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!2008 ASHRAE 45

ABSTRACT

A detailed Computational Fluid Dynamics (CFD) study

of the flow around a Computer Simulated Person (CSP) in anotherwise empty displacement ventilated room is presented.

Both Reynolds Averaged Navier-Stokes (RANS) and Large

Eddy Simulation (LES) methods are included in this study.

The study identifies the requirements of several computational

aspects that are needed for accurate CFD simulations of the

personal micro-environment, which include issues related to

grid size and iterative convergence monitoring, turbulence

modeling, and radiation modeling. Using the benchmark test

for evaluating CFD in the indoor environment of Nielsen et al.

(2003), very good agreement between CFD results and test

data was obtained using the standard with wall treatment

and a reduced-order radiation model.

INTRODUCTION

For ventilation systems other than an ideal mixing

system, e.g. displacement and personal ventilation systems,

the well-mixed assumption can not be applied because spatial

gradients of the flow, temperature and pollutant fields can be

large in the vicinity of the Personal Micro Environment

(PME). Here, the PME is the region around a person that

affects the air he/she breathes. In a displacement ventilation

system, human exposure to pollutants is influenced by the

convective and diffusive transport mechanisms found in the

thermal plume around the person. The flow in the thermal

plume is dominated by the buoyancy forces arising from the

higher temperature of the human body, and this flow field is

rather complex even in a situation where the person is standing

in an empty room (Clark and Edholm 1985).

The PME and the surrounding environment have a sophis-

ticated relationship that is rarely amenable to simple analytical

models. Analytical methods are not without merit as they are

powerful tools for understanding the fundamental features(Awbi 1991) of a real scenario but the interactions of these

features are not trivial. This concept is elucidated by Melikov

and Kaczmarcyzk (2007) who state, The measurement at a

point in a room, without a person present, would not define

accurately the quality of the air that the person would inhale

when present at this location. As a result, sophisticated tools

and methods are needed to extract a deeper understanding of

the PME.

Beyond analytical, the two remaining approaches are

experimental and computational. Experiment has traditionally

been the most common and reliable method to study the indoor

environment. The experimental approach could be character-ized by two distinct strategies: field study and detailed

measurement. Field study involves placing sensors in a rela-

tively non-intrusive manner within a real environment, statis-

tically analyze the data obtained and making conclusions

based on the analysis (Ferro et al. 2003). While this strategy

provides the most accurate representation of the actual

scenario, the lack of control of input variables makes quanti-

tative inference a dubious task. The alternative experimental

strategy is detailed measurements. Again, sensors are used to

obtained information about the pertinent quantities, but here

the experiment is carried out in a more controlled manner with

higher resolution equipment. For the indoor environment and

the PME, the types of detailed experimental equipment vary

widely depending on the desired quantity. For flow velocity,

common techniques are hot-wire, hot-sphere, particle image

velocimetry (PIV) and laser-doppler anemometry (LDA), in

k-"

Verification and Validation of CFD for thePersonal Micro-Environment

Chris N. Sideroff, PhD Thong Q. Dang, PhD

Chris N. Sideroffis a technical sales engineer at Pointwise, Inc., Fort Worth, TX. Thong Q.Dang is a professor of mechanical and aerospace

engineering, Syracuse University, Syracuse, NY.

SL-08-005

2008, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org).

Published in ASHRAE Transactions Vol. 114, Part 2. For personal use only. Additional reproduction, distribution, or transmission

in either print or digital form is not permitted without ASHRAEs prior written permission.

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46 ASHRAE Transactions

order of increasing accuracy and sophistication. For tempera-

ture, common techniques are thermal couples, thermistors and

infra-red imaging. The drawback of such experimental

systems is that they can be expensive, complex to operate and

have other limits. Recent examples of detailed experiments

with thermal manikins in the indoor environment are Bjrn

and Nielsen (2002) to study the interaction of multiple people,Melikov and Kaczmarcyzk (2007) to examine personal venti-

lation devices on the PME, Cermak et al. (2006) to identify

transmission of infectious agents between occupants and Marr

(2007) to investigate the influence of body motion.

With the advent of high performance computers at

commodity prices, computational tools are becoming ever

more popular. More specifically, Computational Fluid

Dynamics or CFD has been used with success in a variety of

areas in the indoor environment community; office buildings

(Cheong et al. 2003), homes (Huang et al. 2004), hospitals

(Brohus et al. 2006) and aircraft (Zhang and Chen 2001) are

examples of a few of these areas. To be able to use CFD as a

design tool, one first must have confidence that it can predict

the desired quantities with a certain degree of accuracy. To do

this, two important questions need to be answered: First, is

CFD capable of predicting the flow in question and second,

what is needed to do so? Flows around humans in an indoor

environment can be particularly difficult to predict because of

the complex interaction between many different factors. To

properly answer these questions, standard or canonical bench-

mark cases are needed so the individual issues may be identi-

fied along with providing a consistent approach for others

researchers to use.

The collaborative efforts of Nielsen et al. (2003) have

culminated in a benchmark test for evaluating CFD in the

indoor environment. They have proposed two canonical build-

ing environment scenarios: mixing and displacement venti-

lated rooms with a centrally situated manikin. Results and

discussion of the displacement ventilation case are presented

in this work. Verification and validation of CFD for the

personal micro-environment (PME) is necessary for it to

become a reliable tool. The objective using the benchmark

case is to identify the key requirements needed to achieve an

accurate prediction of the detailed flow field around the PME

of a lifelike Computer Simulated Person (CSP) or manikin.

Previous studies of Topp (2002) and Topp et al. (2002) have

examined the differences of simplified and detailed CSP. Theyconcluded that while variations between the two were incon-

siderable at some distance from the CSP, very near the CSP,

and more importantly in the personal micro-environment, the

distinctions were much more apparent. They provided exam-

ples highlighting how CSP details can affect calculations of

contaminant transport, heat-transfer coefficients and view

factors need for radiative heat-transfer. Specifically, Topp

(2002) provided conclusive evidence that the contaminant

distribution in the personal micro-environment of the manikin

is a strong function of geometry detail.

The CSP geometry used for this study is a digitization of

a female manikin in the standing position. The data file was

obtained from Katos research group at the University of

Tokyo. The surface area of the manikin was approximately

1.48 m2, a value within the known measured range for females.

Diminutive body details such as ears, fingers and toes were

removed to disburden grid generation while maintaining asufficient level of surface description. Furthermore, aspects

such as hair and clothes were also not included to alleviate

further uncertainties (e.g., heat transfer through clothing).

Therefore the manikin represents a female of average body

surface area situated in the standing posture.

The original summary of the scenario setup, boundary

conditions and suggested reporting method of the two bench-

mark cases presented in this paper are outlined in Nielsen et al.

(2003). CFD results were extracted and compared at the same

locations where experimental data was measured. The exper-

imental data, in addition to further information, for each case

is openly available at http://www.cfd-benchmarks.com.

COMPUTATIONAL MODEL

All CFD simulations were performed using the commer-

cial CFD software FLUENT (version 6.3), where the incom-

pressible Navier-Stokes equations (Equation 1) are solved

with the SIMPLEC pressure-velocity coupling method along

with the energy equation (Equation 2).

(1)

(2)

The overbar represents averaged quantities whereas

primed variables are fluctuating quantities. The second last

term in Equation 1 is the Boussinesq approximation for ther-

mal buoyancy effects and the last terms in Equations 1 and 2

are the Reynolds stress tensor and heat-flux vector, respec-

tively. To close the problem the Reynolds stress tensor and

heat-flux vector are related to the mean velocities and temper-

atures through the gradient-diffusion hypothesis

(3)

(4)

where is the mean strain-rate tensor and

is the turbulence kinetic energy. The turbulent viscosity, , is

determined from characteristic velocity and length or times

scales.

(5)

D v

Dt--------

1

#o----- P$ $+ %$ v& ' g 1 () T& 'k $ v 'v '& '**=

DT

Dt-------- $ +$ T& ' $ T'v'& '**=

v 'v '& ' %TS2

3---kI+=

T'v'& ' +T$T=

S1

2--- $ v $ v

T

+, -. /= k

%T

%T C0VL ; %T C0V2T==




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ASHRAE Transactions 47

The turbulent thermal diffusivity, and

. The specification of the characteristic scales are

computed by the various turbulence models.

The numerical convective scheme used for all transport

equations was a 2nd order accurate upwind scheme, while

diffusion terms are discretized using the 2nd order accurate

central difference scheme. Pressure interpolation wasachieved with a 2nd order accurate scheme similar to the 2nd

order upwind convective scheme. Computational grids were

generated using the commercial grid-generation software

Gridgen. A Beowulf cluster with 64 1.6 GHz processors (x86-

64 architecture) and 64 Gbytes of total system memory made

this type of analysis possible. Thirty-two processors were

typically used, which took anywhere from 48 to 72 hours

depending on the grid resolution and turbulence models, the

latter include the model with enhanced wall treatment and

the model for the Reynolds-Averaged Navier Stokes

(RANS) equations, and the Large Eddy Simulation (LES)

method.

In displacement ventilation systems, clean and cool air is

introduced into the lower portion of the room at a low velocity

so not to cause draught discomfort. The cool supply air then

spreads throughout the occupied zone, i.e. the zone occupied

by people. Heat sources present in the room cause the air to

rise due to thermal buoyancy. As the warming air rises,

contaminants picked up along the way are carried above the

occupied zone. The warm, dirty air is then exhausted in the

upper portion of the room. Figure 1 illustrates the benchmark

displacement ventilation setup used (Nielson et al. 2003). The

room has dimensions of 2.5 m wide, 3.5 m deep and 3.0 m high

(width, depth and height correspond to the x,y andz coordi-

nates respectively). Air is supplied through a 0.4 m wide by 0.2m high rectangular hole located on the floor and is discharged

through a hole of equivalent shape and size at the ceiling on the

opposite wall. Measured from the top of the head, the CSP is

located 1.75 m downstream of the inlet wall, centered in thex-

direction and 1.75 m from the floor. Experimental data

included PIV data measured in three windows. These three

windows are the small gray rectangles indicated in Fig. 1.

Within each window, velocity components in the plane of

measurement were provided along a 0.2 m long line. Theselines are labeled L1, above the head, L2, projecting from

the center of the mouth and L3, projecting from the center of

the torso. All three horizontal locations are in thex mid-plane.

These test data are used for CFD validation.

In the CFD calculations, the computational domain

consists of the entire room shown in Figure 1. Several compu-

tational grids of different mesh size and topology are gener-

ated in this work (to be discussed in details later). The

following boundary conditions were used for all simulations.

The velocity and temperature at the inlet were 0.2 m/s and

22C respectively. A turbulence intensity of 30% and length

scale of 0.1 m were experimental values suggested by Nielsen

et al (2003). The only variable specified at the outlet was static

pressure and was set to zero. The no-slip condition along with

zero heat-flux (insulated) was applied to all the room walls.

Along with the no-slip condition on the remaining bound-

ary, the manikin surface, a boundary condition for the energy

equation is required that approximates a human body. The

human body is a dynamic thermoregulatory system (Fiala et

al. 1999; Tanabe et al. 2002). It has the ability to adjust heat

output in response to global and local changes in skin temper-

ature. The objective of this work was not to predict the thermal

response of a human but to evaluate the ability of CFD to

predict the flow in the personal micro-environment. As a

result, a thermoregulation model was not used to control the

heat output of the body. Rather, a constant (spatially and

temporally) heat-flux was chosen to mimic the heat exchange

of the body with its surroundings. The net heat loss by a human

is not only affected by their local environment but also can

vary widely depending on gender, age and physiological

makeup. The manikin used in this work represents a young

adult female with a BMI in the normal range1. A characteristic

heat loss for a human of this makeup is around 76 W. Using

this value along with the surface of area of the manikin (1.48

m2), a heat-flux of 51.2 W/m2 is obtained. This value is the

total heat-flux per unit area, where the fraction due to convec-

tion and radiation are determined during the calculation. It iswidely accepted that roughly half of human heat loss is due to

convective means while the remainder is due to radiation. An

often used approach is to ignore radiation to avoid the

perceived difficulties associated with radiation calculations.

For cases in which only convection was modeled, half of the

aforementioned heat-flux per unit area value was assumed

(25.6 W/m2).

+T %T PrT1=PrT 0.85=

k-"%2-f

1. BMI, body-mass index, is a measure of body fat based on heightand weight.Figure 1 Displacement ventilation room configuration.




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VERIFICATION

Following the definitions of Roache (1997), verification

can be thought of assolving the equations rightwhereas vali-

dation would be solving the right equations. Verification

involves quantifying the error induced by solving the chosen

equations using discrete approximations. The total error

includes those due to coding, discretization, grid convergenceand iterative convergence.

Because a commercial CFD code was used and access to

the source code is not possible, code verification could not be

performed. While, the author recognizes this as a potential

source of error, due to the large FLUENT user base, it is

assumed that any unreported coding errors negligibly affect

the solution. A list of known resolved and unresolved errors in

FLUENT are available on their supported user website. Solu-

tions to the equations were computed using a well-docu-

mented second-order discretization scheme but no verification

of the observed order of accuracy was performed. The author

recognizes this as a potential source of error but believes it tobe reasonable assumption again due to large FLUENT user

base that accept the implementation of this discretization

scheme to be second-order or close to second-order.

The verification of FLUENT performed in this work

involves grid and iterative convergence studies. Grid conver-

gence will be demonstrated by comparing relevant quantities

on the sequence of grids at strategically chosen locations. A

more rigorous approach to determine grid convergence is the

Richardson Extrapolation (RE) method (Richardson and

Gaunt 1927). Two requirements of RE are constant grid refine-

ment ratio and values at the same location. While the later is

possible through interpolation, the former is not for the typesof grids used in this work. Furthermore, the reliability of these

methods on complex, unstructured grids remains unclear. As

such error estimation using the RE method was not used. Iter-

ative convergence for all solutions was performed and an

example highlighting the strategies of monitoring conver-

gence will be discussed.

Grid Convergence Study

Due to the unknown behavior of the global and local flow

features in both cases, determining the appropriate grid strat-

egy was non-trivial. Traditionally the number of grid cells has

not exceeded several hundred thousands, due in large extent tolack of computational resources (Posner et al. 2003; Xing et al.

2001; Murakami 2004; Zhu et al. 2005; Srebric et al. 2007). In

the present study, grids consisting of up to seven million cells

were investigated. However, even with a seemingly indispens-

able amount of processing power, care should be exercised

when determining the global resolution (total cells), local

resolution (clustering around the CSP) and topology (cell

type) for the grids in these scenarios.

The approach to creating each grid began with meshing

the surface of the manikin. A consequence of the complex

manikin surface was a non-uniform distribution of triangles.

This was done to ensure all the details of the geometry were

represented. Next, the walls, inlets and outlets were meshed

uniformly. Finally, the volume grid was created where a

growth rate factor (or the rate at which the cell size increases)

of 1.2 or less was used to gradually increase the cell size away

from the manikin. Some grids included an additional stepwhere several layers of prismatic cells on the manikin were

created to sufficiently resolve the boundary layer (called

boundary layer grid here). In all cases, the equi-volume skew-

ness values of the interior cells (or the quality of the cells) were

monitored to ensure that they fall within the guidelines of the

solver FLUENT.

To establish grid independent solutions for the displace-

ment ventilation case four grids were used. A summary of the

four grids is provided in Table 1. The four grids consisted of

two with strictly tetrahedral cells and two with the boundary

layer cells added near the manikin. The important parameters

that differentiate these grids include the number of triangles

used to define the manikin geometry, the average value on

the manikin surfaces2, and the type of grid (with or without

boundary layer prismatic cells). Recall that the growth factor

of the cell volume was kept under 1.2 and grid quality as

measured by the equi-volume skewness was within the recom-

mended value of the CFD solver. Illustrations of each grid type

can be found in Sideroff (2007).

The solutions from each grid used for the grid dependency

study were obtained using the standard turbulence model

with enhanced wall treatment, and only the convective portion

of heat-transfer. Since convection alone was included, only

half the heat-flux value was applied to the manikin surface.

The three measurement stations (head, face, and torso)

detailed in Figure 1 are used to compare solutions from the

four grids. Besides being located where the data were

measured, these stations are meaningful because they pene-

trate the thermal plume at three distinctly different locations.

Comparisons of the vertical velocity were made at the

three stations illustrated in Figure 1 for the four grids, and the

largest differences between these solutions occurred at the

torso (station L3). These results are illustrated in Figure 2,

which show that Grid C and Grid D appear to exhibit grid inde-

pendence while Grid A and Grid B do not. In particular, the

steep gradient of the near-wall velocity is difficult to capture

when a strictly tetrahedral grid is used, unless of courseextremely small tetrahedrons are used. Employing strictly

tetrahedral to resolve the boundary layer would result in grids

well in excess of ten million cells.

2. Where is the distance from wall adjacent cell-

center to the wall, the friction velocity and is the

kinematic viscosity.

y+

y+ypu

2

v----------- : yp=

u23wall

#-----------= %

k-"




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Iterative Convergence Study

When steady-state RANS simulations are used, conver-

gence is typically done by monitoring the average residualsduring the iterative process of the transport equations (mass,

momentum energy, and turbulence model equations). Resid-

uals were monitored and typically dropped four orders of

magnitude for the continuity equation (two to three orders

lower for other equations). The number of iterations required

to reach convergence varied but was at least several thousands.

For the test case studied here, it was noted that average resid-

uals alone were not good indicators of convergence. Averag-

ing of the residuals can hide regions where the local residual

may be many orders of magnitude larger. It was found that

along with residuals, velocity magnitude should be monitored

at strategically chosen points to give a more accurate indica-

tion that the solution had indeed converged. For the presentproblem, two points were chosen: one in the thermal plume

(referred to as point A), and another away from and behind the

CSP to monitor the room airflow (referred to as point B).

During the iteration process, two distinct flow structures

developed: the thermal plume, which was expected, and

another not so obvious structure was a rather complex re-

circulating flow around the room and behind the CSP gener-

ated by the inlet vent. The momentum of the inlet vent created

a low-speed jet that progressed along the floor, and instead of

rising upon hitting the warm feet of the CSP, it proceeded

along to the back wall. In fact, the flow circulated several times

behind the CSP, three or more times in some instances, before

being entrained in the thermal plume. The development of

these two flow structures was not independent of each other

thus making judgment of convergence non-trivial.

As mentioned, FLUENT uses averaged residuals to moni-

tor convergence of the transport equations. In the present prob-

lem, the continuity residual typically dropped about four

orders of magnitude and leveled out after about 10,000 itera-

tions, and in this case, falsely indicating convergence. It is

noted that, since the velocity magnitude is highest in the ther-

mal plume, the average residual is basically a convergence

indicator of the flow structure in the thermal plume. When the

velocity magnitudes at Points A and B were monitored during

the iteration process, it was observed that convergence was not

yet reached after 10,000 iterations. Figure 3 shows the velocity

in the plume (Point A) declines monotonically, stops changing

at about iteration 9,000, and remained constant until about

iteration 10,000 where it gradually increases back to about

0.035 m/s from a value of 0.01 m/s. At iteration 14,000, the

velocity magnitude began to slowly decline again and eventu-

ally leveling out to a value of 0.02 m/s at roughly iteration

27,000. Along the floor (Point B), the velocity magnitude

made a couple of large oscillations during the first 7,000 iter-

ations and then began to oscillate at a much higher frequency

but at a constant mean value. Eventually the oscillations died

away and the velocity became steady near iteration 27,000.

During the first several thousands iterations (

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be very large if the sources of contaminants are located behind

the CSP in the vicinity of the re-circulating flows.

VALIDATION

It is validation when one wants to determine how well the

computational model can represent reality. Through verifica-

tion, one gains confidence that the CFD code can produce

solutions to the discrete equations of known error but provides

no guarantee these equations sufficiently captures the physics

of the problem. To validate CFD codes, experimental data

must be used because experiments themselves do not selec-

tively exclude the relevant physics. When validating a compu-

tational model, the user must now account for not only the

error associated with the computational model but also theerror associated with the experiment. Therefore error due to

measurement uncertainty and error to facility biasing should

be also accounted for.

Katos research group at the University of Tokyo has

obtained experimental data of the displacement ventilation

case studied here. The setup of Katos experiment is similar to

the computational model shown in Figure 1 where the manikin

is suspended slightly above the floor. Two velocities compo-

nents were measured with a particle image velocimetry (PIV)

system near the manikin and values for each were provided

along the lines indicated in Figure 1. Velocity magnitude,

turbulent intensity and temperature were measured at several

locations away from the manikin including the inlet. Unfortu-nately no estimates of uncertainty or error were provided.

Turbulence Modeling

Due to our inability to compute the entire range of flow

scales for all but the most trivial problems, modeling of turbu-

lence has become a research science of its own. The most ubiq-

uitous approach to modeling turbulence is the RANS method

while the more robust but computationally demanding

approach is the LES method. Two RANS models as well as an

LES model were investigated in this work.

Eddy-viscosity RANS model are the most popular class

of turbulence model utilized for indoor environment simula-

tions. They are attractive because they offer the best balance

between accuracy, complexity and computational cost. The

most popular of these, the standard (Jones and Launder

1972), was used in this work. The transport equations for the

turbulence kinetic energy, , and turbulence dissipation rate,

, respectively are as follows:

(6)

(7)

where is the turbulent viscosity, is

thermal buoyancy induced production and is the time

scale. Complete details of these equations, including the

model constants, can be found in many other books on turbu-lence (Pope 2000; Tennekes and Lumley 1972).

To extend the applicability of the standard model,

FLUENT has made available an enhanced wall treatment

option. The enhanced wall function is a near-wall modeling

approach that enables the standard equations to be inte-

grated all the way to the wall. Essentially, this provides the

standard with the ability to resolve the boundary layer

through the buffer layer into the viscosity affected sub-layer

without the need for an explicit wall function. To allow this, a

two-layer model is used to specify and in the viscous sub-

layer. Providing the standard with the ability to resolve the

boundary layer imposes requirements on , i.e. less than

one. Complete details of the enhanced wall treatment are

found in the FLUENT manual.

A state-of-the-art RANS model, dubbed the , with

some noteworthy improvements over the standard , was

also used in this work. Regardless of the ability to full resolve

the boundary layer, it is well known that the standard

model over-predicts the production of turbulent kinetic energy

near solid walls. The performance of the definition of the

eddy viscosity degrades rapidly as solid walls are approached

primarily due to incorrect scaling of turbulent kinetic energy.

The model of Durbin (1991) changes the definition of the

velocity scale to primarily because scales as

as it approaches solid walls whereas scales as (Durbin1991); thus providing stronger damping as the wall is

approached. Furthermore, an elliptic relaxation function, , is

included to account for the non-local damping effects of solid

boundaries. Through this approach the elliptic relaxation

function can account for anisotropy present near solid bound-

aries. There have been various modifications to the model

and the versions of the and equations incorporated in

FLUENT are identical to Model 3 of Sveningsson (2003).

Along with the Equations 6 and 7, the remaining equations that

constitute this version of the are as follows:

Figure 3 Convergence history of velocity at Points A and B.

k-"

k

"

Dk

Dt------- $ %

%T4k-----+, -

. / $k, -. / 2%TS

2 " Pb+ + +*=

D"Dt------- $ %

%T4"-----+, -

. / $", -. / C1"

T-------- 2%TS

2 C3" Pb+& ' C2""T---+*=

%T C0k

"--= Pb g+T(

5T5z------=

T k"--=

k-"

k-"

k-"

" %tk-"

y+ y+

%2-fk-"

k-"

k-"

%2-fv'2& '1 21

2v' y4

k y2

%2-fv2

%2-f




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(8)

(9)

where is the turbulent viscosity. The time scale,T, defined to allow adjustment near walls and model constants

can be found in Sveningsson (2003).

While the standard employs ad-hoc wall treatments,

the model instead handles the near-wall behavior through

a more physical approach: the and equations. Without the

need for wall functions, the turbulence model requires

that the boundary layer be fully resolved and should be less

than one.

Eddy-viscosity RANS models, such as the standard

and , are known to be deficient for low Reynolds

numbers flow. The majority of the assumptions on which

they are based can be traced to the fully turbulent approxi-

mation. Furthermore, turbulence production from thermal

gradients is a particularly challenging issue for typical RANS

models. While there has been considerable effort to extend

the capabilities of traditional RANS models (Murakami et al.

1996; Kenjere et al. 2002, 2005), these new models tend to

be overly complex requiring additional equations, more coef-

ficients and typically introduce numerical instability. Despite

their achievements, these models undoubtedly fall well short

of being reliable for a wide range of indoor environment

flows. With this in mind, it seems reasonable to consider

models beyond the RANS approach. LES is a more robust

method of approximating complex turbulent flows than

RANS methods. In contrast to RANS modeling, Large EddySimulation (LES) computes the large-scale motions of the

flow directly. The small-scale, dissipative motions of turbu-

lence tend to more amenable to modeling because of their

more uniform character, whereas the large-scale motions

contain the majority of the energy and anisotropy. As a result,

LES is expected to be more accurate, particularly in complex

flows where the assumptions inherent to RANS models

rarely exist. The drawback is that LES simulations are always

three dimensional, unsteady one. Provided the boundary

layer is resolved and y+ is less than one, a linear stress-strain

relationship is assumed for LES. If however the first cell does

not lie well within the viscous sub-layer, it is assumed the

first cell lies within the logarithmic layer and the traditionallaw-of-the-wall is used.

LES typically does not suffer the drawbacks associated

with RANS models provided the energy-containing length

scales are sufficiently resolved. The question is how to ensure

this happens without a priori knowledge of the flow. Because

LES computes the large scale motions and models the small

scale ones, knowledge or even approximation of the small

scales would be beneficial. From known values of the length

and time scales, estimates of the smallest scales, the Kolmog-

orov scales (Tennekes and Lumley 1972), can be made. The

Kolmogorov length ( ) and time ( ) scales are be expressed

in terms of the kinematic viscosity, %.

(10)

In determining and , only an estimate for e remains.

Following Tennekes and Lumley (1972), an inviscid estimatefor can made through the relationship . The fluc-

tuating velocity, , is determined by the relation .

Here, would be the peak plume velocity, 0.3 m/s. The turbu-

lent intensity, , and turbulent length scale m

of the plume were obtained from Marr and Glauser (2006) and

Marr (2007). Using these values, m2/s3. From this,

the estimated Kolmogorov scales of the thermal plume are

mm and .

Now that approximations of the smallest scales are avail-

able, determination of the appropriate grid spacing and time

step for LES can be made. If a DNS of this flow was

performed, a grid spacing and time step would be chosen to

match the Kolmogorov values. However, since LES models

the small scales a larger grid spacing and time step can be used.

Meyers et al. (2003) recommends the LES sub-grid scale

cutoff, i.e., grid spacing, to be around 1020 Kolmogorov

scales. This would suggest a grid spacing of about 6 mm would

be sufficient for LES. The time step would be determined in a

similar manner but numerical concerns must also be consid-

ered. The recommendation of Meyers et al. (2003) applied to

the time step would yield 0.25 s but the flow time for a 6 mm

cell with a velocity of 0.3 m/s would be 0.02 san order of

magnitude smaller than . It is unlikely that the maximum

velocity would occur in the smallest cell, since the smallest

cells are located adjacent that walls. The appropriate time stepsize would lie somewhere between 0.02 and 0.25.

The dynamic Smagorinsky sub-grid scale model of

Germano et al. (1991) was used in this work. The sub-grid

scale viscosity and length scale are defined as

(11)

(12)

where the over-tilde denotes spatial average (as opposed to

temporal averaging for RANS models) and the filter width,

. Complete details along with the model constants

can be found in Germano et al. (1991).As previously mentioned, results from the turbulence

models were compared with the experimental data at the loca-

tions indicated in Figure 1. Upon examining the vertical veloc-

ity profiles in Figure 4 above the head, significant differences

are revealed between not only the turbulence models but also the

experimental values. The general profile shapes appear reason-

able, but only a small the portion of the profile near the head

(

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by 0.1 m/s. It is evident from Figure 4 that LES provides

marginal improvement. Near the head, the LES profile is consis-

tent with the slope of the data. Beyond the near-wall region, theLES profile compares better to the test data than either RANS

models, but the improvement is marginal. The LES results over-

predict the magnitude by as much as 0.05 m/s.

At the face shown in Figure 5, the RANS results yielded

considerably different trends. Overall, the model under-

predicts the thickness of the thermal plume, while the

model over-predicts it. Near the wall (

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side walls and floor without radiation are several degrees lower

than with radiation, while the converse is true on the ceiling.

Indubitably, the incorporation of radiation has consequences

on not only on the individual contribution of heat transfer

modes but also on the surface temperatures.

To evaluate the effect of radiation more definitively,

results were compared to the test data at the three locationsindicated in Figure 1. Upon inspection of the results of Figure

9 above the head, it is immediately obvious the influence radi-

ation has on the thermal plume. The over-prediction of the

magnitude seen in Figure 4 without radiation appears to be

remedied by the inclusion of radiation. The LES profile is in

excellent agreement with the data, and the standard and

yield more than satisfactory results.

The results at the face with radiation included shown in

Figure 10. While not in agreement to the degree seen above the

head, these results still provide improvement over predictions

without radiation included. Here, it could be argued the LES

provides no considerable benefit over the standard or

. All numerical profiles show roughly the same peak value

albeit higher than the data0.125 m/s for the , 0.11 m/s

for LES and standard versus 0.08 m/s for the data.

However, beyond about 0.03 m the numerical profiles follow

the data remarkably close.

The final location at the torso indicates similar trends as

seen at the face. As shown in Figure 11, the peak value is over-

predicted by both models but beyond there they follow the data

reasonably well. The standard does not predict the change

in slope seen in the data or the and LES but overall yields

acceptable results.

Reduced-Order Model for Radiation

The calculations with radiation provided evidence that

radiation modeling cannot be ignored, but the inclusion of

radiation modeling did not come without a cost. For surface-

to-surface radiation calculations, the view factors are needed.

Although purely a pre-processing step, computing the view

factors can be computationally expensive (Sideroff 2007). It

would be beneficial if the effects of radiation could be

included without actually performing the radiation modeling.

If the surface temperatures were somehow known a priori, the

effects of radiation can be included without the difficulties of

actually computing radiative energy transfer. Unfortunately,

determining a detailed spatial (or temporal) description of the

surface temperature from experiment is exceedingly difficult

or simply not possible, nor it is the case in practice.

It was postulated that perhaps a reduced-order or low-

order description of the surface temperature would be

adequate. And if a low-order description of the surfacetemperature were used, how would this affect the flow in the

PME? To answer this question, an examination of the impact

of a reduced surface temperature description was carried out.

The simplest way is to reduce the surface temperature of each

surface to an average value.

Figure 6 Vertical velocity at torso (station L3).

Figure 8 Surface temperatures with radiation; LES model

on grid D.

k-"%2-f

k-"%2-f

%2-fk-"

k-"%2-f

Figure 7 Surface temperatures without radiation; LES

model on grid D.




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Using the solution from the standard on grid D, an

area-weighted average of the temperature distribution was

computed for each surface. The resulting average surface

temperatures and those subsequently used for boundary

conditions are tabulated in Table 2.

A calculation using the standard on grid D was

performed using the average surface temperatures from

Table 2 and compared against the results from the standard

with the unaltered surface temperatures from radiationmodeling, along with the test data. Comparing the solutions at

the three stations where test data are available, it was found

that excellent agreement were obtained at station L1 (above

the head) and station L2 (at face). At station L3 or the torso

shown in Figure 12, more noticeable differences are observed.

The peak value of the profile with the reduced-order model is

marginally lower than with the full radiation modeling

included. However, the shapes of the profiles are very similar.

CONCLUSIONS

A detailed verification and validation study using a

commercial CFD code (FLUENT) of the flow around a

Computer Simulated Person in a displacement ventilation

room was carried out. Following the guidelines of the bench-

mark displacement ventilation case of Nielsen et al. (2003)

several recommendations concerning the verification and vali-

Figure 9 Vertical velocity above head with radiation

(station L1).

Figure 11 Vertical velocity at torso with radiation

(station L3).

Table 2. Average Surface Temperatures

Surface Average Temperature (K)

manikin 303.9

floor 297.9

ceiling 298.5

side walls 298.3

front wall 298.3rear wall 298.4

k-"

k-"

k-"

Figure 10 Vertical velocity at face with radiation

(station L2).

Figure 12 Vertical velocity at torso comparing radiation

modeling and averaged surface temperatures

(station L3).




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dation of CFD for the PME were elucidated by examining grid

dependency, iterative convergence, turbulence modeling and

radiation modeling.

Four grids of increasing resolution and varying topologies

were constructed to demonstrate grid independence. Due to

the complex geometry of the CSP, the grids used were of the

unstructured type. It was found that achieving grid indepen-

dent solutions while maintaining an acceptable cell countusing a strictly tetrahedral topology was exceedingly difficult.

The two finest grids included a technique where several layers

of thin triangular prism cells were created by extruding the

surface triangles away from the CSP. These layers of prismatic

cells allowed full resolution of the boundary layer without

significant increase in the number of cells. To achieve grid

independent solutions, approximately 100,000 surface trian-

gles are needed on the CSP, at least several layers of prismatic

cells around the CSP to achieve values less than one and a

maximum growth rate of 1.2 for the remaining tetrahedral

cells around the CSP.

To achieve convergence for steady-state (RANS) calcu-

lations, quantities other than average residual needed to bemonitored. Because two distinct flow structures developed,

averaged residual was not a sufficient convergence parameter.

Velocities were monitored at strategically chosen pointsone

in the plume and the other away from the CSP in the recircu-

lating room flowduring the iteration process. While the

velocity in the thermal plume appeared to reach steady-state at

approximately the same number of iterations as the residualsthis was not so. The velocity of the recirculating flow near the

floor continued to oscillate for several thousand iterations

beyond the apparent steady state of the plume. Nearly

30,000 iterations were needed to achieve convergence. It was

noted that if the velocity in the PME of CSP were of interest,

the error incurred by incomplete convergence may be incon-sequential. However, if, for example, contaminant transport

from a source away from the CSP in the recirculating flow

were of interest, iterative convergence error may be important.

Due to the perceived effort required to include it, radia-

tion modeling is commonly avoided by assuming half the

CSP heat loss for convection only. This approach requires

using a heat-flux (first derivative) boundary condition.

Through careful examination of the coupling of surface-to-

surface radiation equations to the flow equations and results

that include radiation modeling it was found that neglecting

radiation modeling when heat-flux boundary conditions are

used is erroneous. While the actual radiative to convective

heat transfer ration was closer to 60/40 (not 50/50), it wasconcluded that the significant change in wall temperatures

due to radiation caused the differences and not the lower

convective component.

If somehow the actual surface temperatures were known

a priori, then the effects of radiation could be included without

actually including a radiation model. The actual surfacetemperatures would need to be obtained from experiment

because reality does not disclude radiation. However, obtain-

ing a detailed description of the surface temperatures experi-

mentally would be exceptionally difficult or simply not

possible. By applying spatially averaged values of surface

temperatureobtained from the calculations with radiation

includedit was found that velocities in the PME were rela-

tively insensitive to this approach. This suggests that measur-ing the surface temperature at few points on all the

participating walls and using those as temperature boundary

conditions for CFD calculations would yield satisfactory solu-

tions.

Turbulence models tend to be the most unreliable aspect

of CFD, particularly for low Reynolds, thermally buoyant

flows encountered in the PME. Results from turbulence

models were validated with high-resolution PIV data suppliedby Katos research group at the University of Tokyo. The stan-

dard with an enhanced wall-treatment, the model of

Durbin (1999) and dynamic Smargorinsky LES turbulence

models were utilized. Without radiation (or the effects)

included none of the three turbulence models provided satis-

factory results. Only when radiation (or the effects) were

included did any turbulence yield reasonable comparison to

the data. Regardless of the innovative improvements of the

, it did not yield improvement over the standard . LES

does not suffer from the drawbacks of RANS models butdespite its wider applicability did not offer any benefit over

the standard . When an enhanced wall treatment was usedwith a grid that resolves the boundary layer, the standard

model was found to provide solutions as accurate as the

or LES.

ACKNOWLEDGMENTS

This work was supported by the US Environmental

Protection Agency (EPA) through the STAR Center for Envi-

ronmental Quality Systems (www.eqstar.org) and the Center

of Excellence in Environmental Systems (www.coees.org) atSyracuse University.

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