gives the lowest error at the coarsest resolution while CHARM gives the lowest error at higher resolution This is one reason why Superbee is recommended for LES and CHARM is the default for DNS 29 3 6 Scalar Transport move slug In this section we demonstrate the qualitative behavior of the Superbee flux limiter scheme for transport of a square wave The diffusivity is set to zero and the advecting velocity is constant and uniform u 1 0 1 0 The domain is the unit square with a passive scalar marker initialized to zero everywhere except for two slugs of mass The first slug is set to unity over the region x x z 0 125 0 375 x 0 125 0 375 The second slug is set to 1 2 over the region x x z 0 500 0 750 x 0 500 0 750 With th
64. ions played a role in the verification process of FDS Thanks to Chris Lautenburger and Carlos Fernandez Pello for their assistance with the two reaction test case Matthias M nch of the Freie Universit t Berlin provided useful test cases for the basic flow solver Susanne Kilian of hhpberlin Germany helped to debug the improved pressure solver Clara Cruz a student at the University of Puerto Rico and Summer Undergraduate Fellow at NIST helped developed useful Matlab scripts to automate the process of compiling this Guide Bryan Klein of NIST developed the source code version control system that is an essential part of the verification process Anna Matala of VTT Finland designed the surf mass pyrolysis cases Danielle Antonellis a student at Worcester Polytechnic Institute and Summer Undergraduate Fellow at NIST added the pulsating scalar verification test case vi Contents Preface About the Authors Acknowledgments 1 What is Verification 2 Survey of Past Verification Work 2 1 2 2 2 3 2 4 Analytical TESIS 2 uoce mono moe a wow dog Dow eos qos a ufo Numencal Tests e s bss I II TT sensitivity Analysis coo ore oe Cb a o Ow a ea 23 Ond Senstvily ss a i Sa 2 Se ec lege he or ples eye E Ow Re ak Erwin 2 3 2 Sensitivity of Large Eddy Simulation Parameters ln 2 3 3 Sensitivity of Radiation Parameters lt oo ee ee ee 2 3 4 Sensitivity of Thermophysical Properties of
65. ions with a finite element model 51 6 3 Simple Thermocouple Model thermocouples This example tests the simple thermocouple model in EDS It consists of a box whose walls and gas temper atures are fixed at 500 C Inside the box are three thermocouples with bead diameters of 1 2 and 3 mm Also included in the box are three targets small solid objects whose surfaces are assumed to be com posed of small spheres of the same diameter as the thermocouples Figure 6 3 compares the temperature rise of the objects The thermocouple model is not compared with an analytical solutions This is simply a comparison of the thermally thin thermocouple calculation with the thermally thick target calculation Small differences in temperature are due to slightly different flow conditions in different regions of the box and numerical error due to node spacing and time step size 600 Surface Temperature thermocouples 500 S 400 g 3 300 9 g Thick Target 1 E 200 Thick Target_2 Thick Target_3 100 Thin TC 1 Thin TC 2 Thin TC 3 0 i i i 0 20 40 60 80 100 120 Time s Figure 6 3 Comparison of thermally thin and thick heat conduction into a small sphere 52 Chapter 7 Pyrolysis This chapter tests the routines in FDS that calculate the thermal decomposition of materials Solid surfaces can consist of multiple layers and each layer can consist of multiple material compon
66. is not as important as those in the near field where coverage by the default number of angles is much better Hostikka et al examined the sensitivity of the radiation solver to changes in the assumed soot pro duction number of spectral bands number of control angles and flame temperature Some of the more interesting findings were Changing the soot yield from 1 to 2 increased the radiative flux from a simulated methane burner about 15 Lowering the soot yield to zero decreased the radiative flux about 20 ncreasing the number of control angles by a factor of 3 was necessary to ensure the accuracy of the model at the discrete measurement locations Changing the number of spectral bands from 6 to 10 did not have a strong effect on the results Errors of 100 in heat flux were caused by errors of 20 in absolute temperature The sensitivity to flame temperature and soot composition are consistent with combustion theory which states that the source term of the radiative transport equation is a function of the absorption coefficient mul tiplied by the absolute temperature raised to the fourth power The number of control angles and spectral bands are user controlled numerical parameters whose sensitivities ought to be checked for each new sce nario The default values in FDS are appropriate for most large scale fire scenarios but may need to be refined for more detailed simulations such as a low sooting methane burner
67. is presented in Section 3 1 and is used to verify the spatial and temporal accuracy of momentum equation However to our knowledge there are no similar i e time dependent and periodic in space analytical solutions for the compressible NS equations which could be used for verification of both compressible and variable density low Mach flow solvers The aim of the present work is to take a small step toward developing such analytical solutions The main idea is that given a specified velocity field the continuity equation can be rearranged into a linear hyperbolic PDE for the logarithm of the density Let p denote the density and let u u v denote the velocity The continuity equation conservation of mass can then be written as dlnp ot u Vinp V u 0 3 11 Further for certain simple specifications of the velocity this PDE can be solved using the method of char acteristics In what follows we present 1D and 2D solutions to 3 11 for two basic irrotational flow fields All the solutions are periodic in space The first configuration is a pulsating flow that cycles between compressing the fluid toward the center and then the corners of the domain In the second configuration time periodicity is achieved by using a constant and uniform advection velocity in combination with the compression waves This results in a solution with a qualitatively different character than the first 3 5 1 Pulsating 1D solution We specify the vel
68. ius r specified via THICKNESS is 0 01 m The expected masses are thus 360 1 0 5 x mr 0 00565 kg for charring and 0 0113 kg for non charring materials For spherical particles the expected mass is 360 1 0 5 x 4n 3 7 54 x 107 kg for charring and 1 51 x 1073 kg for non charring materials The analytical and computed results for charring material are compared in 7 3 The analytical and computed results for non charring material are compared in 7 4 57 Mass kg 0 02 0 02 surf mass part char cart fuel surf mass part char cart gas O05 oish 7 e E 0 01r e 1 a 0 01F a 1 x 8 me E nae e Pid T 0 005 PN d 1 0 005 gne Pd Expected Po Expected pa os S 4 4 0 d L L 1 0 le L 0 50 100 150 200 0 50 100 Time s Time s 0 014 T T 0 014 surf mass part char cyl fuel surf mass part char cyl gas 0 0127 Y 1 0 0127 Y P 0 01 E 0 01 3 E 0 008 im E 0 008 icm Z 0 006 amp 0 0065 a a 0 004 0 004 0 002 0 002 Expected Gaseous 0 0 Time s Time s 5X 10 jx 107 surf mass part char spher fuel surf mass part char spher gas 15h 15h 7 8 Ir EN g Lr hy e AAA SM e O a rm y e 0 5 uo 0 5 uo Pd 2 Y di d Expected uv Y Y 0 Y f 1 1 0 Y i 0 20 40 60 0 20 40 60 Time s Time s Figure 7 3 Comparison of analytical mass change and simulated mass changes f
69. l A e FDS Superbee Lm 10 4 FDS CHARM gar O dx Las a E 0 x gt gl a e E a 3 ON A 3 107 0 10 S o 0 2 4 6 8 10 12 10 10 10 Time s Grid Spacing dx m Figure 3 11 Left Time series of p at the position x y 3n 2 37 2 for several grid resolutions using the Superbee limiter Right Convergence plot for central differencing Superbee and CHARM AII schemes are second order accurate 3 5 3 Stationary compression wave in 1D Another problem which can be solved analytically is that of a stationary compression wave In this section we consider a stationary compression wave combined with a constant and uniform advection velocity in 1D The velocity is specified to be u x c sin x 3 27 where c gt 1 is a constant The 1D continuity equation becomes d X c sin x m cos x 0 3 28 A solution to 3 28 1s q x t q xolx t 0 In cos bt 2arctan y x 1 bsin bt 2 arctan y x 1 In 2c cos 2arctan y x t bsin 2arctan y x 1 3 29 where b vV 1 c gt 0 3 30 1 ctan 38840 y x t i E 3 31 and xo x t 2arctan Eran arctan d Heeck 3 i 3 32 c b 2 c 3 5 4 Stationary compression wave in 2D As with the pulsating flow there is a simple extension of the 1D stationary wave solution to 2D In this section we consider the velocity field with components u x ci sin x 3 33 v y co sin y 3
70. l solution is Ya E Y t Y t exp Kopt Kab exp Kapt exp Kpct 7 4 Kbc Kap Kap 1 exp Koct Kpc exp Kapt 1 Kap Koc 1 5 The analytical and numerical solution for the parameters Kap 0 389 and Kpc 0 262 are shown here Solid Density two step solid reaction e o oo Analytical Ya Analytical Yb Analytical Yc FDS Ya FDS Yb FDS Yc 0 5 10 15 20 25 30 Time s Mass Fraction o a d a Figure 7 7 Comparison of a two step solid pyrolysis calculation with an analytical solution 62 7 5 Interpreting Bench Scale Measurements This section describes a method of deriving and applying the values of the kinetic parameters for the thermal decomposition of a solid following the methodology described by Lyon 67 7 5 1 General Theory Consider a small sample of solid material that is heated at a relatively slow constant rate An example of this process is thermal gravimetric analysis TGA Assume that the solid consists of N material components with each component mass fraction denoted by Y t As the solid is heated each component undergoes a reaction to form undetermined gases or a single solid residue whose mass fraction is denoted Y t and whose yield is denoted by v The governing equations for the component mass fractions is then dY udi A Y exp z Y 0 Yo g
71. me Lower right Result for first order upwinding after one flow through time illustrating the relatively low dissipation of the Superbee scheme Note that though the first order scheme is available as an option in FDS it is presented here for comparison purposes only In practice the higher order Superbee scheme is preferred for LES FDS default 31 3 7 Energy Conservation energy_budget The examples in this section check that mass and energy are conserved for relatively simple configurations 3 7 1 The Heat from a Fire energy_budget For the purpose of verifying that the basic FDS algorithm is energy conserving 1t is useful to think of a single compartment as a control volume into which energy is generated by a fire and out of which energy either flows via openings or is conducted through the walls If the fire s heat release rate HRR is steady eventually the system will reach a quasi steady state in an LES calculation there is never a true steady state Two simple cases called energy budget adiabatic walls and energy budget cold walls illustrate that in the quasi steady state the energy generated by the fire is conserved For the case with adiabatic walls a 1200 kW fire is simulated within a compartment that is 10 m by 10 m by 5 m tall There is a single door and a single horizontal vent in the ceiling The walls are assumed to be adiabatic that is there is no net heat flux through them Another way to look at it is that th
72. nd should be Ty To dt if 0 dV mcp 4 9 By setting T 0 C dt 0 01 s m 0 01 kg and cp 1 0 kJ kg the value of Ty should be equal to the volumetric integral of Q The following two plots show comparison of the predicted average droplet temperature and the analytical value in cartesian and cylindrical co ordinate systems Droplet Temperature droplet absorption cart Droplet Temperature droplet absorption cyl 3 5 1 3 5 3 Den 3 pen z 2 PEU E di g 25 E 3 3 2 E 2 d 3 2 27 9 Pr 9 nd g 1 5 2 151 e D Ps D pud Et per EI E 0 5 id 7 Analytical 0 5 Pd Analytical Pr FDS ADT Pris FDS ADT 0 0 a 0 0 002 0 004 0 006 0 008 0 01 0 0 002 0 004 0 006 0 008 0 01 Time s Time s Figure 4 2 Conserversion of absorbed thermal radiation energy into increased average droplet temperature 43 Chapter 5 Species and Combustion This chapter contains examples that test the computations related to species concentrations gas properties and combustion 5 1 Boundary Conditions For most problems involving fire or combustion the most important parameter of a model is the total heat release It is therefore extremely important to assure that the correct amount of fuel is injected into the FDS computational domain Below we present a series of test cases for the species boundary conditions 5 1 1 Specified Mass Flux low_flux_hot_gas_filling
73. ocity as u x t Bsin x cos 0f 3 12 where B is a constant amplitude and is the frequency of the compression cycle The velocity divergence in 1D is then du TE Bcos x cos wt 3 13 Let q Inf this notation is used through out this work The 1D continuity equation can then be written as the following linear hyperbolic PDE dq Bsin x cos r Bcos x cos t 0 3 14 oq ot which can be solved using the method of characteristics to obtain the solution x t 1 tan 24 exp 22 sin ar B q x t q xo x t 0 1n m T sin t 3 15 xox 1 tan 52 where the initial position is given by x B xo x t 2arctan tan s exp Estas 3 16 Note that we have taken the initial time to be zero as is done throughout this work 25 3 5 2 Pulsating 2D solution There is a simple extension of the 1D stationary wave solution to 2D In this section we consider the velocity field u u v with components and velocity divergence given by u x t Bsin x cos 0 3 17 v y t Bsin y cos t 3 18 V u B cos x cos y cos r 3 19 where again B is a constant amplitude and is the compression frequency The 2D continuity equation may then be written as d d d xS Bsin x cos ot 3 Bsin y cos or o B cos x cos y cos r 0 3 20 x y where again q Inp x f The solution to 3 20 can be obtained by adding the solutions of the following two PDEs n Bsin x cos
74. odel can be a source of error in the predicted results The hydrodynamic model within FDS is second order accurate in space and time This means that the error terms associated with the approximation of the spatial partial derivatives by finite differences is of the order of the square of the grid cell size and likewise the error in the approximation of the temporal derivatives is of the order of the square of the time step As the numerical grid is refined the discretization error decreases and a more faithful rendering of the flow field emerges The issue of grid sensitivity is extremely important to the proper use of the model and will be taken up in the next chapter A common technique of testing flow solvers is to systematically refine the numerical grid until the computed solution does not change at which point the calculation is referred to as a Direct Numerical Solution DNS of the governing equations For most practical fire scenarios DNS is not possible on conventional computers However FDS does have the option of running in DNS mode where the Navier Stokes equations are solved without the use of sub grid scale turbulence models of any kind Because the basic numerical method is the same for LES and DNS DNS calculations are a very effective way to test the basic solver especially in cases where the solution is steady state Throughout its development FDS has been used in DNS mode for special applications For example FDS or its core
75. oden fuels is very important and difficult to measure Flame spread over complicated objects like cables laid out in trays can be modeled if the surface area of the simplified object is comparable to that of the real object This suggests sensitivity not only to physical properties but also geometry It is difficult to quantify the extent of the geometrical sensitivity There is little quantification of the observed sensitivities in the study Fire growth curves can be linear to exponential in form and small changes in fuel properties can lead to order of magnitude changes in heat release rate for unconfined fires The subject is discussed in the FDS Validation Guide Volume 3 of the Technical Reference Guide where it is noted in many of the studies that predicting fire growth is difficult Recently Lautenberger Rein and Fernandez Pello 35 developed a method to automate the process of estimating material properties to input into FDS The methodology involves simulating a bench scale test with the model and iterating via a genetic algorithm to obtain an optimal set of material properties for that particular item Such techniques are necessary because most bench scale apparatus do not provide a complete set of thermal properties 2 4 Code Checking An examination of the structure of the computer program can be used to detect potential errors in the nu merical solution of the governing equations The coding can be verified by a third party
76. of time are compared to analytical solutions of the one dimensional heat transfer equation These studies help determine the number of nodes to use in the solid phase heat transfer model Similar studies are performed to check the pyrolysis models for thermoplastic and charring solids Early in its development the hydrodynamic solver that evolved to form the core of FDS was checked against analytical solutions of simplified fluid flow phenomena These studies were conducted at the National Bureau of Standards NBS by Rehm Baum and co workers 5 6 7 8 The emphasis of this early work was to test the stability and consistency of the basic hydrodynamic solver espe cially the velocity pressure coupling that is vitally important in low Mach number applications Many numerical algorithms developed up to that point in time were intended for use in high speed flow applications like aerospace Many of the techniques adopted by FDS were originally developed for l The National Institute of Standards and Technology NIST was formerly known as the National Bureau of Standards 3 meteorological models and as such needed to be tested to assess whether they would be appropriate to describe relatively low speed flow within enclosures A fundamental decision made by Rehm and Baum early in the FDS development was to use a direct rather than iterative solver for the pressure In the low Mach number formulation of the Navier Stokes equations an elli
77. on Tall Buildings pages 507 514 International Council for Research and Innovation in Building and Construction CIB 2003 6 G Heskestad SFPE Handbook of Fire Protection Engineering chapter Fire Plumes Flame Height and Air Entrainment National Fire Protection Association Quincy Massachusetts 3rd edition 2002 6 72 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 N M Petterson Assessing the feasibility of reducing the grid resolution in fds field modeling Fire Engineering Research Report 2002 6 University of Canterbury Christchurch New Zealand March 2002 6 A Musser K B McGrattan and J Palmer Evaluation of a Fast Simplified Computational Fluid Dynamics Model for Solving Room Airflow Problems NISTIR 6760 National Institute of Standards and Technology Gaithersburg Maryland June 2001 6 K B McGrattan S Hostikka J E Floyd H R Baum R G Rehm W E Mell and R McDermott Fire Dynamics Simulator Version 5 Technical Reference Guide Volume 1 Mathematical Model NIST Special Publication 1018 5 National Institute of Standards and Technology Gaithersburg Maryland October 2007 7 20 W Zhang A Hamer M Klassen D Carpenter and R Roby Turbulence Statistics in a Fire Room Model by Large Eddy Simulation Fire Safety Journal 37 721 752 2002 7 J Smagorinsky General Circulation Experiments with the Primitive Equations I The Ba
78. or charring surfaces asso ciated with particles 58 8 Mass k 0 02 surf mass part nonchar cart fuel 0 02 surf mass part nonchar cart gas n 28 n A Y 3 Y 0015 5 y J 0015 pd L A a s 7 eb 2 L Expected c im 2 Expected The et Gaseous g KA Pd Gaseous 0 01r EN 2 Solid QOO0lr E ooo p Solid Sa Pid S s P Pd te 0 005 2 J 0 005 yd Pd Pd Mirch oo cece ee hg Tenge TUS 0 L L Ba ose L 0 ites L 0 20 40 60 80 100 60 80 100 Time s Time s 0 015 0 015 surf mass part nonchar cyl fuel surf mass part nonchar cyl gas 0 01 0 01 L7 feb feb ao cei Ej m e e 5 V 0 005 0 005 Rf x Ld A Expected V EN Expected de Gaseous Y ug Gaseous Pd oco Solid md Da 0 20 40 60 80 100 0 20 40 60 Time s Time s 3 3 10 10 ap S surf mass part nonchar spher fuel surf mass part nonchar spher gas 2r 2t a AAA a aa D LT S E rr T E eer E venenum p di p d E 7 E e a d zi S 1 i Y 7 Y T d a d a Y e 05E a J 0 5 7z i 4 m Expected Y m Expected P EN Gaseous P Em Gaseous E RAPERE aaa Solid 7 a rt AA Solid 0 Y L pte ses L L 0 le n Ys e ke L 0 20 40 60 80 100 0 20 40 60 80 100 Time s Time s Figure 7 4 Comparison of analytical mass change and simulated mass changes for non charring surfaces associated
79. orted financially via internal funding at both NIST and VTT Finland In addition support is provided by other agencies of the US Federal Government The US Nuclear Regulatory Commission Office of Research has funded key validation experiments the preparation of the FDS manuals and the development of various sub models that are of importance in the area of nuclear power plant safety Special thanks to Mark Salley and Jason Dreisbach for their efforts and support The Office of Nuclear Material Safety and Safeguards another branch of the US NRC has supported modeling studies of tunnel fires under the direction of Chris Bajwa and Allen Hansen The Micro Gravity Combustion Program of the National Aeronautics and Space Administration NASA has supported several projects that directly or indirectly benefited FDS development The US Forest Service has supported the development of sub models in FDS designed to simulate the spread of fire in the Wildland Urban Interface WUT Special thanks to Mark Finney and Tony Bova for their support The Minerals Management Service of the US Department of the Interior funded research at NIST aimed at characterizing the burning behavior of oil spilled on the open sea or ice Part of this research led to the development of the ALOFT A Large Outdoor Fire plume Trajectory model a forerunner of FDS Special thanks to Joe Mullin for his encouragement of the modeling efforts The following individuals and organizat
80. pheres with a diameter of 1 cm and temperature of 500 C are situated within a smaller volume that is 0 5 m on a side One of the open volumes contains 10 spheres the other contains 50 000 The simulation lasts for 10 s In the first volume the heat loss is just the sum of the areas of the spheres multiplied by 07 emissivity is specified as unity in this case See the upper left plot in Fig 4 1 In the second volume the region is densely packed and it is expected that the collection of spheres will radiate like a solid cube that is 0 5 m on a side and whose temperature is 500 C This is just under 30 kW as shown in the upper right of Fig 4 1 The plot in the lower left of Fig 4 1 shows the incident heat flux to a gauge positioned at the center of the densely packed volume It is expected that this gauge would register a heat flux of oT 20 26 kW m Finally the plot in the lower right of Fig 4 1 indicates the integrated intensity 4074 81 04 kW m 0c Or r r r r n Loose Pack Radiation Loss hot spheres 10 E Tight Pack Radiation Loss hot_spheres 10L 1 0 02F J 1 o y o 20r 1 i E MT Lt 7 004 S30 1 m e a t wr 3 is E 40r 1 2 T le 2 1 Is NL LLL LLL 2 sok y E a 1 I E E 60L 1 0 08 H Exact Rad Loss 1 70t 1 1 Exact Rad Loss 2 4 FDS rad loss 1 1 tl FDS rad loss 2 0 1 1 1
81. ptic partial differential equation for the pressure emerges often referred to as the Poisson equation Most CFD methods use iterative techniques to solve the governing conservation equations to avoid the necessity of directly solving the Poisson equation The reason for this is that the equation is time consuming to solve numerically on anything but a rectilinear grid Because FDS is designed specifically for rectilinear grids it can exploit fast direct solvers of the Poisson equation obtaining the pressure field with one pass through the solver to machine accuracy FDS employs double precision 8 byte arithmetic meaning that the relative difference between the computed and the exact solution of the discretized Poisson equation is on the order of 107 The fidelity of the numerical solution of the entire system of equations is tied to the pressure velocity coupling because often simulations can involve hundreds of thousands of time steps with each time step consisting of two solutions of the Poisson equation to preserve second order accuracy Without the use of the direct Poisson solver build up of numerical error over the course of a simulation could produce spurious results Indeed an attempt to use single precision 4 byte arithmetic to conserve machine memory led to spurious results simply because the error per time step built up to an intolerable level 2 2 Numerical Tests Numerical techniques used to solve the governing equations within a m
82. put parameters that describe the geometry materials combustion phenomena etc By design the user is not expected to provide numerical parameters besides the grid size although the optional numerical parameters are described in both the Technical Reference Guide and the User s Guide FDS does not limit the range of most of the input parameters because applications often push beyond the range for which the model has been validated FDS is still used for research at NIST and elsewhere and the developers do not presume to know in all cases what the acceptable range of any parameter is Plus FDS solves the fundamental conservation equations and is much less susceptible to errors resulting from input parameters that stray beyond the limits of simpler empirical models However the user is warned that he she is responsible for the prescription of all parameters The FDS manuals can only provide guidance The grid size is the most important numerical parameter in the model as it dictates the spatial and tem poral accuracy of the discretized partial differential equations The heat release rate is the most important physical parameter as it is the source term in the energy equation Property data like the thermal conduc tivity density heat of vaporization heat capacity etc ought to be assessed in terms of their influence on the heat release rate Validation studies have shown that FDS predicts well the transport of heat and smoke when the HRR is pres
83. r a is 4 2 Y z 607 5 d 405 20 Analytical Rel Hum FDS humid 0 1 1 1 1 0 1 2 3 4 5 Time s 30 r h Gas Temperature water evaporation N CM gt 25 BS H ib A ELS mi E 9 E E 20 Analytical temp FDS Temp 15 n n 1 1 0 1 2 3 4 5 Time s 0 03 Evaporated Mass water evaporation OOP oe ee Sie 0 022 7 b l a f a 0 015 YN E e 0 01 0 099 Analytical vapor FDS WATER VAPOR 0 n n 1 1 0 1 2 3 4 Time s Figure 8 2 Output of the test case called water_evaporation 70 Bibliography 1 2 3 4 5 6 7 8 9 10 11 K B McGrattan S Hostikka and J E Floyd Fire Dynamics Simulator Version 5 User s Guide NIST Special Publication 1019 5 National Institute of Standards and Technology Gaithersburg Mary land October 2007 1 American Society for Testing and Materials West Conshohocken Pennsylvania ASTM E 1355 04 Standard Guide for Evaluating the Predictive Capabilities of Deterministic Fire Models 2004 i 1 9 W Mell K B McGrattan and H Baum Numerical Simulation of Combustion in Fire Plumes In Twenty Sixth Symposium International on Combustion pages 1523 1530 Combustion Institute Pittsburgh Pennsylvania 1996 3 K B McGrattan H R Baum and R G Rehm Large Eddy Simulations of Smoke Movement Fire Safety Journal 30 161 178 1998 3 H R Baum R G Rehm P D Barnett and D M Corley
84. r r Temperature isentropic2 Enthalpy isentropic2 140r it a 600 t Pa ae nn D0r i Pd c ka CADCM AS fet p 1 e e 550r 1 pt 1 d EJ 1 2 100p 1 P E n P E p Bsp y ge z 80r i a 4 E Ni g 1 H i 60 e m 450r A Pd 1 1 a 40 A E Pd Analytical Temperature 400 2 sid Analytical Enthalpy le FDS temperature_1 hog FDS enthalpy 1 20 T FDS temperature_2 e FDS enthalpy 2 ER 350 4 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Time s Time s Figure 3 16 Density pressure temperature and enthalpy rise due to the injection of nitrogen into a sealed compartment 35 3 8 Checking for Coding Errors symmetry_test This example is a very simple test to determine if there are coding errors in the basic flow solver A closed box 1 m on a side has 6 injection vents one centered on each face Air is pumped into the box at a rate of 0 5 m s Anything that might lead to an asymmetry in the flow field is turned off for example gravity atmospheric stratification natural convection and random noise The resulting flow field is shown at the left in Fig 3 17 On the right are plots of the three components of velocity at equidistant corners of the enclosure Ideally there should be two equal and opposite time histories of the three components Even the slightest error in coding will throw this off almost immediately Component Velocity symmetry test 0 57 Velo
85. re 5 1 45 0 035f Low Flux Hot Gas Filling 120 0 03r kg 0 025 0 02f 0 015 0 01f Accumulated Mass 0 005 Specified FDS 0 10 20 30 40 50 60 Time s Figure 5 1 Test of specified mass flux boundary condition for low mass flux and specified temperature on the face of the vENT Left Image of the domain showing contours of propane mass fraction Right Comparison of the accumulated mass of propane with the FDS values reported in the mass file 5 2 Fractional Effective Dose FED Device The Fractional Effective Dose index FED developed by Purser 63 is a commonly used measure of human incapasitation due to the combustion gases The present version of FDS uses only the concentrations of the gases CO CO and O to calculate the FED value as FED FEDco x HVco FEDo 5 3 The fraction of an incapacitating dose of CO is calculated as FEDco 4 607 x 107 Cco 996 5 4 where t is time in seconds and Cco is the CO concentration ppm The fraction of an incapacitating dose of low O hypoxia is calculated as t FEDo 0 60exp 8 13 0 54 20 9 Co 5 5 where Co is the O2 concentration volume per cent The hyperventilation factor induced by carbon dioxide is calculated as 0 1930C 2 0004 HVco apo ZR ub where Cco is the CO concentration percent The FED values were computed from specified constant ga
86. re positive in that nothing points to coding errors 16 0 05 Time 0 045 o e E 2 m 2 o a a t EDS zero vise e FDS mol visc 8 FDS Smag i d O filtered CBC data 5 0 03 kinetic energy o o e o N N un 0 0157 0 005 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 time s FDS Smag 0 06 O filtered CBC data 2 2 Ss gt E a kinetic energy m7 s o S E k m s 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 time s k 1 m Figure 3 5 Left Time histories of integrated kinetic energy corresponding to the grid resolutions on the right side of the figure In the 32 case top the CBC data open circles are obtained by applying a filter to the CBC energy spectra at the Nyquist limit for an N 32 grid Similarly for the 64 case bottom the CBC data are obtained from filtered spectra for an N 64 grid Notice that the integrated FDS results for the 32 case compare better with the filtered CBC data than the 64 results This is a well known limitation of the constant coefficient Smagorinsky model namely that the eddy viscosity does not converge to zero at the appropriate rate as the filter width here equivalent to the grid spacing is decreased Right Energy spectra for the 32 case top and the 64 case bottom The solid black lines are the spectral data of Comte Bellot and Corrsin at three different points in time corre
87. ric initial and boundary conditions For example put a hot cube in the exact center of a larger cold compartment turn off gravity and watch the heat diffuse from the hot cube into the cold gas Any simple error in the coding of the energy equation will show 9 up almost immediately Then turn on gravity and in the absence of any coding error a perfectly symmetric plume will rise from the hot cube This checks both the coding of the energy and the momentum equations Similar checks can be made for all of the three dimensional finite difference routines So extensive are these types of checks that the release version of FDS has a routine that generates a tiny amount of random noise in the initial flow field so as to eliminate any false symmetries that might arise in the numerical solution The process of adding new routines to FDS is as follows typically the routine is written by one person not necessarily a NIST staffer who takes the latest version of the source code adds the new routine and writes a theoretical and numerical description for the FDS Technical Reference Guide plus a description of the input parameters for the FDS User s Guide The new version of FDS is then tested at NIST with a number of benchmark scenarios that exercise the range of the new parameters Provisional acceptance of the new routine is based on several factors 1 it produces more accurate results when compared to experimental measurement 2 the theoretical descrip
88. rticle drag F i T im amp E 100 E D 1 d li 50 Q A O Analytical 0 Me oo 9 9 D ll 0 0 5 1 1 5 2 Time s Figure 8 1 Outputs of the particle_drag test cases compared with analytical solutions 68 8 2 Water Droplet Evaporation water_evaporation The test case called water evaporation involves stationary water droplets in a box with dimensions of 1 m on a side The walls of the box are assumed adiabatic meaning that there are no leaks or heat losses The air within the box is stirred to maintain uniform conditions Initially the air temperature is 20 C the median volumetric diameter of the droplets is 100 um the water temperature is 90 C and the total mass of water droplets is 0 2 kg It is expected that a steady state will be achieved after about 5 s Figure 8 2 displays the average enthalpy humidity density pressure temperature and mass of water of the gas The horizontal lines denote the expected initial and steady state values respectively The plot of enthalpy includes the gas reference temperature is 0 K and the liquid water droplets reference temperature is 0 C The decrease in the enthalpy of the water droplets should equal the increase in the enthalpy of the gas minus the work performed due to increasing pressure It is the internal energy of the system that is conserved The internal energy can be expressed in terms of the enthalpy pressure and density p e h 8 2 p In differential form
89. s concentrations using an external spread sheet The gas concentrations are listed in the following table and the FDS and spreadsheet predictions of FED values are compared in the figures below 46 FED FED 0 1 100 FED 02 depletion 0 08 0 06 0 04 0 02 FED Spreadsheet FDS FED 0 i i 7 7 0 20 40 60 80 Time s FED CO24 CO 0 17 0 05 gt FED Spreadsheet FDS FED 0 i i 7 7 0 20 40 60 80 Time s Figure 5 2 Comparison of FED index predictions with spreadsheet computations 100 47 FED FED 100 0 1 T r r r FED CO 0 08f 0 06 0 04 0 02 FED Spreadsheet FDS FED 0 i i 7 7 0 20 40 60 80 Time s FED All gases 0 17 0 05 FED Spreadsheet FDS FED 0 i i 7 7 0 20 40 60 80 Time s 100 48 Chapter 6 Heat Conduction This chapter contains examples that test the one dimensional heat conduction solver in FDS A one dimensional heat conduction equation for the solid phase temperature T x t is applied in the direction x pointing into the solid the point x 0 represents the surface OT OTs m k T 6 1 PsCs t Jx s 3x ds 6 1 In cylindrical and spherical coordinates the heat conduction equation is written oT 10 OT Wi oT 10 4 OT ii Kem de 5 Cs k 6 2
90. s exercise Note that REFERENCE TEMPERATURE is 7 but in units of C REFERENCE RATE is actually r Yo in units of s HEATING RATE is B in units of K min NU RESIDUE is V and NU FUEL is 1 v Table 7 1 lists all of the kinetic parameters for the cable insulation and jacket materials The peak temperatures are easy to estimate and the values of rp Yo can be fine tuned to closely match the data Note that it is possible to compute values of A and E and input them directly into FDS rather than inputting those listed in the table However the values of A and E are fairly large numbers and have little meaning in their own 65 Table 7 1 Parameters used to derive the kinetic constants for cable materials The heating rate for both is 60 C min Parameter Insulation v 0 06 Jacket v 0 49 1 2 1 2 3 Tpi CC 355 485 300 345 450 Fail Tia sb 0 0384 0 2426 0 0064 0 3500 0 0156 7 5 3 Using TGA Data birch_tga This is an example of a comparison of a candidate solid phase model with TGA Thermo gravimetric Analy sis data The sample cases called birch tga 1step 2 and birch tga 1step 20 simulate two standard TGA experiments in which small samples of birch wood are heated up slowly at constant rates of 2 C min and 20 C min respectively The model of the wood only involves one reaction that converts virgin wood to char and fuel gases Th
91. s the characteristic mesh spacing of the CBC wind tunnel and x is the downstream location of the data station Considering the mean velocity in the CBC wind tunnel experiment these correspond to dimensional times of t 0 00 0 28 and 0 66 seconds in our simulations The initial condition for the FDS simulation is generated by superimposing Fourier modes with random phases such that the spectrum matches that of the initial CBC data An iterative procedure is employed where the field is allowed to decay for small time increments subject to Navier Stokes physics each wavenumber is then injected with energy to again match the initial filtered CBC spectrum The specific filter used here is discussed in 40 To provide the reader with a qualitative sense of the flow Figure 3 4 shows the initial and final states of the velocity field in the 3D periodic domain The flow is unforced and so if viscosity is present the total energy decays with time due to viscous dissipation Because the viscous scales are unresolved a subgrid stress model is required Here the stress is closed using the gradient diffusion hypothesis and the eddy viscosity is modeled by the constant coefficient Smagorinsky model with the coefficient taken to be C 0 2 see the Technical Reference Guide for further details The decay curves for two grid resolutions are shown plotted on the left in Figure 3 5 For an LES code such as FDS which uses a physically based subgrid model an import
92. sic Experi ment Monthly Weather Review 91 3 99 164 March 1963 7 J W Deardorff Numerical Investigation of Neutral and Unstable Planetary Boundary Layers Journal of Atmospheric Sciences 29 91 115 1972 7 M Germano U Piomelli P Moin and W H Cabot A Dynamic Subgrid Scale Eddy Viscosity Model Physics of Fluids A 3 7 1760 1765 1991 7 D K Lilly A Proposed Modification of the Germano Subgrid Scale Closure Method Physics of Fluids A 4 3 633 635 1992 7 J Hietaniemi S Hostikka and J Vaari FDS Simulation of Fire Spread Comparison of Model Results with Experimental Data VTT Working Papers 4 VTT Building and Transport Espoo Finland 2004 8 C Lautenberger G Rein and C Fernandez Pello The application of a genetic algorithm to estimate the material properties for fire modeling from bench scale fire test data Fire Safety Journal 41 204 214 2006 8 J C Adams W S Brainerd J T Martin B T Smith and J L Wagener Fortran 95 Handbook Com plete ISO ANSI Reference MIT Press Cambridge Massachusetts 1997 9 R McDermott A nontrivial analytical solution to the 2 d incompressible Navier Stokes equations http randy mcdermott googlepages com NS exact soln pdf 2003 11 G Comte Bellot and S Corrsin Simple Eularian time correlation of full and narrow band velocity signals in grid generated isotropic turbulence J Fluid Mech 48 273 337 1971 15 Stephen M de Bruyn Kops Numerical
93. simulation of non premixed turbulent combustion PhD thesis The University of Washington 1999 15 R McDermott A Kerstein R Schmidt and P Smith Characteristics of 1D spectra in finite volume large eddy simulations with one dimensional turbulence subgrid closure In 58th Annual Meeting of the American Physical Society Division of Fluid Dynamics Chicago Illinois November 2005 http randy mcdermott googlepages com implied_filter pdf 15 16 73 41 Y Morinishi T S Lund O V Vasilyev and P Moin Fully conservative high order finite difference schemes for incompressible flow J Comp Phys 143 90 124 1998 15 42 F E Ham F S Lien and A B Strong A fully conservative second order finite difference scheme for incompressible flow on non uniform grids J Comp Phys 177 117 133 2002 15 43 R McDermott Discrete kinetic energy conservation for variable density flows on staggered grids In 60th Annual Meeting of the American Physical Society Division of Fluid Dynamics Salt Lake City Utah November 2007 http randy mcdermott googlepages com aps2007 notes pdf 15 44 R McDermott and S B Pope A particle formulation for treating differential diffusion in filtered density function methods J Comp Phys 226 1 947 993 2007 18 45 M Germano U Piomelli P Moin and W Cabot A dynamic subgrid scale eddy viscosity model Phys Fluids A 3 7 1760 1765 1991 18 20 46 M Pino Martin U Piomell
94. sponding to downstream positions in the turbulent wind tunnel The initial condition for the velocity field spectra shown as black dots in the FDS simulation is prescribed such that the energy spectrum matches the initial CBC data The FDS energy spectra corresponding to the subsequent CBC data are shown by the red and blue dots The vertical dashed line represents the wavenumber of the grid Nyquist limit 17 Smokeview Test 3187 Jan 30 2009 Slice 0 30 0 27 0 24 0 21 0 18 0 15 0 12 0 09 0 06 0 03 0 00 Frame 91 Time 0 313 mS Figure 3 6 Smagorinsky coefficient for a 64 simulation of the CBC experiment 3 3 The Dynamic Smagorinsky Model In the previous section all calculations were performed with a constant and uniform Smagorinsky coeffi cient C 0 2 For the canonical case of homogeneous decaying isotropic turbulence at sufficiently high Reynolds number this model is sufficient However we noticed that even for the isotropic turbulence problem when the grid Reynolds number is low i e the flow is well resolved the constant coefficient model tends to over predict the dissipation of kinetic energy see Figure 3 5 This is because the eddy viscosity does not converge to zero at the proper rate so long as strain is present in the flow the magnitude of the stain rate tensor is nonzero the eddy viscosity will be nonzero This violates a guiding principle in LES development that the method shoul
95. sults from a model when applied for a specific use The model evaluation process consists of two main components verification and validation Verification is a process to check the correctness of the solution of the governing equations Verification does not imply that the governing equations are appropriate only that the equations are being solved correctly Validation is a process to determine the appropriateness of the governing equations as a mathematical model of the physical phenomena of interest Typically validation involves comparing model results with experimental measurement Differences that cannot be explained in terms of numerical errors in the model or uncertainty in the measurements are attributed to the assumptions and simplifications of the physical model Evaluation is critical to establishing both the acceptable uses and limitations of a model Throughout 1ts development FDS has undergone various forms of evaluation both at NIST and beyond This volume provides a survey of verification work conducted to date to evaluate FDS 11 About the Authors Randall McDermott joined the research staff of the Building and Fire Research Lab in 2008 He received a B S degree from the University of Tulsa in Chemical Engineering in 1994 and a doctorate at the University of Utah in 2005 His research interests include subgrid scale models and numerical meth ods for large eddy simulation adaptive mesh refinement Lagrangian particle methods
96. t i 1 N 7 6 dY dY d Tay oque an In the TGA apparatus the temperature of the sample is increased linearly in time dT dt B Because TGA results are usually expressed as a function of temperature rather than time it is convenient to rewrite Eq 7 6 as dY Ai E dT po FT 0 Yo 7 8 The decomposition rate dY dt peaks at a temperature denoted by T with a value denoted by r j At this temperature the second derivative of Y is zero dY Aj dY E Ai y ox E Y E _ MA E E o gar Xu BO OU SERO ar B RE RE Next Eq 7 8 can be integrated from Yo to Y the value of Y at the peak and T to T Ypi dY A i E A RT E ra F E T id exp dT e et exp 7 10 Yo Y p To RT p E F 2RT 3 RT i Using Eq 7 9 to eliminate A yields 0 7 9 Y E Inf 2 1 E gt 2RT 7 11 E 2RT pe pi or more simply Y Yo e Now the activation energy can be evaluated using Eqs 7 6 and 7 9 2 2 E RT2 i exp Ei Pri tps Roi erp 7 12 TB RT D Ypi D Yoi Then A can be evaluated directly from Eq 7 6 A pi exp m pi exp 7 13 Y RT i Yo RT Note that the formulae for A and E can be evaluated with parameters that are obtained directly by inspection of the plot of mass loss rate versus temperature For each peak the values of T and rp are obvious The values of Yo can be estimated
97. te it is assumed by most that the model suitably describes via its mathematical equations what is happening It is also assumed that the solution of these equations must be correct So why do we need to perform model verification Why not just skip to validation and be done with it The reason is that rarely do model and measurement agree so well in all applications that anyone would just accept its results unquestionably Because there is inevitably differences between model and experiment we need to know if these differences are due to limitations or errors in the numerical solution or the physical sub models or both Whereas model validation consists mainly of comparing predictions with measurements as documented for FDS in Volume 3 of the Technical Reference Guide model verification consists of a much broader range of activities from checking the computer program itself to comparing calculations to analytical exact solutions to considering the sensitivity of the dozens of numerical parameters The next chapter discusses these various activities and the rest of the Guide is devoted mainly to comparisons of various sub model calculations with analytical solutions Chapter 2 Survey of Past Verification Work This chapter documents work of the past few decades at NIST VTT and elsewhere to verify the algorithms within FDS 2 1 Analytical Tests Most complex combustion processes including fire are turbulent and time dependent There are
98. terms are negligible and the sgs stress is of critical importance The quality of the sgs model still influences the wall stress however since other components of the sgs tensor affect the value of the near wall velocity and hence the resulting viscous stress determined by the wall model In particular it is important that the sgs model is convergent in the sense that the LES formulation reduces to a DNS as the filter width becomes small so that as the grid is refined we can expect more accurate results from the simulation For smooth walls the model used for ty t o in this work is the Werner and Wengle model 56 which is described in detail in the FDS Tech Guide For rough walls the momentum flux normal to the wall is balanced by inviscid drag forces on the surface elements 59 In this case FDS models the stress by a rough wall log law see Pope 50 Details are provided in the Tech Guide 20 10 LO BO 0 aset E Later E107 8 ia 310 9 a 4 10 FDS Q amp ol 10 107 Grid Spacing z m Figure 3 8 FDS exhibits second order convergence for laminar Poiseuille flow in a 2D channel 3 4 2 Results Laminar As verification of the no slip boundary condition and further verification of the momentum solver in FDS we perform a simple 2D laminar Poiseuille flow calculation of flow through a straight channel The height of the channel is H 1 m and the length of t
99. tion is sound and 3 any empirical parameters are obtainable from the open literature or standard bench scale apparatus If the new routine is accepted it is added to a test version of the software and evaluated by external users and or NIST grantees whose research is related to the subject Assuming that there are no intractable issues that arise during the testing period the new routine eventually becomes part of the release version of FDS Even with all the code checking performed at NIST it is still possible for errors to go unnoticed One remedy is the fact that the source code for FDS is publicly released Although it consists of on the order of 30 000 lines of Fortran statements various researchers outside of NIST have been able to work with it add enhancements needed for very specific applications or for research purposes and report back to the developers bugs that have been detected The source code is organized into 27 separate files each containing subroutines related to a particular feature of the model like the mass momentum and energy conservation equations sprinkler activation and sprays the pressure solver etc The lengthiest routines are devoted to input output and initialization Most of those working with the source code do not concern themselves with these lengthy routines but rather focus on the finite difference algorithm contained in a few of the more important files Most serious errors are found in these files for they
100. tions weather forecasting is a typical example For a 32 LES the test filter width in the dynamic model falls at a resolution of 16 clearly outside the inertial range A tacit assumption underlying the original interpretation of the dynamic model is that both the grid filter scale and the test filter scale should fall within the inertial range since this is the 18 FDS Smag 0 045r O filtered CBC data m 004r 4 N as 0 035 amp lis A za 0 03 a D A S 0 025 2 2 m o 002r S x 0 015F 0 01r 0 005 i i i 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 time s 0 07 T T 1 FDS Smag 0 06 O filtered CBC data S 0 05 F e z 2 004r an A 5 0 03 Z m 9 E 002r X 0 01r 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 time s o Figure 3 7 Dynamic Smagorinsky model results analogous to Figure 3 5 for integrated kinetic energy left and spectra right range in which the scales of turbulent motion in theory exhibit fractal like scale similar behavior recently the procedure has been derived from other arguments 51 With this in mind it is perhaps not surprising that the dynamic model does not perform optimally for the low resolution case In the higher resolution 64 case however the dynamic model does perform better than the constant coefficient model and this is the desired result we want better performance at higher resolution As can
101. two series of tests which demonstrate the second order accuracy of the FDS numerical scheme and thus provide a strong form of code verification for the advective and viscous terms which are exercised The physical domain of the problem is a square of side L 27 The grid spacing is uniform 6x dy L N in each direction with N 8 16 32 64 for each test series The staggered grid locations are denoted x idx and y jy and the cell centers are marked by an overbar x x 6x 2 and y y 6y 2 First we present qualitative results for the case in which v 0 Thus only the advective discretization and the time integration are being tested Figure 3 1 shows the initial and final t 2x numerical solution for the case N 64 As mentioned with v 0 the solution is periodic in time and this figure demonstrates that as should be the case the FDS numerical solution is unaltered after one flow through time 11 Figure 3 1 Initial and final states of the u component of velocity Next in Figure 3 2 we show time histories of the u component of velocity at the center of the domain for the case in which v 0 1 It is clearly seen that the FDS solution thin line converges to the analytical solu tion thick line Note that the analytical solution is evaluated at the same location as the FDS staggered grid location for the u component of velocity xy 2 Yw 2 which is different in each case N 8 16 32 64 Figure 3 3 is t
102. ty in the x direction The summation is over all N particles The common parameters used in all the simulations are 8 1 Cp 10 ra 0 005 The initial velocity uo for each case is listed in Table 8 1 Comparisons of computed and analytical results are shown in Figure 8 1 Table 8 1 Parameters used in the particle drag cases Case uo N A 10 16 B 50 16 C 100 16 D 50 1600 E 100 1600 F 150 1600 67 Velocity m s Velocity m s Velocity m s 12 Gas phase velocity particle drag A 108 Y 8L v L O Analytical a FDS E AF Se o L T9 2 eo Mene 0 L L L L 0 20 40 60 80 100 Time s 60 Gas phase velocity particle drag B 509 i 1 40n L O Analytical 30r FDS y 20r a S e a 10 ge ba ENS o o o 0 1 L L 0 10 20 30 40 50 Time s 120 T r r Gas phase velocity particle drag C 1009 i 1 80n L O Analytical 60r FDS y 407 a N a 20 Es o o o o 2 39 3 0 sf L L L 0 5 10 15 20 25 Time s Gas phase velocity particle drag D Velocity m s 1 201b Li V 120 Gas phase velocity particle drag E 10 am sor E gt 60 5 2 I 40b n 20 5 R 5 O Analytical o 9 9 e Fg FS I 0 0 5 1 1 5 2 Time s 200 T r Gas phase velocity pa
103. us Fuel S 2L We ox E a a 2 s 458 1 lr 4 Y 3 0 2 L 04 1 dl L 0 50 100 150 200 0 50 100 150 200 Time s Time s 2L surf mass vent nonchar cyl fuel j 2F surf mass vent nonchar cyl gas d 1 5 15r e ss W Y x Id E Y Expected Gaseous x Gaseous IE Solid l 8g vf Gascous Gaseous Fuel m y e L s 05r y 50 100 150 0 50 100 150 Time s Time s 1 5 T T T T 1 5 surf mass vent nonchar spher fuel surf mass vent nonchar spher gas 1 Ej Expected Ej Expected pod Gaseous tae p DE A IEA olid 2 amp yl Gaseous Fuel amp gt pA 0 St E 3 Fi ue B ti 0 20 40 60 80 100 Time s Time s Figure 7 2 Comparison of analytical mass change and simulated mass changes for non charring surfaces associated with vents 56 7 1 2 Pyrolysis of Discrete Particles For lagrangian particles the expected values of the mass are obtained by multiplying the material density by the particle volume by the residue fraction For cartesian surfaces the particle area is two times the product of the parameters LENGTH and WIDTH on the SURF line both of which are given a value 0 05 m As a result the expected masses for particles with cartesian surfaces are 360 1 0 5 x 26LW 0 009 kg for charring and 0 018 kg for non charring materials Note that the half thickness 6 0 01 m is specified on the SURF line as THICKNESS For cylindrical particles the LENGTH is 0 1 m and the rad
104. we describe the model formu lation Then in Section 3 4 2 we conduct a verification study of the wall boundary conditions for laminar and turbulent flows in FDS From this study we are able to draw quantitative conclusions in Section 3 4 3 about the accuracy of the channel flow simulations for smooth and rough walls 3 4 1 Formulation Details of the FDS formulation are given in the Technical Guide 28 Here we provide only the salient components of the model necessary for treatment of constant density channel flow The filtered continuity and momentum equations are Qi X 0 3 7 Oi 4 gi u 1 dp op OT n ovi ot Ox E p dx l Ox Ox Ox j 3 8 where vi p uju iiji is the subgrid scale sgs stress tensor here modeled by gradient diffusion with dynamic Smagorinsky 45 used for the eddy viscosity In this work we specify a constant pressure drop dp dx in the streamwise direction to drive the flow The hyrdrodynamic pressure p is obtained from a Poisson equation which enforces 3 7 When 3 8 is integrated over a cell adjacent to a smooth wall in an LES it turns out that the most difficult term to handle is the viscous stress at the wall e g 7 p because the wall normal gradient of the streamwise velocity component cannot be resolved Note that the sgs stress at the wall is identically zero We have therefore an entirely different situation than exists in the bulk flow at high Reynolds number where the viscous
105. with particles 59 7 2 Development of surface emissivity emissivity For thermally thick materials the surface emissivity is computed as a mass weighted sum of the individual values of the emissivity in the first condensed phase grid cell In this verification test the initial material having emissivity of 1 0 is converted to another material having emissivity of 0 0 at a constant rate of 0 1 s7 As a result the surface emissivity should change linearly from 1 0 to 0 0 in 10 s Surface Emissivity emissivity Emissivity Analytical Emissivity FDS EMISSIVITY 0 2 4 6 8 10 Time s Figure 7 5 Testing the emissivity of solid materials 60 7 3 Enthalpy of solid materials enthalpy Consider a thin plate of conductive material that is exposed on one side to an elevated temperature heat source and exposed on the other to an ambient temperature void In the thermally thin limit the temperature of the slab is governed by the following equation dT Qon Gees dt Cs Ps 7 1 In this example the initial exposure to the front side of the slab is 3 kW m The original material call it A undergoes a reaction to form material B The reaction rate is constant 0 2 s l which in this case means that material A disappears in exactly 5 s This is achieved by setting ns and E to 0 and A to 0 2 in the reaction rate term E r B4 A exp 7 2 Ps0 RT The density and con

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