ABSTRACT 

This report investigates the use of the Fire Dynamics Simulator (FDS), for coarse grid modeling of non-fire 

and fire situations. FDS is a large eddy simulation computational fluid dynamics program that was 

developed to model fires in enclosures. One goal of this study was to compare its predictions with 

experimental data and other published CFD studies of test rooms without fires in them. Four such 

experiments are considered. The first three are idealized test rooms designed to demonstrate forced, natural, 

and mixed convection. The fourth is a more realistic room setup with furniture, a displacement ventilation 

system, and a contaminant release. The results of these simulations agree reasonably with the experimental 

data, provided that care is taken in defining boundary conditions and inputs in a way that is consistent with 

the intention and capabilities of the model. In particular, some care is needed to define convection 

coefficients for heated or cooled surfaces. A second goal of this study was to determine the effects of using 

very coarse grids on both the computational results and computing time. The results of this comparison show 

that non-fire simulations are generally much faster than fires because the simulation times step is limited by 

the convective motion. In many cases, the coarse grid solutions agreed with the experimental data nearly as 

well as could be accomplished with a much finer grid and could be modeled in real time or faster. However, 

accurate contaminant dispersal modeling did require a significantly finer grid. 

ACKNOWLEDGEMENT 

The work described in this report was undertaken while the first author held a National Research Council 

Postdoctoral Research Associateship. The assistance of that program is gratefully acknowledged. 
1

Evaluation of a Fast, Simplified Computational Fluid Dynamics Model for Solving Room Airflow Problems 

TABLE OF CONTENTS 

ABSTRACT....................................................................................................................................................... i 

ACKNOWLEDGEMENT.................................................................................................................................. i 

1. INTRODUCTION.........................................................................................................................................3

2. SIMPLIFIED CFD MODELING OF ROOM AIRFLOW............................................................................4

2.1. Types of CFD Models ............................................................................................................................4

2.2. The Fire Dynamics Simulator (FDS)......................................................................................................4

2.3. Constructing an FDS Model...................................................................................................................6

3. VERIFICATION SIMULATIONS...............................................................................................................8

3.1 Forced Convection ..................................................................................................................................8

3.2. Natural Convection...............................................................................................................................17

3.3. Mixed Convection ................................................................................................................................22

3.4. Displacement Ventilation .....................................................................................................................29

3.5 Ventilated Fire.......................................................................................................................................37

3.6. Corner Fire ...........................................................................................................................................45

4. DISCUSSION .............................................................................................................................................51

4.1. Computing Time...................................................................................................................................51

4.2. Results Comparison..............................................................................................................................52

5. CONCLUSIONS.........................................................................................................................................53

REFERENCES.................................................................................................................................................54

APPENDIX A: Sample input files ..................................................................................................................56

A.1. Forced convection (case 14)................................................................................................................56

A.2. Natural convection (case 2) .................................................................................................................56

A.3. Mixed convection (case 1)...................................................................................................................56

A.4. Displacement ventilation (case 2)........................................................................................................57

A.5 Ventilated Fire (case 4) ........................................................................................................................59

A.6 Corner Fire (case1)..............................................................................................................................61

FIGURE LIST 

Figure 1. Geometry for the forced convection case. 

Figure 2. Grid transformations used in the forced convection case. 

Figure 3. CPU time per cell per time step for the forced convection case. 

Figure 4. CPU time per cell per second of simulated time for the forced convection case. 

Figure 5. Airflow pattern generated for the forced ventilation case. 

Figure 6. Forced convection results for non-transformed grids. 

Figure 7. Forced convection results for cases with polynomial transformation. 

Figure 8. Forced convection results for piecewise linear transformation. 

Figure 9. Problem description for the natural convection case. 

Figure 10. CPU time per cell per time step for the natural convection case. 

Figure 11. CPU time per cell per second of simulated time for the natural convection case. 

Figure 12. Dimensionless temperatures for two dimensional natural convection cases without grid 

transformation. 

Figure 13. Dimensionless temperatures for three dimensional natural convection cases with polynomial grid 

transformation. 

Figure 14. Velocities from two dimensional natural convection cases without grid transformation. 

Figure 15. Geometry for the mixed convection case. 

Figure 16. Grids transformations used in the mixed convection case. 

Figure 17. CPU time per cell per time step for the mixed convection case. 

Figure 18. CPU time per cell per second for the mixed convection case. 

Figure 19. Mixed convection results for the piecewise linear transformations. 

Figure 20. Mixed convection results for the polynomial transformations. Figure 21. Geometry for the 

displacement ventilation case. 
2

Figure 22. Measurement locations for the displacement ventilation case. 

Figure 23. CPU time per cell per time step for the displacement ventilation case. 

Figure 24. CPU time per cell per second of simulated time for the displacement ventilation case. 

Figure 25. Temperatures predicted for the displacement ventilation case. 

Figure 26. SF6 concentration predicted for the displacement ventilation case. 

Figure 27. Velocities predicted for the displacement ventilation case. 

Figure 28. Geometry for the Ventilated Fire. 

Figure 29. Smokeview Wire Frame of the Ventilated Fire. 

Figure 30. Grid transformations used in the ventilated fire (x- direction) 

Figure 31. CPU time per cell per time step for ventilated fire 

Figure 32. CPU time per cell per second of simulated time for the ventilated fire 

Figure 33. Normalized Error Fraction for the ventilated fire with no grid transformation 

Figure 34. Normalized Error Fraction for the ventilated fire with grid transformation 

Figure 35. Normalized Error Fraction for the ventilated fire, radiation calculations enabled 

Figure 36. Plan view of experimental layout for the corner fire. 

Figure 37. Wire frame view of corner fire experiment. 

Figure 39. CPU time per cell per time step for corner fire. 

Figure 40. CPU time per cell per second of simulated time for corner fire. 

Figure 41: Fast corner fire normalized error fraction 

Figure 42: Slow corner fire normalized error fraction. 

Figure 43. Average time step. 

Figure 44. CPU time per cell per timestep.

Figure 45. CPU time per cell per second.

TABLE LIST 

Table 1. Simulations performed for the forced convection case. 

Table 2. Simulations performed for the natural convection case. 

Table 3. Simulations performed for the mixed convection case. 

Table 4. Surface Convection Coefficients Relevant to Room Airflow. 

Table 5. Simulations performed for the displacement ventilation case. 

Table 6 Simulations Performed for Ventilated Fire
3

1. INTRODUCTION 

Many types of building design and analysis would benefit from a more detailed understanding of building 

airflow patterns, contaminant dispersal, and thermal stratification. Computational Fluid Dynamics (CFD) 

models provide this type of information and have been available for many years, however, their application 

has historically been limited by their need for extensive computational resources. Historically, then, two 

modeling techniques have evolved: CFD models to represent a single room or small set of rooms when 

much detail is needed, and whole-building models that are less detailed but consume fewer computational 

resources. 

Many airflow problems require analysis of the entire building, since pressure-driven flows generated by 

forces such as weather and the building mechanical system influence the migration of contaminants between 

rooms. Often, this macroscopic view of building airflows is adequate to characterize contaminant behavior. 

However, when stratified or poorly mixed spaces are present within the building, the details of contaminant 

migration within these rooms begin to influence its interaction with surrounding rooms. A CFD modeling 

approach allows this room or group of rooms to be modeled in a more detailed way. A fast, simplified CFD 

simulation could be integrated into the whole-building simulation or possibly used on its own to model many 

rooms simultaneously. 

This sort of integrated simulation approach would offer the building design community an enhanced ability 

to predict and model the performance of complicated spaces, and to simulate events more realistically. As 

computing time and resources become faster and less costly, emulation of building or system behavior in 

response to an event such as a fire or a contaminant release also becomes possible. However, before such an 

undertaking is begun, the CFD software must first be evaluated for its intended usage. In addition to the 

verification of results with experimental data, issues such as computing time, model construction, and output 

data must be investigated. 

This report compares results of simulations performed using the Fire Dynamics Simulator (FDS) with 

published experimental data, covering a wide range of conditions that are encountered in buildings. 

Whenever possible, these results have also been qualitatively compared with published simulations from 

other CFD programs. The issues of computing time and model assembly have also been investigated in 

detail. The overall focus is to simultaneously consider both experimental verification and computing time, 

allowing users to build improved models and develop realistic expectations regarding speed and accuracy. 

Issues of concern with regard to FDS model development, execution, and application are documented for 

situations relevant to the modeling of fire scenarios, indoor air quality, and thermal comfort. The report 

offers guidance, identifies weaknesses, and evaluates the effectiveness of the model for situations beyond the 

fire and smoke applications for which it was originally developed. Verification of results with experimental 

data and qualitative comparison with published predictions of other CFD programs provide a context from 

which potential users may evaluate FDS according to the needs of a specific project. 
4

2. SIMPLIFIED CFD MODELING OF ROOM AIRFLOW 

Computational fluid dynamics (CFD) models have been used to predict room air motion since the mid-1970s. 

Since they provide a very detailed prediction of velocities, temperatures, and species concentration in rooms, 

CFD models are potentially useful for many types of building analysis. Some examples include indoor air 

quality studies, fire modeling, thermal comfort evaluations, and predicting air distribution patterns. 

Unfortunately, it can be difficult to construct realistic CFD models of building airflows because diffuser 

flows, heat fluxes, and other boundary conditions may not be well understood or easily defined (Chen 1997). 

In addition, room airflows typically require turbulence modeling. 

2.1. Types of CFD Models 

CFD models are often categorized according to the way in which turbulence is addressed. Direct numerical 

simulation of the Navier-Stokes equations is possible, but requires very fine grid resolution and small time 

steps that demand computing capacity far exceeding what is currently available. Therefore, two groups of 

methods have been developed to reduce the computing effort associated with turbulence. These methods 

differ in the way that turbulence is approximated. The first solves a time averaged set of Navier-Stokes 

equations. The other method solves directly for the transient behavior of the large scale turbulent motion and 

approximates small scale activity to reduce computing time. 

Reynolds Averaged Navier-Stokes (RANS) methods divide the flow into mean and fluctuating components, 

solving a time averaged set of Navier-Stokes equations. These methods save computing time by allowing 

coarser grids to be used and because they produce time independent solutions for steady flows. If a transient 

solution is desired, a quasi-steady solution is obtained at each time step. While the standard k-epsilon model 

may be the most well known and widely used method to approximate the effects of turbulence, models with 

varying degrees of complexity are available and have been successfully used to model various types of room 

airflow (Nielsen 1998). The simplest of these is the zero equation turbulence model. In these models, a 

turbulent viscosity component is represented by a simple algebraic function of the fluid density, average 

velocity, and mixing length. This does not add to the number of equations to be iteratively solved, resulting 

in very fast simulation times appropriate for a simplified model (Chen et al. 1998). 

Large eddy simulation (LES) provides an alternative method of accounting for turbulence. LES seeks to 

filter out and directly calculate the large-scale turbulent motion, which tends to have the greatest impact on 

turbulent transport (McGrattan et al. 1994). Smaller-scale turbulent motion (those eddies smaller than the 

grid cell size chosen) is taken into account with a subgrid scale eddy viscosity model. Because the Navier 

Stokes equations are not time averaged, this method is inherently time dependent. LES methods are 

therefore best suited to solving transient flow problems, but results can be averaged over time for comparison 

with steady-state experimental data. LES has traditionally been more time consuming than RANS methods. 

However, by limiting the solution to regular geometries, a very fast solver can be used. This technique has 

been employed to develop a simplified LES model, Fire Dynamics Simulator (FDS), to predict room air 

motion in fires (McGrattan et al. 2000). This model has also been used to solve some room airflow 

problems (Emmerich and McGrattan 1998). 

2.2. The Fire Dynamics Simulator (FDS) 

The Building and Fire Research Laboratory at NIST has recently released version 1.0 of the Fire Dynamics 

Simulator (FDS). Previous versions of the model were referred to as LES, LES3D and most recently IFS 

(Industrial Fire Simulator). The name Fire Dynamics Simulator was chosen because model development is 

heading in a number of different directions; some of which are not necessarily ``industrial'' in nature. Below 

is a brief description of the numerical model. Further details can be found in McGrattan et al. (2000). 

Consider a thermally expandable mixture of ideal gases driven by a prescribed heat source. The equations of 

motion governing the fluid flow can be written in a form suitable for low Mach number applications (Rehm 

and Baum 1978). Sometimes, this form of the equations is referred to as ``weakly compressible'' or 
5

``thermally expandable'' to emphasize that the divergence of the gas mixture is governed only by the 

introduction of heat or a change in the composition of the mixture. High speed compressibility effects are not 

admitted. The low Mach number approximation is achieved by replacing the spatially and temporally varying 

pressure in the energy conservation and state equations by an average or background pressure, po, that 

depends only on time. This is done to filter out acoustic waves. The efficiency of the numerical solution of 

the equations is dramatically increased by this approximation because the speed of sound is assumed infinite 

and small pressure perturbations need not be tracked in the numerical procedure. The conservation equations 

are written as follows: 

Conservation of Mass 

0

t

+ ∇ ⋅ ρ = ∂

∂ρ u (1) 

Conservation of Species 

( ) Y Y ( ) D Y

t

i i ρ i + ∇ ⋅ ρ i = ∇ ⋅ ρ ∇

∂

∂

u (2) 

Conservation of Momentum 

 ( )  + ∇ = ρ + ∇ ⋅ τ 

 



 + ⋅∇

∂

∂

ρ u u g

u

p t

 (3) 

Conservation of Energy 

 ( ) q' ' ' k T h ( ) D Y dt

dp h h

t

i i

i

i

0 ρ + ∇ ⋅ ρ − = +∇ ⋅ ∇ + ∇ ⋅ ∑ ρ ∇

∂

∂ ⋅

u (4) 

Equation of State 

 p = TR∑( ) Yi M i / 0 ρ (5) 

Here, all symbols have their usual fluid dynamical meaning: ρ is the density, u the velocity vector, Yi and Di

the mass fraction and diffusion coefficient of the ith gas species, p the pressure, ∇⋅ τ the viscous stress tensor, 

g the gravity vector, h the enthalpy, T the temperature, k the thermal conductivity, t the time, q''' the 

volumetric heat release rate, and R the universal gas constant. 

What distinguishes CFD models from one another is how each treats the diffusive terms in the species, 

momentum and energy equations. Most formulations start with the viscous terms in the momentum 

equations, and relate other diffusive coefficients to the viscosity. 

The components of the viscous stress tensor are given by 

 



 





∂

∂ − δ

∂

∂

+

∂

∂

τ = μ

k

k

ij

i

j

j

i

ij

x

u

3

2

x

u

x

u

 (6) 

For a Large Eddy Simulation (LES) where the grid resolution is not fine enough to capture the mixing 

processes at all relevant scales, a sub-grid scale model for the viscosity is applied. Following the analysis of 

Smagorinsky (1963), the viscosity can be modeled as 
6

( ) Cs S2

μLES = ρ ∆ (7) 

where CS is an empirical constant, ∆ is a length on the order of the size of a grid cell, and S is the 

magnitude of the deformation tensor 

















∂

∂

+

∂

∂  + 

 





∂

∂

+

∂

∂

+ 















∂

∂

+

∂

∂  + 

 





∂

∂

+ 















∂

∂  + 

 





∂

∂ = y

w

z

v

x

w

z

u

x

v

y

u

z

w 2

y

v 2

x

u S 2

2 2 2 2 2 2

2

 (8) 

The thermal conductivity and material diffusivity are related to the turbulent viscosity by 

( ) Sc ; D

Pr

c

k LES

l,LES

LES p

LES

μ ρ = μ = (9) 

The Prandtl number Pr and the Schmidt number Sc are assumed to be constant for a given scenario. 

There have been numerous refinements of the original Smagorinsky model [Deardorff 1972, Germano et al. 

1991, Lilly 1992] but it is difficult to assess the improvements offered by these newer schemes in the context 

of flow simulations in volumes on the order of hundreds or thousands of cubic meters. 

There are two reasons for this. First, the dominant flow features, like a fire plume or ventilation jet, is so 

dominated by the large scale resolvable eddies that even a constant eddy viscosity gives results almost 

identical to those obtained using the Smagorinsky (Baum et al. 1997). Second, the lack of precision in most 

large scale experimental data sets makes it difficult to assess the relative accuracy of each model. The 

Smagorinsky model with constant Cs produces satisfactory results for most large scale applications where 

boundary layers are not well resolved. 

A second distinguishing feature of CFD models involving fire or combustion is the way it treats the 

combustion and heat transfer processes. Because the FDS model is intended to be used to evaluate the effect 

of fires on buildings, the combustion model is extremely simple because in most cases the user prescribes the 

fire size. The fire is represented by introducing a large number of Lagrangian elements which release heat as 

they are convected about by the thermally induced motion. Since the fluid motion determines where the heat 

is actually released, and the heat release determines the motion, the large scale features of the coupling 

between the fire and the smoke transport are retained. It should be noted, however, that the heat release rate 

is not predicted, but is an input parameter in the computer programs implementing this model. The smoke is 

simulated by tracking the convected elements after fuel burnout is complete. A specified percentage of the 

fuel consumed is assumed to be converted to smoke particulate. Thus, knowledge of the spatial distribution 

of the Lagrangian elements is equivalent to a specification of the smoke particulate density at any instant of 

time. In short, this method of introducing fire into the calculation ensures that the total heat release rate of the 

fire is as the user specifies, but it allows the heat of the fire to be released in a way that mimics reality. 

2.3. Constructing an FDS Model 

The FDS input file is a simple text file that describes the domain, boundary conditions, run control 

parameters, and output data that are needed. The format of the file is simple enough that a typical room 

could be described by less than a page of text. Sample problems and a full explanation of the input file are 

available in a user’s manual (McGrattan and Forney 2000). A brief description is presented here. 

The first few command lines describe the computational domain, which must be rectangular. Another 

requirement of the fast solver is that the number of grid cells in each of the coordinate directions must be a 

multiple of 2, 3, and 5. By default, grid cells are evenly spaced. However, this can be adjusted in up to two 

of the three coordinate directions using a transformation. Two types of transformations are possible: 

polynomial and piecewise linear. Transformations using polynomial functions must be monatonic and must 
7

map the endpoints of the domain onto themselves. They are specified by setting values of the polynomial 

function and its first or second derivatives at various points throughout the domain. Piecewise linear 

transformations specify the portion of the total number of grid cells belonging to each segment of the 

coordinate axis. Within each segment, the grid cells are evenly distributed. 

Next, various run control quantities are specified. Here, the Smagorinsky constant, ambient temperature, and 

other default values can be set. The total simulated time and initial time step are also specified. If the initial 

time step is too large, FDS will automatically reduce it (within limits) until stability constraints are satisfied. 

If the initial time step is smaller than is needed for stability, the specified time step will be used throughout 

the simulation. Therefore, it is worthwhile to carefully choose an initial time step so that the simulation time 

is not increased by imposing a smaller than necessary time step. 

Input parameters describing the boundary conditions are also needed. Rectangular obstructions and vents 

(places where fluid can enter or leave the domain) are specified, and if their dimensions do not automatically 

match the computational grid, their sizes are altered automatically by FDS. The default surface condition is 

adiabatic and inert. If velocity, thermal, or species boundary conditions are desired, the surface condition 

must be described and assigned to the corresponding wall, vent, or obstruction. A fire is also specified as a 

surface condition. 

Other details available to describe the computational domain include sprinklers, heat detectors, particles, 

species, and chemical reactions. In a fire scenario, particles are emitted from the burning surface and emit 

heat as they are convected about the room. They can also be used in non-fire scenarios to represent a 

contaminant, or can simply be inserted into the domain to allow visualization of the airflow pattern. Particles 

consume considerable computational resources, so a number of options are also available to manage and 

reduce their impact. 

Finally, the format and content of output data may be specified. Files for diagnostic output, sprinkler data, 

heat release rates, and masses of all species present are automatically generated. Several other optional data 

files are available. “Thermocouple” data files are comma delimited files that contain a point measurement of 

temperature, species, velocity, or some other quantity at a regular specified time interval. “Slice” files record 

data for a specified quantity over a plane or three-dimensional portion of the domain, also at designated time 

intervals. This data is unformatted and can be time averaged using a companion routine that generates an 

ASCII output file. Data for two scalar quantities and the three components of velocity can be archived at 

specified time intervals in plot3d format. Plot3d is a widely used share-ware data analysis program. If 

particles are used, their information is saved in a separate particle file, which can become quite large. If a 

boundary quantity is desired, it can be archived in a boundary file. 

For post-processing, NIST has developed SMOKEVIEW (Forney and McGrattan 2000) as a companion 

program to FDS. SMOKEVIEW is able to read all of the various forms of output data generated by FDS, 

and allows the computational domain and results to be displayed as color graphics and animations. The 

program is operated through a menu-driven interface. 
8

3. VERIFICATION SIMULATIONS 

FDS simulation results were compared with six published experiments. Three of the data sets represent 

simple test rooms in which forced, natural, and mixed convection were investigated in room-like settings. A 

fourth case models a more complex room with a real diffuser, furniture, and a pollutant source. All of these 

data sets were collected under steady state conditions and have been modeled with many other CFD 

programs. These data sets are intended to test the capability of the program to address room airflow 

problems in a non-fire setting. This type of verification is needed not only for application of the model to 

solve problems outside of fire simulation, but also for the modeling of smoldering fires, in which ordinary 

room airflow phenomena can dominate the initial stages of the fire. 

Two additional cases involve fires. These data sets have been used by others for verification of the FDS 

program, and are included here to provide a side by side comparison with the non-fire results. The effects of 

fire on execution times and grid refinement required were of particular interest. Since fire is a transient 

phenomenon, both of these data sets included time series data, allowing the transient capabilities of FDS to 

be utilized. 

FDS is a FORTRAN code that can be compiled for a number of different operating systems. These 

computations were performed using a personal computer with a 400 MHz Pentium II processor and 128 Mb 

RAM, using the Windows 98 operating system. FDS was run in a DOS shell from the Windows operating 

system rather than rebooting the system in DOS. This was done because the traditional DOS operating 

system is not able to handle the long names of the output files generated by the current version of FDS. The 

program could be modified to generate appropriate filenames, but it was not expected that such a 

modification would significantly reduce computing time, so it was not undertaken. No other applications 

were run on this machine during the timing runs, so that effects of the operating system on timing of the 

simulations were expected to be minimal, or at least uniform between simulations. 

3.1 Forced Convection 

Problem Description

The forced convection validation case takes the form of a single, isothermal, three-dimensional room, as 

shown in Figure 1. Experimental measurements for this configuration were done by Restivo (1979), and 

have been used in validation of many CFD codes (Davidson and Nielsen 1996, Zhang and Chen 1999), 

including FDS (Emmerich and McGrattan 1998). The inlet air enters the room along the ceiling with a 

velocity of 0.455 m/s and a uniform, "top hat" profile. A passive exhaust is located near the floor on the 

opposite wall, with conditions specified such that there is no buildup of pressure in the enclosure. For the 

FDS simulation, the initial conditions included no air motion, and a background temperature, density, and 

pressure throughout the room. 

Figure 1. Geometry for the forced convection case. 

Grid Selection

Inlet 

Uin = 0.455 m/s 

h = 0.168 m 

Exhaust 

L=9 m h = 0.48 m H=3 m 

W= 3 m 

z 

x y 
9

To illustrate the effect of grid refinement on both the simulation results and computing time, several grids 

were investigated. In total, sixteen cases were run, and are shown in Table 1. Cases 1 through 5 were 

performed without any grid transformation: the domain was divided into evenly spaced cells in the x, y, and 

z directions. These simulations did not produce good results, however, due to the small inlet height in 

relation to the overall height of the room. In these cases, the inlet and outlet dimensions had to be adjusted to 

fit the closest available grid cell. This required at least eighteen total cells in the z direction to represent the 

inlet by just one cell of the proper height. Therefore, some sort of grid refinement was needed in the zdirection. 

Both piecewise linear and polynomial grid transformations were investigated. Because the length of the time 

step calculated by FDS is related to velocity and the cell size, it was anticipated that the nature of the grid 

refinement might impact computing time by influencing the number of time steps required. Piecewise linear 

transformations of the z-axis were used in cases 7, 8, and 13. In case 7, the inlet was represented by six cells 

of uniform size, the outlet by twelve, and the remaining portion of the room height by fourteen. Case 8 used 

a similar transformation, with eight cells over the inlet height, sixteen over the outlet height, and forty cells to 

describe the remainder of the room. Case 13 was also similar, with a somewhat finer grid. 

A seventh order polynomial transformation of the z-axis was used for the remaining cases. Cases 6 and 9 

were specified with first derivative of 0.5 at the floor and ceiling, second derivative of 0 at the floor and 

ceiling, with 12 % of the grid cells used to define the inlet, and 25% of the grid cells used to describe the 

outlet. In cases 10, 11, 12, 14, 15, and 16, 15 % of the grid cells were used to define the inlet, and 30% of the 

grid cells used to describe the outlet. Note that cases 14 and 15 are identical to cases 12 and 11, except that 

the initial time step specified was larger. Figure 2 shows the locations of the inlet and outlet vents, the 

vertical locations in which experimental data were collected, the piecewise linear grid transformations used 

in cases 7 and 8, and the polynomial transformations with the largest and smallest number of grid cells (cases 

6 and 12). 

Case Refinement Transform 

type (z-direction) 

Smallest 

cell size (m) 

Average 

time step (s) 

1 144 x 50 x 50 none 0.06 x 0.06 x 0.06 >0.1 

2 96 x 32 x 32 none 0.09 x 0.09 x 0.09 >0.1 

3 64 x 20 x 20 none 0.14 x 0.15 x 0.15 >0.1 

4 45 x 15 x 15 none 0.2 x 0.2 x 0.2 >0.1 

5 36 x 12 x 12 none 0.25 x 0.25 x 0.25 >0.1 

6 96 x 32 x 32 polynomial 0.09 x 0.09 x 0.05 >0.1 

7 96 x 32 x 32 piecewise linear 0.09 x 0.09 x 0.03 >0.1 

8 96 x 64 x 64 piecewise linear 0.09 x 0.05 x 0.02 0.076 

9 60 x 32 x 32 polynomial 0.15 x 0.09 x 0.04 >0.1 

10 60 x 20 x 20 polynomial 0.15 x 0.15 x 0.07 >0.1 

11 45 x 15 x 20 polynomial 0.2 x 0.2 x 0.07 >0.1 

12 36 x 12 x 20 polynomial 0.25 x 0.25 x 0.07 >0.1 

13 108 x 45 x 45 piecewise linear 0.08 x 0.07 x 0.03 >0.1 

14 36 x 12 x 20 polynomial 0.25 x 0.25 x 0.07 0.329 

15 45 x 15 x 20 polynomial 0.2 x 0.2 x 0.07 0.263 

16 40 x 15 x 20 polynomial 0.225 x 0.2 x 0.07 0.288 

Table 1. Simulations performed for the forced convection case. 
10

0

1

2

3

4

5

6

7

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Height (m)

Case 6

Case 12

Case 8

Case 7

Data 

vents

Figure 2. Grid transformations used in the forced convection case. 

Computing Times

The ratio of simulated time to computing time was desired as a measure of computational speed. However, 

this depends on both the time step size and the computing time consumed by the airflow calculation at each 

time step. The maximum time step is related to the grid refinement, so these effects are not necessarily 

independent. Obtaining the ratio of simulated to computed time is also complicated by the process that FDS 

uses to adjust the time step. For each simulation, the user specifies a time step size with which to begin the 

simulation. If the initial time step is too large, the program will automatically reduce its size until the CFL 

condition is satisfied. However, if the initial time step is smaller than necessary, the program will not 

automatically increase the time step. Therefore, it would be possible to double the computing time for a 

problem simply by cutting the initial time step in half (which would double the number of time steps). Many 

of the simulations shown in Table 2 were run for a time step somewhat less than that necessary to satisfy the 

CFL condition, so these computing times do not reflect the minimum time in which the simulation could 

have been completed. However, another relevant computing time metric can be obtained by dividing the 

CPU time by the number of grid cells and by the number of time steps in the simulation. The CPU time per 

cell per time step is shown in Figure 3. 

For these simulations, CPU time per cell per time step increased with the number of cells in an approximately 

linear fashion. This was not expected based on past simulations and others in this report, in which this 

measure of computing time was nearly constant. The fine grid simulations in this set contained the largest 

numbers of grid cells and longest computing times in this study. It is likely that inefficiencies related to the 

operating system developed when memory intensive calculations continued for a long time without 

rebooting. Therefore, this effect might be reduced with the use of a memory management software package 

when long simulations with large numbers of grid cells are performed. 
11

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

0 100000 200000 300000 400000

Number of grid cells

CPU time (s)

CPU time per cell

per timestep

Figure 3. CPU time per cell per time step for the forced convection case. 

Four of the simulations listed in Table 1 were given an initial time step larger than was needed to satisfy the 

CFL condition, and the largest allowable time step was used. An average time step is listed for these cases in 

Table 1. In general, the average time step tends to increase as the grid cell dimensions get larger. Therefore, 

not only is the computation at each time step faster for coarse grids, but fewer time steps are needed as well. 

Figure 4 shows the computing time per cell per second of simulation time for cases 14, 15, and 16. These 

simulations used coarse grids with polynomial transformation of the z-axis. The dashed line on this plot 

shows the upper limit for a "real time" simulation, which occurs when the CPU time and simulated times are 

equal. Points that fall on or below this curve indicate simulations that occur at "real time" or faster. For 

these cases, a 1:1 ratio between simulated time and CPU time occurs at approximately 13,000 grid cells. 

Case 14, which uses 8640 grid cells, can be completed in approximately 56% of real time (100 seconds of 

simulated time can be calculated in about 56 seconds). 

0.0E+00

5.0E-05

1.0E-04

1.5E-04

2.0E-04

2.5E-04

5000 7000 9000 11000 13000 15000

Number of grid cells

CPU time (s)

CPU time per cell

per second

Upper limit for real

time simulation

Figure 4. CPU time per cell per second of simulated time for the forced convection case. 

Comparison with Experimental Data

The experimental data measured by Restivo (1979) are for a steady-state condition, while the FDS results are 

inherently transient. Therefore, the FDS simulation must be run long enough to no longer be influenced by 

the initial condition, and the results averaged over a period long enough to average out time-dependent 

variations. This is accomplished by comparing various averaging periods until nearly identical results are 

obtained. The appropriate averaging period was determined by investigating cases 6, 14, and 7. Cases 6 and 
12

14 are the finest and coarsest grids used with polynomial z-axis transformation, and case 7 is the coarsest grid 

used with the piecewise linear transformation. Dependence on the initial condition no longer influenced the 

results of these cases after 1000 s of simulated time. Averaging of velocities over successive 500 s time 

periods produced profiles with slight time-dependent variation, while a 1000 s averaging period produced 

nearly identical profiles. This finding differs from the experience of Emmerich and McGrattan (1998) with 

the same simulation, and might be related to changes in the FDS program since that work was completed. 

Based on the investigation of these three cases, all simulations were run for 2000 s, and results averaged 

between 1000 s and 2000 s. 

Figure 5 shows the airflow vectors generated for a vertical cross section of the room by the 45 x 15 x 20 grid 

with polynomial transformation. The flow, as recorded in the experiment, consists of a ceiling jet and a 

clockwise circulation pattern throughout the bulk of the room, with a small area of recirculation in the upper 

right hand corner. Simulations performed with the standard k-epsilon turbulence model (Chen, Glicksman, 

and Srebric 1998) have failed to predict this area of recirculation. 

Figure 5. Airflow pattern generated for the forced ventilation case. 

Figures 6, 7, and 8 show simulation results plotted with the measured experimental data. The u-component 

of velocity was measured in four arrays: two vertical arrays located at x=3.0 m and x=6.0 m along the 

centerline of the room, and two horizontal arrays located near the floor (h=0.084 m) and ceiling (h=2.916 m). 

These measurements were taken using hot-wire anemometers. While data on the specific instrumentation 

used are not readily available, hot-wire systems tend to have limitations at low velocities, with typical 

thresholds of 0.1-0.15 m/s. It is important to keep these limitations in mind when working with experimental 

data, particularly when low velocities are present. 

Figure 6 shows results for the cases in which no transformation was used in the z-direction. The limitation of 

this approach becomes obvious when the vertical arrays are examined (6a and 6b). Velocities in the inlet 

region are not well predicted because they are defined by too few grid cells. The data series are plotted with 

symbolic markers representing the velocity at each grid cell. For the coarsest grid (36x12x12), the inlet is 

described by only one cell, and since the grid is too coarse, FDS increases the inlet height to fit the grid. To 

maintain the correct flow rate, the velocity of the flow at the inlet is reduced, and the simulation predicts 

much lower velocities near the inlet than are measured experimentally. Even for the finest grid used 

(144x50x50), there are only three grid cells used to describe the inlet, and in all of these cases, the size of the 

inlet had to be altered to match the computational grid. Therefore, the predicted near-ceiling velocities 

shown in Figure 6d became a strong function of the grid that was used. Although the outlet is somewhat 

larger than the inlet, a similar phenomenon can be observed with the outlet and the near-floor flows shown in 

Figure 6c. These results clearly indicate the need for grid refinement to properly define the inlet and outlet 

regions, which strongly influence the flow in this room. 

Figure 7 shows results obtained for the cases in which a polynomial transformation was used to add grid 

refinement near the floor and ceiling. These transformations were defined such that the location of the grid 

cells matched the inlet and outlet locations, so that FDS did not need to adjust the size of the vents. With the 

exception of the 60x32x32 grid, all of these simulations produce results that reasonably resemble the 

experimental data. It is interesting to note that the finer grids did not necessarily produce results that more 
13

precisely match the experiment, and that the results generated by the 36x12x20 grid were not significantly 

less accurate than those generated by the 96x32x32 grid. All of these results produce recirculation in the 

upper right hand corner of the room, which is best seen in Figure 7d as a negative horizontal velocity 

component near the wall at x = 9.0 m. The extent of this recirculation seems to be slightly overpredicted by 

all of the grids, and is much larger for the 60 x 32 x 32 grid. In that case, the inlet jet separates from the 

ceiling and the secondary recirculation in the upper right corner becomes much larger than was shown in the 

experiment. There is no obvious reason why this would occur only for the 60x32x32 case. The possible 

influence of time step was investigated, but identical results were obtained using a much smaller time step. 

Therefore, the difference must be related to the grid in some way. The most likely cause is the aspect ratio of 

some of the grid cells, which pushes the rule of thumb limit of three to one. This case illustrates the need to 

check solutions for grid independence, particularly when grids with high aspect ratios must be used. 

In general, the agreement of these results with the experimental data seems to be weakest in the near wall 

region. This could be attributed to one of two factors. First, more detailed wall functions are available, but 

they have not been incorporated into the FDS model to preserve its simplicity. Second, the output data from 

the FDS simulation is given as an average taken at the nearest cell corner to the point specified. The actual 

measurements were taken very close to the floor and ceiling, and since these locations do not exactly match 

the computational grid the results are averaged at the nearest cell corner. This dependence on grid cell 

location may explain why, particularly in Figures 7c and 7d, simulations with coarser grids sometimes more 

closely match the experimental data. Therefore, the vertical arrays are probably the best indicator of an 

accurate computational solution. 

The piecewise linear transformations shown in Figure 8 also agree reasonably with the experimental data. 

These transformations were also implemented such that the inlet and outlet match up with the computational 

grid, and near floor and near ceiling measurement locations (Figures 8c and 8d) averaged at the nearest cell 

corner. Agreement with the experimental data was generally not better than that which was obtained by 

polynomial transformations using coarser grids. 
14

0.1 0.2 0.3 0.4 0.5

U-Velocity (m/s)

Experiment36x12x1245x15x1564x20x2096x32x32144x50x50

0

0.5

1

1.5

2

2.5

3

-0.2 -0.1 0 0.1 0.2 0.3 0.4

U-Velocity (m/s)

Height (m)Experiment 36x12x12 45x15x15 64x20x20

96x32x32144x50x50

(a) x=3.0 m (b) x=6.0 m 

2468

Distance (m)

xperiment 36x12x12

5x15x15 64x20x206x32x32 144x50x50

-0.2-0.1

0

0.10.20.30.40.50.6

02468

Distance (m)

U-Velocity (m/s) Experiment 36x12x12 45x15x15 64x20x20

96x32x32 144x50x50

(c) near-floor (d) near-ceiling 

Figure 6. Forced convection results for non-transformed grids. 
15

0 0.1 0.2 0.3 0.4

U-Velocity (m/s)

Experiment36x12x2045x15x2060x20x2060x32x3296x32x32

0

0.5

1

1.5

2

2.5

3

-0.2 -0.1 0 0.1 0.2 0.3 0.4

U-Velocity (m/s)

Height (m)Experiment 36x12x20 45x15x20 60x20x20

60x32x3296x32x32

(a) x=3.0 m (b) x=6.0 m 

2468

Distance (m)

Experiment 36x12x2045x15x20 60x20x2060x32x32 96x32x32

-0.3-0.2-0.1

0

0.10.20.30.40.50.6

02468

Distance (m)

U-Velocity (m/s) Experiment 36x12x20 45x15x20 60x20x20

60x32x32 96x32x32

(c) near-floor (d) near-ceiling 

Figure 7. Forced convection results for cases with polynomial transformation. 
16

1 0 0.1 0.2 0.3 0.4

U-Velocity (m/s)

Experiment 96x32x3296x64x64108x45x45

0

0.5

1

1.5

2

2.5

3

-0.1 0 0.1 0.2 0.3 0.4 0.5

U-Velocity (m/s)

Height (m) Experiment 96x32x32

96x64x64108x45x45

(a) (b) 

2468

Distance (m)

Experiment 96x32x3296x64x64 108x45x45

-0.3-0.2-0.1

0

0.10.20.30.40.50.6

02468

Distance (m)

U-Velocity (m/s) Experiment 96x32x32

96x64x64 108x45x45

(c) (d) 

Figure 8. Forced convection results for piecewise linear transformation. 
17

3.2. Natural Convection 

Problem Description

The natural convection case is the least realistic of this study, but is a classic problem used for CFD 

verification. The test chamber is closed, with no flow inlets or outlets. The left wall is heated to 35.3°C. 

The right wall is cooled to 19.9°C. All other walls are insulated. This geometry is shown in Figure 9. 

Figure 9. Problem description for the natural convection case. 

Problem Representation

This problem is typically solved as a two dimensional case. In FDS, the domain is specified as one cell thick 

in the y-direction, with a slip boundary condition applied to the front and back walls. FDS does not allow 

grid transformation with two-dimensional geometries. Therefore, additional cases with a thickness of three 

cells were run so that grid transformation in the x-direction could be attempted. All of these transformations 

used polynomials with a first derivative of 0.5 and second derivative of 0.0 at the left and right walls. The 

seven cases are summarized in Table 2. For each case, a large initial time step was specified, and FDS 

allowed to determine the largest appropriate time step during the simulation. 

Case Refinement Transform 

type 

Smallest 

cell size (m) 

Average 

time step (s) 

1 25 x 1 x 8 none 0.32 2.16 

2 50 x 1 x 16 none 0.16 0.95 

3 81 x 1 x 25 none 0.10 0.51 

4 144 x 1 x 50 none 0.05 0.22 

5 50 x 3 x 16 polynomial 0.08 0.69 

6 81 x 3 x 25 polynomial 0.05 0.37 

7 144 x 3 x 50 polynomial 0.03 0.15 

Table 2. Simulations performed for the natural convection case. 

Computing Time

The CPU time per cell per time step is for these simulations is shown in Figure 10. This measure of 

computing time was much larger for the 25 x 1 x 8 grid than for any of the other simulations. A breakdown 

of contribution to computing time from various parts of the program showed that file management and other 

problem setup tasks make up a much larger percentage of overall computing time for this case. Because only 

200 grid cells are present, these "overhead" tasks are spread among fewer grid cells and have a greater impact 

on overall computing time. The effect of increased computing time for finer grids was not seen for these 

7.9 m 

2.5 m 

Hot wall Cold wall

Insulated wall 

Insulated wall 

z

x
18

cases as it was for the forced convection problem. This may be because the finest grid, with 21,600 cells, 

was much smaller than the grids used for most of the forced convection cases. 

0.0E+00

5.0E-05

1.0E-04

1.5E-04

2.0E-04

0 10000 20000 30000

Number of grid cells

CPU time (s)

CPU time per

cell per timestep

Figure 10. CPU time per cell per time step for the natural convection case. 

Figure 11 shows the CPU time per cell per second of simulated time, compared to the upper limit for a "real 

time" simulation. This shows that the two-dimensional cases with grids of 81 x 1 x 25 and smaller and the 

three dimensions with grids of 81 x 3 x 25 and smaller can be completed faster than real time. The coarse 

grid simulations are extremely fast, and can be simulated in as little as 2% of real time. This clearly 

illustrates the potential time saving benefit of being able to represent room airflow using a two-dimensional 

geometry. 

0.E+00

1.E-04

2.E-04

3.E-04

4.E-04

5.E-04

6.E-04

7.E-04

0 10000 20000 30000

Number of grid cells

CPU time (s)

Two dimensional

Three dimensional

Real time upper limit

Figure 11. CPU time per cell per second of simulated time for the natural convection case. 

Simulation results

The vertical temperature profile in the middle of the chamber (x = 3.95 m) has been measured experimentally 

by Olson et al. (1990). The measured temperatures are presented in dimensionless form, with dimensionless 

temperature, Θ, defined as: 

T T

T T

h c

c

−

− Θ = (10) 

with Tc = cold wall temperature, Tn = warm wall temperature, and T = Temperature. 

Figure 12 shows the results of the two dimensional simulations with no grid refinement, plotted with the 

experimental data. The FDS simulations are not grid independent, and the temperature stratification in the 
19

room increases as the grid becomes finer. With the Smagorinsky subgrid scale model, the diffusion 

coefficient is proportional to the grid cell size. When a coarse grid is used, the diffusion may be exaggerated, 

and the temperature profile can be washed out. On the other hand, when a very fine grid is used, the 

simulation may not completely transition to a direct numerical simulation (DNS). FDS sets a lower bound on 

both the viscosity and thermal conductivity so that they cannot go below their actual molecular values. 

However, the heat transfer correlation does not transition to DNS. In the next release of FDS, there are plans 

to deal with this issue. 

FDS was written as a simplified model and with the intention that relatively coarse grids would be used. As 

such, it does not include a detailed model of heat transfer at walls. The user may specify convection 

coefficients for vertical and horizontal surfaces. The heat flux from a constant temperature wall is calculated 

using this convection coefficient and the temperature difference between the wall and the adjacent fluid cell. 

This assumption requires that the grid cell size at the wall be larger than the thermal boundary layer 

thickness. If the grid cell size became too small next to the wall, heat transfer could actually become less 

efficient. However, this effect does not appear to be strong enough to overcome the diffusion effects in this 

case. 

Results from the simulations with the transformed grids are shown in Figure 13. These simulations show 

even greater stratification than was obtained with the untransformed grids in Figure 12. The finer grids near 

the right and left walls lead to less diffusion and a stronger buoyant force near the walls. 

0

0.25

0.5

0.75

1

0 0.25 0.5 0.75 1

Dimensionless temperature

Dimensionless height

25x8

50x16

81x25

144x50

Experiment

Figure 12. Dimensionless temperatures for two dimensional natural convection cases without grid 

transformation. 
20

0

0.25

0.5

0.75

1

0 0.25 0.5 0.75 1

Dimensionless temperature 

Dimensionless height

50x16

81x25

144x50

Experiment

Figure 13. Dimensionless temperatures for three dimensional natural convection cases with polynomial grid 

transformation. 

Since this simulation includes only natural convection created by the heated and cooled walls, these effects 

are obvious in the results of the simulation. The simulation of cases in which mixed convection effects are 

present will indicate the extent of these limitations on modeling more realistic room airflows. There are also 

some steps that the user can take in setting up room airflow problems that might mitigate these effects. 

Instead of specifying a wall temperature, the heat flux at the wall could be specified. In FDS, a constant 

convection coefficient is still used, and the wall temperature is adjusted to provide the correct heat flux. 

Although the issues with regard to diffusion effects still exist, the user can be certain that the amount of heat 

transfer is correct. Another good strategy for this type of problem would be to check the approximate 

boundary layer thickness before choosing the computational grid. In this experiment, the boundary layer on 

the hot and cold walls was estimated through flow visualization to be between 0.05 and 0.125 m (Olsen, et al. 

1990). A rough estimate for the boundary layer thickness can also be obtained from laminar correlations 

(Incropera and DeWitt 1990). For laminar natural convection over an infinite vertical plate, a thermal 

boundary layer thickness of 0.05 m can be calculated. Because the flow in this case is turbulent, a somewhat 

smaller thermal boundary layer would be expected. Using either of these methods to estimate the thermal 

boundary layer thickness, the user would want to choose a grid cell size greater than 0.05 m. This might 

suggest the 81 x 1 x 25 two dimensional grid, which reproduces the experimental result reasonably well. 

Although velocities were not measured in the original experiment, flow visualization provided some 

observations that are also useful in evaluating the model. Olson et al. (1990) report that flow from the warm 

wall reached the ceiling and was observed to move horizontally, slowing down and thickening as it moved 

toward the cold wall. At the cold wall, this jet reversed direction, and part of it formed a secondary flow 

moving in the opposite direction beneath the ceiling jet. Some of the flow was also entrained into the cold 

layer moving downward along the cold wall. Symmetric behavior was observed for the cold jet in the floor 

of the chamber. The thicknesses of jets along the floor and ceiling were observed to be 10-20% of the room 

height when they reached the opposing wall. Also, a stagnant region was identified in the central portion of 

the room; between 40 and 60% of the room height no detectable motion was present. 

Figure 14 shows profiles of the horizontal velocity component at the same location as the temperature 

measurements from Figure 12 for the two-dimensional simulations. All of these simulations show the ceiling 

and floor jets and the recirculation, although they are too large for the coarsest grid. The remaining three 

simulations produce ceiling and floor jets that range from about 8-18 % of the room height, consistent with 

the observation of 10-20% at the far wall. These simulations also show a region of relatively little motion 

near the center of the room. 
21

This problem has been used to evaluate many CFD models. Xu and Chen (1998) simulated this geometry 

with a standard k-epsilon turbulence model and two low Reynolds number models. The standard k-epsilon 

model failed to predict the recirculation, but it was produced by the two low Reynolds number models. 

Simulations performed by Chen, Glicksman, and Srebric (1998) with a zero-equation turbulence model and a 

course grid did produce the recirculation, but it was larger than observed in the experiments. 

0

0.5

1

1.5

2

2.5

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

U-velocity (m/s)

Height (m)

25x8

50x16

81x25

144x50

Figure 14. Velocities from two dimensional natural convection cases without grid transformation. 
22

3.3. Mixed Convection 

Problem Description

The mixed convection simulations are based on experiments conducted by Blay et. al (1992). This case is 

similar to another set of mixed convection experiments conducted by Schwenke (1975). Both data sets have 

been used for verification of CFD results, however, the former was chosen for this study because the data 

provided is more detailed and the original publication is available in English. The geometry of this case is 

similar to the forced convection case, except that the chamber is square. Dimensions and boundary 

conditions are shown in Figure 15. The floor of the chamber is heated to 35.5 °C, and the supply air enters at 

a temperature of 15.0 °C and a velocity of 0.57 m/s. All other walls were maintained at a temperature of 15.0 

°C. 

Figure 15. Geometry for the mixed convection case. 

Grid Selection

The most influential issue in defining the computational grid for this problem was proper representation of 

the inlet and outlet. Although their geometry and flow characteristics are relatively simple, the need for grid 

refinement is dictated by the small height of the inlet and outlet vents relative to the room. If uniform grid 

spacing in the vertical direction were used, 60 cells would be needed to represent the inlet by just one cell of 

the proper height. Therefore, transformations were needed. A total of eight cases (shown in Table 3) were 

investigated. Four of these used piecewise linear transformations, and four used polynomials. In all cases, 

the grid was specified such that the inlet and outlet were modeled at their exact experimental dimensions 

(0.018 m and 0.024 m, respectively). Grid refinement of the vertical axis is shown graphically in Figure 16. 

The FDS simulations were specified with an initial time step larger than was needed to satisfy the 

convergence criteria, and the program chose the largest appropriate time step. The average time steps shown 

in Table 3 are generally much smaller than those obtained for the forced convection case. This is because the 

time step is related to cell size, which is much smaller for these cases. 

This strategy of allowing FDS to find its maximum acceptable time step produced an unstable result for Case 

6. This was initially rather puzzling, since stable results were obtained for a similar polynomial grid 

transformation for both coarser and finer grids. Imposing a smaller time step (0.05 s) for the simulation 

eliminated the instability, and produced results that were similar to those obtained with the other grids. This 

was the only simulation in this study that experienced this problem, but it does suggest a potential pitfall of 

this strategy. One possible explanation is that the stability constraint δt<<δx2

/ν may not have been satisfied. 

FDS only checks this constraint for DNS simulations, but it could become important for LES simulations 

with small grid cells, such as those that were needed to correctly model the inlet and outlet in this problem. 

This is yet another reason why checking results against those generated with different grids and smaller time 

steps is essential when experimental data are not available. 

Inlet 

Uin = 0.57 m/s 

h = 0.018 m 

T = 15°C 

L=1.04 m 

H=1.04 m 

W= 0.7 m 

Exhaust 

Floor, h = 0.024 m 

T = 35.5 °C

z 

x y 
23

Case Refinement Transform 

type (z-direction) 

Cells representing 

inlet, outlet 

Smallest 

cell size (m) 

Average 

time step (s) 

1 10 x 8 x 10 piecewise linear 1, 1 0.10 x 0.09 x 0.018 0.16 

2 20 x 15 x 20 piecewise linear 2, 2 0.05 x 0.05 x 0.009 0.04 

3 40 x 30 x 40 piecewise linear 2, 2 0.03 x 0.02 x 0.009 0.04 

4 40 x 30 x 40 piecewise linear 4, 4 0.03 x 0.02 x 0.004 0.02 

5 10 x 8 x 10 polynomial 1, 1 0.10 x 0.09 x 0.018 0.19 

6 15 x 10 x 15 polynomial 1, 1 0.07 x 0.07 x 0.018 >0.05* 

7 20 x 15 x 20 polynomial 2, 2 0.05 x 0.05 x 0.008 0.04 

8 40 x 30 x 40 polynomial 4, 4 0.03 x 0.02 x 0.004 0.02 

*Unstable solution with code-determined time step 

Table 3. Simulations performed for the mixed convection case. 

-1

1

3

5

7

9

0.00 0.25 0.50 0.75 1.00

Height (m)

Case 8

Case 7

Case 6

Case 5

Case 4

Case 3

Case 2

Case 1

Data

Vents

Figure 16. Grids transformations used in the mixed convection case. 

Computing Times

Figure 17 shows computing time per cell per time step for the mixed convection case. For these simulations, 

this measure of computing time only varied only by about 10%, and showed very little relationship to the 

number of grid cells. 

In Figure 18, the computing time per cell per second is plotted for the coarse grid cases. Cases 1 and 5, with 

the 10 x 8 x 10 grids, can be simulated in approximately 20% of real time. Case 6 appears to be much 

slower, consuming about 150% of real time. This is partially because the time step for this simulation had to 

be reduced to produce a stable solution. The original solution was obtained at a speed that was faster than 

real time, and it might be possible to "fine tune" the time step to obtain a faster, stable solution. Since the 

results obtained did not seem significantly better than those generated by the 10 x 8 x 10 grids, this was not 

pursued. 
24

0.0E+00

5.0E-06

1.0E-05

1.5E-05

2.0E-05

2.5E-05

3.0E-05

3.5E-05

4.0E-05

4.5E-05

0 20000 40000 60000

Number of grid cells

CPU time (s)

CPU time per cell

per timestep

Figure 17. CPU time per cell per time step for the mixed convection case. 

0.0E+00

5.0E-04

1.0E-03

1.5E-03

2.0E-03

0 2000 4000 6000 8000

Number of grid cells

CPU time (s)

CPU time per

cell per s

Real time

upper limit

Figure 18. CPU time per cell per second for the mixed convection case. 

Comparison With Experimental Data

The experiments included several cases in which the floor temperature and inlet velocity were varied. They 

documented two different flow patterns that were related to the Froude number of the flow: at high Froude 

numbers, a counterclockwise flow pattern developed, while at lower Froude numbers the inlet jet separated 

from the ceiling and a clockwise flow pattern formed. This was a result of reduced inlet jet momentum in 

relation to the buoyancy force caused by the heated floor. In decreasing and increasing the Froude number 

until the flow switched between flow regimes, a significant hysteresis effect was noted. However, in all 

cases the counterclockwise flows were produced below Fr=1.92 and clockwise flows were produced above 

Fr=3.41. 

The Froude number for the data set that is presented here is 5.31, well above the threshold at which a 

counterclockwise flow pattern is expected. Blay et al.(1992) present computational results obtained for this 

data set using two different low Reynolds number k-epsilon turbulence models. The Jones and Launder 

model incorrectly produced a counterclockwise flow because it overestimated heat transfer from the floor. 

The Lam and Bremhorst model with modifications by Davidson produced the correct clockwise flow pattern. 

Likewise, all of the FDS simulations performed for this study correctly produced a clockwise flow pattern 

with the exception of the original case 6 simulation. The problem with that simulation was corrected by 

reducing the time step. 
25

Figures 19 and 20 show the simulation results compared with velocity and temperature data collected from 

poles located at x=0.502 and z=0.502 m. The x-component of velocity was measured at the pole located at 

x=0.502 m, and the z-component measured at z=0.502 m. 

The velocities predicted by FDS resemble the experimental data reasonably well, although the predicted 

temperature profile is slightly more linear than the measured one. It is interesting to note that there is little 

difference between the results obtained with piecewise linear and polynomial grid transformation, nor is there 

a clear improvement related to number of grid cells. Cases 3 and 4 differed only in the number of cells used 

to define the inlet and outlet, and the additional detail in that region does not appear to improve the result 

significantly. 

There does seem to be more variation in the temperature profiles generated using different levels of grid 

refinement. Again, the heat transfer in this problem is not independent of the grid. The bulk temperature in 

the room tends to decrease as the number of grid cells increases. Cases 3 and 4 had the same total number of 

grid cells, but the size of grid cells adjacent to the floor and ceiling was smaller in case 4 than in case 3, and 

the bulk temperature was lower in case 4 as well. Therefore, it seems that making the grid cells near the floor 

smaller reduces the heat transfer from the floor. Given the small size of the grid cells in this case, this is 

most likely due to violation of the assumption that the boundary layer is smaller than the first grid cell. FDS, 

a coarse grid model, calculates the heat transfer based on a constant heat transfer coefficient and the 

temperature difference between the wall and the first grid cell. This means that the conventional expectation 

of improved results with a finer grid may be incorrect. In this case, the wall heat transfer would be better 

modeled using a coarse grid. Unfortunately, a fine grid was needed to adequately define the inlet and outlet 

flows for this problem. 

Choice of convection coefficient is another factor that strongly influences the heat transfer from constant 

temperature walls. Additional tests with these data showed that the results were very sensitive to the choice 

of these coefficients. Since the experimental data was available, it would have been possible to "tune" the 

CFD model to more closely reproduce the measured temperatures. However, this was not done since it was 

felt that the results would not be representative of the kinds of predictions that could be produced by a 

practitioner using the model in a situation for which experimental data were not available. 

Choosing a convection coefficient to represent room airflows is not an easy task, but it can have a significant 

impact on the results generated by the simulation. In FDS, convection coefficients are expressed in the form, 

 h=C(∆T)1/3 (11) 

where h is the heat transfer, ∆T is the temperature difference, and C is an empirical convection coefficient. 

The default values used in FDS are taken from Holman (1989), which gives a simplified relationship for air 

in which Cv=0.95 W/m2

K4/3 and Ch=1.43 W/m2K4/3 for idealized, infinite vertical and horizontal surfaces. 

However, FDS allows the user to specify horizontal and vertical convection coefficients that are applied to all 

heated or cooled surfaces in the enclosure. 

Convection coefficients published elsewhere can be quite different from these values, and may be more 

appropriate for indoor air situations. Incropera and Dewitt (1990) give relationships, also for idealized 

situations, that produce Cv=1.18 W/m2

K4/3 and Ch=1.78 W/m2K4/3 using properties of air at 27°C. The heat 

transfer section of the 1997 ASHRAE Handbook of Fundamentals gives Cv=1.31 W/m2

K4/3 and Ch=1.52 

W/m2

K4/3, however, it is noted that these relationships may not be entirely appropriate for convection in 

rooms, citing experiments conducted by Bauman et. al (1993) that suggest even higher coefficients may often 

be appropriate. 

The thermal transmission section of the ASHRAE Handbook of Fundamentals and a number of HVAC texts 

give overall constant heat transfer coefficients of 8.29 W/m2

K (vertical) and 9.26 W/m2K (horizontal) for still 

air next to a wall. These include radiation: once it is subtracted out, they become 3.08 and 4.05 W/m2

K, 

respectively. It is noted that these values were calculated for ∆T=5.56 °C and an ambient temperature of 

21°C. This temperature difference is higher than usually occurs in indoor situations. 

Bauman et. al (1993) conducted experiments to calculate heat transfer coefficients in room-like situations. 

However, the tests themselves were actually done in water and similarity relationships used. They found that 
26

the flows did not transition to turbulence as soon as was expected, so the relationship that they developed for 

vertical walls takes the form of a correlation for laminar flow. 

In reality, the convection in real rooms is probably influenced by both forced and natural convection. 

Especially near the diffuser, the flow may not be well approximated by the idealized situation of still, cool air 

exposed to an infinite, heated plate. In this type of situation, it may be appropriate to use a higher convection 

coefficient. 

Table 4 summarizes the published convection coefficients relevant to room airflow problems. For this 

problem horizontal and vertical coefficients of Ch=4.05 and CV=2.03 were selected based on experience and 

judgement. This selection produced very good results when used with a coarse grid. If a fine grid were 

needed for some reason, one might attempt to increase the convection coefficient in an attempt to obtain the 

same heat transfer rate. This would be a rather un-scientific approach: it would be better in such a case to 

simply specify the desired heat flux at the wall. 

Source correlation Cv Ch For ∆T=2°C 

Qv Qh

Holman h=C(∆T)1/3 0.95 1.43 2.39 3.60 

Incorpera & Dewitt h=C(∆T)1/3 1.18 1.78 2.97 4.49 

ASHRAE 

Fundamentals (Sec. 3) 

h=C(∆T)1/3 1.31 1.52 3.30 3.83 

ASHRAE 

Fundamentals (Sec. 22) 

h=C 3.08 4.05 6.16 8.10 

Bauman, et.al h=C(∆T/H)0.22 2.03 na 3.80 na 

Table 4. Surface Convection Coefficients Relevant to Room Airflow. 
27

0.4 0.6 0.8 1

Length (m)

10x8x10 (i,o=1)20x15x20 (i,o=2)40x30x40 (i,o=2)40x30x40 (i,o=4)Experiment

) W-velocity at z=0.502 

0 0.2 0.4 0.6

X-velocity (m/s)

10x8x10 (i,o=1) 20x15x20 (i,o=2) 40x30x40 (i,o=2)40x30x40 (i,o=4)Experiment

) X-Velocity at x=0.502 

17.017.518.018.519.019.520.020.5

0 0.2 0.4 0.6 0.8 1

Length (m)

Temperature (C) 10x8x10 (i,o=1) 20x15x20 (i,o=2) 40x30x40 (i,o=2) 40x30x40 (i,o=4)

Experiment

(b) Temperature at z=0.502 

0

0.20.40.60.8

1

15 17 19 21 23 25 27

Temperature (C)

Height (m)

10x8x10 (i,o=1)20x15x20 (i,o=2)40x30x40 (i,o=2)40x30x40 (i,o=4)Experiment

(d) Temperature at x=0.502 

Figure 19. Mixed convection results for the piecewise linear transformations. 
28

0.4 0.6 0.8 1

Length (m)

10x8x1015x10x1520x15x2040x30x40Experiment

) W-velocity at z=0.502 

-0.2 0 0.2 0.4

X-velocity (m/s)

10x8x10 15x10x15 20x15x2040x30x40Experiment

) X-Velocity at x=0.502 

16.016.517.017.518.018.519.019.520.020.5

0 0.2 0.4 0.6 0.8 1

Length (m)

Temperature (C) 10x8x10 15x10x15 20x15x20 40x30x40

Experiment

(b) Temperature at z=0.502 

0

0.20.40.60.8

1

16 18 20 22 24 26

Temperature (C)

Height (m)

10x8x1015x10x1520x15x2040x30x40Experiment

(d) Temperature at x=0.502 

Figure 20. Mixed convection results for the polynomial transformations. 
29

3.4. Displacement Ventilation 

Problem Description

The most complex and realistic non-fire validation case is modeled after a displacement ventilation test room 

described by Yuan et al. (1998). This three dimensional room, shown in Figure 21, contains computers, 

furniture, and lighting fixtures as well as heated rectangular boxes intended to represent occupants. The 

room is ventilated with cool supply air introduced via a diffuser that is mounted on a side wall, near the floor. 

Displacement ventilation systems distribute cool supply air in the lower portion of the room. This air rises as 

it is warmed by heat sources and exits through a return located in the upper part of the room. The flow 

pattern is intended to remove contaminants by sweeping them upward at the source and removing them from 

the room. 

Figure 21. Geometry for the displacement ventilation case. 

Computational results are compared with a steady-state experimental result obtained with a ventilation rate of 

4 air changes per hour and a supply air temperature of 17.0°C. The total heat load introduced by six lamps, 

two computers, and two occupants (represented using boxes heated by incandescent lamps) was 636 W. 

Sulphur hexafluoride (SF6) was introduced as a tracer gas near the breathing zone of the occupants at a rate 

of 0.00023 kg/hr each. Wall, floor, and ceiling temperatures were measured during the experiment, and these 

values were used to specify boundary conditions for the CFD simulation. Temperature, SF6 concentration, 

and velocity were measured using vertical sensor arrays mounted on nine poles with locations shown in 

Figure 22. 

Figure 22. Measurement locations for the displacement ventilation case. 

Pole a 

(0.78 m, 1.83 m)

Pole b 

(1.74 m, 1.83 m)

Pole c 

(2.70m, 1.83 m)

Pole d 

(3.66 m, 1.83 m)

Pole e 

(4.62 m, 1.83 m)

Pole f 

(2.70 m, 0.61 m)

Pole g 

(2.70 m, 1.22 m)

Pole h 

(2.70 m, 2.44 m)

Pole i 

(2.70 m, 3.05 m)

Desk 

Occupant 

Computer 

Computer 

Occupant 

Supply 

diffuser 

Box Desk 
30

Problem representation

When the problem definition begins to include objects and obstacles in the room, a finer grid is often needed 

to properly define these objects. To represent this geometry using relatively coarse grids, there were two 

options. The first would be to specify a grid transformation that would allow each object to be defined at its 

proper dimensions. This would have required grid transformation in all three directions, and would have 

been mathematically complicated due to the number of objects present. This strategy was ultimately rejected 

because undesirable aspect ratios would be needed to maintain a coarse grid while properly representing 

objects such as the desks, which are very thin in the vertical direction. Instead, a regular grid was specified 

and the size of obstacles adjusted to fit the grid. This resulted in significant changes in the dimensions of 

some objects for the cases with coarse grids. 

Heated objects were defined using an FDS feature that allows the user to specify a uniform heat release rate 

per unit surface area. For example, the heat release associated with each occupant was 75 W. For the 

computational model, 75 W was divided by the surface area of the occupant, and this rate specified for all of 

its surfaces. When FDS adjusts the dimensions of an object to accommodate the grid, the heat release rate 

per unit area is adjusted by the program as well, so that the intended quantity of heat is released. 

The tracer gas sources were defined in much the same way. FDS requires contaminants to be introduced 

either at a vent or at the surface of an object that is at least two cells thick. In the actual experiment, the 

tracer gas was introduced through a small tube, just in front of the occupants. This had to be simulated in 

FDS as a contaminant release from the surface of an object defined by at least two grid cells. In the coarsest 

grid case, the occupants were defined by only four cells; therefore, the best strategy was to specify a uniform 

mass release flowing from the surface that represented the top of the occupants' heads. A mass flux per unit 

surface area was specified, and was adjusted as necessary by FDS for each case to provide the correct influx 

of SF6 based on the surface area of the grid-adjusted occupants. 

Real diffusers present another difficulty when modeling realistic situations. The velocity profile of flow 

leaving an inlet diffuser typically has a major influence on the flow pattern in the room, so it is important to 

model the diffuser appropriately. Since their geometry is often complicated, diffusers may require rather 

detailed specifications and grid refinement. For this case, the flow leaving the diffuser was evenly 

distributed over the face area of the diffuser, and modeled as a unidirectional, "top hat" profile. This method 

was chosen after comparing results obtained using a few slightly more sophisticated methods, without 

obtaining superior results. 

Four levels of grid refinement were investigated, as shown in Table 5. The coarsest grid represented the 

room by only 1,728 cubic cells of approximately 0.3 m x 0.3 m x 0.3 m. This required significant 

adjustments to the size of most objects within the room, as a single grid cell was approximately the same size 

as one of the computers. The largest adjustment was made to the thickness of the desks, which increased by 

a factor of 30 from an actual thickness of 0.01 m. Significant adjustments were also made to larger objects 

such as the occupants, with actual dimensions of 0.4 m x 0.35 m x 1.1 m modeled as 0.3 m x 0.3 m x 1.2 m. 

The finest grid represented the room by 86,400 cells with dimensions 0.08 m x 0.08 m x 0.08 m. This 

representation allowed the occupants to be modeled as 0.40 m x 0.32 m x 1.13 m, very close to their actual 

size. Even with this much finer grid, however, the thickness of the desk was multiplied by a factor of eight 

so that it could be represented using one grid cell. 

Case Refinement Transform 

type 

Approximate 

cell dimension (m) 

Average 

time step (s) 

1 18 x 12 x 8 none 0.3 x 0.3 x 0.3 1.02 

2 25 x 18 x 12 none 0.2 x 0.2 x 0.2 0.64 

3 50 x 36 x 24 none 0.1 x 0.1 x 0.1 0.22 

4 64 x 45 x 30 none 0.08 x 0.08 x 0.08 0.17 

Table 5. Simulations performed for the displacement ventilation case. 
31

In all four cases the time step was specified so that FDS could determine the largest time step appropriate for 

each case based on stability requirements. Table 5 shows a reduction in average time step size from 1.02 s to 

0.17 s that occurs as the grid becomes finer. This gives the coarse grid a dual advantage with regard to 

computing time, since the larger time steps reduce the total number of calculations that are performed while 

fewer cells also means that each calculation is faster. Figure 23 shows the CPU time consumed per cell per 

time step, which is relatively constant for these cases. The two simulations with the coarsest grids are 

slightly slower on a per cell per time step basis, but the output files again show that this is because "fixed 

costs" associated with file management, prep time, and generation of output files consume a greater 

percentage of the overall computational resources and are spread over a smaller number of time steps. 

It should be noted here that FDS offers the user a variety of ways to report and visualize results, and that 

indiscriminate use can consume substantial computing time. The approach taken for all of the simulations in 

this study was to obtain the results necessary for diagnostics and comparison with experimental data, and to 

omit most of the more time-intensive visualization files. There are four file formats for visualizing and 

reporting output data. The thermocouple file is a comma delimited file that reports time series flow data at 

specified points. For this problem ten points were specified for diagnostic purposes. Slice files record time 

series flow data at specified "slices" through the domain. In this case, 27 slice files were specified to record 

temperature, velocity, and SF6 concentration at each of the nine instrumentation pole locations. These results 

were then time averaged for comparison to the experimental data. Two additional slice files were used to 

record temperature and SF6 concentration for an xz-plane centered on the y-axis of the room. These results 

were used for visualization and diagnostics. Data files formatted for the shareware visualization program 

plot3d were also generated every 1000 s, for a total of five plot3d output files. Each of these files archive 

five flow quantities for the entire flow domain at a single time, and can be a useful diagnostic tool. A fourth 

type of output, the particle file, allows the user to visualize Lagrangian particles that are carried by the flow. 

In the case of a fire, these particles may also continue to burn and release heat as they are distributed 

throughout the room. These particles influence the calculation, and have the potential to consume 

considerable computing time and disk space. Their impact can be reduced by saving only a fraction of the 

particles or by setting an age limit, so that particles that have been in the domain for a specified length of 

time are deleted. To reduce computing time, particles were not used in this simulation. For coarse grids, the 

time required to model particles, even with age limitations in place, can be on the order of that required for 

the rest of the simulation. Therefore, the need for output data is something that must be considered when 

computing time is of concern. 

The CPU time consumed per cell per second of simulated time is shown in Figure 24. For this case, the two 

coarsest grids can be simulated at speeds faster than real time. The 18 x 12 x 8 grid can be simulated in 

about 13% of real time, while the 25 x 18 x 12 grid consumes about 61% of real time. 

0.E+00

1.E-05

2.E-05

3.E-05

4.E-05

5.E-05

6.E-05

7.E-05

8.E-05

9.E-05

0 25000 50000 75000 100000

Number of grid cells

CPU time (s)

CPU time per

cell per

timestep

Figure 23. CPU time per cell per time step for the displacement ventilation case. 
32

0.E+00

1.E-04

2.E-04

3.E-04

4.E-04

5.E-04

6.E-04

0 10000 20000 30000 40000 50000

Number of grid cells

CPU time (s)

CPU time per cell

per second

Upper limit for real

time simulation

Figure 24. CPU time per cell per second of simulated time for the displacement ventilation case. 

Each simulation was run for 5,000 s of simulated time. This was done based on investigations of the coarsest 

and finest grid cases (cases 1 and 4), which showed that 5,000 s of simulation was needed to obtain steady 

state velocity, temperature, and species profiles that were independent of the averaging period used. These 

investigations showed significant differences among these three parameters in the averaging period needed to 

obtain a uniform result and in the length of time needed until the result was no longer affected by the initial 

condition. For example, uniform steady state temperature profiles could be generated by averaging data over 

periods of at least 500 s, after the first 1500 s of the simulation. However, an averaging period of 1500 s was 

needed to generate uniform velocity profiles, and an initial period of 3500 s was needed before species 

concentration no longer depended on the initial condition. The efficiency of the data reduction process was 

maximized by using the same averaging period for temperature, velocity, and species concentration. To 

obtain steady state results, all flow variables were averaged between 3500 s and 5000 s. 

Comparison With Experimental Data

Figures 25, 26, and 27 compare the predictions of the four FDS simulations with measured temperature, SF6

concentration and average velocity. Comparisons are shown for three of the nine instrumentation poles at 

locations d, f, and h. These were chosen as a representative sampling of the measurement locations. 

Figure 25 shows temperatures predicted by four FDS simulations. As the computational grid becomes finer, 

the results of the simulations can be seen to converge until the predictions of the two finest grids are very 

similar to one another. This suggests that the flow solution is approaching grid independence. In addition, 

the locations of the heated objects are becoming better defined. For the coarse grids, object and measurement 

locations were modified to fit the grid. Therefore, heat sources may be slightly closer to or further away 

from the measurement location than intended. In all cases, however, the general trend predicted by the 

model matches the experimental data. For the two fine grids, the agreement is quite good. The coarse grid 

results, while not quite as good a match, might be acceptable in exchange for computing speed. 

The results for SF6 concentration, shown in Figure 26, are not quite as good. At all three measurement 

points, the coarse grids tend to predict much higher concentrations near the floor than were measured 

experimentally. This seems to be related to poor grid refinement, and the results obtained using the finer 

grids are in much closer agreement with the experimental data. Still, a 50x36x24 grid is needed to capture 

the general trends of the concentration profile in the lower half of the room, and the 64x45x30 grid gives an 

even better result. In the upper half of the room, the model gives good results at pole h and over-predicts the 

concentration at poles d and f, particularly near the height of the source. The way in which the tracer gas 

sources were defined in the computational model has a significant impact on this result. Instead of a point 

source, the SF6 release is modeled as being spread over a larger area, part of which is closer to poles d and f 

than the original source. Concentrations at these poles are also likely to be more influenced by this change in 
33

source location since the local velocities tend to move air from the area of the source toward the pole. The 

flow pattern in the vicinity of pole h tends to move air from the nearest source away from the pole, so 

localized variations would have less effect on the contaminant concentration there. It is likely that the results 

of the fine grid simulations could have been improved by defining a small object adjacent to the occupant 

from which the tracer gas is introduced. While this would not have been possible for the coarser grids, a fine 

grid would allow it. Overall, the results in Figure 26 indicate a need for fine grids to properly represent both 

contaminant diffusion and to approximate point sources. 

The velocity profiles in Figure 27 also appear to be converging to a uniform solution for the two finer grids. 

While the comparison to the experimental data may not be striking, it is certainly reasonable given the 

limitations of velocity measurement instrumentation at these low velocities. These results also tend to follow 

general trends observed through flow visualization and generated by other CFD programs. The most notable 

of these is the reversal of flow direction that happens in the lower portion of the room. Cool air entering the 

room at the diffuser forms a gravity wave that travels across the lower portion of the room. Above this layer, 

an area of recirculation exists. This reversal in flow direction can be seen in the computational results as the 

velocity dips at about 0.2 m above the floor. This effect is captured throughout most of the room with the 

coarse grid used in Case 1, however, it is best seen in the results of the cases with the finer grids. 
34

20

21

22

23

24

25

26

27

28

0.0 0.5 1.0 1.5 2.0

Height (m)

Temperature (C)

Experiment

18x12x8

25x18x12

50x36x24

64x45x30

(a) 

20

22

24

26

28

30

0 0.5 1 1.5 2

Height (m)

Temperature (C)

Experiment

18x12x8

25x18x12

50x36x24

64x45x30

(b) 

20

22

24

26

28

30

32

0.0 0.5 1.0 1.5 2.0

Height (m)

Temperature (C)

Experiment

18x12x8

25x18x12

50x36x24

64x45x30

(c) 

Figure 25. Temperatures predicted for the displacement ventilation case. 

(a) Pole d (x=3.66 m, y=1.83 m) (b) Pole h (x=2.70 m, y=2.44 m) (c) Pole f (x=2.70 m, y=0.61 m) 
35

0.0E+00

5.0E-07

1.0E-06

1.5E-06

2.0E-06

2.5E-06

3.0E-06

3.5E-06

4.0E-06

0.0 0.5 1.0 1.5 2.0

Height (m)

SF6 Concentration (kg/kg)

Experiment

18x12x8

25x18x12

50x36x24

64x45x30

(a) 

0.0E+00

5.0E-07

1.0E-06

1.5E-06

2.0E-06

2.5E-06

3.0E-06

3.5E-06

0.0 0.5 1.0 1.5 2.0

Height (m)

SF6 Concentration (kg/kg)

Experiment

18x12x8

25x18x12

50x36x24

64x45x30

(b) 

0.00E+00

1.00E-06

2.00E-06

3.00E-06

4.00E-06

5.00E-06

6.00E-06

0.0 0.5 1.0 1.5 2.0

Height (m)

SF6 Concentration (kg/kg)

Experiment

18x12x8

25x18x12

50x36x24

64x45x30

(c) 

Figure 26. SF6 concentration predicted for the displacement ventilation case. 

(a) Pole d (x=3.66 m, y=1.83 m) (b) Pole h (x=2.70 m, y=2.44 m) (c) Pole f (x=2.70 m, y=0.61 m) 
36

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.0 0.5 1.0 1.5 2.0

Height (m)

Velocity (m/s)

velocity

18x12x8

25x18x12

50x36x24

64x45x30

(a) 

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.0 0.5 1.0 1.5 2.0

Height (m)

Velocity (m/s)

velocity

18x12x8

25x18x12

50x36x24

64x45x30

(b) 

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.0 0.5 1.0 1.5 2.0

Height (m)

Velocity (m/s)

velocity

18x12x8

25x18x12

50x36x24

64x45x30

(c) 

Figure 27. Velocities predicted for the displacement ventilation case. 

(a) Pole d (x=3.66 m, y=1.83 m) (b) Pole h (x=2.70 m, y=2.44 m) (c) Pole f (x=2.70 m, y=0.61 m) 
37

3.5 Ventilated Fire 

Problem Description

These simulations were based on full scale fire tests directed by The Sandia National Laboratory (SNL), 

sponsored by the US Nuclear Regulatory Commission (USNRC), and performed by the Factory Mutual 

Research Corporation (FMRC). The ventilated room modeled here is based on their Test #5, described in 

detail by Nowlen (1991). A schematic drawing of the test chamber is shown in Figure 28. 

Friday and Mowrer (2000) first simulated these tests with the Fire Dynamics Simulator (FDS). Their paper 

reported basic information comparing results for a few grid dimensions and comparing computing times on 

various platforms. They illustrated the importance of selecting an appropriate grid to balance result accuracy 

and computational time. This study considers the issues of computing time and grid refinement in more 

depth using a single platform. 

9.37 m

0.51 m

18.8 m (60.0 ft)

12.2 m (40.0 ft)

0.10 m

1.82 m

2.82 m

NOT TO SCALE

2.82 m

8.91 m

0.46 m

0.46 m

15.01 m

11.8 m

5.69 m

5.18 m

0.46 m

0.46 m

0.46 m

0.46 m

0.46 m

0.46 m

0.46 m

0.46 m

0.46 m

0.46 m

0.51 m

0.51 m

Sector 3

Thermocouples

(3.05, 6.10) m

Sector 2

Thermocouples

(9.15, 6.10) m

Sector 3

Thermocouples

(15.2, 6.10) m

Plume

Thermocouple

(12.2, 6.10) m

supply

vent

supply

vent

supply

vent

supply

vent

supply

vent

supply

vent

burner

return

vent

Figure 28 Geometry for the Ventilated Fire. 

The test chamber was 18.3 m by 12.2 m by 6.1 m, with a concrete floor. Wall and ceiling panels were 

constructed of 25.4 mm heat-treated, inorganic calcium silicate board supported by an external wood frame. 

Forced ventilation entered the chamber via six 0.61 m square inlet ducts extending 1.2 m below the ceiling. 

Four-way air deflector caps partially blocked the flow below the ducts. One 0.61 m by 1.83 m exhaust vent 

was located on the ceiling Figure 29 shows this arrangement in a wireframe view generated by Smokeview. 

Some additional unintended air leakage was also observed during the test, but was not accounted for by the 

model. 

Over 200 data channels recorded temperature, velocity, and species concentration at five second intervals 

during the 10-minute fire test. Figure 28 shows the measurement locations. Gas quantities were not modeled 

in this study, since this adds an extra equation and increases the computational time. Friday and Mowrer 

noted difficulty comparing their results with the experimental velocity measurements. Therefore, this report 
38

considers only the measured temperatures. Since this report draws from the original simulations run by 

Friday and Mowrer (2000), the reader may wish to refer to that report for more extensive details of the 

simulation setup. 

supply vent

burner

return vent

deflector

thermocouple

sector

Figure 29. Smokeview Wire Frame of the Ventilated Fire. 

Friday and Mowrer noted a 60 second lag between the start of the fire and detection of the temperature rise 

by the centerline plume thermocouple. They also noted that shifting the data by 60 seconds improved early 

predictions but deteriorated later predictions, although no reason for this shift was apparent. Therefore, the 

timing of the experiment may be uncertain. The analysis in this report presents the data as it was reported by 

Nowlen (1991) and does not attempt any data correction techniques. 

Grid Selection

The computational grid must be specified to properly define the features of the room. This test chamber did 

not contain many objects, however, the supply vents are 0.46 m square. This suggests a maximum grid cell 

size. The fire source is roughly this size, and the return vent is larger. The supply and return vents are 

scattered throughout the room, in locations that do not suggest an obvious grid transformation. It might be 

beneficial to create a transformed grid that is smaller near a fire event. The fire will be the largest driving 

force to the flow, and finer grid cells might give better results in the vicinity of the fire. 

The computational domains for both of the fire experiments are full-size rooms with fires in them. 

Therefore, the grid cells are much larger than used in many of the indoor air quality cases. The smallest cell 

dimension used for this case was 0.15 m, an order of magnitude larger than the finest grid used for the indoor 

air quality cases. Despite the larger grid cells, the fire cases required a much shorter time step. This happens 

because the time step is determined in part by how quickly a particle travels across a grid cell. A particle 

cannot move more than one grid cell per time step. If the particles are moved by a strong convective force, 

as with a large fire, the allowable time step is greatly reduced. This increases overall computing time since 

more steps are needed for the simulation. 

Table 6 shows the 11 cases simulated. Four cases were modeled with no grid transformation. A very coarse 

grid with dimensions 1.5 m x 1.2 m x 0.61 m was chosen for very fast computational time. The size of the 

0.46 m square supply vents was distorted significantly, and FDS reduced the supply velocity to achieve the 

correct volume flux. The fire source size was also increased to accommodate the grid, and its properties 

adjusted to obtain the correct heat release rate. Very coarse grids would have required significant distortion 

of the deflector plates as well. Therefore, some of the simulations were run without modeling the deflector 

plates at all. These cases are shown in Table 6 with an asterisk. 
39

Case Refinement Transformation type 

(x- and y- directions) 

Radiation 

modeled? 

Smallest cell size (m) Average time 

step (s) 

1* 12 x 10 x 10 none no 1.50 x 1.20 x 0.61 0.21 

2* 30 x 20 x 20 none no 0.61 x 0.61 x 0.61 0.064 

3 60 x 40 x 20 none no 0.30 x 0.30 x 0.30 0.044 

4 60 x 40 x 20 piecewise linear no 0.15 x 0.15 x 0.30 0.036 

5* 30 x 20 x 20 piecewise linear no 0.30 x 0.30 x 0.30 0.044 

6 60 x 40 x 20 polynomial no 0.13 x 0.15 x 0.30 0.035 

7* 30 x 20 x 20 polynomial no 0.25 x 0.30 x 0.30 0.044 

8* 30 x 20 x 20 none yes 0.61 x 0.61 x 0.61 0.063 

9* 30 x 20 x 20 piecewise linear yes 0.30 x 0.30 x 0.30 0.045 

10* 30 x 20 x 20 polynomial yes 0.25 x 0.30 x 0.30 0.044 

11 90 x 60 x 30 none no 0.15 x 0.15 x 0.15 0.025 

* Deflector plates on supply vents not modeled. 

Table 6 Simulations Performed for Ventilated Fire 

Grid transformations were also investigated. The number of cells near the fire source was increased in both 

the x- and y-directions to better capture the fire effects. In the case of piecewise linear transformation, twice 

as many grid cells were used in the vicinity of the fire. The polynomial transformations specified a first 

derivative equal to zero and second derivative equal to one at the mid-point of the fire in both the x- and ydirections. The x-direction transformation is shown in Figure 30, along with the supply and return vent 

locations and the fire position. 

0 5 10 15

Case 7

Case 6

Case 5

Case 4

Case 3

Case 2

Case 1

Sensors

return supply supply supply fire Room

Figure 30 Grid transformations used in the ventilated fire (x- direction) 

Three additional cases included radiation calculations. In most cases, the user does not activate the radiation 

calculations because they consume considerable computational time. Since this study focused on results 

versus computational time, the radiation calculations were run for three coarse grids to study their effect on 

both timing and results. 

Computing Times

As with the indoor air quality simulations, these simulations were structured to run quickly. The record data 

was narrowed to only those parameters needed for comparison with the experiment. A large starting time 

step was specified to allow FDS to choose its own time step. 
40

Figure 31 shows the CPU time per cell per time step, plotted against number of grid cells. In this case, there 

was no relationship between number of grid cells and this measure of computing time. A total of six cases 

were run with 12,000 grid cells. The three in which radiation were modeled consume up to five times as 

much CPU time per timestep than the cases in which radiation effects were neglected. Since the radiation 

calculation adds considerable computing time, its effect on the results of the simulation should be carefully 

considered. 

0.0E+00

5.0E-05

1.0E-04

1.5E-04

2.0E-04

2.5E-04

3.0E-04

0 20,000 40,000 60,000 80,000 100,000 120,000 140,000 160,000 180,000

Number of grid cells

CPU time (s)

Without Radiation

With Radiation

Figure 31 CPU time per cell per time step for ventilated fire 

CPU time per cell per second of simulated time is shown in Figure 32. The only case that fell below the real 

time threshold was the extremely coarse grid (12 x 10 x 10). The 30x20x20 grid simulations where slightly 

above the threshold and show promise for achieving real time on a faster computing platform, as long as 

radiation is neglected. 

0.0E+00

5.0E-04

1.0E-03

1.5E-03

2.0E-03

2.5E-03

3.0E-03

3.5E-03

4.0E-03

4.5E-03

5.0E-03

0 10,000 20,000 30,000 40,000 50,000

Number of grid cells

CPU time (s)

Without Radiation

With radiation

Upper limit for real time simulation

Figure 32 CPU time per cell per second of simulated time for the ventilated fire 
41

Comparison with Experimental Data

The fire experiments provide transient results. No time averaging was necessary, and the FDS results are 

reported directly. This report compares average normalized temperatures by grid selection and vertical 

location. 

Tempatures are compared using a Normalized Error Fraction (NEF) that was used by Friday and Mowrer 

(2000). The NEF is defined by the equation: 

measured ambient

measured

T T

T

−

− =

max,

Tpredicted NEF (2) 

where Tpredicted is the temperature predicted by FDS, Tmeasured is the temperature from the experiment, 

Tmax,measured is the maximum measured temperature during that test, and Tambient is the ambient temperature. 

An NEF of zero indicates that the predicted and measured temperatures agree exactly. 

Figures 33 - 35 show Normalized Error Fraction. The closer the results are to zero, the better the agreement 

between the experiment and FDS results. The plume temperature is measured using a single thermocouple at 

0.98 H directly above the burner. The other five data sets represent the average NEF for three thermocouples 

at the given location on the vertical arrays. 

The first set of graphs show results for the non-transformed grids. Graph (a) shows the coarsest grid, with 

NEF between –0.2 and 0.2 for the entire duration of the test. The most notable aspect of this result is the 

underprediction of the plume temperature by FDS. Because the grid is so coarse, temperatures are averaged 

over a larger area, and plume temperature is underpredicted. Although the results for this case may not be 

significantly worse in absolute terms as those from the simulations in which finer grids were used, this 

underprediction could pose a safety threat. The results of these simulations seem to reach grid independence 

with the two finest grids. 

Figure 34 shows the NEF for the cases with grid transformation. The results are only slightly better than the 

equivalent non-transformed grids. For both cases, the plume temperature rises slightly for the finer grid. 

Therefore, the 60 x 40 x 20 grid seems to be needed to resolve the plume behavior. 

The last set of NEF graphs in Figure 35 show the results for the simulations run with the radiation 

calculations. These graphs demonstrate roughly the same degree of agreement between the simulated and 

experimental results as was present in the cases in which radiation was not considered. Given the 

experimental uncertainty associated with the experiments and the complexity of the process being modeled, 

the agreement may be considered reasonable for all cases. The most significant difference between the 

calculations with and without radiation is the dramatic increase in simulation time. 
42

100 200 300 400 500 600

Time (s)

Plume 0.98 H0.9 H 0.7 H0.5 H 0.3 H

-0.4-0.3-0.2-0.1

0

0.10.20.30.4

0 100 200 300 400 500 600

Time (s)

NEF

Plume 0.98 H0.9 H 0.7 H0.5 H 0.3 H

(a) Case 1, 12 x 10 x 10 grid (b) Case 2, 30 x 20 x 20 grid 

100 200 300 400 500 600

Time (s)

Plume 0.98 H0.9 H 0.7 H0.5 H 0.3 H

-0.4-0.3-0.2-0.1

0

0.10.20.30.4

0 100 200 300 400 500 600

Time (s)

NEF

Plume 0.98 H0.9 H 0.7 H0.5 H 0.3 H

(c) Case 3, 60 x 40 x 20 grid (d) Case 11, 90 x 60 x 30 grid 

Figure 33: Normalized Error Fraction for the ventilated fire with no grid transformation 
43

100 200 300 400 500 600

Time (s)

Plume 0.98 H0.9 H 0.7 H0.5 H 0.3 H

-0.4-0.3-0.2-0.1

0

0.10.20.30.4

0 100 200 300 400 500 600

Time (s)

NEF

Plume 0.98 H0.9 H 0.7 H0.5 H 0.3 H

se 5, 30 x 20 x 20 piecewise linear (b) Case 4, 60 x 40 x 20 piecewise linear 

100 200 300 400 500 600

Time (s)

Plume 0.98 H0.9 H 0.7 H0.5 H 0.3 H

-0.4-0.3-0.2-0.1

0

0.10.20.30.4

0 100 200 300 400 500 600

Time (s)

NEF

Plume 0.98 H0.9 H 0.7 H0.5 H 0.3 H

Case 7, 30 x 20 x 20 polynomial (d) Case 6, 60 x 40 x 20 polynomial 

Figure 34: Normalized Error Fraction for the ventilated fire with grid transformation 
44

100 200 300 400 500 600

Time (s)

Plume 0.98 H0.9 H 0.7 H0.5 H 0.3 H

-0.4-0.3-0.2-0.1

0

0.10.20.30.4

0 100 200 300 400 500 600

Time (s)

NEF

Plume 0.98 H0.9 H 0.7 H0.5 H 0.3 H

a) Case 8, untransformed grid (b) Case 9, piecewise linear grid transformation 

-0.4-0.3-0.2-0.1

0

0.10.20.30.4

0 100 200 300 400 500 600

Time (s)

NEF

Plume 0.98 H0.9 H 0.7 H0.5 H 0.3 H

(c) Case 10, polynomial grid transformation 

 Figure 35: Normalized Error Fraction for the ventilated fire, radiation calculations enabled 
45

3.6. Corner Fire 

Vettori (1999) first modeled this set of experiments with the Fire Dynamics Simulator (FDS) and another 

simulation tool. That work compared the output from the two simulations against a large number of 

experiments, including slow and fast burning fires. Here, FDS simulation results are compared with 

experimental data from two of those experimental tests with grid size altered to observe the impact on 

computational time and simulation results. 

Problem Description

Figure 36 shows a plan view of the test chamber, burner, and instrumentation for the experimental setup. 

The rectangular chamber was 9.2 x 5.6 m x 2.4 m with a hollow steel door to the outside that remained 

closed during testing. An open wooden stairway led to an upper floor with the same dimensions as the fire 

compartment. Wooden joists measuring 0.038 m x 0.24 m were spaced at 0.41 m intervals across the ceiling 

and were supported by a single steel beam that spanned the width of the room. A rectangular methane gas 

burner measuring 0.7 m x 1.0 m x 0.31 m was placed in the corner of the chamber. Slow and fast burning 

fires that reached 1055 kW in 600 and 150 s respectively were monitored. Figure 37 shows a wireframe 

view of the room setup that was generated using Smokeview. 

Figure 36. Plan view of experimental layout for the corner fire. 
46

thermocouple arrays burner

stairwell

center I beam ceiling joist

Figure 37 Wire frame view of corner fire experiment. 

All temperature measurements were made using Type K thermocouples with a 0.51 mm nominal diameter, 

with a standard uncertainty of ±2.2 °C based on manufacturer’s data. These were arranged in four vertical 

arrays shown in Figures 36 and 37. For each array, measurements were taken at locations of 0, 25, 50, 75, 

100, 125, 150, 250, 350, 450, 550, and 900 mm below the ceiling. 

Grid Selection

Defining the computational grid for this case was less straightforward than for the ventilated fire 

experiments. In Vettori’s simulations, individual ceiling joists were modeled with four grid cells between 

them, for a total of 113 grid cells in the x-direction. This level of grid refinement requires nearly 300,000 

grid cells for a three dimensional simulation, so it was the finest grid that was investigated for this study. 

Four different grids were used to model the slow and fast burning fires, for a total of eight simulation cases. 

The two finest grids defined the ceiling joists at their proper dimensions via piecewise linear transformation 

of the x-axis. The ceiling joists were not modeled with the two coarsest grids, and no transformation was 

used. Omitting the ceiling joists allowed a significant reduction in the number of grid cells needed; however, 

this would not be a viable option if the flow near the ceiling joists were important, as it might be in a study of 

ceiling mounted detector activation. The eight simulations are summarized in Table 7. Figure 38 shows the 

location of grid cells on the x-axis for the four grids, as well as the locations of joists, vents, and sensor 

arrays. 

Case Refinement Transform type (xdirection) 

Smallest cell size (m) Average time step 

(s) 

Fire 

Speed 

1 113 x 64 x 40 piecewise linear 0.092 x 0.088 x 0.066 0.0044 fast 

2 72 x 32 x 20 piecewise linear 0.11 x 0.18 x 0.13 0.0102 fast 

3 45 x 24 x 16 none 0.20 x 0.23 x 0.16 0.0140 fast 

4 12 x 10 x 10 none 0.77 x 0.56 x 0.26 0.0458 fast 

5 113 x 64 x 40 piecewise linear 0.092 x 0.088 x 0.066 0.0096 slow 

6 72 x 32 x 20 piecewise linear 0.11 x 0.18 x 0.13 0.0254 slow 

7 45 x 24 x 16 none 0.20 x 0.23 x 0.16 0.0367 slow 

8 12 x 10 x 10 none 0.77 x 0.56 x 0.26 0.129 slow 

Table 7. Simulations performed for the corner fire. 
47

02468

Distance (m)

Case 4

Case 3

Case 2

Case 1

Sensors

Geometry

burner open vent

Joist Locations

Figure 38. Grid spacing for the corner fire (x- direction). 

Computing Times

The output information collected for this simulation was again kept to a minimum to reduce effects on 

simulation time, and FDS was again allowed to calculate the maximum permissible time step. Figure 39 

shows the CPU time per cell per time step. Generally, computing times for the fast and slow burning fires 

are very close to one another, except in the case of the coarsest grid. For that case, the fast fire simulation 

was much slower on a per time step basis. Examination of computing time usage broken down by task 

showed that the primary difference between the two simulations was that the sprinklers were activated for the 

fast burning fire, but not for the slow burning fire. This was actually true of all of the fast fire simulations, 

but the additional computing time consumed was much larger on a per grid cell basis for the coarse grid case. 

In the other cases, the penalty associated with sprinkler activation was spread out over many more time steps 

and grid cells. 

0.E+00

1.E-05

2.E-05

3.E-05

4.E-05

5.E-05

6.E-05

7.E-05

8.E-05

9.E-05

1.E-04

0 50,000 100,000 150,000 200,000 250,000 300,000

Number of grid cells

CPU time (s)

Slow Fire

Fast Fire

Figure 39. CPU time per cell per time step for corner fire. 
48

0.E+00

5.E-04

1.E-03

2.E-03

2.E-03

3.E-03

3.E-03

4.E-03

4.E-03

5.E-03

5.E-03

0 10,000 20,000 30,000 40,000 50,000

Number of cells

CPU Time (s)

Slow Fire

Upper limit for real

time simulation

Fast Fire

Figure 40. CPU time per cell per second of simulated time for corner fire. 

Figure 40 shows the computing time in comparison to real time. Only Case 8 with the coarsest grid and slow 

fire was simulated in less than real time. Since the time step is limited by the time required for a particle to 

travel the length of one grid cell, shorter time steps were needed to model the fast burning fire. For the same 

reason, shorter time steps are required for both fire types as the grid becomes finer. As Table 8 shows, the 

average time step for the slow burning fire is roughly twice that required for the fast fire. 

Comparison with Experimental Data

As with the ventilated fire, the NEF is again used to compare the experimental and simulated temperature 

profiles. A NEF of zero indicates that the predicted and measured temperatures agree exactly. Results for 

the fast and slow burning fires are shown in Figures 41 and 42 respectively. 

In Figure 41, all of the simulations show the temperatures as overpredicted by the model, particularly as time 

progresses. This may be attributable to the actual experimental conditions not matching precisely with the 

model inputs. This is suggested by the trend at all of the thermocouple locations to follow a similar pattern. 

Some differences between the coarse and fine grids are apparent, however. When the coarse grid is used, 

temperatures in the lower portion of the room tend to be higher while temperatures in the upper portion of the 

room tend to be lower than those predicted by the finer grids. This is a result of artificial diffusion created by 

the large grid cells. Also, because the ceiling joists are not modeled, the patterns predicted by the simulation 

at points close to the ceiling are sometimes different. 

The agreement between simulation and experiment is much closer in Figure 42, which shows the slow 

burning fire. In these cases, the predictions tend to be within about 10% of the experiment. Again, for the 

coarse grid cases, temperatures at the lower thermocouples tend to be higher than expected, and those at 

upper thermocouples tend to be slightly lower. In general, the finer grids give a narrower range of NEF for 

the various measurement heights.
49

20 40 60 80

Time (s)

0 mm 50 mm100 mm 150 mm350 mm 550 mm

-0.40-0.20

0.000.200.40

0 20 40 60 80

Time (s)

NEF

0 mm 50 mm100 mm 150 mm350 mm 550 mm

a) Case 1, 113 x 64 x 40 grid (b) Case 2, 72 x 30 x 20 grid 

20 40 60 80

Time (s)

0 mm 50 mm100 mm 150 mm350 mm 550 mm

-0.40-0.20

0.000.200.40

0 10 20 30 40 50 60 70 80

Time (s)

NEF 

0 mm 50 mm100 mm 150 mm350 mm 550 mm

(c) Case 3, 45 x 24 x 16 grid (d) Case 4, 12 x 10 x 10 grid 

Figure 41: Fast corner fire normalized error fraction 
50

50 100 150

Time (s)

0 mm 50 mm100 mm 150 mm350 mm 550 mm

-0.40-0.20

0.000.200.40

0 50 100 150

Time (s)

NEF 

0 mm 50 mm100 mm 150 mm350 mm 550 mm

a) Case 5, 113 x 65 x 40 grid (b) Case 6, 72 x 32 x 20 grid 

50 100 150

Time (s)

0 mm 50 mm100 mm 150 mm350 mm 550 mm

-0.40-0.20

0.000.200.40

0 50 100 150

Time (s)

NEF

0 mm 25 mm50 mm 75 mm100 mm 125 mm

(c) Case 7, 45 x 24 x 16 grid (d) Case 8, 12 x 10 x 10 grid 

Figure 42: Slow corner fire normalized error fraction.
51

4. DISCUSSION 

4.1. Computing Time 

The computing time required for each of these simulations depends on both the average time step length and 

the computing time consumed per time step. Figure 43 shows the average time step for all of the simulations. 

In general, time step length is limited to the time required for a particle to travel the length of one grid cell. 

Therefore, for each of the six validation problems, time step increases with the cell dimension. Also, much 

smaller time steps can be used for problems with strong convective motion, such as the fires. This effect is 

also apparent within the corner fire results: for each grid dimension the larger time step represents the slow 

burning fire and the smaller time step represents the fast burning fire. However, both of these fires require 

significantly smaller time steps than the non-fire scenarios. To obtain similar computing times, the fires were 

simulated with coarser grids to partially offset this difference. 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8

Shortest cell dimension (m)

Average time step (s)

Displacement

Forced

Natural

Mixed

Corner fire

Ventilated fire

Vent. fire + radiation

Figure 43. Average time step. 

Clearly, shorter time steps increase overall simulation time because more time steps are needed. A second 

factor affecting overall simulation speed is the CPU time required for each timestep. This quantity, shown in 

Figure 44, generally does not depend on number of grid cells, and is instead related to the equations that must 

be solved. It is possibile that large simulations may be less efficient if system resources are strained. Also 

simulations with a very small number of grid cells sometimes appear to consume more computing time 

simply because there are fewer cells and time steps for “overhead” tasks such as results reporting and 

sprinkler activation to be spread among. Of the scenarios shown, the most CPU time is consumed by the 

radiation cases. This would be expected because of the additional equations involved. The next most time 

consuming simulations are the very coarse mixed convection case and the very coarse fast corner fire case, 

again because of these “overhead” tasks. The shortest CPU time is needed for the forced ventilation 

scenario, which would be expected since this case does not require the energy or species equations to be 

solved. 

Putting both of these factors together, Figure 45 shows the CPU time required per cell per second of 

simulated time for each of the scenarios. This measure of CPU time is referenced against a “real time upper 

limit”, in which the simulated and simulation times would be equal. Three of the four non-fire scenarios 

were simulated in less than real time with reasonable results. A somewhat longer simulation time was 

needed to properly model species diffusion for the displacement ventilation scenario. Using a very coarse 

grid, it was possible to obtain reasonable predictions of temperatures generated by the slow corner fire. This 

may not have been the case, however, if species were also tracked. The stronger convective forces in the fast 

corner fire required longer computing times, however, these are still quite reasonable and could be improved 

even further with a more powerful computer. Likewise, one of the ventilated fire cases is faster than real 
52

time, but the predicted plume temperature is too low. A finer grid is needed to reduce the numerical 

diffusion. 

0.0E+00

5.0E-05

1.0E-04

1.5E-04

2.0E-04

2.5E-04

3.0E-04

0 20000 40000 60000 80000 100000

Number of grid cells

CPU time per cell per 

timestep (s)

Displacement

Forced

Natural

Mixed

Corner fire

Ventilated fire

Vent. fire + Radiation

Figure 44. CPU time per cell per timestep.

0.0E+00

5.0E-04

1.0E-03

1.5E-03

2.0E-03

2.5E-03

3.0E-03

3.5E-03

4.0E-03

0 2000 4000 6000 8000 10000

Number of grid cells

CPU time per cell per second 

(s)

Displacement

Forced

Natural

Mixed

Corner fire

Ventilated fire

Vent. Fire + radiation

Real time upper limit

Figure 45. CPU time per cell per second. 

4.2. Results Comparison 

Comparison with experimental results has identified a number of issues important to building simulations 

and developing expectations for the computational results. Development of the computational model should 

include an investigation of the influence of number of grid cells, grid refinement technique, and time step on 

the results. The need to properly specify obstructions, heat transfer boundary conditions, inlet diffusers, and 

contaminant releases is also clear. In a design situation, it is likely that certain boundary conditions, such as 

surface temperatures or inlet velocity profiles, would not be as well defined. This might require additional 

simulations to assess the sensitivity of the solution to fluctuations in these input parameters. 

It would also have been possible to improve the agreement of the CFD models with the experimental results 

by “fine-tuning” the inputs. For example, the temperature profiles predicted for the displacement ventilation 

case might have better matched the experimental results if another convection coefficient had been used in 

the model. It would have been possible to continually adjust the convection coefficients until the best 

possible result was obtained. However, this would not be possible when modeling a new situation. The 

approach taken here was to choose convection coefficients based on past experience and published studies 

and not adjust them. With a new situation, the modeler should give careful thought to selecting convection 
53

coefficients. Fire simulations tend to be dominated by the fire behavior, so that the convection from other 

surfaces is often less important. However, surface convection can be an important aspect of non-fire flows, 

and the choice of coefficient can become critical. If the heat flux from a surface is known, it should be 

specified directly; otherwise care should be taken to select coefficients from published sources that best 

describe the situation to be modeled. 

The way in which FDS treats surface convection also leads to a departure from the accepted wisdom that a 

finer grid will produce better results. This convection model requires that the grid cell adjacent to a fixedtemperature wall be larger than the thermal boundary layer. Smaller grid cells could lead to under-prediction 

of heat transfer. In certain cases, there could be a trade-off between keeping grid cells large enough to get 

the correct heat transfer and small enough to properly define the room geometry or to predict diffusion 

correctly. Empirical correlations can be used to approximate boundary layer thickness to determine whether 

a conflict might arise. If this is the case, it would be worthwhile to try to specify a surface heat flux instead 

of a fixed temperature. 

In general, the results obtained for these simulations were accurate enough to be useful. However, even 

though the experimental results were generated and measured under controlled conditions, the agreement 

between model and experiment was not always precise and is sometimes best compared qualitatively. The 

results pattern for the fast corner fire suggests that perhaps the original experimental conditions are not 

understood as well as one might want them to be, and that the results are systematically affected. These 

experiences should be used to calibrate expectations of the model. 

5. CONCLUSIONS 

The collective experience of the many simulations performed to model these six flow problems highlights 

several issues relevant to the use of the code for modeling a wider variety of scenarios. The inclusion of both 

fire and non-fire scenarios allows issues specific to each type of modeling to be identified. In general, the 

FDS code was able to produce results that agree reasonably with the experimental data. However, a 

systematic modeling approach that considers the problem solving technique employed by the code is 

essential to obtaining the best results. 

For a single problem, at least a few simulations should be performed to check the influence of the number of 

grid cells, grid refinement technique, and time step on the solution. In particular, grid cell size should be 

checked to verify that it is large enough to properly model heat transfer from constant temperature surfaces, 

and small enough to properly represent diffusion conditions. This should be done in addition to any 

investigation of possible variation in boundary conditions that may also be necessary. 

Some care is also needed to define the model in a way that is appropriate for the program and for the problem 

to be solved. For non-fire scenarios, heat transfer coefficients should be carefully selected and defined in a 

manner that is consistent with a coarse grid model. This may be less important for fire-dominated flows. 

The true power of a simplified model is its ability to produce very fast solutions. Most of the non-fire 

problems cold be solved at faster than real time speeds on a mid-level personal computer. With the exception 

of the displacement ventilation problem, the results obtained at these speeds were nearly as good as those 

obtained with the finer grids at slower computing times. In the displacement ventilation case, a finer grid 

was required to properly capture diffusion of the tracer gas. 

Because the stronger convective forces present in the fire cases required much shorter time steps, these 

simulations tended to consume slightly more computing time. However, these simulations were still quite 

fast, and reasonable results were obtained with coarse grids. These simulations were slower than real time, 

but still fast enough to be convenient and useful in a design environment. With a more powerful computer, 

many of these simulations might be conducted in real time as well. 
54

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Edited by Klein C.R. and Kawano, S., August 1-5, Boston, Massachusetts. 
56

APPENDIX A: Sample input files 

A.1. Forced convection (case 14) 

 &HEAD CHID='forced14', TITLE='Davidson study, 36X12X20, grid xform' / 

 &GRID IBAR=36,JBAR=12,KBAR=20 / 

 &PDIM XBAR=9.0, YBAR=3.0, ZBAR=3.0 / 

 &TRNZ IDERIV=1, CC=0.0, PC=0.5 / 

 &TRNZ IDERIV=1, CC=3.0, PC=0.5 / 

 &TRNZ IDERIV=2, CC=0.0, PC=0.0 / 

 &TRNZ IDERIV=2, CC=3.0, PC=0.0 / 

 &TRNZ IDERIV=0, CC=2.55, PC=2.832 / 

 &TRNZ IDERIV=0, CC=0.90, PC=0.480 / 

 &TIME DT=0.4,TWFIN=2500. / 

 &MISC TMPA=20., ISOTHERMAL=.TRUE., CSMAG=0.14 / 

 &PL3D DTSAM=200, QUANTITIES='VELOCITY', 'U-VELOCITY', 'V-VELOCITY' ,'W-VELOCITY', 

'PRESSURE' / 

 &SURF ID='INLET', VOLUME_FLUX=-0.22932 / 

 &VENT XB=0.0, 0.0, 0.0, 3.0, 2.832, 3.0, SURF_ID='INLET' / 

 &VENT XB=9.0, 9.0, 0.0, 3.0, 0.0, 0.48, SURF_ID='OPEN' / 

 &SLCF XB=3., 3., 1.5, 1.5, 0., 3., QUANTITY='U-VELOCITY', DTSAM=1.0 / 

 &SLCF XB=6., 6., 1.5, 1.5, 0., 3., QUANTITY='U-VELOCITY' / 

 &SLCF XB=0., 9., 1.5, 1.5, 2.916, 2.916, QUANTITY='U-VELOCITY' / 

 &SLCF XB=0., 9., 1.5, 1.5, 0.084, 0.084, QUANTITY='U-VELOCITY' / 

A.2. Natural convection (case 2) 

&HEAD CHID='natural2',TITLE='Sample fire in multiple room layout' / 

&GRID IBAR=50, JBAR=1, KBAR=16 / 

&PDIM XBAR=7.9,YBAR=.16,ZBAR=2.5 / 

&TIME DT=1.0,TWFIN=5000. / 

&MISC TMPA=27.6 / 

&SURF ID='hot' ,TMPWAL=35.3 / 

&SURF ID='cold',TMPWAL=19.9 / 

&SURF ID='slip',VBC=1. / 

&VENT CB='XBAR' ,SURF_ID='hot' / 

&VENT CB='XBAR0',SURF_ID='cold' / 

&VENT CB='YBAR' ,SURF_ID='slip' / 

&VENT CB='YBAR0',SURF_ID='slip' / 

&SLCF XB=0.00,7.90,0.08,0.08,0.00,2.50, QUANTITY='TEMPERATURE' / 

&SLCF XB=0.00,7.90,0.08,0.08,0.00,2.50, QUANTITY='U-VELOCITY' / 

&SLCF XB=0.00,7.90,0.08,0.08,0.00,2.50, QUANTITY='W-VELOCITY' / 

&SLCF XB=0.00,7.90,0.08,0.08,0.00,2.50, QUANTITY='VELOCITY' / 

&SLCF XB=3.95,3.95,0.08,0.08,0.00,2.50, QUANTITY='TEMPERATURE' / 

&SLCF XB=3.95,3.95,0.08,0.08,0.00,2.50, QUANTITY='U-VELOCITY' / 

A.3. Mixed convection (case 1) 

 &HEAD CHID='mixed1', TITLE='mixed convection, blay case, grid 10x8x10' / 

 &GRID IBAR=10, JBAR=8, KBAR=10 / 

 &PDIM XBAR=1.04, YBAR=0.7, ZBAR=1.04 / 

 &TRNZ CC=0.104, PC=0.024 / 

 &TRNZ CC=0.936, PC=1.022 / 

 &TIME DT=0.3, TWFIN=1000. / 

 &MISC TMPA=15., CSMAG=0.14, SURF_DEFAULT='WALL', C_HORIZONTAL=4.0, 

C_VERTICAL=2.03 / 
57

 &PL3D DTSAM=200, QUANTITIES='TEMPERATURE', 'U-VELOCITY', 'V-VELOCITY', 'WVELOCITY', 'PRESSURE' / 

 &SURF ID='INLET', VOLUME_FLUX=-0.007182 / 

 &SURF ID='FLOOR', TMPWAL=35.5 / 

 &SURF ID='WALL', TMPWAL=15.0 / 

 &VENT XB=0.0, 0.0, 0.0, 0.7, 1.0022, 1.04, SURF_ID='INLET' / 

 &VENT XB=1.04, 1.04, 0.0, 0.7, 0.0, 0.024, SURF_ID='OPEN' / 

 &VENT CB='ZBAR0', SURF_ID='FLOOR' / 

 &SLCF XB=0., 1.04, 0.35, 0.35, 0.52, 0.52, QUANTITY='W-VELOCITY', DTSAM=1.0 / 

 &SLCF XB=0., 1.04, 0.35, 0.35, 0.52, 0.52, QUANTITY='TEMPERATURE' / 

 &SLCF XB=0.52, 0.52, 0.35, 0.35, 0., 1.04, QUANTITY='U-VELOCITY' / 

 &SLCF XB=0.52, 0.52, 0.35, 0.35, 0., 1.04, QUANTITY='TEMPERATURE' / 

 &SLCF XB=0., 1.04, 0.35, 0.35, 0., 1.04, QUANTITY='TEMPERATURE' / 

 &SLCF XB=0., 1.04, 0.35, 0.35, 0., 1.04, QUANTITY='VELOCITY' / 

A.4. Displacement ventilation (case 2) 

 &HEAD CHID='disp2', TITLE= 'Data for Chen validation, case 1' / 

 &GRID IBAR=18, JBAR=12, KBAR=8 / 

 &PDIM XBAR=5.16, YBAR=3.65, ZBAR=2.43 / 

 &TIME DT=1.5,TWFIN=5000. / 

 &MISC TMPA=26.7, C_HORIZONTAL=4.05, C_VERTICAL=3.08 / 

 &PL3D DTSAM=1000., QUANTITIES='SF6','U-VELOCITY','V-VELOCITY','WVELOCITY','TEMPERATURE' / 

 &PART NPSAM=500, QUANTITY='SF6', AGE=1, DTSAM=100 / 

 &SPEC ID='SF6', MW=146. / 

 &SURF ID='PERSON', HEAT_FLUX=0.0419 / 

 &SURF ID='COMP1', HEAT_FLUX =0.13563 / 

 &SURF ID='COMP2', HEAT_FLUX =0.2168 / 

 &SURF ID='LAMP', HEAT_FLUX =0.051515 / 

 &SURF ID='CEILING', TMPWAL=25.61 / 

 &SURF ID='FLOOR', TMPWAL=23.56 / 

 &SURF ID='WINDOW', TMPWAL=27.68 / 

 &SURF ID='LOWALL', TMPWAL=24.21 / 

 &SURF ID='UPWALL', TMPWAL=25.72 / 

 &SURF ID='INLET', TMPWAL=17.0, VOLUME_FLUX=-0.05085, MASS_FRACTION(1)=0.0 / 

 &SURF ID='TRACER', HEAT_FLUX=0.0419, VEL=-0.001, MASS_FLUX(1)=7.33E-7 / 

 &OBST XB=2.01,2.29,0.9125,1.21,0.0,1.215,SURF_IDS='TRACER','PERSON','PERSON' / 

 &OBST XB=3.15,3.44,2.43,2.73,0.0,1.215,SURF_IDS='TRACER','PERSON','PERSON' / 

 &OBST XB=1.98, 2.38, 0.1, 0.5, 0.75, 1.15, SURF_ID='COMP1' / 

 &OBST XB=3.13, 3.53, 3.15, 3.55, 0.75, 1.15, SURF_ID='COMP2' / 

 &OBST XB=0.35, 2.58, 0.0, 0.75, 0.74, 0.75 / 

 &OBST XB=2.93, 5.16, 2.90, 3.65, 0.74, 0.75 / 

 &OBST XB=0., 0.33, 0., 0.58, 0., 1.32 / 

 &OBST XB=4.21, 5.16, 0., 0.58, 0., 1.24 / 

 &OBST XB=1.03, 1.23, 0.16, 1.36, 2.18, 2.33, SURF_ID='LAMP' / 

 &OBST XB=2.33, 2.53, 0.16, 1.36, 2.18, 2.33, SURF_ID='LAMP' / 

 &OBST XB=3.61, 3.81, 0.16, 1.36, 2.18, 2.33, SURF_ID='LAMP' / 

 &OBST XB=1.03, 1.23, 2.29, 3.49, 2.18, 2.33, SURF_ID='LAMP' / 

 &OBST XB=2.33, 2.53, 2.29, 3.49, 2.18, 2.33, SURF_ID='LAMP' / 

 &OBST XB=3.61, 3.81, 2.29, 3.49, 2.18, 2.33, SURF_ID='LAMP' / 

 &OBST XB=0.0, 0.28, 1.51, 2.04, 0.03, 1.14 / 

 &VENT XB=0.28, 0.28, 1.51, 2.04, 0.03, 1.14, SURF_ID='INLET' / 

 &VENT XB=2.365, 2.795, 1.61, 2.04, 2.43, 2.43, SURF_ID='OPEN' / 

 &VENT CB='ZBAR0', SURF_ID='FLOOR' / 

 &VENT XB=4.14, 5.16, 0.00, 3.65, 2.43, 2.43, SURF_ID='CEILING' / 
58

 &VENT XB=3.18, 4.14, 0.00, 3.65, 2.43, 2.43, SURF_ID='CEILING' / 

 &VENT XB=2.365, 3.18, 0.0, 1.61, 2.43, 2.43, SURF_ID='CEILING' / 

 &VENT XB=2.795, 3.18, 1.61, 2.04, 2.43, 2.43, SURF_ID='CEILING' / 

 &VENT XB=2.365, 3.18, 2.04, 2.745, 2.43, 2.43, SURF_ID='CEILING' / 

 &VENT XB=2.365, 3.18, 2.745, 3.65, 2.43, 2.43, SURF_ID='CEILING' / 

 &VENT XB=1.26, 2.365, 0.0, 3.65, 2.43, 2.43, SURF_ID='CEILING' / 

 &VENT XB=0.00, 1.26, 0.00, 3.65, 2.43, 2.43, SURF_ID='CEILING' / 

 &VENT XB=5.16, 5.16, 0.15, 3.5, 1.24, 2.10, SURF_ID='WINDOW' / 

 &VENT XB=5.16, 5.16, 0.58, 3.5, 0.94, 1.24, SURF_ID='WINDOW' / 

 &VENT XB=0.0, 0.0, 0.58, 1.51, 0.0, 0.85, SURF_ID='LOWALL' / 

 &VENT XB=0.0, 0.0, 2.04, 3.65, 0.0, 0.85, SURF_ID='LOWALL' / 

 &VENT XB=5.16, 5.16, 0.58, 3.65, 0.0, 0.85, SURF_ID='LOWALL' / 

 &VENT XB=2.58, 4.21, 0.0, 0.0, 0.0, 0.85, SURF_ID='LOWALL' / 

 &VENT XB=0.35, 2.58, 0.0, 0.0, 0.0, 0.74, SURF_ID='LOWALL' / 

 &VENT XB=0.35, 2.58, 0.0, 0.0, 0.81, 0.85, SURF_ID='LOWALL' / 

 &VENT XB=0.33, 0.35, 0.0, 0.0, 0.0, 0.85, SURF_ID='LOWALL' / 

 &VENT XB=0.0, 2.93, 3.65, 3.65, 0.0, 0.85, SURF_ID='LOWALL' / 

 &VENT XB=2.93, 5.16, 3.65, 3.65, 0.81, 0.85, SURF_ID='LOWALL' / 

 &VENT XB=2.93, 5.16, 3.65, 3.65, 0.0, 0.74, SURF_ID='LOWALL' / 

 &VENT XB=0.0, 0.0, 0.0, 0.58, 1.32, 2.43, SURF_ID='UPWALL' / 

 &VENT XB=0.0, 0.0, 0.58, 1.51, 0.85, 2.43, SURF_ID='UPWALL' / 

 &VENT XB=0.0, 0.0, 1.51, 2.04, 1.14, 2.43, SURF_ID='UPWALL' / 

 &VENT XB=0.0, 0.0, 2.04, 3.65, 0.85, 2.43, SURF_ID='UPWALL' / 

 &VENT XB=5.16, 5.16, 3.5, 3.65, 0.85, 2.1, SURF_ID='UPWALL' / 

 &VENT XB=5.16, 5.16, 0.58, 3.5, 0.85, 0.94, SURF_ID='UPWALL' / 

 &VENT XB=5.16, 5.16, 0.15, 3.65, 2.1, 2.43, SURF_ID='UPWALL' / 

 &VENT XB=5.16, 5.16, 0.0, 0.15, 1.24, 2.43, SURF_ID='UPWALL' / 

 &VENT XB=0.33, 4.21, 0.0, 0.0, 0.85, 1.24, SURF_ID='UPWALL' / 

 &VENT XB=0.33, 5.16, 0.0, 0.0, 1.24, 1.32, SURF_ID='UPWALL' / 

 &VENT XB=0.0, 5.16, 0.0, 0.0, 1.32, 2.43, SURF_ID='UPWALL' / 

 &VENT XB=0.0, 5.16, 3.65, 3.65, 0.85, 2.43, SURF_ID='UPWALL' / 

 &THCP XYZ=4.0, 1.0, 0.6, QUANTITY='SF6', DTSAM=1.0 / 

 &THCP XYZ=1.5, 2.65, 0.6, QUANTITY='SF6' / 

 &THCP XYZ=1.5, 1.0, 2.0, QUANTITY='SF6' / 

 &THCP XYZ=4.5, 3.0, 2.0, QUANTITY='SF6' / 

 &THCP XYZ=2.58, 1.825, 2.40, QUANTITY='SF6' / 

 &THCP XYZ=4.0, 1.0, 0.6, QUANTITY='TEMPERATURE' / 

 &THCP XYZ=1.5, 2.65, 0.6, QUANTITY='TEMPERATURE' / 

 &THCP XYZ=1.5, 1.0, 2.0, QUANTITY='TEMPERATURE' / 

 &THCP XYZ=4.5, 3.0, 2.0, QUANTITY='TEMPERATURE' / 

 &THCP XYZ=2.58, 1.825, 2.40, QUANTITY='TEMPERATURE' / 

 &SLCF XB=0.78, 0.78, 1.83, 1.83, 0.0,2.43, QUANTITY='TEMPERATURE', DTSAM=1.0 / 

 &SLCF XB=1.74, 1.74, 1.83, 1.83, 0.0,2.43, QUANTITY='TEMPERATURE' / 

 &SLCF XB=2.7, 2.7, 1.83, 1.83, 0.0,2.43, QUANTITY='TEMPERATURE' / 

 &SLCF XB=3.66, 3.66, 1.83, 1.83, 0.0,2.43, QUANTITY='TEMPERATURE' / 

 &SLCF XB=4.62, 4.62, 1.83, 1.83, 0.0,2.43, QUANTITY='TEMPERATURE' / 

 &SLCF XB=2.7, 2.7, 0.61, 0.61, 0.0,2.43, QUANTITY='TEMPERATURE' / 

 &SLCF XB=2.7, 2.7, 1.22, 1.22, 0.0,2.43, QUANTITY='TEMPERATURE' / 

 &SLCF XB=2.7, 2.7, 2.44, 2.44, 0.0,2.43, QUANTITY='TEMPERATURE' / 

 &SLCF XB=2.7, 2.7, 3.05, 3.05, 0.0,2.43, QUANTITY='TEMPERATURE' / 

 &SLCF XB=0.78, 0.78, 1.83, 1.83, 0.0,2.43, QUANTITY='SF6' / 

 &SLCF XB=1.74, 1.74, 1.83, 1.83, 0.0,2.43, QUANTITY='SF6' / 

 &SLCF XB=2.7, 2.7, 1.83, 1.83, 0.0,2.43, QUANTITY='SF6' / 

 &SLCF XB=3.66, 3.66, 1.83, 1.83, 0.0,2.43, QUANTITY='SF6' / 

 &SLCF XB=4.62, 4.62, 1.83, 1.83, 0.0,2.43, QUANTITY='SF6' / 

 &SLCF XB=2.7, 2.7, 0.61, 0.61, 0.0,2.43, QUANTITY='SF6' / 
59

 &SLCF XB=2.7, 2.7, 1.22, 1.22, 0.0,2.43, QUANTITY='SF6' / 

 &SLCF XB=2.7, 2.7, 2.44, 2.44, 0.0,2.43, QUANTITY='SF6' / 

 &SLCF XB=2.7, 2.7, 3.05, 3.05, 0.0,2.43, QUANTITY='SF6' / 

 &SLCF XB=0.78, 0.78, 1.83, 1.83, 0.0,2.43, QUANTITY='VELOCITY' / 

 &SLCF XB=1.74, 1.74, 1.83, 1.83, 0.0,2.43, QUANTITY='VELOCITY' / 

 &SLCF XB=2.7, 2.7, 1.83, 1.83, 0.0,2.43, QUANTITY='VELOCITY' / 

 &SLCF XB=3.66, 3.66, 1.83, 1.83, 0.0,2.43, QUANTITY='VELOCITY' / 

 &SLCF XB=4.62, 4.62, 1.83, 1.83, 0.0,2.43, QUANTITY='VELOCITY' / 

 &SLCF XB=2.7, 2.7, 0.61, 0.61, 0.0,2.43, QUANTITY='VELOCITY' / 

 &SLCF XB=2.7, 2.7, 1.22, 1.22, 0.0,2.43, QUANTITY='VELOCITY' / 

 &SLCF XB=2.7, 2.7, 2.44, 2.44, 0.0,2.43, QUANTITY='VELOCITY' / 

 &SLCF XB=2.7, 2.7, 3.05, 3.05, 0.0,2.43, QUANTITY='VELOCITY' / 

 &SLCF XB=0.0, 5.16, 1.61, 1.58, 1.58, 2.43, QUANTITY='TEMPERATURE' / 

 &SLCF XB=0.0, 5.16, 1.61, 1.58, 1.58, 2.43, QUANTITY='SF6' / 

A.5 Ventilated Fire (case 4) 

&HEAD CHID='FMSNL4',TITLE='FMSNL Test #5- 1ft grid with piecewise linear transformation' / 

&GRID IBAR=60,JBAR=40,KBAR=20 / 

&PDIM XBAR=18.29,YBAR=12.19,ZBAR=6.10 / 

&TRNX CC=9.14,PC=10.67 / 

&TRNX CC=15.24, PC=13.72 / 

&TRNY CC=3.05,PC=4.57 / 

&TRNY CC=9.15, PC=7.62 / 

&TIME DT=0.5,TWFIN=600. / 

&PART QUANTITY='TEMPERATURE',DTPAR=0.05 / 

&MISC TMPA=21.0 / 

&SURF ID='burner',HRRPUA=787.,TBO=0.5,TAU_Q=-240. / 

&SURF ID='wall',ALPHA=1.55E-7,KS=0.1035,DELTA=0.0254, RADIATION=.FALSE. / 

&SURF ID='port',TMPWAL=21,VOLUME_FLUX=-0.63 / 

&OBST XB=2.82,3.28,2.82,3.28,4.88,6.10 /#1 injection port 

&OBST XB=2.82,3.28,2.82,3.28,4.57,4.57 /deflector plate 

&OBST XB=8.91,9.37,2.82,3.28,4.88,6.10 /#2 injection port 

&OBST XB=8.91,9.37,2.82,3.28,4.57,4.57 /deflector plate 

&OBST XB=15.01,15.47,2.82,3.28,4.88,6.10 /#3 injection port 

&OBST XB=15.01,15.47,2.82,3.28,4.57,4.57 /deflector plate 

&OBST XB=2.82,3.28,8.91,9.37,4.88,6.10 /#4 injection port 

&OBST XB=2.82,3.28,8.91,9.37,4.57,4.57 /deflector plate 

&OBST XB=8.91,9.37,8.91,9.37,4.88,6.10 /#5 injection port 

&OBST XB=8.91,9.37,8.91,9.37,4.57,4.57 /deflector plate 

&OBST XB=15.01,15.47,8.91,9.37,4.88,6.10 /#6 injection port 

&OBST XB=15.01,15.47,8.91,9.37,4.57,4.57 /deflector plate 

&OBST XB=11.79,12.60,5.69,6.50,0.00,0.30 /sand burner 

&VENT CB='EAST',SURF_ID='wall' / 

&VENT CB='WEST',SURF_ID='wall' / 

&VENT CB='NORTH',SURF_ID='wall' / 

&VENT CB='SOUTH',SURF_ID='wall' / 

&VENT CB='TOP',SURF_ID='wall' / 

&VENT XB=2.82,3.28,2.82,3.28,4.88,4.88,SURF_ID='port' / 

&VENT XB=8.91,9.37,2.82,3.28,4.88,4.88,SURF_ID='port' / 

&VENT XB=15.01,15.47,2.82,3.28,4.88,4.88,SURF_ID='port' / 

&VENT XB=2.82,3.28,8.91,9.37,4.88,4.88,SURF_ID='port' / 

&VENT XB=8.91,9.37,8.91,9.37,4.88,4.88,SURF_ID='port' / 

&VENT XB=15.01,15.47,8.91,9.37,4.88,4.88,SURF_ID='port' / 

&VENT XB=11.79,12.60,5.69,6.50,0.30,0.30,SURF_ID='burner' / propylene burner 

&VENT XB=0.10,0.61,5.18,7.01,6.10,6.10,SURF_ID='OPEN' / exhaust vent 
60

&THCP XYZ=3.05,6.1,5.98,QUANTITY='TEMPERATURE',LABEL='Sector3 Ch11',DTSAM=5 / 

&THCP XYZ=3.05,6.1,5.49,QUANTITY='TEMPERATURE',LABEL='Sector3 Ch12' / 

&THCP XYZ=3.05,6.1,4.27,QUANTITY='TEMPERATURE',LABEL='Sector3 Ch13' / 

&THCP XYZ=3.05,6.1,3.05,QUANTITY='TEMPERATURE',LABEL='Sector3 Ch14' / 

&THCP XYZ=3.05,6.1,1.83,QUANTITY='TEMPERATURE',LABEL='Sector3 Ch15' / 

&THCP XYZ=9.15,6.1,5.98,QUANTITY='TEMPERATURE',LABEL='Sector2 Ch6' / 

&THCP XYZ=9.15,6.1,5.49,QUANTITY='TEMPERATURE',LABEL='Sector2 Ch7' / 

&THCP XYZ=9.15,6.1,4.27,QUANTITY='TEMPERATURE',LABEL='Sector2 Ch8' / 

&THCP XYZ=9.15,6.1,3.05,QUANTITY='TEMPERATURE',LABEL='Sector2 Ch9' / 

&THCP XYZ=9.15,6.1,1.83,QUANTITY='TEMPERATURE',LABEL='Sector2 Ch10' / 

&THCP XYZ=15.25,6.1,5.98,QUANTITY='TEMPERATURE',LABEL='Sector1 Ch1' / 

&THCP XYZ=15.25,6.1,5.49,QUANTITY='TEMPERATURE',LABEL='Sector1 Ch2' / 

&THCP XYZ=15.25,6.1,4.27,QUANTITY='TEMPERATURE',LABEL='Sector1 Ch3' / 

&THCP XYZ=15.25,6.1,3.05,QUANTITY='TEMPERATURE',LABEL='Sector1 Ch4' / 

&THCP XYZ=15.25,6.1,1.83,QUANTITY='TEMPERATURE',LABEL='Sector1 Ch5' / 

&THCP XYZ=15.25,1.52,5.98,QUANTITY='TEMPERATURE',LABEL='Station1 Ch16' / 

&THCP XYZ=15.25,1.52,5.49,QUANTITY='TEMPERATURE',LABEL='Station1 Ch41' / 

&THCP XYZ=15.25,1.52,4.27,QUANTITY='TEMPERATURE',LABEL='Station1 Ch42' / 

&THCP XYZ=15.25,1.52,3.05,QUANTITY='TEMPERATURE',LABEL='Station1 Ch43' / 

&THCP XYZ=15.25,1.52,1.83,QUANTITY='TEMPERATURE',LABEL='Station1 Ch44' / 

&THCP XYZ=9.14,1.52,5.98,QUANTITY='TEMPERATURE',LABEL='Station2 Ch17' / 

&THCP XYZ=9.14,1.52,5.49,QUANTITY='TEMPERATURE',LABEL='Station2 Ch45' / 

&THCP XYZ=9.14,1.52,4.27,QUANTITY='TEMPERATURE',LABEL='Station2 Ch46' / 

&THCP XYZ=9.14,1.52,3.05,QUANTITY='TEMPERATURE',LABEL='Station2 Ch47' / 

&THCP XYZ=9.14,1.52,1.83,QUANTITY='TEMPERATURE',LABEL='Station2 Ch48' / 

&THCP XYZ=3.05,1.52,5.98,QUANTITY='TEMPERATURE',LABEL='Station3 Ch18' / 

&THCP XYZ=3.05,1.52,5.49,QUANTITY='TEMPERATURE',LABEL='Station3 Ch49' / 

&THCP XYZ=3.05,1.52,4.27,QUANTITY='TEMPERATURE',LABEL='Station3 Ch50' / 

&THCP XYZ=3.05,1.52,3.05,QUANTITY='TEMPERATURE',LABEL='Station3 Ch51' / 

&THCP XYZ=3.05,1.52,1.83,QUANTITY='TEMPERATURE',LABEL='Station3 Ch52' / 

&THCP XYZ=12.19,3.05,5.98,QUANTITY='TEMPERATURE',LABEL='Station4 Ch19' / 

&THCP XYZ=12.19,3.05,5.49,QUANTITY='TEMPERATURE',LABEL='Station4 Ch53' / 

&THCP XYZ=12.19,3.05,4.27,QUANTITY='TEMPERATURE',LABEL='Station4 Ch54' / 

&THCP XYZ=12.19,3.05,3.05,QUANTITY='TEMPERATURE',LABEL='Station4 Ch55' / 

&THCP XYZ=12.19,3.05,1.83,QUANTITY='TEMPERATURE',LABEL='Station4 Ch56' / 

&THCP XYZ=6.10,3.05,5.98,QUANTITY='TEMPERATURE',LABEL='Station5 Ch20' / 

&THCP XYZ=6.10,3.05,5.49,QUANTITY='TEMPERATURE',LABEL='Station5 Ch57' / 

&THCP XYZ=6.10,3.05,4.27,QUANTITY='TEMPERATURE',LABEL='Station5 Ch58' / 

&THCP XYZ=6.10,3.05,3.05,QUANTITY='TEMPERATURE',LABEL='Station5 Ch59' / 

&THCP XYZ=6.10,3.05,1.83,QUANTITY='TEMPERATURE',LABEL='Station5 Ch60' / 

&THCP XYZ=12.19,9.14,5.98,QUANTITY='TEMPERATURE',LABEL='Station6 Ch21' / 

&THCP XYZ=12.19,9.14,5.49,QUANTITY='TEMPERATURE',LABEL='Station6 Ch61' / 

&THCP XYZ=12.19,9.14,4.27,QUANTITY='TEMPERATURE',LABEL='Station6 Ch62' / 

&THCP XYZ=12.19,9.14,3.05,QUANTITY='TEMPERATURE',LABEL='Station6 Ch63' / 

&THCP XYZ=12.19,9.14,1.83,QUANTITY='TEMPERATURE',LABEL='Station6 Ch64' / 

&THCP XYZ=6.10,9.14,5.98,QUANTITY='TEMPERATURE',LABEL='Station7 Ch22' / 

&THCP XYZ=6.10,9.14,5.49,QUANTITY='TEMPERATURE',LABEL='Station7 Ch65' / 

&THCP XYZ=6.10,9.14,4.27,QUANTITY='TEMPERATURE',LABEL='Station7 Ch66' / 

&THCP XYZ=6.10,9.14,3.05,QUANTITY='TEMPERATURE',LABEL='Station7 Ch67' / 

&THCP XYZ=6.10,9.14,1.83,QUANTITY='TEMPERATURE',LABEL='Station7 Ch68' / 

&THCP XYZ=15.24,10.67,5.98,QUANTITY='TEMPERATURE',LABEL='Station8 Ch23' / 

&THCP XYZ=15.24,10.67,5.49,QUANTITY='TEMPERATURE',LABEL='Station8 Ch69' / 

&THCP XYZ=15.24,10.67,4.27,QUANTITY='TEMPERATURE',LABEL='Station8 Ch70' / 

&THCP XYZ=15.24,10.67,3.05,QUANTITY='TEMPERATURE',LABEL='Station8 Ch71' / 

&THCP XYZ=15.24,10.67,1.83,QUANTITY='TEMPERATURE',LABEL='Station8 Ch72' / 

&THCP XYZ=9.14,10.67,5.98,QUANTITY='TEMPERATURE',LABEL='Station9 Ch24' / 
61

&THCP XYZ=9.14,10.67,5.49,QUANTITY='TEMPERATURE',LABEL='Station9 Ch73' / 

&THCP XYZ=9.14,10.67,4.27,QUANTITY='TEMPERATURE',LABEL='Station9 Ch74' / 

&THCP XYZ=9.14,10.67,3.05,QUANTITY='TEMPERATURE',LABEL='Station9 Ch75' / 

&THCP XYZ=9.14,10.67,1.83,QUANTITY='TEMPERATURE',LABEL='Station9 Ch76' / 

&THCP XYZ=3.05,10.67,5.98,QUANTITY='TEMPERATURE',LABEL='Station10 Ch25' / 

&THCP XYZ=3.05,10.67,5.49,QUANTITY='TEMPERATURE',LABEL='Station10 Ch77' / 

&THCP XYZ=3.05,10.67,4.27,QUANTITY='TEMPERATURE',LABEL='Station10 Ch78' / 

&THCP XYZ=3.05,10.67,3.05,QUANTITY='TEMPERATURE',LABEL='Station10 Ch79' / 

&THCP XYZ=3.05,10.67,1.83,QUANTITY='TEMPERATURE',LABEL='Station10 Ch80' / 

&THCP XYZ=16.76,4.57,5.98,QUANTITY='TEMPERATURE',LABEL='Station11 Ch26' / 

&THCP XYZ=1.52,4.57,5.98,QUANTITY='TEMPERATURE',LABEL='Station12 Ch27' / 

&THCP XYZ=12.19,6.1,5.98,QUANTITY='TEMPERATURE',LABEL='Station13 Ch28' / 

&THCP XYZ=6.10,6.10,5.98,QUANTITY='TEMPERATURE',LABEL='Station14 Ch29' / 

&THCP XYZ=16.76,7.62,5.98,QUANTITY='TEMPERATURE',LABEL='Station15 Ch30' / 

&THCP XYZ=1.52,7.62,5.98,QUANTITY='TEMPERATURE',LABEL='Station16 Ch31' / 

A.6 Corner Fire (case1) 

&HEAD CHID='OBSCOR1',TITLE='Obstructed Ceiling, corner, fast. fire, piecewise linear transformation' / 

&GRID IBAR=113,JBAR=64,KBAR=40 / 

&PDIM XBAR=9.20,YBAR=5.60,ZBAR=2.64 / 

&TRNX CC= .326,PC= .368 / 

&TRNX CC= .407,PC= .405 / 

&TRNX CC= .733,PC= .773 / 

&TRNX CC= .814,PC= .810 / 

&TRNX CC=1.140,PC=1.178 / 

&TRNX CC=1.221,PC=1.214 / 

&TRNX CC=1.547,PC=1.582 / 

&TRNX CC=1.628,PC=1.619 / 

&TRNX CC=1.954,PC=1.987 / 

&TRNX CC=2.035,PC=2.024 / 

&TRNX CC=2.361,PC=2.392 / 

&TRNX CC=2.442,PC=2.429 / 

&TRNX CC=2.768,PC=2.797 / 

&TRNX CC=2.850,PC=2.834 / 

&TRNX CC=3.175,PC=3.202 / 

&TRNX CC=3.257,PC=3.238 / 

&TRNX CC=3.582,PC=3.606 / 

&TRNX CC=3.664,PC=3.643 / 

&TRNX CC=3.989,PC=4.011 / 

&TRNX CC=4.071,PC=4.048 / 

&TRNX CC=4.396,PC=4.416 / 

&TRNX CC=4.478,PC=4.453 / 

&TRNX CC=4.804,PC=4.821 / 

&TRNX CC=4.885,PC=4.858 / 

&TRNX CC=5.211,PC=5.226 / 

&TRNX CC=5.292,PC=5.262 / 

&TRNX CC=5.618,PC=5.630 / 

&TRNX CC=5.699,PC=5.667 / 

&TRNX CC=6.025,PC=6.035 / 

&TRNX CC=6.106,PC=6.072 / 

&TRNX CC=6.432,PC=6.440 / 

&TRNX CC=6.513,PC=6.477 / 

&TRNX CC=6.839,PC=6.845 / 

&TRNX CC=6.920,PC=6.882 / 

&TRNX CC=7.246,PC=7.250 / 
62

&TRNX CC=7.327,PC=7.286 / 

&TRNX CC=7.653,PC=7.654 / 

&TRNX CC=7.735,PC=7.691 / 

&TRNX CC=8.060,PC=8.059 / 

&TRNX CC=8.142,PC=8.096 / 

&TRNX CC=8.467,PC=8.464 / 

&TRNX CC=8.549,PC=8.501 / 

&TRNX CC=8.874,PC=8.869 / 

&TRNX CC=8.956,PC=8.906 / 

&TIME DT=0.50,TWFIN=150. / 

&MISC TMPA=20.,DATABASE='database' / 

&PART NPSAM=7,DTPAR=0.05,AGE=5. / 

&SURF ID='BURNER',HRRPUA=2930.,TBO=0.30, RADIATIVE_FRACTION=0.14,RAMP_Q='fast' / 

&SURF ID='WALL',ALPHA=0.00000016,KS=0.17,DELTA=0.0127,RADIATION=.FALSE. / 

&SURF ID='CEILING',ALPHA=0.00000009,KS=0.11,DELTA=0.0254,RADIATION=.FALSE. / 

&SURF ID='WOOD BEAM',ALPHA=0.00000009,KS=0.11,RADIATION=.FALSE. / 

&SURF ID='STEEL BEAM',ALPHA=0.00001482,KS=54.0,DELTA=0.5,RADIATION=.FALSE. / 

&OBST XB=0.00,0.70,0.00,1.00,0.00,0.30 / 

&OBST XB=0.00,9.20,2.72,2.80,2.22,2.40,SURF_ID='STEEL BEAM' / 

&OBST XB=0.3680,0.4048,0.00,5.60,2.40,2.64,SURF_ID='WOOD BEAM' / 

&OBST XB=0.7728,0.8096,0.00,5.60,2.40,2.64,SURF_ID='WOOD BEAM' / 

&OBST XB=1.1776,1.2144,0.00,5.60,2.40,2.64,SURF_ID='WOOD BEAM' / 

&OBST XB=1.5824,1.6192,0.00,5.60,2.40,2.64,SURF_ID='WOOD BEAM' / 

&OBST XB=1.9872,2.0240,0.00,5.60,2.40,2.64,SURF_ID='WOOD BEAM' / 

&OBST XB=2.3920,2.4288,0.00,5.60,2.40,2.64,SURF_ID='WOOD BEAM' / 

&OBST XB=2.7968,2.8336,0.00,5.60,2.40,2.64,SURF_ID='WOOD BEAM' / 

&OBST XB=3.2016,3.2384,0.00,5.60,2.40,2.64,SURF_ID='WOOD BEAM' / 

&OBST XB=3.6064,3.6432,0.00,5.60,2.40,2.64,SURF_ID='WOOD BEAM' / 

&OBST XB=4.0112,4.0480,0.00,5.60,2.40,2.64,SURF_ID='WOOD BEAM' / 

&OBST XB=4.4160,4.4528,0.00,5.60,2.40,2.64,SURF_ID='WOOD BEAM' / 

&OBST XB=4.8208,4.8576,0.00,5.60,2.40,2.64,SURF_ID='WOOD BEAM' / 

&OBST XB=5.2256,5.2624,0.00,5.60,2.40,2.64,SURF_ID='WOOD BEAM' / 

&OBST XB=5.6304,5.6672,0.00,5.60,2.40,2.64,SURF_ID='WOOD BEAM' / 

&OBST XB=6.0352,6.0720,0.00,5.60,2.40,2.64,SURF_ID='WOOD BEAM' / 

&OBST XB=6.4400,6.4768,0.00,5.60,2.40,2.64,SURF_ID='WOOD BEAM' / 

&OBST XB=6.8448,6.8816,0.00,5.60,2.40,2.64,SURF_ID='WOOD BEAM' / 

&OBST XB=7.2496,7.2864,0.00,5.60,2.40,2.64,SURF_ID='WOOD BEAM' / 

&OBST XB=7.6544,7.6912,0.00,5.60,2.40,2.64,SURF_ID='WOOD BEAM' / 

&OBST XB=8.0592,8.0960,0.00,5.60,2.40,2.64,SURF_ID='WOOD BEAM' / 

&OBST XB=8.4640,8.5008,0.00,2.80,2.40,2.64,SURF_ID='WOOD BEAM' / 

&OBST XB=8.8688,8.9056,0.00,2.80,2.40,2.64,SURF_ID='WOOD BEAM' / 

&VENT XB=0.00,0.60,0.00,0.60,0.30,0.30,SURF_ID='BURNER' / 

&VENT XB=8.30,9.20,2.90,5.60,2.64,2.64,SURF_ID='OPEN' / 

&VENT CB='ZBAR' ,SURF_ID='CEILING' / 

&VENT CB='XBAR' ,SURF_ID='WALL' / 

&VENT CB='XBAR0',SURF_ID='WALL' / 

&VENT CB='YBAR' ,SURF_ID='WALL' / 

&VENT CB='YBAR0',SURF_ID='WALL' / 

&SPRK XYZ=2.40,1.40,2.375,MAKE='VETTORI' / 

&SPRK XYZ=6.80,1.40,2.375 / 

&SPRK XYZ=6.80,4.20,2.375 / 

&SPRK XYZ=2.40,4.20,2.375 / 

&THCP XYZ=2.40,1.40,2.400,QUANTITY='TEMPERATURE',DTSAM=0.2 / 

&THCP XYZ=2.40,1.40,2.375,QUANTITY='TEMPERATURE' / 

&THCP XYZ=2.40,1.40,2.350,QUANTITY='TEMPERATURE' / 

&THCP XYZ=2.40,1.40,2.325,QUANTITY='TEMPERATURE' / 
63

&THCP XYZ=2.40,1.40,2.300,QUANTITY='TEMPERATURE' / 

&THCP XYZ=2.40,1.40,2.275,QUANTITY='TEMPERATURE' / 

&THCP XYZ=2.40,1.40,2.250,QUANTITY='TEMPERATURE' / 

&THCP XYZ=2.40,1.40,2.150,QUANTITY='TEMPERATURE' / 

&THCP XYZ=2.40,1.40,2.050,QUANTITY='TEMPERATURE' / 

&THCP XYZ=2.40,1.40,1.950,QUANTITY='TEMPERATURE' / 

&THCP XYZ=2.40,1.40,1.850,QUANTITY='TEMPERATURE' / 

&THCP XYZ=2.40,1.40,1.500,QUANTITY='TEMPERATURE' / 

&THCP XYZ=6.80,1.40,2.400,QUANTITY='TEMPERATURE' / 

&THCP XYZ=6.80,1.40,2.375,QUANTITY='TEMPERATURE' / 

&THCP XYZ=6.80,1.40,2.350,QUANTITY='TEMPERATURE' / 

&THCP XYZ=6.80,1.40,2.325,QUANTITY='TEMPERATURE' / 

&THCP XYZ=6.80,1.40,2.300,QUANTITY='TEMPERATURE' / 

&THCP XYZ=6.80,1.40,2.275,QUANTITY='TEMPERATURE' / 

&THCP XYZ=6.80,1.40,2.250,QUANTITY='TEMPERATURE' / 

&THCP XYZ=6.80,1.40,2.150,QUANTITY='TEMPERATURE' / 

&THCP XYZ=6.80,1.40,2.050,QUANTITY='TEMPERATURE' / 

&THCP XYZ=6.80,1.40,1.950,QUANTITY='TEMPERATURE' / 

&THCP XYZ=6.80,1.40,1.850,QUANTITY='TEMPERATURE' / 

&THCP XYZ=6.80,1.40,1.500,QUANTITY='TEMPERATURE' / 

&THCP XYZ=6.80,4.20,2.400,QUANTITY='TEMPERATURE' / 

&THCP XYZ=6.80,4.20,2.375,QUANTITY='TEMPERATURE' / 

&THCP XYZ=6.80,4.20,2.350,QUANTITY='TEMPERATURE' / 

&THCP XYZ=6.80,4.20,2.325,QUANTITY='TEMPERATURE' / 

&THCP XYZ=6.80,4.20,2.300,QUANTITY='TEMPERATURE' / 

&THCP XYZ=6.80,4.20,2.275,QUANTITY='TEMPERATURE' / 

&THCP XYZ=6.80,4.20,2.250,QUANTITY='TEMPERATURE' / 

&THCP XYZ=6.80,4.20,2.150,QUANTITY='TEMPERATURE' / 

&THCP XYZ=6.80,4.20,2.050,QUANTITY='TEMPERATURE' / 

&THCP XYZ=6.80,4.20,1.950,QUANTITY='TEMPERATURE' / 

&THCP XYZ=6.80,4.20,1.850,QUANTITY='TEMPERATURE' / 

&THCP XYZ=6.80,4.20,1.500,QUANTITY='TEMPERATURE' / 

&THCP XYZ=2.40,4.20,2.400,QUANTITY='TEMPERATURE' / 

&THCP XYZ=2.40,4.20,2.375,QUANTITY='TEMPERATURE' / 

&THCP XYZ=2.40,4.20,2.350,QUANTITY='TEMPERATURE' / 

&THCP XYZ=2.40,4.20,2.325,QUANTITY='TEMPERATURE' / 

&THCP XYZ=2.40,4.20,2.300,QUANTITY='TEMPERATURE' / 

&THCP XYZ=2.40,4.20,2.275,QUANTITY='TEMPERATURE' / 

&THCP XYZ=2.40,4.20,2.250,QUANTITY='TEMPERATURE' / 

&THCP XYZ=2.40,4.20,2.150,QUANTITY='TEMPERATURE' / 

&THCP XYZ=2.40,4.20,2.050,QUANTITY='TEMPERATURE' / 

&THCP XYZ=2.40,4.20,1.950,QUANTITY='TEMPERATURE' / 

&THCP XYZ=2.40,4.20,1.850,QUANTITY='TEMPERATURE' / 

&THCP XYZ=2.40,4.20,1.500,QUANTITY='TEMPERATURE' / 

&THCP XYZ=2.40,1.40,2.375,QUANTITY='VELOCITY' / 

&THCP XYZ=2.40,1.40,2.325,QUANTITY='VELOCITY' / 

&THCP XYZ=2.40,1.40,2.275,QUANTITY='VELOCITY' / 

&THCP XYZ=2.40,1.40,2.150,QUANTITY='VELOCITY' / 

&THCP XYZ=6.80,1.40,2.375,QUANTITY='VELOCITY' / 

&THCP XYZ=6.80,1.40,2.325,QUANTITY='VELOCITY' / 

&THCP XYZ=6.80,1.40,2.275,QUANTITY='VELOCITY' / 

&THCP XYZ=6.80,1.40,2.150,QUANTITY='VELOCITY' /