TOWARDS SUBGRID SCALE MODELING OF SUPPRESSANT FLOW 

IN ENGINE NACELLE CLUTTER* 

P. E. DesJardin, J. M. Nelsen, L. A. Gritzo 

A. R. Lopez, and J. M. Suo-Anttila 

Sandiil National Laboratories 

P. J. Disimile 

Wright-Patterson Air Force Base 

D. R. Keyser and T. A. Ghee 

NAVAlR 

J. R. Tucker 

Applied Research Associates 

INTRODUCTION 

The release and transport of a suppressant agent into an enclosed compartment is sensitive to local geometrical features or “clutter” that is difficult to resolve numerically without using an excessively large 

CFD grid. Such examples include wire bundles or hydraulic lines in engine compartments of either 

ground vehicles or aircraft. Capturing these features on a grid will result in extremely small time steps 

for explicit time-accurate numerical simulations of agent release and subsequent fire suppression. An 

alternative approach is to use a subgrid scale (SGS) model to represent the macroscopic effects of these 

small features using reasonably sized CFD grid cells. 

The focus of this research is to develop engineering models of flow, fire, and fire suppression and extinguishment in cluttered environments. These models will advance the fundamental knowledge of fire 

dynamics and suppression and provide a foundation for optimizing the distribution of suppressants for 

newly designed or retrofit fire safety systems in aircraft eugine nacelles. This work is being carried out in 

a joint, iterative computational/experimental approach to develop engineering subgrid models for use in 

integral CFD and fire field simulations. These subgrid models will be used to represent phenomena too 

small to resolve using a computational mesh (with sinaller length scales on the order of 10 cm). Models 

will he developed using detailed CFD calculations performed at SNL and discovery and validation 

experiments performed at Air Force and Naval laboratories. Only gaseous agents will he investigated 

initially. The end goal is to provide computational tools to improve suppressant delivery by reducing the 

need to model the fine geometries in the cluttered regions of the engine in the nacelle. 

For agent dispersal in a cold flow environment the effects of subgrid clutter have two main effects on the 

macroscopic flow field. The first is to provide a momentum sink due to viscous and pressure drag forces 

due to the gas flowing through clutter. The second is to either increase or decrease the turbulent kinetic 

energy levels depending on the local clutter size, IC, relative to the characteristic length scale of turbulence, IT. In general, if IC c I7 the turbulent kinetic energy will decrease and if IC > IT the turbuleiit kinetic 

energy will increase. For flame suppression the clutter also serves as either a mechanism for flame 

attachment or local extinction depending on the local time scales of the heat transfer to the clutter and 

chemical kinetics for ignition, although these issues will not be the focus of this paper. 

A literature search reveals little available information in the area of subgrid modeling of cluttered spaces. 

The closest to cluttered environments is numerical modeling of rigid porous structures for high Reynolds 

number flow. Readers interested in the state-of-the-art in this area can consult these papers [ 1-61, which 

provide details of the available means to define the time and phase averaged trausport equations for 

momentum transport as well as derivations of the turbulent kinetic energy transport appropriate for 

porous flows. This effort is to extend these approaches to clutter environments for which the length scale 

of the clutter is not small relative to the size of the system. 

* This work was performed in part at Sandia National Laboratories, a multiprogram laboratory operated by Sandia 

Corporation, a Lockheed-Martin Company, for the US Department of Energy, contract DE-AC04-94AL85000. 

Halon Options Technical Working Conference 24-26 April 2001 99 
The rest of the paper starts with the mathematical formulation of the clutter model based on spatial filtering concepts. The filtering of the governing equations result in unknown correlations that require modeling. Constitutive models are formulated based on a linear combination of porous media and bluff body 

lift and drag relations along with results showing predictions using these models for a density and loosely 

packed clutter. Results are then presented of macroscopic predictions of turbulent flow in the limit of 

porous media with comparisons to detailed CFD calculations available from the literature. Next, experimental measurements of a cylinder in a turbulent cross flow are presented along with detailed CFD 

predictions. Finally conclusions are drawn and future efforts summarized. 

MATHEMATICAL MODEL FORMULATION 

The following mathematical description is limited to a summary of the development of stationary clutter. 

The section starts with an introduction to the two-phase (ie., spatial) averaging and time averaging. The 

reasons for reviewing these mathematical formalities are to familiarize the reader with the concepts of 

spatial filtering and, more importantly, highlight the restrictions imposed by this approach with respect to 

the implementation of the clutter model into a CFD code. Next, these averaging concepts are applied to 

the conservation equations of momentum turbulent kinetic energy transport resulting in unknown second 

order correlations and surface integral terms, which represent subgrid physics that must be closed with a 

clutter model. Requirements for the clutter model are provided based on both physical and computational 

requirements. The end result of this section is to provide a closed set of phase and time averaged transport equations for momentum, turbulent kinetic energy, and turbulent kinetic energy dissipation rate. 

TWO-PHASE AVERAGING 

The formal averaging for two-phase media was first introduced by Anderson and Jackson [7] through the 

use of a local filtering function and later refined by Gray and Lee [8] and Gough and Zwarts [9] as presented in textbook form by Kuo [IO]. Alternatively, Slattery [1 I ] offers a different derivation based on a 

spatially dependent volume of integration. The presentation here follows the outline of Kuo. Figure 1 

illustrates a typical phase averaging volume showing the total volume of interest, Y,., the volume of the 

solid clutter, V,, and the volume of the gas, V, . 

Figure 1. Phase averaging volume. 

Phase averaged properties are obtained by first defining a spatial filtering function, G[(x, - x;)/A,], 

with the normalization property: JG[(. - x;)/~fbv’ = 1. For volume averaging using a cubic volume of 

length L, = (V,)”’ on a side then A, = L, andG is defined as 

v. 

100 Halon Options Technical Working Conference 24-26 April 2001 
l3 

v, 1=1 

G = -n[H(x: - x, +A, 12)- H(x: - x, - A, /2)] where His the Heaviside function. Convoluting G 

with the a gas property of interest, p , yields a gas phase average quantity, 

which physically represents a spatially averaged property over the volume, 4.. It should be emphasized 

that the volume of integration,V,-, represents all of regions occupied by the gas and so does not depend 

on the location,^, , where the averaging takes place. Of more value is the intrinsic average, (p) , defined 

as the local average of p over the gas phase volume, v,, for which constitutive and thermodynamic 

properties are well defined. The intrinsic average is defined as: (p) = b/# and is the variable of 

interest to solve for after phase averaging the transport equations for mass, momentum and energy. The 

variable, 4, is the void fraction and is defined as the volume of gas divided by the averaging volume, i.e., 

4 = v, 1VT. 

TEMPORAL AND SPATIAL DERIVATIVES FOR PHASE AVERAGING 

Applying the spatial filtering function to the transport equations requires expressing the phase averaged 

time and spatial partial derivatives in terms of temporal and spatial derivatives of phase averaged quantities. In the following development, the volume of the gas phase is assumed to change as a function of 

both time and space to accommodate the complexities that may be included in future efforts (e.g., decomposing or burning clutter). Simplifications are then imposed to limit the scope to the focus of this work 

on turbulence modeling on rigid, non-burning clutter. 

Time Derivatives 

Relations for the temporal derivative are obtained by taking the partial derivative of+. 

Since the volume ofthe gas is assumed to be a function of time, Leibnitz rule [ 121 has to be applied to 

commute the temporal derivative term inside the volume averaging operator as follows: 

In Eq. (3), the first term on the right hand size is simply the definition of the phase averaged time rate in 

change ofp , Le., mt . The second term is a surface integral that accounts for material crossing the 

boundary of the phase averaging volume as a function of time wherew, is the velocity of the surface 

(pointing into the solid clutter [Figure 11) of the gas phase volume, V,, on the surface, A, . The gas 

phase surface can be further broken into the contribution associated with the clutter, A,, and rest of the 

surface area associated with the phase averaging volume, A,-‘. Since G goes to zero at the boundary on 

the surface Ag-c then that contribution of the surface integral is equal to zero leading to the following 

relation for the phase averaged time derivative that will become useful when dcriving the phase averaged 

transport equations. 

Halon Options Technical Working Conference 24-26 April 2001 IO 1 
In addition, the clutter surface is assumed rigid and non-porous so that the normal velocity to the clutter 

surface is identically zero (i.e., w, = 0) allowing for the temporal derivative to commute with the filter 

operation resulting in the simple relation. 

Space Derivatives with Uniform Filter Width (Le., A/ = const ) 

Analogous to the time derivatives, a spatial derivative relation is obtained by taking the divergence of a 

phase averaged vector quantity. 

Since the volume averaging is independent of the location the partial derivative can be brought inside the 

integration and applied directly to the filtering function G . 

For uniform filter size &e., A, = const ) then aG/ax, = - aG/&;. and using the chain rule of 

differentiation then Eq. (7) can be expressed as: 

The first term on the right side of Eq. (8) is the two-phase average ofthe gradient of the vector quantity; 

the second term can be further expressed in terms of a surface integral using the divergence theorem. Rearranging terms leads to an expression for the phase averaged divergence of a vector quantity in terms of 

the divergence of a phase averaged quantity and a surface integral to account for microscopic clutter 

effects. 

An important assumption in the derivation of Eq. (9) is thefilrer width is assumed to be constant; i.e., the 

filter width is assumed to be invariant with space and time. Alternatively, the development of a nonuniform filter width could be pursued for which aG/axj # -aG/axl . However, the introduction of such a 

filter brings in commutation error that has been discussed in the Large Eddy Simulation (LES) literature 

[13, 14, 153 as well a surface integral error term. The former of these two sources of error has been 

somewhat mitigated using filter functions that satisfy commutivity up to some order of accuracy [ 151. 

However, the second source of error is more difficult to treat and leads to a violation of mass, momentum, and energy conservation when these quantities are exchanged among phases [16]. These issues are 

not merely academic. Often in practice the filter width is assumed to be proportional to the local grid 

size, e.g., A/ = CA, , where Ax is the local grid cell size and C is a constant that is greater or equal to 

one. Therefore, in a practical engineering problem where the CFD grid cell size changes in space, then 

102 Halon Options Technical Working Conference 24-26 April 2001 
the assumption of A, = consf is violated! In order to avoid this contradiction, thefiNer width is ussumed to be independenffrom the grid. This choice also has the added benefit to allowing for grid convergence (see requirement 4, discussion below). The disadvantages of a filter width independent of the grid 

are two fold, First, the clutter model must be able to capture the relevant physics over a wide range of 

filter to clutter size ratios (see requirement 1 of discussion below). Second, the coding of the clutter 

model is further complicated with the introduction of an integral of the clutter source terms to account for 

the effects of intermittency (see requirement 3, discussion below). 

Only phase averaging concepts have been briefly reviewed. In addition, it is also desirable to time average the governing equations of mass, momentum and energy transport to remove any remaining high 

frequency turbulence signal and to be compatible with the Reynolds Averaged Navier Stokes (RANS) 

transport equations that are commonly used for solving practical engineering applications. Time averaging issues are not reviewed in this paper since excellent discussions of time averaging concepts are provided in several introductory texts on turbulence [I 71. * 

PHASE AND TIME AVERAGING OF TRANSPORT EQUATIONS 

Applying the phase averaging relations given by Eqs. (5) and (9) in addition to time averaging to the 

transport equations of momentum, turbulent kinetic energy and turbulent dissipation leads to the following set of transport equations. 

Momentum 

Turbulent Kinetic Energy 

Turbulent Kinetic Energy Dissipation (Le., E = /ax# 18.1 /ax,)lp) 

wt re the (:)notation refers to a time and phase averaged quantity. The terms involving (...)' i '( ...) 

represent higher order correlation terms of fluctuating quantities in time and space, respectively, which in 

* DesJardin, P.E., and Gritzo, L.A., On the Development ofa Clutter Modelfor Turbulenr Flows, 2001. Copy on 

file with the author. 

Halon Options Technical Working Conference 24-26 April 2001 103 
general are unknown and require modeling. The surface integral term in Eq. (IO) represents momentum 

exchange between the surface of the clutter and the surrounding gas due to viscous and pressure drag 

forces, and the term requires modeling. Note, the surface integral terms only arise in the momentum 

transport due to assumption that the clutter is rigid (i.e., no melting or burning of clutter). Also, in the 

derivation the density is assumed to be constant, and second order correlations associated with mass and 

momentum diffusion have also been neglected. 

In Eq. (IO), the term ui uj 

defined as: ui' 'uj = (Zj)(Zj) -(G). This term, the correlations of Eqs. (1 1) and (12), and the 

surface integrals of Eq. (IO) are closed using models that satisfy a set of guiding principles based on the 

requirements for modeling the clutter in engine nacelles. These requirements are illustrated below. 

represents the effects of the subgrid fluctuations in time and space and is 

(' ' ' ') 

(' ') 

I 

*=ANI 1. The constitutive model(s) should be I 

y=L,l able to accommodate a spectrum of 

clutter object (i.e., sizes bluff ranging body from drag) a single to many FJ4* relalivelo fillerwidth 

objects that are randomly placed (Le., 

clutter that resembles porous media) 

since the filter width of the phase 

averaging is assumed to be constant. L Ai, - 4- 

00 

AfT2. The constitutive model(s) should Anisobapic clutter 

provide a mechanism to represent 

isotropic (Le., rotationally invariant) as 

well as anisotropic (rotationally 

dependent) clutter with minimal 

amount of user input. 

3. The constitutive model(s) should allow 

for intermittency within the filtering 

volume so that non-periodic SGS 

clutter may be addressed. 

Periodic clutter pi 00 

Non-periodic duller 

Applying the above guidelines, the final form for the closure terms needed for the phase and time 

averaged momentum transport equations is as follows: 

104 Halon Options Technical Working Conference 24-26 April 2001 
S, = Bluff body dragilift term 

modified Darcy-Forchheimer Law) 

The first term on the right side of Eq. (13) represents the effects of microscopic dispersion and turbulent 

fluctuations using Brinkman [I 8,191, ,us, and turbulent eddy 1201, pr, viscosity models, respectively. 

On the second line of Eq. (l3), v (= IC /Af) is a the ratio the length scale of the clutter to the size of the 

filtering volume and serves as a linear weighting function to blend constitutive models from the porous 

media literature [21,22,23] with simple bluff body lift and drag models [24,25]. A linear blending is not 

unique and other weightings could be chosen. An assessment of using a linear blending of constitutive 

models from the porous media and bluff body drag is investigated for a collection of spheres. Figure 2 

(a) and (b) show results ofthe drag force per unit volume using a modified Darcy-Forchheimer Law (Le., 

F, /A,' @'(u,)~Ti)/K+C,,~((u;,)I/JiT]) for and a bluff body drag for a linear superposition of a 

collection of spheres (i.e., F, /Af? = (2/3)Npl(is,)/(iij)(1 -+)C',> / D). In the Darcy-Forchheimer 

relation, K (= -p@(u,)/(@/&J))is the permeability and is determined using the empirical relation 

K = b3D2 /[C,,(l -4)2] where C,, is set equal to 147 [5] andC,, is set to two values of either 1.75 

corresponding to the values suggested by Kuwahara et al. [5] for spheres or 2.3 from the classical result 

of Ergun 1261 which is considered independent of local geometry. The results show that the porous 

media and bluff body drag have a similar functional dependence on the Reynolds number with the two 

predicting almost the same force per unit volume for either low porosity at high Reynolds number or for 

high porosity at low Reynolds number. This suggests that the linear blending of these two limits is a 

reasonable approach to span the possible range of clutter sizes. 

Porosity = 0.1 Porosity = 0.9 

Id 

10- 

$0' 

a, IO' 

- BluR body drag 

_____. Porous flow drag, C, ~1.75 

___ Porous flow drag, C,:=2.3 5 t"' 

$ rd 

- 

0 Id 

2 10 

0 

d 

I" 

10= 

(a) (b) 

Figure 2. Forceivolume using constitutive models for a collection of spheres from porous media 

and bluff body drag relations using a porosity of (a) 0.1 and (b) 0.9. 

Halon Options Technical Working Conference 24-26 April 2001 I05 
Due to space constraints, the details of the closure k and E equations will be omitted. Instead, a summary 

of the modeled form of the right side (RHS) of Eqs. (1 1) and (12) is provided below. Details of these 

closure terms can be found in Refs. [I] and [I 71. 

NUMERICAL IMPLEMENTATION 

The clutter models discussed in the previous section are implemented in a general-purpose fire simulation 

code, VULCAN, which is based on the KAMELEON-Fire code [27]. VULCAN uses a RANS-based 

model suite including a k-E turbulence model 1281. Numerical discretization is on a staggered, blockstructured grid with second-order upwind differencing for the convective terms using a version of the 

SIMPLE algorithm [29]. Previous studies using VULCAN for pool fire simulations can be found in 

references [30,3 1,321. The source terms appearing in Eq. (13) for momentum transport are treated in a 

semi-implicit nature to maintain numerical stability. The source terms appearing in Eqs. (14) and (15) are 

implemented in an explicit manner. 

RESULTS 

Two limiting cases are under consideration for assessing the clutter model. The first is unidirectional 

flow in periodic porous media (Figure 3). Figure 4 (a) and (b) show predictions of normalized turbulent 

kinetic energy and its dissipation rate as a function of downstream locations using the macroscopic clutter 

model. The initial kinetic energy and dissipation rate are chosen to be 10 and 30 times the steady-state 

Periodic Porous Media 

Flow direction 4 :@jc 4 4 4 

Figure 3: Schematic of periodic porous media problem 

values, respectively, in order to match the previous studies of the same problem [I, 41. Predictions using 

the clutter model agree well with these previous studies in this limiting where the clutter model degenerates to just the porous media contribution. 

The second problem under consideration is a cylinder in well-characterized homogeneous turbulent flow. 

The cylinder shape was chosen since this shape is representative of the class of clutter objects typically 

encountered in aircraft engine nacelles. Experimental measurements are taken at the US Naval Academy 

(USNA) using their low-speed (0 to 20 m/s) tunnel (Figure 5), for which high turbulence (-10%) could 

be obtained. Hot wire anemometry is used to measure instantaneous stream-wise velocity to obtain mean 

106 Halon Options Technical Working Conference 24-26 April 2001 
Figure 4. Normalized turbulent kinetic energy and its dissipation rate verses dllfusing 

clutter model in the limit of porous media. 

(4 (b) 

Figure 5. (a) USNA wind tunnel facility and (b) blow up region ofcylinder representing 

clutter object under highly turbulent flow conditions. 

and RMS profiles before and after the cylinder. Figures 6 and 7 include measurements (shown with symbols) of mean and RMS stream-wise velocity, respectively. Based on a momentum balance calculation, 

the coefficient of drag (C,) is determined to be 0.97, which is 24% lower than the coefficient of drag of 

1.28 calculated without the turbulence generator in place. This result indicates that the effects of upstream turbulence on the drag characteristics of clutter (Le., the C, in Eq. (13)) are significant. 

In Figures 6 and 7,2D CFD predictions using the CFD-ACE software package [33] (shown with lines) 

are detailed. The purpose of conducting the detailed CFD calculations is to provide full flow field details 

to construct phase-averaged quantities that cannot be obtained experimentally. These details are needed 

for calibration of the unknown clutter model coefficients in the bluff body drag limit. As shown in these 

figures, good qualitative agreement to the experimental data is observed for the mean and RMS. 

Quantitatively, the numerical predictions do appear to underpredict the extent of the velocity deficit profile as well as the wake region ofthe cylinder. These differences may be attributed to the limitations 

performing a 2D calculation (i.e., no streamwise vorticity generation captured for enhanced mixing) and 

the use of the k-E turbulence model in strongly recirculating flows (Le., k-E model assumes local isotropy). Both of these issues are currently being explored by performing 3D calculations using more 

Ilalon Options Technical Working Conference 24-26 April 2001 IO7 
m=-2 x/D = 112 x/D=l x/D=2 x/D=4 fl=6 

150 

100 

v 50 

- 

E 

E 

k? 

00 

a 

5 

a -100 

I- 

- -50 lu 

.- u 

c 

-1 50 

Mean Velocity (mk) 

Figure 6. Comparisons of mean streamwise velocity profiles at several down stream locations. 

Solid lines are CFD predictions and symbols are experimental measurements. 

x/D = -2 x/D= 112 dD=l xID=2 x/D=4 x/D=6 

t 

---

RMS Velocity 

-

(mh) -- 

Figure 7. Comparisons of RMS streamwise velocity profiles at several down stream locations. 

Solid lines are CFD predictions and symbols are experimental measurements. 

advanced turbulence models. The reasonable agreement of the CFD predictions to the experimental data 

in Figures 6 and 7 supports the use of detailed CFD for clutter model calibration. 

CONCLUSIONS 

A preliminary clutter model has been formulated based on the use of two-phase averaging concepts. 

The implementation of phase averaging introduces constraints onto the requirements of the clutter model. 

The most stringent of these constraints is that the model must be able to represent a wide range of clutter 

length scales ranging from a porous media limit to bluff body drag. This requirement is satisfied using a 

108 Halon Options Technical Working Conference 24-26 April 2001 
linear combination of constitutive models from the porous media literature and relations for bluff body 

drag. Based on this formulation, two simplified problems are considered for calibration ofthe model 

constants: (1) the first is turbulent flow in a porous media for which a preliminary version of the clutter 

model is able to reproduce established trends taken from the literature; (2) the second is subjecting a 

cylinder to a highly turbulent cross flow for which there are little existing published data. Results of 

experimental measurements show a significant decrease in drag coefficient due to the highly turbulent 

inflow. Detailed numerical predictions of the same problem show good qualitative agreement to experimental measurements indicating that the use of detailed spatial information from CFD results is a valid 

approach for clutter model calibration. Future work is to perform this calibration so that the macroscopic 

model will be able to reproduce the trends in the bluff body limit. In addition, the model will be extended 

beyond the unidirectional treatment presented here to anisotropic cluttered environments. 

ACKNOWLEDGMENTS 

This work is supported by the US Department of Defense Program under the Next-Generation Fire 

Suppression Program. 

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1 ] 0 Halon Options Technical Working Conference 24-26 April 2001 

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