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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.
8/2/2019 SL-08-005 Final
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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==
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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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.
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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48 ASHRAE Transactions
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-"
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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ASHRAE Transactions 49
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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50 ASHRAE Transactions
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
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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ASHRAE Transactions 51
(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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52 ASHRAE Transactions
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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ASHRAE Transactions 53
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.
2008, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org).
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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).
2008, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org).
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ASHRAE Transactions 55
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.
REFERENCES
Awbi, H.B. 1991. Ventilation of Buildings. E & FN Spon
Publishing.
Bjrn, E. and Nielsen, P.V. 2002. Dispersal of exhaled air
and personal exposure in displacement ventilated rooms.
Indoor Air 12(2): 147-164.
Cermak, R. Melikov, A. Forejt, L. and Kovar, 0. 2006. Per-
formance of personalized ventilation in conjunction
with mixing and displacement ventilation.International
Journal of HVAC Research. 12: 295-311.
Cheong, K.W.D., Djunaedy, E., Pho, T.K., Tham, K.W.,
Sekhar, S.C., Wong, N.H. and Ullah, M.B. 2003. Mea-
surements and computations of contaminants distribu-
tion in an office environment. Building and
Environment. 38: 135-145.
Clark, R.P. and Edholm, O.G. 1985. Man and His Thermal
EnvironmentLondon, UK: Edward Arnold.
Durbin, P.A., 1991. Near-wall turbulence closure modeling
without damping functions. Theoretical and Computa-
tional Fluid Dynamics 3: 1-13.
Fenske, J.D., Paulson, S.E. 1999. Human breath emissions of
VOCs.Journal of Air and Waster Management49: 594-
598.
y+
k-" %2-f
%2-f k-"
k-"k-"
%2-f
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.
8/2/2019 SL-08-005 Final
12/12
56 ASHRAE Transactions
Ferro, A., Kopperud, R.J., and Hildeman, L. 2004. Source
strengths for indoor human activities that resuspend par-
ticulate matter. Environmental Science & Technology38(6): 1759-1764.
Fiala, D., Lomas, K.J. and Stohrer, M. 1999. A computer
model of human thermoregulation for a wide range of
environmental conditions: the passive system. Journal
of Applied Physiology 87(5): 1957-1972.
Germano, M., Piomelli, U., Moin, P. and Cabot, W.H. 1991.
A dynamic sub-grid scale eddy viscosity model.Physics
of Fluids A 3: 1760-1765.
Huang, J.M., Chen, Q., Ribot, B., and Rivoalen, H. 2004.
Modeling contaminant exposure in a single-family
house.Indoor and Built Environment13: 5-19.
Jones, W.P. and Launder, B.E. 1972. The prediction of lami-
narization with a two-equation model of turbulence.
International Journal of Heat and Mass Transfer 15:
301-314.
Kenjere, S., Hanjalic, K. and Gunjaro, S.B. 2002. A T-
RANS/VLES approach to indoor climate simulations.
Proceedings of ASME 2002 Fluids Engineering Divi-sion Summer Meeting, Montreal, CA.
Kenjere, S., Gunjaro, S.B. and Hanjalic, K. 2005. Contribu-
tion to elliptic relaxation modelling of turbulent natural
and mixed convection. International Journal of Heat
and Fluid Low 26:. 569-586.
Marr, D.R. and Glauser, M.N. 2006. Length scale propaga-
tion along a joint inlet and thermal buoyancy driven
Flow.AMSE International MeetingPaper 98532.
Marr, D.R. 2007. Length scale propagation along a joint inlet
and thermal buoyancy driven flow. PhD Thesis, Syra-
cuse University, Dept. of Mechanical and Aerospace
Engineering.
Melikov, A. and Kaczmarcyzk, J. 2007. Measurement andprediction of indoor air quality using a breathing ther-
mal manikin.Indoor Air 17: 50-59.
Meyers, J. Geurts, B.J. and Baelmans, M. 2003. Databaseanalysis of errors in large-eddy simulation. Physics of
Fluids 15(9): 2740-2755.
Modest, M.F. 2003. Radiative Heat Transfer. San Diego,
CA, USA: Academic Press.
Murakami, S., Kato, S., Chikamoto, T., Laurence, D. andBlay, D. 1996. New low-Reynolds number k-e model
including damping effects due to buoyancy in a strati-
fied flow field. International Journal of Heat and Mass
Transfer 39(16): 3483-3496.
Murakami, S. 2004. Analysis and design of micro-climatearound the human body with respiration by CFD.Indoor
Air 14(Suppl. 7): 144-156.
Nielsen, P.V., Murakami, S., Kato, S., Topp, C. Yang, J-H.
2003. Benchmarks test for a computer simulated person.
Aalborg University, Indoor Environmental Engineering
(see http://www.cfd-benchmarks.com).
Pope, S.B. 2000. Turbulent Flows. Cambridge, UK: Cam-
bridge University Press.
Posner, J.D., Buchanan, C.R. and Dunn-Rankin, D. 2003.
Measurement and prediction of indoor air flow in a
model room.Energy and Building. 35: 515-526.Richardson, L.F. and Gaunt, J.A. 1927. The deferred
approach to the limit. Philosophy Transactions of the
Royal Society of London, Ser. A. 226: 299-361.
Roache, P.J. 1997. Quantification of uncertainty in computa-
tional fluid dynamics.Annual Review of Fluid Mechan-
ics 29: 123-160.
Sideroff, C.N. 2007. Detailed examinations of the human
micro-environment by CFD.PhD Thesis, Syracuse Uni-
versity, Dept. of Mechanical and Aerospace Engineer-
ing.
Srebric, J., Vokovic, V., He, G. and Yang, X. 2007. CFD
boundary conditions for contaminant dispersion, heat
transfer and airflow simulations around human occu-pants in indoor environments. Building and Environ-
mentArticle in Proof.
Sveningsson, A. 2003. Analysis of the performance of differ-
ent -f turbulence models in a stator vane passage flow.
Ph.D Thesis, Chalmers University of Technology ISSN
1101-9972.
Tanabe, S., Kobayashi, K., Nakano, J., Ozeki, Y., and Koni-
shi, M. 2002. Evaluation of thermal comfort using com-
bined multi-node thermoregulation (65N) and radiation
models and computational fluid dynamics (CFD).Energy and Buildings 34: 637-646.
Tennekes, H. and Lumley, J.L. 1972. A First Course in Tur-
bulence. Cambridge, MA, USA: MIT Press.
Topp, C. 2002. Influence of geometry of a computer simu-
lated person on contaminant distribution and personal
exposure.ROOMVENT 2002. 1: 265-268.
Topp, C., Nielsen, P.V., and Srensen, D. 2002. Applicationof computer simulated persons in indoor environmental
modeling.ASHRAE Transactions 108(2): 1084-1089.
Xing, H., Hatton, A. and Awbi, H.B. 2001. A study on the air
quality in the breathing zone in a room with displace-
ment ventilation. Building and Environment 36: 809-
820.
Zhang, T. and Chen, Q. 2007. Novel air distribution systems
for commercial aircraft cabins. Building and Environ-ment42: 1675-1684.
Zhu, S., Kato, S., Murakami, S. and Hayashi, T. 2005. Study
on inhalation region by means of CFD analysis and
experiment.Building and Environment40: 1329-1336.
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.