Heat and Mass Transfer of a Energy
Recovery Ventilator (ERV)
by
Roy Pastor
An Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING
Major Subject: MECHANICAL ENGINEERING
Approved:
_________________________________________
Norberto Lemcoff, Primary Project Adviser
_________________________________________
Ernesto Gutierrez-Miravete, Secondary Project Adviser
Rensselaer Polytechnic Institute
Hartford, Connecticut
December, 2010
(For Graduation January 2011)
i
© Copyright 2010
by
Roy Pastor
All Rights Reserved
ii
CONTENTS
LIST OF TABLES ............................................................................................................. v
LIST OF FIGURES .......................................................................................................... vi
ACKNOWLEDGMENT ................................................................................................. vii
NOMENCLATURE ....................................................................................................... viii
ABSTRACT ..................................................................................................................... ix
1. INTRODUCTION ....................................................................................................... 1
1.1
Background ........................................................................................................ 1
1.2
Previous Work.................................................................................................... 2
1.3
Problem Description........................................................................................... 3
2. METHODOLOGY ...................................................................................................... 5
2.1
Physical Model ................................................................................................... 5
2.2
Mathematical Model .......................................................................................... 5
2.2.1
Fluid Dynamics ...................................................................................... 6
2.2.2
Heat Transfer .......................................................................................... 6
2.2.3
Mass Transfer ......................................................................................... 6
2.2.4
Boundary Conditions ............................................................................. 7
2.2.5
Heat Transfer Effectiveness ................................................................... 8
3. FINITE ELEMENT MODEL ...................................................................................... 9
3.1
ERV Dimensions and Parameters ...................................................................... 9
3.2
Fluid Dynamics ................................................................................................ 10
3.3
Heat Transfer .................................................................................................... 11
3.4
Convection and Diffusion ................................................................................ 11
3.5
Meshing ............................................................................................................ 11
4. RESULTS .................................................................................................................. 13
4.1
Problem Scenarios............................................................................................ 13
4.2
Summer and Winter Conditions with Equal Supply and Exhaust Flow .......... 13
iii
4.3
4.4
4.5
4.2.1
Summer Conditions.............................................................................. 13
4.2.2
Winter Conditions ................................................................................ 19
Summer and Winter Conditions with Varying Exhaust Flow ......................... 22
4.3.1
Summer Conditions.............................................................................. 22
4.3.2
Winter Conditions ................................................................................ 25
ERV Effectiveness as the Exhaust Height is Varied ........................................ 27
4.4.1
Summer Conditions.............................................................................. 27
4.4.2
Winter Conditions ................................................................................ 27
ERV Effectiveness as the Diffusion through the Membrane is Varied ........... 28
4.5.1
Summer Conditions.............................................................................. 28
4.5.2
Winter Conditions ................................................................................ 28
5. CONCLUSION.......................................................................................................... 29
6. REFERENCES .......................................................................................................... 30
7. APPENDIX A ............................................................................................................ 31
7.1
Sensible and Latent Effectiveness Calculation ................................................ 31
iv
LIST OF TABLES
Table 1. ERV Basic Dimensions ....................................................................................... 9
Table 2. Supply Parameters for Summer and Winter Seasons ......................................... 9
Table 3. Exhaust Parameters for Summer and Winter Seasons ...................................... 10
Table 4. Membrane Properties and Parameters .............................................................. 10
Table 5. Elements Spacing of the ERV .......................................................................... 11
Table 6. Sensible and Latent Effectiveness for Summer Conditions at Equal Speed .... 13
Table 7. Sensible and Latent Effectiveness for Winter Conditions at Equal Speed ....... 19
Table 8. Sensible and Latent Effectiveness at Varying Exhaust Flow (Summer) .......... 22
Table 9. Sensible and Latent Effectiveness at Varying Exhaust Flow (Winter) ............ 26
v
LIST OF FIGURES
Figure 1. Schematic of a Cross-Flow Membrane ERV [2] .............................................. 3
Figure 2. Schematic of a Quasi-Counter Flow Membrane ERV [4] ................................ 3
Figure 3. Schematic of a Countercurrent Flow Membrane ERV ..................................... 4
Figure 4. Schematic of a Cocurrent Flow Membrane ERV.............................................. 4
Figure 5. Pictorial Description of the Mathematical Model ............................................. 7
Figure 6. Summer Sensible Effectiveness for ERVs ...................................................... 14
Figure 7. Summer Latent Effectiveness for ERVs ......................................................... 14
Figure 8. Countercurrent Flow Temperature Profile at Varying Channel Location....... 15
Figure 9. Cocurrent Flow Temperature Profile at Varying Channel Location ............... 16
Figure 10. Countercurrent Flow Concentration Profile at Varying Channel Location .. 17
Figure 11. Cocurrent Flow Concentration Profile at Varying Channel Location........... 18
Figure 12. Winter Sensible Effectiveness for ERVs ...................................................... 20
Figure 13. Winter Latent Effectiveness for ERVs .......................................................... 20
Figure 14. ERV’s Temperature Profile at x = 1.25 m .................................................... 21
Figure 15. ERV’s Concentration Profile at x = 1.25 m .................................................. 21
Figure 16. Temperature Profile at Varying Exhaust Flows (Countercurrent) ................ 23
Figure 17. Temperature Profile at Varying Exhaust Flows (Cocurrent) ........................ 23
Figure 18. Concentration Profile at Varying Exhaust Flows (Countercurrent) .............. 24
Figure 19. Concentration Profile at Varying Exhaust Flows (Cocurrent) ...................... 24
Figure 20. Summer Sensible Effectiveness for ERVs with Varying Exhaust Flow ....... 25
Figure 21. Summer Latent Effectiveness for ERVs with Varying Exhaust Flow .......... 25
Figure 22. Winter Sensible Effectiveness for ERVs with Varying Exhaust Flow ......... 26
Figure 23. Winter Latent Effectiveness for ERVs with Varying Exhaust Flow ............ 27
vi
ACKNOWLEDGMENT
Type the text of your acknowledgment here.
vii
NOMENCLATURE
c
water concentration in membrane (kg/m3)
cp
specific heat, J / kg K
d
channel height or membrane spacing, m
D
diffusivity, m2/s
F
volume force field, N
h
convective heat transfer coefficient, m/s
k
thermal conductivity, W/m K
L
channel length
Q
heat source, W
R
reaction rate, mol/m3 s
T
temperature, C or K
U
overall heat transfer coefficient, W / m2 K
u
velocity field, m/s
x,y,z
coordinates
Greek Symbols
ts
time scaling coefficient

Density, kg/m3

dynamic viscosity, kg/m s
Subscripts
ave
average
e
exhaust
i
inlet
L
latent
o
outlet
s
supply
S
sensible
viii
ABSTRACT
The purpose of this project is to evaluate the effectiveness of an energy recovery
ventilator (ERV) during the summer and winter seasons. The two configurations that
were used for this analysis are the countercurrent and cocurrent flows.
To better
understand the ERV, the following parameters were varied: flows through the supply
and exhaust duct, flows through the exhaust duct only, height difference through one of
the duct, and diffusion through the membrane. Based on the analysis, it was determined
that the countercurrent flow configuration is more effective than the cocurrent flow
configuration. The effectiveness increases as the velocity decreases given equal and
supply and exhaust channel flows. If the exhaust flow is varied from the supply channel
flow, the effectiveness increases as the exhaust flow decreases.
The effectiveness
through the ERV increases as the height of the exhaust channel decreases at a constant
mass flow rate.
Lastly, as the diffusion rate through the membrane increases, the
effectiveness of the ERV also increases.
ix
1. INTRODUCTION
1.1 Background
In recent years, there was an increase in the need to conserve energy. Therefore, there is
a push in many engineering systems to use less energy, while maintaining the same
functions and exceeding the performance required by earlier systems. As in the case for
heating, ventilating, and air conditioning (HVAC) systems, that are required to provide
comfort and quality air for occupants in buildings or offices, within reasonable
installation, operation, and maintenance costs.
A traditional HVAC system will typically consists of coils, fans, heaters, ducts, and
filters. The purpose of the coil is to reduce the air temperature and control the humidity
of the incoming air, which is vital for dehumidification. The fan is the driving force to
allow the conditioned air to flow through the ducts in buildings or offices. A heater is
used to control the thermal comfort in the space, and heat the cool air that passes through
the cooling coil. The ducts are used to distribute conditioned air to various locations in a
building. To provide quality air, a filter is be used to prevent airborne bacteria, dust, or
odors that may exist in the outside air, to be distributed in the conditioned spaces.
Using a traditional HVAC system for buildings that require high volume of outside air
for heating and cooling will require more powerful ventilation systems to meet the
demands of newer buildings. This can be accomplished by using larger coils, fans,
and/or heaters. Superior ventilation systems will increase operating and equipment
costs. Therefore, a larger system is not a viable solution for conserving energy and
meeting system needs.
In fact, one of the major costs for ventilation systems is the dehumidification of
incoming air from the outside environment. That reason is because the outside air must
first past through a cooling coil where it is cooled below the saturation temperature of
the air to allow condensation. The cold air must then be reheated, since the conditioned
space requires a higher temperature to meet the proper thermal comfort (21°C, 30-60%
Relative humidity [1]). As a result, limiting the usage of cooling coils and heaters not
only reduces the energy cost but also the maintenance cost required to maintain a proper
HVAC system.
1
1.2 Previous Work
To reduce the energy consumption of ventilation systems, research in areas such as airto-air energy recovery ventilator (ERV) or enthalpy exchanger is being carried out. The
ERV allows ventilation systems to reduce energy consumption because it uses
conditioned air that is normally exhausted out of the buildings, to either heat or cool
(sensible heat) and humidify or dehumidify (latent heat) incoming air taken from
outside. Therefore, this allows the ERV to be used during all the seasons. The moisture
and heat transfer is possible because the water vapor-permeable membrane or plate
located between the conditioned and supplied air, allows the heat and moisture to pass
through the membrane or plate. The cost of a ventilation system will also be reduced,
because an ERV does not have the complexity generally found in rotary dehumidifiers or
cooling coils. The simplified design of the ERV also reduces the maintenance cost,
because it does not have any moving parts that can wear over time and only routine
cleaning is required. Therefore the ERV allows the ventilation system demands to grow,
while maintaining air quality required by buildings and offices mandated by state and
local codes based on ASHRAE standards, but does not increase the energy consumption
of a ventilation system.
The most common ERV design found in the market is the cross flow design, due to its
simplified design, and the ease of duct sealing required for ERV systems. A depiction of
a cross flow ERV design is shown below in Figure 1. Due to the popularity of cross
flow ERV systems Zhang et al. [2] analyzed the heat and mass transfer in an ERV
through the use of numerical analysis and conducting a test of a commercial product in a
test lab. Min et al. [3] analyzed the performance of ERV by changing the membrane
spacing and thickness of the ventilator through numerical computation.
2
Figure 1. Schematic of a Cross-Flow Membrane ERV [2]
Another type of ERV design that has been studied is a quasi-counter flow design ERV.
A schematic of a quasi-counter flow design is shown in Figure 2. Due to the lack of
research in countercurrent flow ERV design, Zhang [4] conducted a study of an ERV
with a quasi-counter flow design, because a countercurrent flow membrane ERV has a
much higher effectiveness than a cross flow design.
Figure 2. Schematic of a Quasi-Counter Flow Membrane ERV [4]
1.3 Problem Description
Based on previous research of ERV systems, it was determined that countercurrent and
cocurrent flows ERV have not been evaluated significantly. Therefore, in this paper the
effectiveness of countercurrent and cocurrent flows will be evaluated and compared to
each other. This paper will not focus on the complexity of creating a countercurrent or
cocurrent flow membrane ERV or the cost required to build it. It is assumed that
implementation of countercurrent and cocurrent flows ERV will be feasible. In the
countercurrent flow membrane ERV, the exhaust and supply air flow in opposite
direction, as shown in Figure 3.
3
d
Exhaust Air

Porous Membrane
d
Supply Air
L
Figure 3. Schematic of a Countercurrent Flow Membrane ERV
In a cocurrent flow membrane ERV, the exhaust and supply air flow in the same
direction, as shown in Figure 4:
d
Exhaust Air
Porous Membrane
d

Supply Air
L
Figure 4. Schematic of a Cocurrent Flow Membrane ERV
One study that is conducted in this project is to evaluate the impact of ERV’s
performance by varying the air speed through the supply and exhaust channels. In
addition, the ERV is evaluated by varying the exhaust channel air speed only. This
study is conducted because in most ventilation system some of the conditioned air is
discharged directly out to the environment, in lieu of using the system exhaust ducts.
Another study is to vary the height of the exhaust channel, while maintaining the air
speed through the ERV.
Lastly, the ERV is evaluated by varying the diffusion
coefficient through the membrane. The studies mentioned above will be evaluated for
both summer and winter conditions.
To model the ERV’s performance, the
countercurrent and cocurrent flow will be analyzed in COMSOL.
4
2. METHODOLOGY
2.1 Physical Model
A typical membrane-based ERV with countercurrent or cocurrent flows are shown in
Figures 3 and 4, respectively. The ERV design that will be analyzed is a core that
contains alternate layers of membranes to separate and seal the exhaust and supply
airstream passages. As described above, a countercurrent flow ERV is designed such
that the exhaust and supply airstreams flow in opposite direction, while a cocurrent flow
ERV is designed that the exhaust and supply airstreams flow in the same direction. As
the exhaust and supply air flow through the ERV, the airstream will exchange heat and
moisture through the membrane. Since the ERV has a symmetric design, the domain
that will be evaluated will contain only half of the channel volume of the supply and
exhaust airstreams and the membrane, as shown in Figure 3 for countercurrent flow
ERV and Figure 4 for cocurrent flow ERV.
2.2 Mathematical Model
Based on the physical model described above, several assumptions will be made to assist
in the modeling of the countercurrent and cocurrent flow ERV:

Heat and mass transfer process are in steady state

The physical properties of the air and membrane are constant

Heat conduction and vapor diffusion in the two air streams are negligible
compared to the energy transport and vapor convection by bulk flow

Water vapor diffusion in the membrane only occurs in the thickness direction

Temperature and concentration distribution in the thickness direction in
membrane are linear

Heat conductivity and water diffusivity in the membrane are constant
The guideline that was used for the mathematical model was using the modeling guide
documentation provided in the COMSOL software [5].
5
2.2.1
Fluid Dynamics
The governing fluid dynamics equations for the ERV are the momentum transport
equations and the equation of continuity for incompressible fluids:



u
T
   u   u      u    u  p  F


t
 u  0
(1)
(2)
where  is the density,  is the dynamic viscosity, u is the velocity field, p is the
pressure, t is the time, and F is the volume force field. In equation (1), for steady state
problems the first term of the equation is zero. In addition, assuming that the ERV flow
is laminar, no pressure gradient along the channel flow, and free of any force field, then
equation (1) will simplify to:
2u    u   u  0
2.2.2
(3)
Heat Transfer
The governing heat transfer equation (conduction and convection) for the ERV is shown
below:
 ts  c p
T
    k T   Q   c pu  T
t
(4)
where cp is the heat capacity, k is the thermal conductivity, T is the temperature, ts is the
time scaling coefficient, and Q is the heat source. For steady state problems, the first
term of equation of equation (4) is zero. Also, assuming no heat source in equation (4),
the heat transfer equation simplifies to:
  kT    c pu  T
2.2.3
(5)
Mass Transfer
The governing mass transfer equation (diffusion and convection) for the ERV is shown
below:
 ts
c
     Dc  cu   R
t
(6)
6
where c is the concentration, D is the diffusion coefficient, and R is the reaction rate.
Additionally, for steady state problems the first term of equation (6) is zero. Assuming
reaction rate is also zero, then equation (6) simplifies to:
   Dc  cu   0
(7)
A pictorial description of the equations describe above is shown in Figure (5).
Heat
Convection
Desorption
Exhaust Air
Heat Conduction
Heat
Convection
Porous Membrane
Water Diffusion
Supply Air
Adsorption
Figure 5. Pictorial Description of the Mathematical Model
2.2.4
Boundary Conditions
The boundary conditions for the ERV based on the assumptions and the equations
described for the heat and mass transfer are the following for countercurrent flow:
Supply Air:
us
x 0
 usi
Ts
x 0
 Tsi
cs
x 0
 csi
(8)
Exhaust Air:
ue
xL
 u ei
Te
xL
 Tei
ce
x L
 cei
(9)
where e, i, and s in the subscript are the exhaust, inlet, and supply, respectively. For
cocurrent flow, the same boundary conditions are used, however, for the exhaust flow
the boundary is located at x = 0, in lieu of x = L.
7
2.2.5
Heat Transfer Effectiveness
The heat transfer effectiveness of the ERV is a way to measure its ability to transfer
sensible and latent heat. In order to calculate the sensible heat transfer effectiveness, the
sensible heat transfer of the supply and exhaust flow will be divided by two times the
maximum sensible heat transfer possible for this system. The sensible heat transfer
effectiveness is shown below:
S 
 s c psus Tsi  Tso    e c peue Teo  Tei 
2   c pu min Tsi  Tei 
(7)
where o in the subscript is the outlet.
For the latent heat transfer effectiveness a similar approach to that described for the
sensible heat transfer effectiveness will be used, except that the latent heat transfer is
used in lieu of the sensible heat transfer, as the equation is shown below:
L 
 sus  csi  cso    eue  ceo  cei 
2   u  min  csi  cei 
(8)
8
3. FINITE ELEMENT MODEL
3.1 ERV Dimensions and Parameters
Based on the mathematical model described above, a finite element software will be
used to model the ability of the ERV to transfer sensible and latent heat. The software
that will be used for this analysis is COMSOL. The ERV basic dimensions were taken
from Reference [3] and are shown in Table 1.
Table 1. ERV Basic Dimensions
Length (mm)
Height (mm)
Membrane Height (mm)
250
2
0.1
The supply and exhaust parameters for both the summer and winter season were found
by using the data from Reference [6] for air properties typically found on ERV designs.
References [7] and [8] were used to evaluate other parameters required for the finite
element model, based on the data provided by Reference [6].
The data found in
References [6], [7], and [8] are shown in Tables 2 and 3 for the supply and exhaust
streams, respectively.
Table 2. Supply Parameters for Summer and Winter Seasons
Inlet Dry Bulb Temperature (C)
Inlet Dry Bulb Temperature (K)
Inlet Wet Bulb Tempearture (C)
Inlet Dry Bulb Temperature (K)
Relative Humidity (%)
Pressure (mbar)
Density (kg/m^3)
Dynamic Viscosity (kg/m*s)
Thermal Conductivity (W/m*K)
Diffusion (m^2/s)
Concentration Air (mol/m^3)
Concentration Water (mol/m^3)
9
Summer
Winter
35.000
1.700
308.150 274.850
26.000
0.600
299.150 273.750
49.340
82.020
56.280
6.910
1.145
1.284
1.895E-05 1.738E-05
0.026
0.024
2.680E-05 2.120E-05
39.550
44.342
1.085
0.248
Table 3. Exhaust Parameters for Summer and Winter Seasons
Exhaust Dry Bulb Temperature (C)
Exhaust Dry Bulb Temperature (K)
Exhaust Wet Bulb Tempearture (C)
Exhaust Wet Bulb Tempearture (K)
Relative Humidity (%)
Pressure (mbar)
Density (kg/m^3)
Dynamic Viscosity (kg/m*s)
Thermal Conductivity (W/m*K)
Diffusion (m^2/s)
Concentration Air (mol/m^3)
Concentration Water (mol/m^3)
Summer
Winter
24.000
21.000
297.150 294.150
17.000
14.000
290.150 287.150
49.590
45.866
29.850
24.877
1.188
1.200
1.844E-05 1.830E-05
0.025
0.025
2.484E-05 2.436E-05
41.014
41.432
0.600
0.467
The membrane parameters were determined using the average temperatures of the dry
bulb and wet bulb temperatures found for the supply and exhaust data found in Table 3
and 4. To determine the other parameters of the membrane, Reference [7] was used.
The diffusion and the thermal conductivity through membrane were taken from
Reference [4].
Table 4. Membrane Properties and Parameters
Inlet Dry Bulb Temperature (C)
Inlet Dry Bulb Temperature (K)
Inlet Wet Bulb Tempearture (C)
Inlet Dry Bulb Temperature (K)
Density (kg/m^3)
Thermal Conductivity (W/m*K)
Diffusion (m^2/s) Membrane
Concentration (mol/m^3)
Diffusion (m^2/s) Air to H20
Summer
Winter
29.500
11.350
302.650
284.500
21.500
7.300
294.650
280.450
1.160
1.240
0.130
0.130
8.000E-06 8.000E-06
40.269
42.838
2.680E-05 2.272E-05
3.2 Fluid Dynamics
The initial stage of the finite element modeling is to resolve the flow through the ERV
for both countercurrent and cocurrent flows.
The fluid dynamics model that was
selected is the incompressible Naiver-Stokes, steady state model in COMSOL. It was
assumed in this model that the wall of the membrane has a no slip condition, and the
symmetry plane at the center of the channels of the supply and exhaust flows are the
system boundary. The fluid dynamics model is used, because it allows the heat transfer
and convection and diffusion models to be defined. The other two models may be
10
defined by the fluid dynamics model, because the velocity profile is required in their
input to evaluate the heat transfer and convection and diffusion models.
3.3 Heat Transfer
For the heat transfer of the ERV, the conduction and convection, steady state model in
COMSOL was used. In this multiphysics model, COMSOL will solve the heat transfer
in the ERV, by providing data such as the temperature, temperature gradient, and heat
flux. It was assumed in this model that the inner boundaries have continuity through the
membrane and the symmetry plane at the center of the channels of the supply and
exhaust flow has thermal insulation. It will also be assumed that there will be no
velocity flow through the membrane. The heat transfer model will be used to calculate
the sensible effectiveness of the ERV
3.4 Convection and Diffusion
In the final stage of the analysis, the convection and diffusion, steady-state model will be
selected in COMSOL. This model will be used to determine the ability of the ERV to
humidify or dehumidify the air, by defining the diffusion constant for the membrane and
air, and the vapor concentration in the air for both supply and exhaust. In this model the
inner boundaries will also have continuity through the membrane, and the symmetry
plane at the center of the channels of the supply and exhaust flow will be defined as
insulation/symmetry.
3.5 Meshing
To mesh the model, the mapped mesh parameters was be used. This provides more
flexibility and the user has better control in preventing the meshing of the model from
exceeding the computer’s memory that can be used with COMSOL. In order to solve
the ERV in COMSOL, quadrilateral meshes were used, and were divided into equal
spaces as defined below:
Table 5. Elements Spacing of the ERV
d

L
10
10
200
11
Based on the division above, the ERV will have 6000 elements in a quadrilateral meshed
in the model.
12
4. RESULTS
4.1 Problem Scenarios
In order to evaluate the effectiveness of the ERV, various scenarios will be evaluated.
The first scenario is to evaluate the ERV with velocities through both channels of the
ERV between 1.0 - 1.5 m/s. The ERV will then be evaluated when the supply velocity is
held at 1.5 m/s, while the velocity through the exhaust is varied from 1.0 to 1.5 m/s. The
ERV will also be evaluated as the height of the exhaust channel is reduced to 1.33 x 10-3
m, while the velocity through the channels is 1.5 m/s. The final analysis is to vary the
diffusion coefficient through the membrane from 8 x 10-6 to 8 x 10-8 m2/s. The ERV is
evaluated for both summer and winter conditions, and for each season the countercurrent
and cocurrent flow configuration is analyzed.
4.2 Summer and Winter Conditions with Equal Supply and Exhaust
Flow
4.2.1
Summer Conditions
Through the use of COMSOL and the methods described in section 3, the sensible and
latent effectiveness of the ERV were evaluated for the summer conditions using the data
from Tables 1-4. The effectiveness of the ERV was calculated using equations (12) and
(13). A summary of the results for the summer condition is shown Table 6
Table 6. Sensible and Latent Effectiveness for Summer Conditions at Equal Speed
Speed
(m/s)
1
1.25
1.5
Countercurrent Concurrent Countercurrent Concurrent
S
S
L
L
0.605
0.474
0.609
0.478
0.553
0.451
0.555
0.456
0.509
0.427
0.511
0.433
It can be seen from the results that for both countercurrent and cocurrent flow the latent
effectiveness of the ERV is nearly equal to the sensible effectiveness. The difference
between the sensible and latent effectiveness of the ERV were ranging from 0.002 to
0.006. The effectiveness of the ERV is nearly equal, because the diffusion coefficient
used in the membrane allows a greater mass transfer. The effect of changing the
diffusion coefficient through the membrane is evaluated later in the report. The results
13
also show that as the velocity increases, the sensible and latent effectiveness of the ERV
decreases. For countercurrent flow, the sensible effectiveness decreases by 0.096 as the
velocities through the channel increases, while for the cocurrent flow the sensible
effectiveness decreases by 0.047. The latent effectiveness of the ERV for countercurrent
flow decreases by 0.098 from the lowest to highest velocity, while the cocurrent flow
decreases by 0.045. This phenomenon occurs because at slower velocities it allows a
greater heat and mass transfer through the membrane of the ERV.
Plots for the sensible and latent effectiveness for the countercurrent and cocurrent flow
are shown in Figure 6 and 7, respectively.
Sensible Effectiveness
0.620
0.600
0.580
0.560
e
0.540
Countercurrent
0.520
Concurrent
0.500
0.480
0.460
0.440
0.420
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
Speed (m/s)
Figure 6. Summer Sensible Effectiveness for ERVs
Latent Effectiveness
0.620
0.600
0.580
0.560
e
0.540
Countercurrent
0.520
Concurrent
0.500
0.480
0.460
0.440
0.420
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
Speed (m/s)
Figure 7. Summer Latent Effectiveness for ERVs
It can be seen that for both sensible and latent effectiveness the countercurrent flow ERV
is more effective than the cocurrent flow configuration, which is the expected results
14
based on the configuration evaluated. The countercurrent flow is more effective because
the heat and mass transfer for this configuration is better when compared to the
cocurrent flow. The cocurrent flow is also faster to reach the equilibrium temperature or
concentration between the two channels. As a result, the heat and mass transfer between
the channels is zero. Therefore, for the same size ERV the countercurrent flow will have
a greater temperature or concentration change as the air flows from inlet to outlet, when
compared to the cocurrent flow. The sensible effectiveness of the countercurrent flow
was 0.082-0.131 better than the cocurrent flow as the channel velocities decreased. For
the latent effectiveness, the countercurrent flow was 0.078-0.138 more effective than the
cocurrent flow as the channel velocities decreased.
The full details of the calculation of the sensible and latent effectiveness may be found in
Appendix A of the report.
To better understand the results for the sensible and latent effectiveness of the ERV, the
temperature and concentration profiles for the ERV is plotted. The results obtained for a
channel flow of 1.25 m/s at various axial positions (x = 0, 0.125, and 0.250 m), is plotted
as a function of the vertical distances. The plot of the temperature profile is shown in
Figures 8 and 9 for countercurrent and cocurrent flow, respectively.
Temperature vs y for Summer Countercurrent Flow
310
308
306
304
T (K)
x= 0
x = 0.125
x = 0.25
302
300
298
296
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
0.0045
y (m)
Figure 8. Countercurrent Flow Temperature Profile at Varying Channel Location
The result shows that at the inlet of the supply channel the temperature is approximately
308K. However, the temperature gradually decreases at the membrane, and a larger
temperature variation at the outlet of the exhaust channel. The average temperature at
15
the outlet of the exhaust channel is approximately 303 K (using COMSOL boundary
integration and the calculation of average temperature in Appendix A). At the channel
axial midpoint (x = 0.125 m) the temperature gradually decreases from the bottom of the
supply channel to the top of the exhaust channel. The temperature at the bottom of the
ERV is approximately 306 K, and decreases to approximately 299 K at the top of the
ERV. At the end of the ERV (x = 0.250 m) the same behavior can be seen as it was
identified at x =0 m, however, the profile starts from the top of the exhaust channel to
the bottom of the supply channel. The temperature at the exhaust inlet is approximately
297 K, while the average supply outlet temperature is 302 K. It can be seed that the
maximum temperature change occurs for the supply flow at x = 0.250 m, while for the
exhaust flow is at x = 0 m. Therefore, for the countercurrent flow ERV the temperature
changes by approximately 6 K from the inlet to the outlet of the ERV, for both supply
and exhaust flow.
Temperature vs y for Summer Concurrent Flow
310
308
306
x= 0
T (K)
304
x = 0.125
x = 0.25
302
300
298
296
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
0.0045
y (m)
Figure 9. Cocurrent Flow Temperature Profile at Varying Channel Location
The results for the cocurrent flow shows that at the inlet of the ERV (x = 0 m), there is a
small temperature change for the supply and exhaust flows. However, at the membrane
a larger temperature variation exists. The supply and exhaust inlet temperature for the
cocurrent flow is identical to the countetercurrent flow, which are approximately 308 K
and 297 K, respectively. At the channel axial midpoint, the same behavior occurs for the
cocurrent flow when compared to the countercurrent flow. However, the temperature
variation is not as steep as for the countercurrent flow. The temperature at the bottom of
16
the ERV is approximately 305 K and it decreased to 300 K at the bottom of the ERV. At
the outlet of the ERV, it shows that for the cocurrent flow the supply and exhaust outlet
temperature is almost equal. The supply outlet temperature is approximately 303 K, and
the exhaust outlet temperature is approximately 302 K. Therefore, for the cocurrent flow
the temperature changes from inlet to outlet of the ERV by approximately 5 K, for both
supply and exhaust flows.
The results for the countercurrent and cocurrent flows as shown in Figures 8 and 9,
proves that the countercurrent flow is more effective than a cocurrent flow ERV. Since
the cocurrent flow results in a 5 K temperature change from inlet to outel, while for the
same size ERV the countercurrent flow has a temperature change of 6 K. In addition, if
the length of the ERV was increased, the countercurrent flow outlet temperature still has
a potential to change by 5 K, while the cocurrent flow may change by only 0.5 K.
Therefore, the countercurrent flow configuration is a more ideal ERV to be used in
HVAC system, when compared to the cocurrent flow configuration.
A similar plot was also created for the concentration profile along the channel as
describe above for the temperature profile. The countercurrent and cocurrent flow cases
are show in Figures 10 and 11, respectively.
Concentration vs y for Summer Countercurrent Flow
1.2
1.1
c (mol/m^3)
1
0.9
x= 0
x = 0.125
x = 0.25
0.8
0.7
0.6
0.5
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
0.0045
y (m)
Figure 10. Countercurrent Flow Concentration Profile at Varying Channel
Location
The plot for the countercurrent flow shows that at the inlet of the ERV, the supply inlet
concentration is approximately 1.1 mol/m3, while the exhaust outlet average
17
concentration is approximately 0.865 mol/m3.
At the channel axial midpoint, the
concentration at the bottom of the ERV is approximately 1.0 mol/m3, and gradually
decreases to approximately 0.7 mol/m3. At the end of the ERV, the supply average
outlet concentration is approximately 0.821 mol/m3, while the exhaust inlet
concentration is 0.6 mol/m3. Therefore, for the supply flow the concentration decreases
by 0.264 mol/m3 from inlet to outlet, while the exhaust flow shows an increase of
concentration by 0.265 mol/m3.
Concentration vs y for Summer Concurrent Flow
1.2
1.1
c (mol/m^3)
1
0.9
x= 0
x = 0.125
x = 0.25
0.8
0.7
0.6
0.5
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
0.0045
y (m)
Figure 11. Cocurrent Flow Concentration Profile at Varying Channel Location
The plot for the cocurrent flow shows that at the inlet for both supply and exhaust flows
of the ERV the concentration is identical to the countercurrent flow, which are 1.1
mol/m3 and 0.6 mol/m3, respectively. Similar to the temperature profile, at the inlet of
the ERV, there is a large variation of concentration at the membrane, when moving from
supply to exhaust channel boundaries. At the outlet of the ERV, it shows that the supply
average concentration is approximately 0.868 mol/m3, and the outlet average
concentration is approximately 0.817 mol/m3. Therefore, for both supply and exhaust
flows it showed that there was a variation of 0.217 mol/m3 from inlet to outlet of the
ERV.
The results from the concentration profile for both countercurrent and cocurrent flow are
similar to the temperature profile. Therefore, the concentration profile also shows that
the countercurrent flow configuration is more effective than the cocurrent flow
configuration.
18
4.2.2
Winter Conditions
Through the same approached used for the summer conditions, the winter conditions was
also evaluated. A summary of the results for the winter condition is shown below:
Table 7. Sensible and Latent Effectiveness for Winter Conditions at Equal Speed
Speed
(m/s)
1
1.25
1.5
Countercurrent Concurrent Countercurrent Concurrent
S
S
L
L
0.552
0.441
0.553
0.444
0.501
0.416
0.502
0.420
0.460
0.392
0.461
0.395
The results for the winter conditions shows that the latent effectiveness of the ERV for
both countercurrent and cocurrent flow also have a similar behavior as described for the
summer conditions. However, the sensible and latent effectiveness are slightly lower to
the winter conditions. The countercurrent flows sensible effectiveness for the winter
condition is 0.053-0.049 lower than the summer conditions as the velocity increases,
while the latent effectiveness is 0.056-0.050 lower as the velocity increases. For the
cocurrent flow winter conditions, the sensible effectiveness is 0.033-0.035 lower than
the summer conditions as the velocities increases, while the latent effectiveness is 0.0340.038 lower as the velocities increases. This variation is due to the operating conditions
assumed for the supply and exhaust flows during the winter conditions. The results also
show that as the velocity increases, the sensible and latent effectiveness of the ERV
decreases, which is the same behavior as for the summer conditions. It can be seen that
for the countercurrent flow the sensible and latent effectiveness of the ERV decreases by
0.091 and 0.092, respectively, as the velocity increases. However, for the cocurrent
flow, the sensible and latent effectiveness decreases by 0.049 for both as the velocity
increases.
The sensible and latent effectiveness for the countercurrent and cocurrent flow are
plotted in Figures 12 and 13, respectively.
19
Sensible Effectiveness
0.560
0.540
0.520
0.500
Countercurrent
0.460
Concurrent
e
0.480
0.440
0.420
0.400
0.380
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
Speed (m/s)
Figure 12. Winter Sensible Effectiveness for ERVs
Latent Effectiveness
0.560
0.540
0.520
0.500
Countercurrent
0.460
Concurrent
e
0.480
0.440
0.420
0.400
0.380
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
Speed (m/s)
Figure 13. Winter Latent Effectiveness for ERVs
The plot shows that for both sensible and latent effectiveness the countercurrent flow
ERV is more effective than the cocurrent flow configuration. This behavior is similar to
that observed for the summer conditions. The sensible effectiveness of countercurrent
flow is shown to be 0.111-0.069 higher than the cocurrent flow, as the velocity
increases. However, for the latent effectiveness the countercurrent flow is shown to be
0.109-.065 higher than the cocurrent flow, as the velocity increases.
The countercurrent and cocurrent flow ERV temperature profiles at the channel axial
midpoint, and for increasing vertical distances, at a speed of 1.25 m/s, for both summer
conditions are shown in Figure 14.
20
Temperature vs y at Midpoint of Channel
310
305
300
Countercurrent Flow Summer
Concurrent Flow Summer
Countercurrent Flow Winter
Concurrent Flow Winter
T (K)
295
290
285
280
275
0
0.001
0.002
0.003
0.004
0.005
y (m)
Figure 14. ERV’s Temperature Profile at x = 1.25 m
It can be observe that for countercurrent flow for summer and winter conditions, the
temperature gradient from the bottom of the ERV’s channel to the top channel is slightly
greater than for the cocurrent flow.
This indicates that the heat transfer of the
countercurrent flow is greater, which leads to a higher sensible effectiveness.
The corresponding concentration profiles are plotted in Figure 15.
Concentration vs y at Midpoint of Channel
1.1
1
0.9
T (K)
0.8
Countercurrent Flow Summer
Concurrent Flow Summer
Countercurrent Flow Winter
Concurrent Flow Winter
0.7
0.6
0.5
0.4
0.3
0.2
0
0.001
0.002
0.003
0.004
0.005
y (m)
Figure 15. ERV’s Concentration Profile at x = 1.25 m
The same behavior as that for the temperature profiles is observed for the concentration
profiles. Therefore, this also indicates that the countercurrent flow is more effective than
the cocurrent flow configuration.
21
4.3 Summer and Winter Conditions with Varying Exhaust Flow
4.3.1
Summer Conditions
Using the same approach as used in section 4.2, the ERV was analyzed for supply flow
at 1.5 m/s, while the exhaust flow was varied from 1 to 1.5 m/s. A summary of the
results for the summer condition is shown below:
Table 8. Sensible and Latent Effectiveness at Varying Exhaust Flow (Summer)
Speed Inlet
(m/s)
1.5
1.5
1.5
Speed Outlet Countercurrent Concurrent Countercurrent Concurrent
(m/s)
S
S
L
L
1
1.25
1.5
0.674
0.581
0.509
0.551
0.482
0.427
0.673
0.582
0.511
0.552
0.485
0.433
Based on the results, it can be seen that a similar trend is observed to that shown in Table
6 when the supply and exhaust flows are equal. The countercurrent flow effectiveness is
higher than the cocurrent flow, and the sensible and latent effectiveness are almost
identical. However, as the exhaust flow decreases the sensible and latent effectiveness
increase. Slower exhausts flow than the supply is more effective than an ERV with
equal channel flows, because the temperature and concentration variation is much
higher, which results in a higher heat and mass transfer.
Analyzing the results, it can be seen that the sensible and latent effectiveness increases
by 0.164 and 0.161, respectively, as the velocity of the outlet flow decreases for the
countercurrent flow configuration.
For the cocurrent flow, the sensible and latent
effectiveness increases by 0.123 and 0.120, respectively, as the velocity decreases.
The temperature profiles for both countercurrent and cocurrent at x = 0.125 m and at
different channel flows are shown in Figures 16 and 17, respectively.
22
Temperature vs y for Countercurrent Flow at Varying Exhaust Speed
307
306
305
304
303
T (K)
Exhaust 1.5
Exhaust 1.25
Exhaust 1
302
301
300
299
298
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
0.0045
y (m)
Figure 16. Temperature Profile at Varying Exhaust Flows (Countercurrent)
Temperature vs y for Concurrent Flow at Varying Exgaust Speed
306
305
304
303
T (K)
Exhaust 1.5
Exhaust 1.25
Exhaust 1
302
301
300
299
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
0.0045
y (m)
Figure 17. Temperature Profile at Varying Exhaust Flows (Cocurrent)
Figures 16 and 17 shows that the temperatures variations in the supply channel are
almost equal to the different exhaust flows. For the countercurrent flow, the variation of
supply temperature is approximately 0.2 K as the velocity decreases, while for the
cocurrent flow, the variation of supply temperature is approximately 0.1 K. However,
there is a higher temperature gradient as it moves closer to the membrane and to the top
of the ERV, which indicates a greater heat transfer. The variation of temperature at the
exhaust channel is approximately 0.5 K as the velocity decreases, for both
countercurrent and cocurrent flow configuration. Since, a slower exhaust flow shows a
23
greater temperature variation, the sensible effectiveness will be higher than channels
with equal flow.
The concentration profiles are plotted for both countercurrent and cocurrent flow in
Figures 18 and 19, respectively.
Concentration vs y for Countercurrent Flow at Varying Exhaust Speed
1.05
1
0.95
c (mol/m^3)
0.9
Exhaust 1.5
Exhaust 1.25
Exhaust 1
0.85
0.8
0.75
0.7
0.65
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
0.0045
y (m)
Figure 18. Concentration Profile at Varying Exhaust Flows (Countercurrent)
Concentration vs y for Concurrent Flow at Varying Exgaust Speed
1.05
1
0.95
c (mol/m^3)
0.9
Exhaust 1.5
Exhaust 1.25
Exhaust 1
0.85
0.8
0.75
0.7
0.65
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
0.0045
y (m)
Figure 19. Concentration Profile at Varying Exhaust Flows (Cocurrent)
We observe the same outcome as that described for the temperature profiles, where the
countercurrent flow is more effective than the cocurrent flow.
The concentration
variation for the countercurrent flow at decreasing exhaust flow is approximately 0.01
mol/m3, while for the cocurrent flow is lower than 0.01 mol/m3. It can also be seen that
the concentration gradient is much higher for the exhaust channel as compared to the
24
supply channel. The concentration variation for both countercurrent flow and cocurrent
flow at the top of the ERV is approximately .025 mol/m3, as the velocity decreases.
The sensible and latent effectiveness for both countercurrent and cocurrent flow are
plotted in Figures 20 and 21.
Sensible Effectiveness
0.720
0.670
0.620
e
Countercurrent
0.570
Concurrent
0.520
0.470
0.420
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
Speed (m/s)
Figure 20. Summer Sensible Effectiveness for ERVs with Varying Exhaust Flow
Latent Effectiveness
0.720
0.670
e
0.620
Countercurrent
0.570
Concurrent
0.520
0.470
0.420
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
Speed (m/s)
Figure 21. Summer Latent Effectiveness for ERVs with Varying Exhaust Flow
It also shows that the effectiveness is greater when the exhaust flow decreases.
4.3.2
Winter Conditions
Through the use of COMSOL and the methods described in section 3, the sensible and
latent effectiveness of the ERV were evaluated using the data from Tables 1-4 for the
winter conditions when the supply flow is held at 1.5 m/s and the exhaust flow were
25
varied from 1 to 1.5 m/s. The effectiveness of the ERV was calculated using equations
(12) and (13). A summary of the results for the summer condition is shown below:
Table 9. Sensible and Latent Effectiveness at Varying Exhaust Flow (Winter)
Speed Inlet Speed Outlet Countercurrent Concurrent Countercurrent Concurrent
(m/s)
(m/s)
S
S
L
L
1.5
1
0.605
0.504
0.611
0.509
1.5
1.25
0.524
0.441
0.526
0.446
1.5
1.5
0.460
0.392
0.461
0.395
Based on the data shown in Table 9, the winter condition also has the same results as the
summer conditions. The sensible and latent effectiveness for both countercurrent and
cocurrent flow are almost equal, due to the high diffusion rate to the membrane. The
effectiveness of the countercurrent flow is higher than the cocurrent flow as shown in
Figures 22 and 23, for sensible and latent effectiveness, respectively. The table also
shows that as the velocity through the exhaust flow decreases, the effectiveness increases
when compared to a system with equal supply and exhaust channel flow.
Sensible Effectiveness
0.630
0.580
0.530
e
Countercurrent
Concurrent
0.480
0.430
0.380
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
Speed (m/s)
Figure 22. Winter Sensible Effectiveness for ERVs with Varying Exhaust Flow
26
Latent Effectiveness
0.630
0.580
0.530
e
Countercurrent
Concurrent
0.480
0.430
0.380
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
Speed (m/s)
Figure 23. Winter Latent Effectiveness for ERVs with Varying Exhaust Flow
As indicated above Figures 22 and 23 shows that the countercurrent flows are more
effective than the cocurrent flow, for both sensible and latent effectiveness.
The
temperature and concentration profile will not be plotted for the winter conditions,
because the gradient will be similar as shown for the summer conditions.
4.4 ERV Effectiveness as the Exhaust Height is Varied
4.4.1
Summer Conditions
Through the use of COMSOL and the methods described in section 3, the sensible and
latent effectiveness of the ERV were evaluated using the data from Tables 1-4 for the
summer conditions when the supply flow is held at 1.5 m/s and the height of the exhaust
channel was reduced, while keeping the mass flow rate constant as the lowest flow. The
effectiveness of the ERV was calculated using equations (12) and (13). A summary of
the results for the summer condition is shown below:
d
(m)
1.33E-03
2.00E-03
4.4.2
Speed Countercurrent Concurrent Countercurrent Concurrent
(m/s)
S
S
L
L
1.5
0.602
0.472
0.601
0.478
1.5
0.509
0.427
0.511
0.433
Winter Conditions
Through the use of COMSOL and the methods described in section 3, the sensible and
latent effectiveness of the ERV were evaluated using the data from Tables 1-4 for the
winter conditions when the supply flow is held at 1.5 m/s and the height of the exhaust
channel was reduced, while keeping the mass flow rate constant as the lowest flow. The
27
effectiveness of the ERV was calculated using equations (12) and (13). A summary of
the results for the summer condition is shown below:
d
(m)
1.33E-03
2.00E-03
Speed Countercurrent Concurrent Countercurrent Concurrent
(m/s)
S
S
L
L
1.5
0.547
0.439
0.539
0.437
1.5
0.460
0.392
0.461
0.395
4.5 ERV Effectiveness as the Diffusion through the Membrane is
Varied
4.5.1
Summer Conditions
Through the use of COMSOL and the methods described in section 3, the sensible and
latent effectiveness of the ERV were evaluated using the data from Tables 1-4 for the
summer conditions when the supply flow is held at 1.5 m/s and the exhaust flow were
varied from 1 to 1.5 m/s. The effectiveness of the ERV was calculated using equations
(12) and (13). A summary of the results for the summer condition is shown below:
4.5.2
Winter Conditions
Through the use of COMSOL and the methods described in section 3, the sensible and
latent effectiveness of the ERV were evaluated using the data from Tables 1-4 for the
summer conditions when the supply flow is held at 1.5 m/s and the exhaust flow were
varied from 1 to 1.5 m/s. The effectiveness of the ERV was calculated using equations
(12) and (13). A summary of the results for the summer condition is shown below:
28
5. CONCLUSION
Based on the results, it was determined that the countercurrent flow ERV is more
effective than a countercurrent flow ERV. Summer and winter conditions do not affect
the overall performance of the ERV, since it is dependant on the inlet and outlet flow of
the ERV. For equal supply and exhaust flow, the effectiveness increases as the flow
through the channel decreases. However, if the supply and exhaust flow are not equal,
the effectiveness increases as the exhaust flow decreases, assuming that the supply flow
is held constant. The ERV is also more effective when the exhaust flow is varied from
the supply flow as shown in section 4.3. It was also shown that the as the height of the
exhaust channel decrease and keeping the supply channel the same as the previous
scenarios, the sensible and latent effectiveness also increases. Finally, if the diffusion
rate through membrane increases, the latent effectiveness also increases.
For further analysis, the ERV may also be compared with a cross flow configuration.
The cross flow configuration will require a three dimensional analysis in COMSOL,
which will be more complex. This analysis may be used to determine if the cross flow
ERV is more effective than the countercurrent or cocurrent flow ERV. The cross flow
model in COMSOL may also be used to compare previously analyzed cross flow model,
such as the research done by Zhang et al. [2] and Min et al. [3].
29
6. REFERENCES
[1] “Thermal Comfort”, Wikipedia, September 26, 2010
http://en.wikipedia.org/wiki/Thermal_comfort, Web. November 11, 2010
[2] Zhang, L.Z.; Jiang, Y., Heat and mass transfer in a membrane-based energy recovery
ventilator, Elsevier Ltd., Journal of Membrane Science (1999) 29-38
[3] Min, Jingchun; Su, Ming, Performance analysis of a membrane-based energy
recovery ventilator: Effects of membrane spacing and thickness on the ventilator
performance, Elsevier Ltd., Applied Thermal Engineering 30 (2010) 991-997
[4] Zhang, Li-Zhi, Heat and mass transfer in quasi-counter flow membrane-based total
heat exchanger, Elsevier Ltd., International Journal of Heat and Mass Transfer 53
(2010) 5478-548
[5] COMSOL Multiphysics Modeling Guide, COMSOL Version 3.5a, COMSOL AB,
1998-2008
[6] ANSI/AHRI Standard 1060 2005 Standard for Performance Rating of Air-to-Air
Exchangers for Energy Recovery Ventilation, Air Conditioning, Heating, and
Refrigeration Institute (AHRI), 2005
[7] Cengel, Yunus, Heat and Mass Transfer A Practical Approach, Third Edition,
McGraw-Hill Companies, New York, 2007, Pages 782 and 860
[8] “Psychometric Calculations”, Sugar Engineers,
http://www.sugartech.co.za/psychro/index.php, Web. November 16, 2010
30
7. APPENDIX A
7.1 Sensible and Latent Effectiveness Calculation
In order to calculate the sensible and latent effectiveness, the boundary integration of
COMSOL was used to aid in the calculation of the average temperature and
concentration at the supply and exhaust, inlet and outlet boundaries.
The average
temperatures and concentrations were calculated using the following equations,
respectively.
d
Tave 
 T  u  dy
0
(A1)
d
 u  dy
0
d
cave 
 c  u  dy
0
(A2)
d
 u  dy
0
Based on equations (A1) and (A2), the latent and sensible effectiveness were calculated
for varying conditions. The calculation actual calculations for the effectiveness may be
found in the excel file ERV Properties and Calculations.xls along with the report.
31