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Simplified Numerical Models for Complex Air Supply
Diffusers
Jelena Srebric a & Qingyan Chen b c
a Department of Architectural Engineering , Pennsylvania State University
b Massachusetts Institute of Technology
c Purdue University
Published online: 03 Mar 2011.
To cite this article: Jelena Srebric & Qingyan Chen (2002) Simplified Numerical Models for Complex Air Supply Diffusers,
HVAC&R Research, 8:3, 277-294
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VOL. 8, NO. 3
HVAC&R RESEARCH
JULY 2002
Simplified Numerical Models for
Complex Air Supply Diffusers
Jelena Srebric, Ph.D.
Qingyan Chen, Ph.D.
Member ASHRAE
Member ASHRAE
Correct description of the flow and thermal information for an air supply diffuser is important
for reliably predicting room air distribution by using computational fluid dynamics. Simplified
methods that can be used to describe flow and thermal information from eight commonly used
diffusers were developed in this study. The investigation used the box and momentum methods.
The corresponding experimental data on airflow and temperature distributions from an environ-
mental chamber have been used to validate the numerical methods. The box method with an
appropriate box size is satisfactory for most of the diffusers. The momentum method performs
well for five diffusers. Because the momentum method is simpler than the box method, the
momentum method should be used whenever it is applicable.
INTRODUCTION
Computational fluid dynamics (CFD) is a popular tool for indoor environment design. CFD
modeling can greatly improve our knowledge of the performance of ventilation systems. Unfor-
tunately, a major bottleneck to this modeling is that most diffusers are small compared to the
size of the room and have high flow velocities. The requirements for modeling the flow inside a
diffuser to predict the outflow characteristics are much different from, and often incompatible
with, the requirements for modeling the corresponding room airflow.
On the other hand, to model the room airflow, it is necessary to know the boundary conditions
that describe the inlet jet airflow from a supply diffuser. The information that one typically can
assume as an inflow boundary condition is usually limited to a profile in the inlet neck. Air sup-
ply diffusers often have complex geometries. Actual modeling of the flow from the inside neck
of the diffuser through and out of the diffuser is needed. Although modeling the flow might be
theoretically possible, the codes that are efficient and available for modeling the room airflows
are not capable of modeling the airflow in the diffuser. The boundary conditions and their loca-
tions must be specified to model the airflow in a room, which requires specification of the inlet
boundary conditions. Most of the current room airflow simulations only use simple diffusers
because of this problem. Many researchers have identified modeling the airflow supplied from
the diffuser as a major limiting factor in applying CFD to room airflow (Jacobsen and Nielsen
1993; Moser 1991; Regard et al. 1995; Vogel et al. 1993; Zhang et al. 1992).
Several recent studies have focused on this issue and have suggested potential solutions to
this problem. For example, Skovgaard and Nielsen (1991) compared two techniques of mod-
eling diffuser flow, including modeling the diffuser directly, and modeling the resulting flow
pattern in a volume in front of the diffuser (box method). They concluded that the box method
had better performance, although this depends on the diffuser-specific data. More recently,
Emvin and Davidson (1996) discussed four methods of representing a diffuser with multiple
jets. They concluded that further work is needed to develop a simplified inlet model without
Jelana Srebric is an assistant professor in the Department of Architectural Engineering at Pennsylvania State University.
Qingyan Chen was an associate professor at the Massachusetts Institute of Technology, and is now a professor in the
School of Mechanical Engineering at Purdue University.
277

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HVAC&R RESEARCH
performing any measurements or sacrificing accuracy. Huo et al. (1996) also proposed a new
method to describe diffuser boundary conditions that takes advantage of existing diffuser
characteristic equations and manufacturer data. They concluded that the method may be used
to accurately specify diffuser boundary conditions without describing the complicated dif-
fuser geometry, thereby saving simulation time by using a coarser grid. Other recent reports
on diffuser studies include work from Chen and Jiang (1996), Heikkinen and Piira (1994), and
Joubert et al. (1996). Most of the studies have been limited to one or two diffusers and lead to
contradictory conclusions.
This project builds on the work cited above by focusing on the identification of a simple and
practical method that can be used by CFD modelers (ranging from designers to researchers) to
model the airflow in a room supplied by a variety of real air supply devices. This investigation
seeks a general method that can be applied to most commercial CFD codes.
RESEARCH METHODOLOGY
Through an extensive literature review (Chen and Srebric 2000; Srebric 2000), it was found
that it is not possible to use jet relations to provide boundary conditions for air supply diffusers
for CFD modeling of room airflow. The review concluded that simplified methods, such as
Skovgaard and Nielsen (1991) and Chen and Moser (1991), have promise for modeling diffuser
airflow using resultant momentum. These methods provide the boundary conditions from the
supply diffusers without modeling the detailed diffuser geometry. The methods can be grouped
in two basic categories (Fan 1995):
• Momentum modeling at the air supply devices, such as Chen and Moser (1991)
• Momentum modeling in front of the air supply devices, such as Skovgaard and Nielsen (1991)
The momentum modeling approach at the air supply device imposes the initial jet momentum
as a boundary condition for CFD simulations. This approach is relatively easy to use because the
initial momentum is normally available. On the other hand, the approach for momentum model-
ing in front of the air supply device uses the momentum downstream from the diffuser. This
approach determines the momentum in front of the air supply device by using jet relations or
measured data. The jet relations can be applied only in some special cases, such as fully devel-
oped free or attached diffuser jets, assuming that formulas are available for those types of diffus-
ers. Unfortunately, for many practical applications, jets are neither free nor attached, and the
transition region tends to be large. Furthermore, the main region of the jet is influenced by room
airflow. Therefore, application of the momentum modeling in front of the diffuser requires mea-
surements in many cases. However, not every diffuser manufacturer provides sufficient data for
their product. Therefore, it is not easy to use the momentum modeling in front of the air supply
devices.
Among the methods of momentum modeling at the air supply devices developed through an
international effort (IEA 1993), the momentum method (Chen and Moser 1991) seems most
promising. This method decouples momentum and mass boundary conditions for the diffuser in
a CFD simulation. The diffuser is represented with an opening that has the same gross area,
mass inflow, and momentum flux as a real diffuser. This model enables specification of the
source terms in the conservation equations over the real diffuser area. The air supply velocity for
·
the momentum source term is calculated from the mass flow rate m and the diffuser effective
area A :
o
·
m
ρA
---------
U
Z
(1)
o
o

VOLUME 8, NUMBER 3, JULY 2002
279
Figure 1. Box and Tiny Box Models for Nozzle Air Supply Diffuser
The momentum method requires data on airflow rate, discharge jet velocity or effective dif-
fuser area, supply air turbulence properties, and supply air temperature and contaminant con-
centrations.
The approach for momentum modeling in front of the air supply diffuser has also been used in
many studies. Its variations include the box model (Nielsen 1989, 1997), the prescribed velocity
model (Nielsen 1989), and the diffuser specification model (Huo et al. 1996). Srebric (2000) and
Chen and Srebric (2000) compared these methods and concluded that the box method was the
most appropriate.
The box model (Nielsen 1989, 1997) represents the diffuser boundary conditions on an imag-
inary box surface around the diffuser. The flow field within the box is ignored. An example of
the box method shown in Figure 1 illustrates how the method imposes boundary conditions for a
nozzle diffuser in a two-dimensional form. One of the box surfaces (the front surface) uses jet
profiles as boundary conditions, and the others use a free boundary with zero gradients for flow
parameters. To specify the boundary conditions, either suitable jet formulas should be applied or
air velocity, temperature, and gas concentration profiles must be measured. Nielsen (1997) used
the box method for a diffuser and obtained results in good agreement with the measured data.
However, another study found that the box method overpredicted the maximum jet velocity
more than other simplified methods (Heikkinen 1991). Another problem with the box model is
the determination of the box size. The box should be sufficiently large to have the boundaries in
the fully developed jet region where the velocity and temperature profiles are similar. On the
other hand, the box has to be small enough to avoid the impact of room air recirculation and
thermal plumes on the jet.
In a CFD simulation, the box method needs information on the distribution of air velocities,
the turbulence properties, and the distributions of temperature and contaminant concentrations.
The box method has a more solid physical background than the momentum method. How-
ever, it requires much more time to impose the boundary conditions. The box method also needs
some measured data for all the parameters simulated. Therefore, the momentum method is pre-
ferred, as it is easier to implement in a CFD simulation. Nevertheless, this investigation uses
both methods to examine their performance in room airflow prediction.
The present investigation used the CFD technique to solve a set of partial differential equa-
tions for the conservation of mass, momentum, energy, and species concentrations. These equa-
tions govern flow, heat, and mass transport in a room. Because airflow in the room is turbulent,
the CFD technique used a turbulence model [the renormalized-group k-ε model from Yakhot

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Table 1. Internal Heat Sources in Environmental Chamber
Internal Heat Sources
Btu/h (W)
Each human simulator
Computer 1
256 (75)
368 (108)
590 (173)
116 (34)
Computer 2*
Each fluorescent lamp
Total
1934 (567)
*Close to window
et al. (1992)] to reduce the computing costs. With the turbulence model, the airflow, tempera-
ture, and species concentration transport can be described by the following unsteady time-aver-
aged Navier-Stokes equation:
∂(ρΦ)
----------------
∂t
H div(ρVΦ Ó Γ
gradΦ) Z S
(2)
Φ,eff
Φ
Many textbooks [e.g., Versteeg and Malalasekera (1995)], have detailed the CFD theory. The
governing equations can be closed with appropriate thermofluid boundary conditions at all the
boundaries such as air inlets, outlets, and wall surfaces. The values of velocity, temperature,
kinetic energy, the dissipation rate of kinetic energy, and species concentration were set at the
boundaries.
A commercial CFD program (CHAM 1998) was used in the present investigation to solve the
time-dependent conservation equations together with the corresponding boundary conditions.
The program discretized the indoor space into nonuniform computational cells, and the discrete
equations were solved with the SIMPLE algorithm (Patankar 1980). The computed room air-
flows were validated with the measured data obtained from a full-scale environmental chamber
(Yuan et al. 1999) and from the literature for a number of classic cases (Chen 1995).
SIMULATIONS OF COMMONLY USED AIR SUPPLY DIFFUSERS
Eight different diffusers are commonly used in U.S. buildings: nozzle, slot (linear), valve, dis-
placement, round ceiling, square ceiling, vortex, and grille diffusers, as shown in Figure 2. Dif-
ferent types of diffusers generate different airflow distributions, and may have fundamental
differences in the jet flow structure tested.
Figure 3 shows how the diffusers were installed in an environmental chamber that is 17 ft
(5.18 m) long, 12 ft (3.66 m) wide, and 8 ft (2.44 m) high. The nozzle and valve diffusers were
not installed in the chamber because experimental data for those diffusers were available from
the literature. In addition to the internal heat gains shown in Table 1, there were 341 to 580
Btu/h (100 to 170 W) of cooling load from the window, depending on the diffuser type and ven-
tilation rate. The ventilation rate studied ranged from 3.0 to 9.2 air changes per hour. More
detailed descriptions of the experimental setup are available from Yuan et al. (1999), Srebric
(2000), and Chen and Srebric (2000).
In the experiments the distributions of air velocity, air temperature, and the tracer gas (SF )
6
concentration used to simulate a contaminant were measured. The major measuring equipment
included a flow visualization system by smoke for observing the airflow patterns, a hot-sphere
anemometer system for measuring the air velocity and temperature, a thermocouple system for
measuring the wall and air temperatures, and a tracer-gas system for measuring concentration.
ASHRAE Standard 55 specifies the low-velocity range to be between 0.05 and 0.5 m/s (10 and
100 fpm) and requires an accuracy for the mean velocity measurements of 0.05 m/s ( 10 fpm).

VOLUME 8, NUMBER 3, JULY 2002
281
Figure 2. Eight Commonly Used Air Supply Diffusers: (A) Nozzle, (B) Valve,
(C) Displacement, (D) Grille, (E) Slot, (F) Square Ceiling,
(G) Round Ceiling, and (H) Vortex
The omnidirectional hot-sphere anemometers were calibrated for a velocity as low as 0.05 m/s
(10 fpm). However, the data were more reliable for a velocity higher than 0.1 m/s (20 fpm). The
measuring errors for air temperature were 0.8°F ( 0.4 K), including the errors introduced by the
data acquisition systems. The wall and air temperature measurements with the thermocouples and
data logger system have the same errors as the anemometers. The tracer gas was used to simulate
the contaminants released from the two occupants at their head level. The gas detection threshold
–3
was around 10 ppm, which should provided good accuracy for the present investigation.
This paper presents only the results of the slot diffuser and the square ceiling diffuser in
detail, because these two diffusers are very widely used and have different flow characteristics.
They are good representatives of the eight diffusers studied. The results for other diffusers will
be discussed to draw general conclusions.

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HVAC&R RESEARCH
Slot (Linear) Diffuser
Figure 3 shows the installation position of the slot diffuser and the chamber layout used for
the CFD simulations. The number of control volumes used for the simulations were 44 × 26 ×
24, 59 × 38 × 33, and 72 × 53 × 44; because grid independence was found with a grid resolution
of 59 × 38 × 33 and finer, the results with this resolution are presented. This grid number is com-
parable to that used for a room without diffusers, such as for natural convection. This also
implies that the method to simulate the diffuser does not increase the computing time. There-
fore, this method provides good grid economy and is computationally efficient.
Figure 2E shows the slot (linear) diffuser. The diffuser has openings that discharge parallel
plane jets. The jets merged at a short distance from the diffuser because of the small separation
distance (3/4 in. or 19 mm) between the openings. According to the manufacturer’s catalog, the
jet will be discharged horizontally without separation, as shown in Figure 4. Smoke visualiza-
tion showed that the jet was about 45° downward to the rear wall (x = 0 plane in Figure 3) before
Figure 3. Positions of Supply Diffusers in Test Chamber
Figure 4. Airflow Pattern from Slot Diffuser Manufacturer’s Catalog

VOLUME 8, NUMBER 3, JULY 2002
283
Figure 5. Simulation of Slot Diffuser with (A) Momentum Method,
(B) Box Method, and (C) Tiny Box Method
it was reattached to the ceiling at 8 in. (203 mm) from the diffuser. Because the jet attached to
the upper sidewall as well (y = 0 plane in Figure 3), the overall jet flow was towards the upper
right corner of the room.
Both the momentum and box methods were used to simulate the diffuser. The momentum
method set the initial jet at 45° downwards over an area of 4 × 46 in. (100 × 1168 mm), as shown
in Figure 5A.
With the box method, the measured data close to the diffuser were used to specify the boundary
conditions because no jet formulas are available for this diffuser. This study used two types of box
methods. The first method uses the measured data of the air temperature and velocity at 14 in. (356
mm) downstream from the diffuser, as shown in Figure 5B. At this position, the jets have merged
into an attached single jet. The box height shown in Figure 5B covers the downstream section,
because our measurements in the opposite direction found very low air velocities [an average of
60 fpm (0.3 m/s)] at 2 in. (51 mm) underneath the diffuser. The low velocity is because of jet
entrainment. The experiment measured the air velocity and temperature at 15 points on the box
front surface. The data were used directly as the boundary conditions for the CFD simulation. The
other box surfaces were modeled as zero-pressure, zero-gradients boundaries.
One major problem associated with the box method is how to specify the SF concentration at
6
the box surface. The tracer-gas distribution was not uniform in front of the diffuser. It would
take a long time to measure the SF concentration at the 15 points where the air velocity and
6
temperature were measured, so this method is likely to be impractical. Therefore, the tracer-gas
concentration was not simulated with the box method.
This investigation also used a tiny box for the slot diffuser. The box was so small that the tem-
perature and tracer-gas concentration at the box surface could be estimated without measure-
ments from the energy and species balance. The average air velocity over the entire supply
surface was used as the boundary condition for the CFD modeling. Srebric and Chen (2001a)
showed details on how to determine the box size and the corresponding flow and thermal bound-
ary conditions with the tiny box method. With this method, peripheral jet velocities at the front
surface of the box lower than 80 fpm (0.4 m/s) are neglected. Figure 5C shows the dimension of
the tiny box. Although the size of the two boxes is very close, they are very different: the tiny
box does not contain any recirculated flow, so the boundary conditions for temperature and SF
6
concentration can be easily determined, according to the method described in Srebric and Chen
(2001a).
Figures 6, 7, and 8 present the calculated results of the air velocities, air temperatures, and
SF concentrations in the room, respectively. The corresponding experimental data are used in
6
the figures for the validation of the numerical results.

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HVAC&R RESEARCH
Figure 6. Comparison of Calculated and Measured Velocity Profiles for
Slot Diffuser at Five Positions in Room
Z = height/total room height (H), U = velocity/supply velocity (U ),
0
H = 2.43 m, U = 3.9 m/s
0
The calculated air velocities agree reasonably with the measured data, as shown in Figure 6.
The discrepancies between the computed and measured results appear larger for poles 4 and 5
than for the other poles. In fact, the discrepancies are the same order of magnitude, but both
poles 4 and 5 use a smaller coordinate scale. Most of the discrepancies are within the error
caused by the omnidirectional anemometers [10 fpm (0.05 m/s)]. The computed velocity pro-
files with the box method and the tiny box method do not show correct results on the upper part
of pole 3 because pole 3 is located within the box, and so no computed data are available. There-
fore, zero velocity is plotted in the figure, although the measurements and the momentum
method show a high velocity.
The momentum method failed to predict the jet development. The jet decay predicted was too
fast, as shown in the upper part of poles 1 and 2, and the results are much worse if the grid num-
ber is reduced. In many cases, the jet may drop earlier than the designed value in a variable air
volume system. Correct prediction of the jet is crucial for thermal comfort design. Therefore, the
performance of the momentum method is not satisfactory in predicting the air velocity. The
exact reason for the error in the momentum method is not clear.

VOLUME 8, NUMBER 3, JULY 2002
285
Figure 7. Comparison of Calculated and Measured Temperature Profiles
for Slot Diffuser at Five Positions in Room
Z = height/total room height (H), θ = (T – T )/(T – T )
in
out
in
H = 2.43 m, supply air temperature T = 16.3°C, exhaust air temperature T = 21.4°C
in
out
The tiny box method could not predict the jet flow because of the flat velocity profile used at
the supply surface. Figure 6 clearly shows that the flat jet velocity profile occurs at pole 2, which
is 1.5 ft (0.45 m) in front of the box. The flat velocity profile also has a significant impact on the
calculated jet temperatures (Figure 7). To improve the results, the measured velocity profiles
should be used in the tiny box method, which would require more time because of the need for
more data. Nevertheless, the balance treatment for the temperature and concentration can be
used in the tiny box method to predict a reasonably good concentration profile, as shown in
Figure 8.
Figure 7 shows the computed and measured temperature profiles. The computed profiles are
in agreement with data in the recirculation region. However, the performance in predicting the
temperature in the jet region is very different. The momentum method and the tiny box method
predicted too low an air temperature profile (see poles 1 and 2 in Figure 7). The jet temperatures
were underpredicted because the calculated jet velocities were higher than the measured ones,
implying a poorer mixing with the surrounding air. The results with the tiny box method
improved if a velocity profile at the box surface is used instead of a single value. Using the
box method with the velocity profile, which was simulated by 15 patches, allowed accurate

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HVAC&R RESEARCH
Figure 8. Comparison of Calculated and Measured SF Concentration Profiles
6
for Slot Diffuser at Five Positions in Room
Z = height/total room height (H), C = (c – c )/(c – c ), H = 2.43 m, supply SF concentration
in
out
in
6
c = 0.0327 ppm (mg/kg), exhaust SF concentration c = 0.5546 ppm (mg/kg)
in
6
out
description of the boundary conditions for this diffuser. Clearly, the box method performs better
than the momentum method in this case.
Because of the difficulties in specifying the boundary conditions for the box method, only the
momentum and the tiny box method were used to calculate the tracer-gas concentration profiles
(see Figure 8). With the momentum method, the supply boundary condition from the diffuser,
such as the zero concentration, was easily specified at the inlet. The tiny box method can use a
zero concentration, because the flow at the box surface has not mixed with the room air. How-
ever, the zero-concentration assumption cannot be used in the box method, because some room
air has mixed with the inflow at the box surface.
Even the sharp gradient of the tracer-gas in pole 1 where the tracer gas source is closely
located was well predicted (see Figure 8). Normally, a point source creates a locally high gradi-
ent of tracer gas concentration that is difficult to predict numerically. The momentum method
failed to predict the tracer-gas concentration at pole 2 because the method overpredicts the con-
vection around the tracer gas source due to the overpredicted jet momentum. The performance
of the tiny box method was better.
The results from the momentum method, the box method, and the tiny box method establish
that accuracy in simulating boundary conditions for a complex diffuser is proportional to the

VOLUME 8, NUMBER 3, JULY 2002
287
Figure 9. (A) Flow Visualization for Square Ceiling Diffuser, (B) Velocity Information
for Momentum Method, and (C) Box Size for Box Method
labor in describing the diffuser. There is always a tradeoff between accuracy and labor for this
particular diffuser. For better accuracy, the box method or the tiny box method with supply
velocity profile should be used for the slot diffuser.
Square Ceiling Diffuser
The square ceiling diffuser discharges jets in four cross and four diagonal directions, as shown
in Figure 9A. The simulation of the square diffuser used both the momentum and the box meth-
ods. Figure 9B shows schematically how the flow direction needs to be described for the diffuser
in the momentum method, and Figure 9C shows the box size used in the box method for the dif-
fuser. The box method requires a high labor effort because it specifies flow information in four
surfaces, whereas the momentum method requires only the flow information on one surface.
Because the jets from the diffuser are very thin [around 2 in. (50 mm)], the sharp velocity gra-
dient makes measurement more difficult. In this case, the box method used 40 measured veloci-
ties and a uniform temperature obtained from the heat balance for the box boundaries. The
momentum method used a discharge velocity for the entire diffuser surface as the momentum
source. The discharge velocity is an averaged maximum velocity measured at the perimeter of
the diffuser. The flow direction specified in the momentum method was obtained from the
smoke visualization. The air temperature used was the same as the supply air temperature in the
duct.
The calculations used a 48 × 40 × 33 grid distribution that is grid-independent with a grid res-
olution comparable to a case without diffuser so that it is computationally efficient. Figure 10
compares the measured and calculated air velocities with the two methods at five positions in
the room. The right bottom figure shows the floor plan. The two methods gave similar results,
although the momentum method performed better in areas near poles 4 and 5, which were close
to the diffuser. Because the velocity was measured with omnidirectional anemometers, the ane-
mometers have a great uncertainty in measuring low air velocity because the natural convection

288
HVAC&R RESEARCH
Figure 10. Comparison of Calculated and Measured Velocity Profiles
for Square Ceiling Diffuser at Five Positions in Room
Z = height/total room height (H), U = velocity/supply velocity (U ),
0
H = 2.43 m, U = 5.2 m/s
0
from the heated probes generated a false velocity of the same magnitude. The estimated measur-
ing error is also shown in the figure.
The box method overpredicted the air velocity along the jet region, although the measured
data were used to specify the boundary conditions. The reason is not clear. Because of this over-
predicted velocity in the jet region, the corresponding temperature predicted with the box
method is lower than the measured one, as shown in Figure 11. However, the two methods cor-
rectly predicted the air temperature in the occupied zone. This was expected, because the room
airflow is well mixed and the energy balance ensures a correct mean air temperature.
This investigation also validated the predicted tracer-gas concentration using the experimen-
tal data, as illustrated in Figure 12. The computed results are only for the momentum method.
The results show a uniform distribution of the tracer-gas concentration in the entire chamber,
and the agreement between the computed results and the experimental data is good. The box
method can also be used to calculate the tracer-gas concentration distribution with species bal-
ance, because the box used is very small. Because it is a well-mixed condition, a similar result is
anticipated, as indicated in the temperature prediction.

VOLUME 8, NUMBER 3, JULY 2002
289
Figure 11. Comparison of Calculated and Measured Temperature Profiles
for Square Ceiling Diffuser at Five Positions in Room
Z = height/total room height (H), θ = (T – T )/(T – T ), H = 2.43 m,
in
out
in
supply air temperature T = 14.5°C, exhaust air temperature T = 24.1°C
in
out
The results show that both the momentum and box methods predicted good results for the
square ceiling diffuser. The momentum method is recommended because it is simpler to specify
the boundary conditions for this method.
This study also used another square ceiling diffuser from a different manufacturer. The pur-
pose of the added study was to identify whether the results obtained for the first diffuser were
universal. The results, although not shown here, indicated that the difference in room air veloc-
ity is within the measuring errors. The two temperature fields are nearly identical.
DISCUSSION
The slot and square ceiling diffusers produced well-mixed flow field in the entire chamber
that resulted in uniform velocity, temperature, and tracer-gas concentration distributions. The
simplified methods for diffuser simulations were able to predict the main properties of the flow,
temperature, and contaminant concentration fields. However, the accuracy of the simplified
methods is a function of the amount of data incorporated in the modeling. Two simplified meth-
ods for diffuser modeling, the box and momentum methods, were tested.
The box method, that requires measured resultant velocities, temperatures and concentration
distribution at the box surface is the most accurate, although probably not very practical. For

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HVAC&R RESEARCH
Figure 12. Comparison of Calculated and Measured SF Concentration Profiles
6
for Square Ceiling Diffuser at Five Positions in Room
Z = height/total room height (H), C = (c – c )/(c – c ), H = 2.43 m, supply SF concentration
in
out
in
6
c = 0.0492 ppm (mg/kg), exhaust SF concentration c = 1.0496 ppm (mg/kg)
in
6
out
example, the square ceiling diffuser has attached ceiling jets that are very thin [about 2 in. (50
mm)], and the gradients for all air parameters in the jet region are very large. Therefore, taking
accurate measurements to obtain the data for the box method is tedious, and the flow directions
may not be as easily determined with the smoke visualization due to the high velocities. Further-
more, the specification of the box boundary conditions is time consuming because the jets
spread in all radial directions from the square diffuser.
A modified version of the box method called the tiny box method was developed that used a
relatively small box and a measured resultant velocity field to specify the diffuser boundary con-
ditions. The boundary conditions for supply temperature and contaminant concentration are cal-
culated from energy and species balance for the tiny box (Srebric and Chen 2001a). The tiny box
method produces similar results as the original box method, while using a minimal amount of
measured data.
The momentum method requires only a discharge velocity or effective diffuser area, which is
sometimes available in manufacturer catalogs; it is the simplest method and produced good
results for the square diffuser. Therefore, the momentum method is preferred and recommended
over the box method for this diffuser. However, if the jet development in front of a diffuser is

VOLUME 8, NUMBER 3, JULY 2002
291
Table 2. Summary for Simplified Diffuser Modeling
Diffusers
Box Method
Good
Momentum Method
Recommended Method
Box
Nozzle
Poor
Poor
Slot (linear)
Valve
Good
Box
Good
Poor
Box
Displacement
Square ceiling
Round ceiling
Vortex ceiling
Grille
Poor
Good
Good
Good
Good
Good
Momentum
Momentum
Momentum
Momentum
Momentum
Good
Good
Good
Good
complex, such as in the case of slot diffuser, then the momentum method is not sufficiently
accurate and the box method is recommended.
Only results for slot (linear) and square ceiling diffusers are presented here, although eight dif-
ferent kinds of diffusers have been investigated. Table 2 shows the recommended methods for
each of the eight different diffusers we have studied. It is possible to classify diffusers into three
groups based on the method to employ: only the momentum method, only the box method, and
both methods. The diffusers for which these methods are suitable are discussed in the following.
The Momentum Method
The table shows that only the momentum method can be used for the displacement diffuser.
Yuan et al. (1999) used the momentum method to predict airflow, air temperature, and contami-
nant concentration in a room with the displacement diffuser. The results are in very good agree-
ment with the experimental data. Figure 13 presents the computed and measured velocity profile
in the middle of the room for the present study, also available in Srebric and Chen (2001b). The
displacement diffuser produces stratified distributions of air temperature and contaminant con-
centrations. The agreement between measured and calculated temperatures is very good, even in
the jet region. The prediction of the contaminant concentrations shows some discrepancies
between measurements and calculations. The discrepancies are due to difficulties in simulating
contaminant sources that are point sources and have an initial momentum.
The reason for the failure of the box method is that the buoyancy force plays an important role
in the jet development. The jet flow and air temperature change rapidly in the diffuser vicinity.
Measurements for the jet development would have to be performed under nonisothermal condi-
tions. For nonisothermal conditions, the data could only be used to simulate the diffuser in a
room with the same thermal conditions as the measured ones. Any change in the room geometry
and/or heat sources could have a significant influence on the data. The application would be
very limited, so the box method is not recommended for the displacement diffuser.
The Box Method
For the nozzle, slot, and valve diffusers, the box method can simulate the boundary conditions
better than the momentum method: the flow mixing is too complex for the momentum method
to handle. The flow develops, merges, and combines in front of the diffusers to form a devel-
oped jet. The momentum method may not be appropriate to represent the complexity of the flow
field in front of the diffusers. To simulate this flow properly, a very fine grid resolution is
required, although it may not provide a correct prediction of the airflow pattern, as in the case of
the nozzle diffuser (Emvin and Davidson 1996). Furthermore, for the valve diffuser, the
momentum method was very sensitive to the discharge angle. Therefore, the box method is rec-
ommended for simulating these complex diffusers, as it is more stable and reliable.

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Figure 13. Comparison of Calculated and Measured Velocity Profiles
for Round, Vortex, Grille, Displacement, and Nozzle in Typical Location in Room
Z = height/total room height (H), U = velocity/supply velocity (U )
0
Figure 13 shows the velocity profiles in the middle of a room predicted with the box method
for the nozzle diffuser, in addition to the slot diffuser reported in Figure 6. The valve diffuser
had only qualitative comparison between calculated and measured velocities and airflow pattern
because the detailed measured data were available only in the vicinity of the diffuser. The
present study used the experimental data from the literature for the nozzle and valve diffuser.
The corresponding room size and thermal and flow conditions are different from those used for
the other diffusers. The results shown in Figure 13 confirm that the box method is capable of
providing satisfactory results for room air distribution design. Srebric (2000) and Chen and
Srebric (2000) have provided more detailed validation of the nozzle and valve diffusers.
Momentum and Box Methods
Among the eight diffusers studied, both the momentum and box methods can be used to pre-
dict room airflow with the square ceiling, round ceiling, vortex, and grill diffusers. The round
ceiling diffuser discharges a radial jet attached to the ceiling in a very thin layer [around 2 in.
(50 mm)]. The jet is similar to the one created by the square ceiling diffusers. The momentum
and box methods are expected to perform the same for the round ceiling diffuser as for the
square diffuser. Figure 13 illustrates the velocity profile in the middle of the room with the dif-
fuser, predicted with the momentum method by Srebric and Chen (2001b). Figure 13 also shows
the velocity profiles in the middle of the room for the vortex and grille diffuses. The results were

VOLUME 8, NUMBER 3, JULY 2002
293
obtained with the momentum method. Again, they agree with the experimental data. The calcu-
lated temperature field agreed very well with the measured data for all diffusers in this group.
The calculations and measurements of the contaminant concentrations show discrepancies simi-
lar to the one in Figure 12. The probable cause of the discrepancies is the nature of the contami-
nant sources used for the experiments that are point sources with an initial momentum.
With the box method (Chen and Srebric 2000), the computed airflow agreed with the experi-
mental data. The accuracy is similar to that with the momentum method. Although both methods
are good, the momentum method is recommended because it is simpler.
The present study has limitations. Although the eight diffusers tested represent a wide variety
of the diffusers available on the market, this investigation does not ensure that the results can be
extended to a diffuser of similar kind. In some cases, cluster diffusers may be used for a large
space. The impact of one diffuser on the other has not been examined. Furthermore, the jets
from the diffusers are free from the interference of obstacles, such as beams and columns. The
impact of the obstacles on the two methods needs further study. Turbulence intensity is a key
parameter for draft impact on airflow and its model formulation needs investigation.
CONCLUSIONS
The objective of this research was to develop a simplified methodology for specifying bound-
ary conditions of air supply diffusers for CFD simulations. Two simplified methods, the
momentum and box methods, have been compared with the measured data to assess their accu-
racy and reliability. The measured data were obtained from a state-of-the-art experimental facil-
ity and from the literature.
Numerical simulations of the diffusers can employ a simplified modeling technique by using
the resultant momentum from the diffusers without the detailed diffuser geometry representa-
tion. The modeling of the resultant momentum can be made at the diffuser surface with the
momentum method, or in front of the diffuser in the direction of the jet discharge with the box
method. The momentum method is simpler than the box method in terms of the effort required
to specify the data for modeling.
The momentum method is recommended for the displacement diffuser and mixing diffusers
that discharge combined jets. Mixing diffusers such as the nozzle, slot, and valve diffusers,
which discharge several jets that merge and combine in front of them, should use the box
method because the momentum method performs poorly.
With a proper box size, the data required for the box method, such as temperature and con-
taminant concentration distributions (but not the air velocity distribution), can be eliminated.
Simplified diffuser modeling requires measurement of some of the parameters necessary for
the simulations or detailed information from a product catalog.
NOMENCLATURE
A
m
diffuser effective area
mass flow rate
Φ
1 for mass continuity
o
·
V ( j = 1, 2, 3) for three components of momentum
j
S
source term
k for turbulent energy
Φ
t
U
V
time
ε for the dissipation rate of k
T for energy transport
air velocity specified in the CFD simulation
velocity vector
o
C for contaminant concentration i
i
Γ
effective diffusion coefficient
ρ
air density
Φ,eff
REFERENCES
ASHRAE. 1992. Thermal Environmental Conditions for Human Occupancy. ANSI/ASHRAE Standard
55-1992. American Society of Heating, Refrigerating and Air-Conditioning Engineers.
CHAM. 1998. PHENICS Version 3.1. CHAM Ltd., London, U.K.

294
HVAC&R RESEARCH
Chen, Q. 1995. ASHRAE Handbook Part B: Fundamentals, Comparison of Different k-ε Models for
Indoor Airflow Computations. Numerical Heat Transfer 28:353-369.
Chen, Q. and Z. Jiang. 1996. Simulation of a Complex Air Diffuser with CFD Technique. Proceedings of
ROOMVENT ’96 1:227-234.
Chen, Q. and A. Moser. 1991. Simulation of a Multiple-Nozzle Diffuser. Proceedings of 12th AIVC Con-
ference 2:1-14.
Chen, Q. and J. Srebric. 2000. Simplified Diffuser Boundary Conditions for Numerical Room Airflow
Models. Final Report for ASHRAE RP-1009. Department of Architecture, Massachusetts Institute of
Technology, Cambridge.
Emvin, P. and L. Davidson. 1996. A Numerical Comparison of the Diffuse in Case E1 Annex20. Proceed-
ings of ROOMVENT ’96, 1:219-226.
Fan, Y. 1995. CFD Modeling of the Air and Contaminant Distribution in Rooms. Energy and Building
23:33-39.
Heikkinen, J. 1991. Modeling of a Supply Air Terminal for Room Airflow Simulation. Proceedings of 12th
AIVC Conference, 3:213-230.
Heikkinen, J. and K. Piira. 1994. CFD Computation of Jets from Circular Ceiling Diffusers. Proceedings of
ROOMVENT ’94, 1:329-344.
Huo, Y., J. Zhang, C. Shaw, and F. Haghighat. 1996. A New Method to Describe the Diffuser Boundary
Conditions in CFD Simulation. Proceedings of ROOMVENT ’96, 2:233-240.
IEA. 1993. Annex 20: Room Air and Contaminant Flow, Evaluation of Computational Methods, Subtask-1,
Summary report. Edited by A.D. Lemaire. TNO Building and Construction Research, Delft.
Jacobsen, T.V. and P.V. Nielsen. 1993. Numerical Modeling of Thermal Environment in a Displace-
ment-Ventilated Room. Proceedings of Indoor Air ’93:5.
Joubert, P., A. Sandu, C. Beghein, and F. Allard. 1996. Numerical Study of the Influence of Inlet Boundary
Conditions on the Air Movement in a Ventilated Room. Proceedings of ROOMVENT ’96, 1:235-242.
Moser, A. 1991. The Message of Annex 20: Air Flow Patterns Within Buildings. Proceedings 12th AIVC
Conference.
Nielsen, P.V. 1989. Representation of Boundary Conditions at Supply Openings. IEA, Annex 20, Research
Item 1.11.
Nielsen, P.V. 1997. The Box Method—A Practical Procedure for Introduction of an Air Terminal Device in
CFD Calculation. Institute for Bygningsteknik, Aalborg Universite, Denmark.
Patankar, S.V. 1980. Numerical Heat Transfer and Fluid Flow. New York: Hemisphere Publishing.
Regard, M., F.R. Carrie, A. Voeltzel, and V. Richalet. 1995. Measurement and CFD Modeling of IAQ
Indices. Proceedings of 16th AIVC Conference.
Skovgaard, M. and P.V. Nielsen. 1991. Modeling Complex Inlet Geometries in CFD—Applied to Airflow
in Ventilated Rooms. Proceedings of 12th AIVC Conference, 3:183-200.
Srebric, J. 2000. Simplified Methodology for Indoor Environment Design. Ph.D. dissertation, Department
of Architecture, Massachusetts Institute of Technology, Cambridge.
Srebric, J. and Q. Chen. 2001a. A Method of Test to Obtain Diffuser Data for CFD Modeling of Room Air-
flow. ASHRAE Transactions 107(2).
Srebric, J. and Q. Chen. 2001b. Boundary Conditions for Diffusers in Room Air Distribution Calculations.
Proceedings of CLIMA 2000, Napoli.
Versteeg, H.K. and W. Malalasekera. 1995. An Introduction to Computational Fluid Dynamics. London:
Longman.
Vogel, P., E. Richter, and M. Rosler. 1993. The Effect of Various Inlet Conditions on the Flow Pattern in
Ventilated Rooms—Measurements and Computations, Proceedings of the 14th AIVC Conference.
Yakhot, V., S.A. Orszag, S. Thangam, T.B. Gatski, and C.G. Speziale. 1992. Development of Turbulence
Models for Shear Flows by a Double Expansion Technique. Physics Fluids A 4(7):1510-1520.
Yuan, X., Q. Chen, L.R. Glicksman, Y. Hu, and X. Yang. 1999. Measurements and Computations of Room
Airflow with Displacement Ventilation. ASHRAE Transactions 105(1):340-352.
Zhang, J.S., L.L. Christianson, G.J. Wu, and R.H. Zhang. 1992. An Experimental Evaluation of a Numeri-
cal Simulation Model for Predicting Room Air Motion, Proceedings of Jacques Cartier Conference.