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Copyright Declaration
I hereby declare that I am the sole author of this thesis.
I authorize Carnegie Mellon University, Pittsburgh, Pennsylvania to lend this thesis to other
institutions or individuals for the purpose of scholarly research.
I authorize Carnegie Mellon University, Pittsburgh, Pennsylvania to reproduce this thesis by
photocopying or by other means, in total or in part, at the request of other institutions or
individuals for the purpose of scholarly research.
Copyright 2008 by Chaoqin Zhai
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Acknowledgment
First and foremost, I gladly acknowledge my debt to Dr. Khee Poh Lam, chair of my thesis
committee, who has been guiding and inspiring me throughout my research. Without his constant
encouragement and advice over these years this thesis would not ever have been completed.
Im especially grateful to Dr. David H. Archer, who generously and continuously offered his time
and effort to provide me solid theoretical and technical support. His insightful thoughts and
strategic ways to problem solving during the numerous times of discussion made it possible for
me to frame the major structure of my thesis and also to detail it with systematic and logical
information.
My special thanks also go to Dr. Volker Hartkopf, Director of CBPD, for offering me the
opportunity to be a member of the fascinating IW team and for his continuous support and
encouragement during my research. I thank Dr. Michael K. Sahm from Carrier for hosting me
during my internship and offering his valuable time to communicate with me on a regular basis
regarding my research, which enabled the successful completion of my thesis in a timely fashion.
Im grateful to Mr. John C. Fischer from SEMCO for helpful discussion and quick responses to my
technical concerns every time. Its an honor of me to have them all sitting in my thesis committee.
I am very thankful to many friends and colleagues, in particular to Yi Chun Huang, Bing Dong and
Yun Gu. Many thanks also go to CBPD staff members, especially to Jim Jarrett for helping me in
my field tests with the SEMCO units.
I am grateful to my parents-in-law for taking care of my daughters, allowing me time to spend on
my research. My thanks extend to my grandparents, my dad, my brother, my brothers- and
sisters-in-law for their continuous care and support. My journey without their support would have
been unimaginable and words are just not enough to express my gratitude to all of them.
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Abstract
Desiccant coated enthalpy recovery and dehumidification devices have the potential to enhance
the dehumidification performance of HVAC systems, and thus meet the needs of improved indoor
air quality. Meanwhile, they can reduce or eliminate the energy penalty, including peak electricity
demand and overall energy consumption, associated with higher ventilation rate and better
humidity control. They make it possible for water based cooling devices such as radiant cooling
panels, water mullion and fan coils to function under humid climatic conditions, by mitigating the
impact on indoor humidity conditions.
In the past, there have been several attempts in modeling the operating performance of the
desiccant wheels. These published models are either applicable to the enthalpy recovery wheel
or the active desiccant wheel. Only a few are claimed to be applicable for both. In addition, there
has been a lack of physical understanding of the desiccant materials despite the different
moisture transport models presented in the previous publications. The practical issues
encountered in the wheel operation, such as the wheel purge, the residual moisture contained in
the desiccant materials and the impact of the wheel supporting structure, have not been
considered. Furthermore, very limited validation information has been provided for the existing
models.
This thesis presents the development of an equation based model to predict the operating
performance of both the enthalpy recovery and the active desiccant wheels, based upon
fundamental scientific and engineering principles. This model has related the desiccant wheels
performance to its design parameters and operating conditions. The moisture transfer processes
have been developed based on the physical analysis of desiccant materials. The effect of the
practical issues on the operating performance of desiccant wheels has also been considered.
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The model has been validated using the experimental data collected from a field installation of the
enthalpy recovery and the active desiccant wheels. Reasonable agreements between the
simulated and the measured performance parameters have been obtained, which indicates that
the model well represents all significant mechanisms occurring in the desiccant wheels. This
model can be used in selecting design parameters and operating variables, and in diagnosing
experimental data for the desiccant wheels.
This model has been applied to evaluate the costs and benefits provided by the enthalpy
recovery wheel. It is shown that the enthalpy recovery is an economic design feature. When
properly applied, its payback is immediate for most climatic conditions.
As a thermally activated device, the active desiccant wheel represents a good candidate for CHP
integration. This performance model has been used to develop operating strategies for the active
desiccant wheel integrated CHP system.
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Table of Contents
Copyright@2008 by Chaoqin Zhai ........................................................................................ i
Acknowledgement................................................................................................................... ii
Dedication ............................................................................................................................... iii
Abstract................................................................................................................................... iv
Chapter 1 Introduction............................................................................................................1
1.1 Background and Motivation ........................................................................................................................1
1.2 Literature Review.........................................................................................................................................21.2.1 Desiccant Wheels.................................................................................................................................2
1.2.2 Solid Desiccant Materials ....................................................................................................................81.2.3 Performance Modeling of Desiccant Wheels.......................................................................................91.2.4 Research Gaps in Desiccant Wheel Modeling ...................................................................................12
1.3 Research Objective ....................................................................................................................................13
1.4 Research Approach....................................................................................................................................14
1.5 Thesis Chapter Overview...........................................................................................................................15
Chapter 2 Development of the Performance Model ...........................................................17
2.1 Problem Formulation ................................................................................................................................182.1.1 Model Assumptions ...........................................................................................................................232.1.2 Governing Equations..........................................................................................................................24
2.1.3 Boundary Conditions .........................................................................................................................262.1.4 The Adsorption Isotherm of the Desiccant ........................................................................................26
2.2 Model Development...................................................................................................................................282.2.1 Convective Heat and Mass Transfer Coefficients..............................................................................292.2.2 The Explicit Finite Difference Formulation.......................................................................................29
2.3 Modeling Results .......................................................................................................................................362.3.1 Modeling Results for the Enthalpy Recovery Wheel .........................................................................382.3.2 Modeling Results for the Active Desiccant Wheel ............................................................................45
2.4 Performance Indicators of Desiccant Wheels............................................................................................542.4.1 Performance Indicators for the Enthalpy Recovery Wheel ................................................................542.4.2 Performance Indicators for the Active Desiccant Wheel ...................................................................562.4.3 Performance Indicators for the Simulated Desiccant Wheels ............................................................58
2.5 Discussion..................................................................................................................................................582.5.1 Step Sizes in Space and Time Domains .............................................................................................582.5.2 Energy and Moisture Storage in the Air.............................................................................................612.5.3 Heat Capacity of the Substrate...........................................................................................................632.5.4 Heat Conduction through the Substrate .............................................................................................642.5.5 Wheel Purge.......................................................................................................................................652.5.6 Residual Water in the Desiccant Material..........................................................................................672.5.7 Wheel Supporting Structure...............................................................................................................692.5.8 Saturation Vapor Pressure..................................................................................................................71
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2.6 Various Uses of the Performance Model .......... .......... ........... ........... .......... ........... .......... ........... .......... .....72
2.7 Summary....................................................................................................................................................74
Chapter 3 Validation of the Performance Model................................................................78
3.1 Experiment Platform..................................................................................................................................78
3.1.1 SEMCO REV 2250............................................................................................................................793.1.2 SEMCO FVR 2000 ............................................................................................................................82
3.2 Experiment Setup.......................................................................................................................................843.2.1 Experiment Setup on the Enthalpy Recovery Wheel .........................................................................853.2.2 Experiment Setup on the Active Desiccant Wheel ............................................................................94
3.3 Validation Results......................................................................................................................................983.3.1 Validation Results of the Enthalpy Recovery Wheel .........................................................................983.3.2 Validation Results of the Active Desiccant Wheel ..........................................................................109
3.4 Uncertainty Analysis................................................................................................................................116
3.5 Summary..................................................................................................................................................121
Chapter 4 Integration of the Enthalpy Recovery Wheel in HVAC System Design.......1244.1 Evaluation Procedure..............................................................................................................................124
4.2 Discussion................................................................................................................................................133
4.3 Summary..................................................................................................................................................135
Chapter 5 Integration of the Active Desiccant Wheel in CHP System Design ..............137
5.1 Operating Performance and Cost of the Active Desiccant Wheel ........... ........... ........... ........... ........... ....137
5.2 Development of Operating Strategies for the Active Desiccant Integrated CHP System ........... ........... ..140
5.3 Discussion................................................................................................................................................145
5.4 Summary..................................................................................................................................................147
Chapter 6 Contribution, Conclusion and Future Work ..................................................148
6.1 Contributions...........................................................................................................................................148
6.2 Conclusions .............................................................................................................................................153
6.3 Future Work.............................................................................................................................................155
Reference ..............................................................................................................................159
Appendix 1............................................................................................................................162
Appendix 2............................................................................................................................165
Appendix 3............................................................................................................................159
Appendix 4............................................................................................................................173
Appendix 5............................................................................................................................181
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List of Figures
Figure 1-1 Rotary Air-to-air Enthalpy Recovery Wheel .......................................................... 3
Figure 1-2 Honeycomb Structure of the Desiccant Wheels...................................................... 3
Figure 1-3 Sorption Isotherms of Various Desiccants.............................................................. 5
Figure 1-4 Desiccant Dehumidification Wheel ........................................................................ 6
Figure 1-5 Purge Section of Desiccant Wheels ........................................................................ 7
Figure 1-6 Supporting Structure of Desiccant Wheels ........................................................... 11
Figure 2-1 Schematic of the Desiccant Wheel and Its Airflow Channel Used in the Model . 19
Figure 2-2 SEM Images of the Desiccant Materials............................................................... 20
Figure 2-3 Moisture Transfer Processes in Desiccant Wheel................................................. 21
Figure 2-4 Schematic of the Finite Difference Representation of the Desiccant Wheel Model
............................................................................................................................... 30
Figure 2-5 Adsorption Isotherm of 3 Molecular Sieves and Silica Gel Used in the
Simulation............................................................................................................. 38
Figure 2-6 Psychrometric Chart Representation of the Enthalpy Recovery Wheel Operation
............................................................................................................................... 39
Figure 2-7 Schematic of the Enthalpy Recovery Wheel Used in the Simulation................... 40
Figure 2-8 Profile of the Air and Desiccant Temperature, with the Rotation of the Enthalpy
Recovery Wheel.................................................................................................... 43
Figure 2-9 Profile of the Water Vapor Concentration in the Air and at the Interface of the Air
and the Desiccant, with the Rotation of the Enthalpy Recovery Wheel............... 44
Figure 2-10 Profile of the Moisture Loading in the Desiccant, with the Rotation of the
Enthalpy Recovery Wheel................................................................................... 44
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Figure 2-11 Psychrometric Chart Representation of the Active Desiccant Wheel Operation 46
Figure 2-12 Schematic of the Active Desiccant Wheel Used in the Simulation .................... 46
Figure 2-13 Profile of the Air and Desiccant Temperature, with the Rotation of the Active
Desiccant Wheel, rpm=0.42 ................................................................................ 50
Figure 2-14 Profile of the Water Vapor Concentration in the Air and at the Interface of the
Air and the Desiccant, with the Rotation of the Active Desiccant Wheel,
rpm=0.42 ............................................................................................................. 51
Figure 2-15 Profile of the Moisture Loading in the Desiccant, with the Rotation of the Active
Desiccant Wheel, rpm=0.42 ................................................................................ 51Figure 2-16 Zoom in to the Water Vapor Concentration in the PA Outlet, with the Rotation
of the Active Desiccant Wheel, rpm=0.42 .......................................................... 52
Figure 2-17 Zoom in to the Water Vapor Concentration in the RgA Outlet, with the Rotation
of the Active Desiccant Wheel, rpm=0.42 .......................................................... 52
Figure 2-18 Profile of the Air and Desiccant Temperature, with the Rotation of the Active
Desiccant Wheel, rpm=1.5 .................................................................................. 53
Figure 2-19 Profile of the Water Vapor Concentration in the Air and at the Interface of the
Air and the Desiccant, with the Rotation of the Active Desiccant Wheel, rpm=1.5
............................................................................................................................. 53
Figure 2-20 The Effect of the Number of Discretization in Space Domain on the Predicted
Performance of the Enthalpy Recovery Wheel ................................................... 59
Figure 2-21 The Effect of the Number of Discretization in Space Domain on the Predicted
Performance of the Active Desiccant Wheel ...................................................... 60
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Figure 2-34 The Impact of the Wheel Supporting Structure on the Predicted Performance of
the Active Desiccant Wheel ................................................................................ 71
Figure 2-35 Deviation in the Saturation Vapor Pressure Calculations ................................... 72
Figure 3-1 SEMCO REV 2250 and FVR 2000 Units Installed in the IW.............................. 79
Figure 3-2 Configuration of SEMCO Revolution Unit .......................................................... 79
Figure 3-3 Flow Diagram of FVR 2000 and REV 2250 Installed in the IW.......................... 80
Figure 3-4 Psychrometric Representation of Semco FVR 2000 and REV 2250.................... 80
Figure 3-5 Solid Desiccant Dehumidification Wheel Installed in the IW.............................. 81
Figure 3-6 FVR 2000 Enthalpy Recovery Module Installed in the IW.................................. 82Figure 3-7 The Purge Section in FVR 2000 Enthalpy Recovery Module .............................. 83
Figure 3-8 Instrumentation on the Enthalpy Recovery Module ............................................. 86
Figure 3-9 External Sensors Used to Measure the Outside Air Outlet Conditions ................ 87
Figure 3-10 External Sensors Used to Measure the Building Exhaust Air Inlet Conditions.. 88
Figure 3-11 Instrumentation on the Active Desiccant Module............................................... 95
Figure 3-12 External Sensors Used to Measure the Process Air Inlet Conditions of the Active
Desiccant Wheel.................................................................................................. 95
Figure 3-13 OA and RA Conditions during the Summer Experiment.................................... 99
Figure 3-14 Sensible Heat Balance during the Summer Experiment ................................... 100
Figure 3-15 Moisture Balance during the Summer Experiment ........................................... 100
Figure 3-16 Enthalpy Balance during the Summer Experiment........................................... 101
Figure 3-17 Simulated and Measured Sensible Heat Exchange........................................... 101
Figure 3-18 Simulated and Measured Sensible Heat Recovery Effectiveness ..................... 103
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Figure 3-19 Difference between Simulated and Measured Sensible Heat Recovery
Effectiveness ..................................................................................................... 104
Figure 3-20 Simulated and Measured Moisture Exchange................................................... 105
Figure 3-21 Simulated and Measured Moisture Recovery Effectiveness............................. 105
Figure 3-22 Difference between Simulated and Measured Moisture Recovery Effectiveness
........................................................................................................................... 106
Figure 3-23 Simulated and Measured Enthalpy Exchange................................................... 107
Figure 3-24 Simulated and Measured Enthalpy Recovery Effectiveness............................. 107
Figure 3-25 Difference between Simulated and Measured Enthalpy Recovery Effectiveness........................................................................................................................... 108
Figure 3-26 Difference between Simulated and Measured Sensible Heat Recovery
Effectiveness during the Winter Experiment .................................................... 109
Figure 3-27 Sensible Heat Balance of the Active Desiccant Wheel during the Winter
Experiment ........................................................................................................ 110
Figure 3-28 Comparison between the Calculated and Measured Regeneration Air Inlet
Temperature of the Active Desiccant Wheel during the Winter Experiment ... 111
Figure 3-29 Difference between Simulated and Measured Sensible Heat Recovery
Effectiveness of the Active Desiccant Wheel during the Winter Experiment .. 112
Figure 3-30 Enthalpy Balance of the Active Desiccant Wheel during the Summer Experiment
........................................................................................................................... 112
Figure 3-31 Comparison between the Calculated and Measured Regeneration Air Inlet
Temperature of the Active Desiccant Wheel during the Summer Experiment. 113
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Figure 3-32 Moisture Balance of the Active Desiccant Wheel during the Summer Experiment
........................................................................................................................... 114
Figure 3-33 Simulated and Measured Regeneration Efficiency........................................... 115
Figure 3-34 Simulated and Measured Heat Carryover Ratio................................................ 115
Figure 3-35 Comparison between the Simulated and Measured Sensible Heat Recovery
Effectiveness with Uncertainty Range during the Summer Experiment........... 117
Figure 3-36 Comparison between the Simulated and Measured Moisture Recovery
Effectiveness with Uncertainty Range during the Summer Experiment........... 118
Figure 3-37 Comparison between the Simulated and Measured Total Heat RecoveryEffectiveness with Uncertainty Range during the Summer Experiment........... 118
Figure 3-38 Comparison between the Simulated and Measured Sensible Heat Recovery
Effectiveness with Uncertainty Range for the Enthalpy Recovery Wheel during
the Winter Experiment ...................................................................................... 119
Figure 3-39 Comparison between the Simulated and Measured Sensible Heat Recovery
Effectiveness with Uncertainty Range for the Active Desiccant Wheel during the
Winter Experiment ............................................................................................ 120
Figure 3-40 Comparison between the Simulated and Measured Regeneration Efficiency with
Uncertainty Range during the Summer Experiment ......................................... 120
Figure 3-41 Comparison between the Simulated and Measured Heat Carryover Ratio with
Uncertainty Range during the Summer Experiment ......................................... 121
Figure 4-1 Hourly Load Reduction on the Cooling Coil ...................................................... 131
Figure 4-2 Hourly Load Reduction on the Regeneration Coil.............................................. 132
Figure 4-3 Predicted Annual Energy Savings at Different Location[9] ............................... 135
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Figure 5-1 Enthalpy Removal Breakdown ........................................................................... 138
Figure 5-2 Moisture Removal Breakdown ........................................................................... 139
Figure 5-3 Operating Cost Breakdown................................................................................. 139
Figure 5-4 Predicted Supply Air Conditions with Relation to Wheel Rotary Speed and
Bypass Ratio, Regeneration Flowrate 0.0944 m3/s............................................. 143
Figure 5-5 Predicted Supply Air Conditions with Relation to Wheel Rotary Speed and
Bypass Ratio, Regeneration Flowrate 0.189 m3/s............................................... 143
Figure 5-6 Predicted Supply Air Conditions with Relation to Wheel Rotary Speed and
Bypass Ratio, Regeneration Flowrate 0.283 m
3
/s............................................... 144Figure 5-7 Predicted Supply Air Conditions with Relation to Wheel Rotary Speed and
Bypass Ratio, Regeneration Flowrate 0.378 m3/s............................................... 144
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List of Tables
Table 1-1 Literature Review of Desiccant Wheel Modeling.................................................. 12
Table 2-1 Design Parameters of the Desiccant Wheels Used in the Simulation .................... 37
Table 2-2 Inlet and Predicted Average Outlet Air Conditions for the Enthalpy Recovery
Wheel...................................................................................................................... 39
Table 2-3 Inlet and Predicted Average Outlet Air Conditions for the Active Desiccant Wheel
................................................................................................................................ 45
Table 2-4 Parameters of the Wheel Supporting Structure ...................................................... 70
Table 3-1 Instrumentation Specification................................................................................. 89
Table 3-2 The Data/Equation for the Enthalpy Recovery Wheel Performance Calculation .. 91
Table 3-3 The Data/Equation for the Active Desiccant Wheel Performance Calculation ..... 97
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SA Supply Air
SEM Scanning Electronic Microscopy
VFD Variable Frequency Drive
VAV Variable Air Volume
Parameters/Variables:
A cross sectional area of the airflow channel, the desiccant or substrate layer, m2
Bi Biot number
C separation factor
Cp specific heat, J/kg-K
D diffusivity, m2/s
F calculated variable
h enthalpy or convective heat transfer coefficient, J/kg or W/m2-K
hm convective mass transfer coefficient, kg/m2-s
H heat of adsorption or vaporization, J/kg
iads number of discretization in the adsorption section
it indicator of the element in t domain
ix indicator of the element in x domain
k thermal conductivity, W/m-K
L depth of the desiccant wheel, m
Le Lewis number
M molecular weight, kg/mole
.
m Mass flowrate, kg/s
No_x number of discretization in the space (x) domain
No_t number of discretization in the time (t) domain
Nu Nusselt number
p perimeter length of the airflow channel or pressure, m or Pa
R universal gas constant, R = 8.314 J/mole-K
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t time or temperature, s oroC
T temperature in Kelvin, K
t timestep, s
u air velocity, m/s
U uncertainty
x distance in axial direction, m
x grid size in x domain, m
moisture loading in the desiccant, kg moisture/kg dry desiccant
sensible, latent heat or enthalpy recovery effectiveness, regeneration efficiency,
heat carryover ratio
density, kg/m3
thickness of the desiccant layer, m
relative water vapor concentration
Subscripts:
amb ambient
c carryover
efan exhaust fan
g air
in inlet
l latent
m desiccant matrix or mass transfer
max maximum
min minimum
out outlet
pair process air
pg purge
r regeneration
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rair regeneration air
s sensible
sub substrate
t enthalpy
v water vapor
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Chapter 1 Introduction
1.1 Backgrou nd and Mot ivat ion
Previous research has associated increasing building ventilation rate with improved occupants health
and productivity[1]. Under some circumstances, increasing ventilation rate can however elevate the
indoor humidity level if the moisture in the ventilation air is not properly managed. Elevated indoor
humidity has negative health impacts such as respiratory diseases and mold growth[2]. With elevated
indoor humidity, the building occupants tend to adjust the thermostat to a lower setting in order to
achieve acceptable indoor comfort, which translates into deteriorated building energy efficiency.
Increasing ventilation rate can also be directly related to more energy consumption since the Heating,
Ventilating and Air Conditioning (HVAC) system has to cool or heat more outside air.
Therefore, building designers and mechanical engineers are faced with two issues. On one hand,
they need to meet the increasing requirement for ventilation rate, which brings in significant amount of
moisture while providing breathing air for the occupants and diluting the indoor pollutants. On the
other hand, they have to meet the needs of better indoor humidity control, and therefore provide
healthier, more comfortable and productive environment for building occupants. Moreover, they would
like to meet both requirements in an energy efficient and environment friendly manner to support the
sustainable building programs.
There are many ways to do building ventilation. Dedicated Outdoor Air System (DOAS) based on
desiccant coated enthalpy recovery and dehumidification devices provides a solution to the above
dilemma encountered by the building professionals. Desiccant coated enthalpy recovery and
dehumidification devices, either deployed together or individually, can enhance the dehumidification
performance of HVAC systems, and thus meet the needs of improved indoor air quality[3,4,5].
Meanwhile, they can reduce or eliminate the energy penalty, including the peak electricity demand
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and overall energy consumption, associated with higher ventilation rate and better humidity control[6].
Desiccant coated enthalpy recovery devices fit well in current green building programs and are
required by ASHRAE 90.1-2004 for systems where the design supply air is above 2.4 m3/s (5000 cfm)
and the outside airflow is above 70% of total airflow[7] in the building. Such a provision excludes
many potential applications, such as office buildings or school facilities, where enthalpy recovery
wheels can be economically justified. In fact, the ASHRAE system capacity requirement is likely to
drop with the next version of the standard.
They make it possible for water-based cooling devices such as radiant cooling panels, water mullions
and fan coils to function effectively under humid climatic conditions, by mitigating the impact on indoor
humidity conditions. It is estimated by TIAX that radiant cooling system together with DOAS has the
potential to save 15-50% on space cooling and 20-30% on air moving (ventilation) power, compared
to conventional Variable Air Volume (VAV) system[8].
Since desiccant coated devices reduce the load on subsequent cooling/heating coils, the required
capacity of the coils can be decreased, which reduces the capital investment and helps to pay for the
deployment of desiccant devices themselves[9]. As a thermally activated device, the active desiccant
equipment provides the opportunity to utilize the rejected heat from power generation or other thermal
processes for regeneration[10], as well as the thermal energy from solar thermal receivers. By
improving the overall system energy efficiency, desiccant coated devices can also reduce the carbon
footprint of the building and its mechanical system.
1.2 Literature Review
1.2.1 Desiccant Wheels
Desiccant coated devices have different forms. A desiccant coated rotary wheel, such as the enthalpy
recovery wheel shown in Figure 1-1, is one of the most common types in commercial applications due
to its high performance as a result of its large heat and mass transfer area. This area results from its
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desiccant wheels used honeycomb paper impregnated with lithium chloride, which functioned as the
desiccant. This type of wheel was relatively easy to manufacture. However, deliquescence, loss of
the desiccant material during operation, is a major problem associated with these wheels due to the
nature of lithium chloride. More recently, silica gel and molecular sieves have been used because
they are stable and do not deliquesce[12]. Compared to lithium chloride, silica gel and molecular
sieves have lower equilibrium capacity as seen from Figure 1-3[14]. Therefore, the loading of silica
gel or molecular sieves has to be higher. The original coating method is no longer applicable. New
manufacturing techniques have emerged. One of them is to mix the desiccant material with pulp and
binder and to make desiccant paper from this mixture. The paper is then corrugated and wound into a
desiccant wheel[13]. The other technique is to form the silica gel in-situ by making a honeycomb
wheel from a glass fiber paper backbone which is first impregnated with concentrated water glass and
then reacted with an acid wash[15].
The airflow channels can have different shapes such as triangle, sinusoidal and square, but the
sinusoidal shape is preferred[16]. The height of the channel ranges from 0.5 to 2.5 millimeters. The
width ranges from 0.7 to 5 millimeters[13].
There are two types of desiccant coated rotary wheels commonly used in HVAC systems: the
enthalpy recovery wheel and the active desiccant wheel. For building ventilation purposes, the
enthalpy recovery wheel operates between the outside and the building exhaust air streams, as
shown in Figure 1-1. During the summer cooling season, the outside air is warmer and, most likely,
more humid. Heat and moisture are transferred from the outside air to the channels of the enthalpy
recovery wheel. Since the building exhaust air is cooler and less humid, heat and moisture are
transferred back from the wheel to the exhaust air. During the winter heating season, heat andmoisture are transferred from the building exhaust air to the wheel and then transferred back from the
wheel to the outside air. Heat and moisture transfer between the outside and the building exhaust air
streams are thus accomplished through the channels of the rotating wheel.
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Figure 1-3 Sorption Isotherms of Various Desiccants[14]
Since there is no external thermal energy input besides the limited amount of power input to rotate
the wheel, the enthalpy recovery wheel is a passive desiccant wheel, in contrast to an active
desiccant wheel, as shown in Figure 1-4. An active desiccant wheel, also known as a
dehumidification wheel, transfers moisture from the outside air supply stream to the heated
regeneration air stream. The regeneration air can be the combustion product from a direct-fired gas
burner. It can also come from a solar thermal collector, or a sensible heat exchanger which recovers
the rejected heat from the power generation process. These alternatives will be explored in Chapter 5
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of this thesis. Since the temperature of this regeneration air is higher than that of the building exhaust
air, the outlet ventilation air humidity from the active desiccant wheel is not limited by the building
exhaust air conditions. The objective of the active desiccant wheel is to remove moisture from the
ventilation air stream, but the associated temperature increase needs to be counteracted for effective
system performance.
Figure 1-4 Desiccant Dehumidification Wheel[12]
For an enthalpy recovery wheel, both the heat and the mass transfer rates are important in most
applications. The desiccant material absorbs moisture and has relatively low heat capacity. The
substrate does not absorb moisture, but has a relatively high heat capacity. The mass fraction of the
desiccant material is relatively low, roughly 15 - 30%[13]. For the enthalpy wheels currently available
in the market, the thickness of the substrate is roughly 50 microns. The desiccant coating is roughly
25 microns on each side of the substrate[13]. The rotary speed of the wheel is approximately 20 - 30
rpm in order for desirable heat and mass transfer performance. The wheel split for the outside and
the building exhaust air streams is about 50/50. In order to prevent cross contamination between the
outside and the building exhaust air streams, the enthalpy wheel is built with a purge section, as
illustrated in Figure 1-5. In this section, the incoming outside air flows into the channels of the wheel
and drives the exhaust air contained in these channels into the incoming building exhaust air stream.
The required purge area is dependent on the depth of the wheel, the velocity of the purge gas flow
and the rotary speed of the wheel.
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Some desiccant materials, such as 3 zeolite molecular sieves, used in the wheel can further prevent
cross contamination between the outside and the building exhaust air streams, as explained in
Chapter 3 of this thesis. As a note both the wheel purge and the selected desiccant material are only
effective to prevent the contaminants in the building exhaust air stream from entering the building
ventilation air. They have no effect on the contaminants that is contained in the outside air.
Figure 1-5 Purge Section of Desiccant Wheels[16]
For the active desiccant wheel, moisture transfer is of higher importance than heat transfer. Therefore
the mass fraction of the desiccant material is relatively high, roughly 50 - 60%, in order to increase
the moisture removal capacity. The desiccant coating is usually thicker than 25 microns[12]. The heat
capacity of the desiccant matrix is relatively low in order to minimize the heat carryover from the
regeneration side, because the regeneration air is a heated stream with a temperature of roughly
100oC. The wheel rotates at a much slower rate than the enthalpy recovery wheel, in order to provide
enough time for the moisture adsorption and to pre cool the regenerated desiccant before it can pick
up moisture again.
In order for better dehumidification capability, the adsorption capacity of the desiccant in the active
desiccant wheel is expected to be higher than that in the enthalpy recovery wheel. Due to the
different operating conditions of the active desiccant and the enthalpy recovery wheels, desired
adsorption characteristics of the desiccant materials for the two applications are different as well. The
desiccant material in the active desiccant wheel functions in a larger range in terms of temperature
and moisture concentration. It has been reported in the literature[17,18] that desiccants with Langmuir
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Moderate Type 1 adsorption isotherm are desirable for the active desiccant wheel. Due to the higher
desorption rate resulting from the elevated temperature of the regeneration air, the regeneration
section of the active desiccant wheel is usually smaller than the adsorption section, resulting in a
shorter desorption period than the adsorption. The different functions of the enthalpy recovery and the
active desiccant wheels are likely to require different wheel design parameters such as the channel
size and wheel depth, and operating conditions such as the air velocity in the channel, which will be
explored in this thesis.
In addition, the building exhaust air stream is needed in the operation of the enthalpy recovery wheel.
Therefore the building outside air intake and the exhaust air outlet need to be located close to each
other.
1.2.2 Solid Desiccant Materials
The desiccant isotherm is usually used to represent the sorption characteristics of a desiccant. As
plotted in Figure 1-3, it shows the equilibrium sorption capacity of a desiccant at a certain temperature
under different humidity conditions. A set of isotherms at different temperatures is required in order to
fully characterize the sorption capacity of a desiccant. The equilibrium capacity is important in terms
of the diffusion limitation and overall heat capacity effects. The shape of the isotherm is dependent on
the dominant sorption mechanisms of the desiccants.
The heat of adsorption, which is equivalent to the heat of vaporization plus the heat of wetting, is
another parameter that affects the performance of desiccant wheels. Adsorption is an exothermic
process and low heat of wetting is desirable in order to achieve better wheel performance.
The adsorption rate is also important for desiccant wheels. It has been reported[17] that the
adsorption rate is very dependent on the desiccant thickness. The adsorption is slower for thicker
desiccant coating. The adsorption rate is also limited for salt-impregnated samples due to the pore
pluggage and the hydration of the salt.
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There are some other factors that need to be considered when selecting desiccant materials:
performance degradation of the desiccant over repetitive adsorption and regeneration cycles, long
term stability and stability with combustion products when used in direct fired systems, the need for
binding material, and safety for using in air conditioning systems, etc.
1.2.3 Performance Modeling of Desiccant Wheels
The performance of desiccant wheels can be modeled by a set of equations, which represent the
conservation of energy and mass, the rates of heat and moisture transfer, and the adsorption
equilibrium. The equations have been solved either by applying the analogy between the heat and
mass transfer or numerically by using finite difference and finite volume techniques.
In early 1970s, the modeling of the enthalpy recovery wheel was based on the analogy between heat
and mass transfer. The sensible heat recovery wheel, also known as the periodic flow heat
exchanger, has been used for a long time in power plants, recovering the sensible heat from the
exhaust air to preheat the incoming combustion air. The heat transfer in these wheels has been
extensively studied. Comprehensive design theory has been presented[20]. By applying the analogy
theory, Maclaine-cross and Banks[21] developed a model for solid desiccant coated enthalpy
exchangers and dehumidifiers. By introducing new dependent variables, known as characteristic
potentials, to replace the enthalpy and the moisture content, the differential equations for coupled
heat and mass transfer were reduced to a set of uncoupled differential equations. Further
assumptions were made to convert the equations to a linear form. The solutions for sensible rotary
heat exchangers, such as the ones presented by Kays and London[20], can be used to solve the
characteristic potentials and thus the enthalpy and the moisture content in the air.
When the computational power was limited, using analogy between heat and mass transfer is
necessary because the solutions for heat transfer are readily available. However, this advantage
became less significant with the development of computers and numerical techniques[22].
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Van den Bulck and Mitchell et al[23,24] developed an Effectiveness-Number of Transfer Units (-NTU)
method for the active desiccant wheel. The model was established in two steps. During the first step,
the governing equations for ideal dehumidifiers with infinite overall heat and mass transfer coefficients
were solved analytically by the method of characteristics and shock wave method. During the second
step, the performance of a silica gel coated rotary dehumidifier with finite heat and mass transfer
coefficients was empirically correlated to that of ideal dehumidifiers by using a finite difference model
MOSHMX. This model was then used to explore the impacts of different operating variables, such as
the regeneration air flowrate, regeneration temperature and wheel rotary speed, in order to maximize
the wheel performance based on the thermal and electrical energy input[25].
Zheng and Worek[26] developed a one dimensional transient model to simulate the simultaneous
heat and mass transport processes involved in the rotary desiccant dehumidifier. The governing
equations were solved using implicit finite difference method, which allowed the numerical scheme to
be unconditionally stable. The simulation results were compared with the predictions from other
programs. As applications of this model, the impacts of certain design parameters, such as the
separation factor and the maximum moisture uptake of the desiccant material and the number of
transfer units, and certain operating variables, such as the inlet temperature and humidity ratio of the
process and regeneration air, on the rotary dehumidifier performance were investigated[27,28,29].
Simonson and Besant[30,31] presented a one dimensional transient model to simulate the heat and
moisture transfer in enthalpy wheels. Different from previous publications, they assumed that part of
the heat of adsorption was conducted to the desiccant matrix and the rest was convected to the air
stream. The model was validated using experimental data and reasonable agreement between theexperiment and the model predictions was achieved. They used this model to study the sensitivity of
certain assumptions of the model and the operating variables of the enthalpy wheel. This model was
also used by Jeong and Mumma[32] to develop simple performance correlations for molecular sieves
and silica gel coated enthalpy wheels under normal operating conditions. These correlations are only
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valid for molecular sieves and silica gel coated enthalpy wheels since the desiccant property
parameters are embedded in the development of these correlations.
The above models only included the convective heat and mass transfer resistance at the gas solid
interface. Besides the resistance at the interface, the solid side resistance for heat and mass transfer
were also considered in Majumdars model[33]. The moisture transport in the desiccant matrix was
represented by gas diffusion and surface diffusion resistances. Zhang and Niu[34]and Sphaier and
Worek[35] presented two dimensional models that considered both heat and mass transfer
resistances in both axial and thickness directions of the solid desiccant. These two models were
claimed to be applicable for both the enthalpy recovery and the active desiccant wheels. Both models
gave some insights into the heat and mass transfer processes in the desiccant matrix, which was not
provided in previous publications. However, both models are more based on abstracted mathematics
than physical understanding of the desiccant material. Whether the models truly described what is
going on in reality remains unknown. As a matter of fact, very limited validation information, if at all,
was provided in these papers.
In addition, none of the previous models considered the practical issues in the wheel operation, which
include the wheel purge shown in Figure 1-5, the residual water contained in the desiccant material
and the wheel supporting structure such as the spokes and the casing shown in Figure 1-6.
Figure 1-6 Supporting Structure of Desiccant Wheels
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The literature review of desiccant wheel modeling is summarized in Table 1-1as follows.
Table 1-1 Literature Review of Desiccant Wheel Modeling
Numerical Application ValidationPracticalissues
Maclaine-crossand Banks [21]
No DWlimited lab
dataNo
Van den Bulck, etal. [23,24]
No DW No No
Zheng and Worek[26]
Yes DW other model No
Simonson andBesant [30,31]
Yes EWfield and lab
dataNo
Majumdar[ref1998]
Yes DW No No
Zhang and Niu[34]
Yes DW, EW No No
Sphaier andWorek [35]
Yes DW, EWlimited lab
dataNo
Zhai Yes DW, EW field data Yes
1.2.4 Research Gaps in Desiccant Wheel Modeling
Desiccant coated enthalpy recovery and active desiccant wheels share many similarities in wheel
structure, the use of solid desiccant materials and the combined heat and mass transfer processes. It
is expected that one performance model will be applicable for both applications, which has been
achieved by very few published models. In addition, modeling of the moisture transport processes is
one of the major tasks in the performance simulation of desiccant wheels. It requires physical
understanding of the desiccant materials, which is not provided in any of the published models.
Furthermore, the investigation of the practical issues is as important as the analysis of the combined
heat and mass transfer processes in determining the operating performance of desiccant wheels in
field installations. As pointed out before, none of the previous publications took these practical issues
into consideration.
A new performance model for both the enthalpy recovery and the active desiccant wheels, which
describes the heat and mass transfer processes based on the physical understanding of the
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desiccant materials and considers the impact of the practical issues, is therefore needed. This model
needs to be validated through extensive field experimental data, since field experiment is the only
way to determine the desiccant wheel performance in a field installation.
In addition, there is a lack of unified performance indicators for the active desiccant wheels. Various
indicators have been used in the published literature: dehumidification effectiveness[34], specific
dehumidification power[34], coefficient of performance[27,28,29], moisture removal capacity[36],
regeneration specific heat input[36], etc. No information has been found on why these indicators have
been chosen. There is a need for unified performance parameters that can be used to make
comparative evaluations of the operating performance regardless of the design and make of the
desiccant wheels and to calculate the outlet air conditions from the desiccant wheels based on the
inlet air conditions.
Given the energy, environment and cost benefits provided by the enthalpy recovery wheels, they
have gained increasing attention from the HVAC engineers and building owners. A procedure that
helps the interested parties to evaluate the applicability and economics of the enthalpy recovery
wheels will be desirable in order for the wider deployment of this device.
As a thermally activated device, the active desiccant wheel makes a great candidate for utilizing the
rejected heat from the power generation processes, in order to improve the overall energy efficiency.
There is a need for a design procedure that integrates the active desiccant wheel in a Combined
Heating and Power (CHP) system and develops the operating strategies for the integrated system.
Such a procedure does not yet exist.
1.3 Research Objec tive
The objective of this thesis is to address the research gaps described in the previous section. More
specifically, the research work in this thesis aims:
to develop and implement an equation based model for the performance modeling of solid
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desiccant wheels based on fundamental scientific and engineering principles, not model
fitting of experimental data. The major features of this model are shown in Table 1-1.
to validate the model using experimental data from field experiments
to compare and contrast the design and operation between the enthalpy recovery and theactive desiccant wheels, and to investigate the applicability of the model to both wheels
to use this model to analyze and diagnose the data collected from field experiments
to outline procedures for selecting and evaluating the costs and benefits of enthalpy
recovery wheels based on the model and experience gained in field experiments
to outline procedures for developing operating strategies for the active desiccant wheel
integrated CHP system.
1.4 Research Ap pro ach
The moisture transport model, an important aspect of the performance simulation of the desiccant
wheels, has been developed by investigating the structure of the solid desiccant materials under the
scanning electronic microscope (SEM). This model, together with heat transfer model, the energy and
material balance as well as the adsorption equilibrium equation at the air and desiccant interface,
have been assembled to form the basis of the performance simulation.
The performance model is one dimensional in the axial direction. It applies a lumped formulation in
the thickness direction of the desiccant and the substrate. The boundary conditions of this problem
represent the inlet outside/process and building exhaust/regeneration air conditions as well as the
adiabatic condition of the two ends of the desiccant composite. The solutions of this model are
iterated until the wheel reaches periodic steady state operation, which means the wheel returns to its
original condition in terms of temperature and moisture loading after one complete cycle. The
modeling results are obtained as the changes of the outside/process and building
exhaust/regeneration air conditions along the wheel depth and the wheel rotation.
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This performance model relates the wheels design parameters, such as the wheel dimension, the
channel size and the desiccant properties, and the wheels operating variables, such as the rotary
speed and the regeneration air flowrate, to its operating performance.
An active desiccant based ventilation unit, together with an enthalpy recovery module, was installed
in the Intelligent Workplace (IW)[37] at Carnegie Mellon University (CMU), as part of its energy supply
system (IWESS)[38]. This machine serves as the experimental platform for the empirical validation of
the performance model. Extensive testing data have been collected using carefully located sensors in
the machine. The testing methods used in this thesis can also be applied to other field installations of
desiccant wheels.
Applying the performance model, an evaluation procedure for the enthalpy recovery wheel and a
design procedure for the active desiccant wheel integrated CHP system have been developed, using
the installed ventilation machine in the IW as a specific example.
1.5 Thesis Chapter Overview
This thesis comprises six chapters:
Chapter 1, Introduction, introduces the motivation of this thesis work and the current research status
of the desiccant wheel modeling. It identifies the research gaps, establishes the research objectives
and approaches used in this thesis.
Chapter 2, Development of the Performance Model, presents the assumptions, governing equations
and boundary conditions used to develop the performance model of the desiccant wheels. It also
presents and interprets the modeling results for both the enthalpy recovery and the active desiccant
wheels, and investigates the impact of different parameters such as the wheel purge, substrate heat
conduction on the operating performance of both wheels. The performance indicators for both wheels
have also been developed in this chapter.
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Chapter 2 Development of the Performance Model
In this chapter, an equation based model has been developed to predict the operating
performance of both the enthalpy recovery and the active desiccant wheels, based upon
fundamental scientific and engineering principles. This model relates the desiccant wheels
performance to its design parameters and operating conditions.
The design parameters include:
the wheel dimension, such as the wheel depth, the wheel diameter and the split between
adsorption and desorption sections;
the channel dimension, such as the channel shape and size;
the desiccant composite, such as the desiccant material properties and coating thickness,
as well as the substrate properties and thickness.
The operating variables include:
the rotary speed of the wheel;
the inlet outside/process air temperature, humidity and flowrate;
the building exhaust/regeneration air temperature, humidity and flowrate;
The results from the model prediction are:
the temperature and humidity of the outside/process and building exhaust/regeneration
air at any given time and location as well as the average values;
the temperature and moisture loading of the desiccant composite at any given time and
location as well as the average values.
The model can be used:
to explore different design alternatives of the enthalpy recovery and the active desiccant
wheels;
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to predict the operating performance of the desiccant wheels once the wheel design and
operating conditions are given;
to select operating variables of the desiccant wheels for a given application.
2.1 Prob lem Formulat ion
The schematic of the desiccant wheel and a cross section of its airflow channel used in the model
development are shown in Figure 2-1. The wheel is a rotating cylinder with depth L and diameter
D. It rotates around its axis at a constant speed and the rotation of the wheel is represented by .
The wheel is split into the adsorption and desorption sections and the area of the two sections are
not necessarily equal. The wheel is sometimes built with a purge section to prevent cross-
contamination between the outside/process and the building exhaust/regeneration air streams,
which is discussed in Section 2.5.5 of this chapter. The outside/process and the building
exhaust/regeneration air streams are in counter flow arrangement.
The structure and composition of the wheel are assumed homogeneous. All the channels in the
wheel are assumed identical. The wheel performance is modeled by tracking the air and
desiccant conditions in a single channel as it rotates. The channel can be of any shape, such as
sinusoidal, rectangular or circular. The channel wall is made of desiccant composite, which
consists of desiccant materials, and perhaps substrate to support the desiccants. Air flows
through the channels in the direction of the wheel axis, exchanging energy and moisture with the
desiccant composite.
Analysis of the moisture transport processes is one of the important tasks in modeling the
performance of the desiccant wheels. This task is facilitated by investigating the structure of the
desiccant materials. Figure 2-2shows the SEM images of two desiccant materials, 3 zeolite
molecular sieves and silica gel, at various magnification levels. The first four images are for the
zeolite at 500, 2,000, 3,000 and 10,000 magnification levels, respectively. The last two are for the
silica gel at 200 and 90,000 magnification levels, respectively. Both the zeolite and the silica gel
samples were supplied by SEMCO Inc. The zeolite is coated on a thin aluminum sheet using
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binder materials, as shown in the first two images. The appearance of this silica gel sample is
different from the dried silica gel powdered crystals found in food or electrics packages, since it is
made in-situ and not dried.
Figure 2-1 Schematic of the Desiccant Wheel and Its Airflow Channel Used in the Model
adsorption section
desiccant compositer
moist air
desiccant composite
x
moist air
desiccant composite
desiccant composite
moist air
Outside/process air outlet
desorption section
Outside /process air inlet
Buildingexhaust/regeneration air
inlet
Buildingexhaust/regeneration air
outlet
D
L
purge section
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3 molecular sieves (x500) 3 molecular sieves (x3,000) Silica gel (x200)
3 molecular sieves (x2,000) 3 molecular sieves (x10,000) Silica gel (x90,000)
Figure 2-2 SEM Images of the Desiccant Materials
Seem from these images, the desiccant composite is a porous matrix consisting of desiccant
particles. There are large pores between the desiccant particles, which are referred to as inter
particle or macro pores. There are also small pores residing in the desiccant particles, which are
referred to as intra particle or micro pores. The intra particle pores in the silica gel can be seen
from the last image in Figure 2-2; they are not uniform in size. The average intra particle pore size
in this silica gel is about 50 . Those in zeolite are not visible even at 10,000 magnification level
since they are only about 3 in diameter. The wall of the intra particle pores are where the
moisture is adsorbed.
The following moisture transfer model is developed by analyzing the structure of the desiccant
materials. The moisture transfers from the air flowing in the wheel channels to the intra particle
pores in two steps. In the first step, the water vapor molecules transport from the air to the
surface of the desiccant composite. This step is called the gas side transfer. In the second step,
the moisture transfers from the surface of the desiccant layer to the inter particle pores and then
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to the intra particle pores. Finally the water molecules get adsorbed on the surface of the intra
particle pores. Heat is released at the location where the adsorption occurs. This step is called
the solid side transfer. No water is adsorbed on the surface of the inter-particle pores. Seen from
Figure 2-2, there is not a well defined separation surface between the gas side and the solid side.
Therefore, the hypothetical surface of the desiccant layer is used. These transfer processes are
illustrated in Figure 2-3.
Figure 2-3 Moisture Transfer Processes in Desiccant Wheel
Gas side transfer is controlled by the convective mass transfer coefficient and the vapor pressure
difference between the air and the desiccant composite. There are three diffusion mechanisms,
namely ordinary diffusion, Knudsen diffusion and surface diffusion, occurring in the desiccant
composite. The solid side transfer is controlled by the diffusion coefficient, diffusion area and the
moisture concentration difference for each diffusion mechanism. The molecules of water vapor
diffuse from the hypothetical surface of the desiccant layer to the surface of the desiccant
particles through ordinary and Knudsen diffusion in the inter particle pores. Then the water
molecules diffuse from the surface of the desiccant particles into the intra particle pores through
surface diffusion of adsorbed water molecules as well as ordinary and Knudsen diffusion of water
vapor molecules in the intra particle pores. Depending on the size of the intra particle pores,
moist air
H2O vapor
H2O vapor
(not to scale)
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ordinary and Knudsen diffusion in the intra particle pores might be neglected. For example, the
intra particle pores in the 3 molecular sieves are 3 in diameter. It is just large enough to hold
the water molecule, which is 2.8 in diameter. In this case, surface diffusion of the adsorbed
water molecule is the primary means to transfer the moisture into the intra particle pores.
Despite the complexity, the controlling process for the moisture transfer in the desiccant wheels is
the moisture transport from the bulk air flowing in the channels to the hypothetical surface of the
desiccant layer, due to the small thickness of the desiccant layer.
The heat transfer Biot number is defined as[39]
Equation 2-1
Similarly, the mass transfer Biot number can be defined as[39]
m
m
mD
hBi
= Equation 2-2
The heat transfer Biot number relates the convective heat transfer resistance between the solid
and the fluid with the resistance to thermal conduction inside the solid material. It is a measure of
the ratio of the temperature drop in the solid material and the temperature drop between the solid
and the fluid. When the heat transfer Biot number is small (Bih
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Figure 2-2is about 25 microns thick and the substrate is 15 microns thick. Therefore, the
temperature and moisture concentration gradient in the thickness direction (r direction in Figure
2-1) is very small. Therefore the analysis can be considered as one dimensional in the axial
direction (x directionin Figure 2-1).
The model is formulated in the same way for both adsorption and desorption sections. Depending
on the airflow direction, the air velocity is either positive or negative. Depending on the vapor
concentration in the air and the desiccant, the moisture either adsorbs onto or desorbs from the
desiccant. Depending on the temperature of the air and the desiccant, the energy either transfers
from the air to the desiccant or from the desiccant to the air.
2.1.1 Model Assumptions
The following assumptions are made in developing the model:
1. The axial heat conduction and water vapor diffusion in the air are negligible.
2. The axial water vapor and adsorbed water diffusion in the desiccant are negligible.
3. The convective heat and mass transfer rates are represented using the bulk mean air
temperature and humidity.
4. Heat conduction in the desiccant is negligible. Heat may be conducted axially through the
substrate.
5. The mid plane, indicated as dash lines in Figure 2-1and two ends of the desiccant composite
are adiabatic and impermeable.
6. The airflow in the channel is fully developed laminar flow.
7. The heat of adsorption is released in the desiccant composite.
8. The inlet air conditions are uniform across the wheel surface, but they can vary with time.
9. Thermodynamic properties of the dry air, desiccant material, and substrate, such as density,
specific heat and heat of adsorption, remain constant during the wheel operation.
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10. The convective heat and mass transfer coefficients remain constant during the wheel
operation. They are determined based on published coefficients between gases and solid
surfaces.
11. There is no heat or moisture storage in the wheel when it completes one rotation.
In essence, the model is one dimensional in the axial direction. It is transient, which means it
calculates the time dependent conditions of the air and the desiccant composite. It models the
simultaneous and coupled heat and mass transfer effect occurring in the wheel. It applies to both
the enthalpy recovery and the active desiccant wheels, since none of the assumptions and the
following governing equations is specific to either application. Furthermore, the wheel is in
periodic steady-state operation, which means the wheel returns to its original condition in terms of
temperature and moisture loading after one complete cycle.
2.1.2 Governing Equations
The governing equations, which describe the material and energy balance as well as the heat
and mass transfer rates, are developed based on above assumptions.
Since it is assumed that the dry air properties remain constant during the wheel operation, the air
velocity remains constant according to the mass balance of dry air. The moisture balance of the
air stream can be written as:
0)( =
+
+
tA
xuAph
vgvg
vmvgm
Equation 2-3
The first term in this equation represents the rate of convective mass transfer between the air and
the desiccant, which is represented by the difference in water vapor concentration between the
bulk mean air and the desiccant, and a constant convective mass transfer coefficient. The second
term represents the rate of moisture flux as a result of airflow. The third term represents the
moisture storage in the air.
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The moisture balance of the desiccant is described as:
0)( =
tAph mmmvmvgm
Equation 2-4
The first term in this equation represents the rate of convective mass transfer between the air and
the desiccant, corresponding to the first term in Equation 2-3. The second term represents the
moisture storage in the desiccant material.
The energy balance of the air stream is described as:
0)( =
t
tCpA
x
tCpuAtthp
g
gg
g
gggm Equation 2-5
The first term in this equation represents the rate of convective heat transfer between the air and
the desiccant composite, which is represented by the temperature difference between the bulk
mean air and the desiccant composite, and a constant convective heat transfer coefficient. The
second term represents the rate of heat flux in the air as a result of airflow, and the third term
represents the energy storage in the air. The sensible heat exchange associated with the
moisture transfer is small compared to the convective heat exchange term and it is ignored.
The energy balance of the desiccant composite is described as:
+
)()(
2
2
gmadsvmvgm
m
subsub tthpHphx
tAk
0)( =
+
t
tCpACpA msubsubsubmmm Equation 2-6
The first term in this equation represents the rate of heat conduction through the substrate, if it is
present in the wheel. If the substrate is not present, this term will be eliminated. The heat
conduction through the desiccant is ignored due to low heat conductivity of the material. The
second term represents the rate of heat generation as a result of moisture adsorption. The rate of
heat generation is represented by the product of the rate of moisture exchange and the heat of
adsorption. As assumed earlier, the heat of adsorption is entirely released in the desiccant
composite. The third term represents the rate of convective heat transfer between the air and the
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concentration in equilibrium with the desiccant vmand moisture loading in the desiccant m.
Another equation is therefore needed in order to solve for the five unknown variables. The fifth
equation is the desiccant adsorption isotherm, which relates the moisture loading in the desiccant
with the relative water vapor concentration of the air that is in equilibrium with the desiccant.
A general adsorption isotherm is described as[17,18]:
cc
m
+
=1
1
max Equation 2-13
satvm
vm
,
= Equation 2-14
The ideal gas law gives
TRM
RTp vv
v
v
v
== Equation 2-15
can be represented by the partial pressure of water vapor as follows.
satvm
vvm
p
TR
,
= Equation 2-16
pvm,sat is a function of temperature only. The relationship between pvm,satand tmcan be
determined by applying the Clausius-Clapeyron equation.
)11
()ln(122
1
TTR
H
p
p vap
= Equation 2-17
The application of this equation is discussed in Section 2.5.8 of this chapter.
Assuming at the standard atmospheric pressure 101,325 Pa, water boils at 373.15 K (100
o
C), the
saturation vapor pressure pvm,satat temperature Tmcan be calculated as
)5196
(11
,
10*12.11
mT
satvm
ep
= Equation 2-18
where Tm= tm+ 273.15 K.
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The following relationship is obtained by combining Equation 2-16 and Equation 2-18.
)5196
(910*09.4 m
T
vmm eT
= Equation 2-19
Equation 2-13 relates the moisture loading of the desiccant material with its temperature and
water vapor concentration through Equation 2-19. It supplements the governing equations shown
in Equation 2-3 through Equation 2-6 and completes the formulation of the combined heat and
mass transfer problem in the performance modeling of desiccant wheels.
In summary, the governing equation set consists of:
four partial differential equations, which describe the energy and moisture balance of the
air and the desiccant composite;
one non linear algebraic equation, which represents the desiccant adsorption isotherm.
This governing equation set is subject to the boundary conditions listed in the previous section,
which represent the inlet outside/process and building exhaust/regeneration air conditions as well
as the adiabatic condition of the two ends of the desiccant composite. The initial conditions are
not critical since the wheel is in periodic steady-state operation.
By solving this governing equation set, the change of the outside/process and the building
exhaust/regeneration air conditions along the wheel depth (x domain) and the wheel rotation (t
domain) can be obtained. The temperature and moisture loading profiles of the desiccant can
also be generated.
2.2 Model Development
In developing the model, care is exercised in determining the convective heat and mass transfer
coefficients.
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- 29 -
2.2.1 Convective Heat and Mass Transfer Coefficients
The convective heat transfer coefficient is calculated based on the Nusselt number for fully
developed laminar flow in a tube with constant heat flux boundary conditions[39].
eff
g
D
Nukh = Equation 2-20
The convective mass transfer coefficient is determined by applying the heat and mass transfer
analogy[39].
LeCp
hh
gg
m
= Equation 2-21
Assuming unity Lewis number, which is related to the mechanisms for heat and mass transfer, hm
is obtained as
gg
mCp
hh
= Equation 2-22
2.2.2 The Explicit Finite Difference Formulation
The governing equation set is solved by numerical analysis using the explicit finite difference
method. The numbers of discretization in space and time domains have been varied to determine
the appropriate grid size and timestep for reasonable computational time and accuracy, as
discussed in Section 2.5.1. The schematic used in developing the finite difference formulation is
shown in Figure 2-4. x is defined such that the velocity of the outside/process air is positive and
that of the building exhaust/regeneration air is negative. t is defined positive with the direction of
the wheel rotation.
For the finite difference analysis, the wheel is divided into No_x elements in the space (x) domain
and No_t elements in the time (t) domain, shown as horizontal and vertical grids in Figure 2-4The
corresponding steps in the space and time domains are x and t. The indexes for the space and
time domains are represented by ix and it. The double line in the time domain in Figure 2-4
indicates the separation between the adsorption and desorption sections, which is represented by
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- 30 -
it = iads+1. The integer iads is determined based on the wheel split ratio for the adsorption and
desorption sections. The wheel adsorbs moisture from the outside/process air when it=2 - iads+1;
the wheel releases moisture into the building exhaust/regeneration air when it=iads+2 - No_t+1.
The wheel is at its initial conditions when it=1.
Figure 2-4 Schematic of the Finite Difference Representation of the Desiccant Wheel Model
The five unknown variables, which are functions of x and t, can now be represented as:
tg(it,ix) temperature of the air;
tm(it,ix) temperature of the desiccant composite;
vg(it,ix) water vapor concentration in the air;
vm(it,ix) water vapor concentration at the desiccant air interface, which is in equilibrium
with the desiccant;
m(it,ix) moisture loading of the desiccant, which is a function of tm(it,ix) and vm(it,ix).
ix
it+1
process air
it=1
it=iads+1
it=No_t+1
it
ix=No_x+1
it-1
ix=1 ix+1ix-1
1/2x 1/2xx
regeneration air
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For the adsorption section, the inlet outside/process air conditions are known boundary conditions.
In the finite difference analysis, the calculations are carried out in the direction of the airflow. The
air and desiccant conditions at the next grid in the space domain are calculated based on the
conditions at the previous grid.
The partial derivatives are represented by the forward differences as follows.
x
ixittixitt
x
t ggg
=
)1,(),( Equation 2-23
t
ixittixitt
t
t ggg
=
),1(),( Equation 2-24
tixittixitt
tt mmm
=
),1(),( Equation 2-25
x
ixitixit
x
vgvgvg
=
)1,(),( Equation 2-26
t
ixitixit
t
vgvgvg
=
),1(),( Equation 2-27
t
ixitixit
t
vmvmvm
=
),1(),( Equation 2-28
22
2 )1,1(),1(2)1,1(
x
ixittixittixitt
x
t mmmm
++=
Equation 2-29
Based on the forward differences, the finite difference form of the energy balance equation of the
air for the adsorption section is:
),(),()( ixithptixittt
CpA
x
CpAuhp
mg
ggggp
+
+
),1()1,( ixittt
CpAixitt
x
CpAug
gg
g
ggp
+
=
Equation 2-30
The finite difference form of the energy balance equation of the desiccant composite:
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),(),()(),( ixitpdHhixittt
CpA
t
CpAhpixithpt vgadsmm
subsubsubmmmg
+
+
+
),1()(),( ixittt
CpA
t
CpAixitpdHh m
subsubsubmmmvmadsm
+
=
)1,1()1,1(),1(2
222 +
+ ixitt
x
Akixitt
x
Akixitt
x
Akm
subsubm
subsubm
subsub
Equation 2-31
The finite difference form of the moisture balance equation of the air:
=
+
+ ),(),()( ixitphixitt
A
x
Auph vmmvg
p
m
),1()1,( ixitt
Aixitx
Auvgvg
p
+ Equation 2-32
As seen in Equation 2-4, the finite difference form of the moisture balance equation of the
desiccant requires the representation of the partial derivative of mwith respect to time. This
partial derivative is obtained from the adsorption isotherm, Equation 2-13, by selecting tmand vm
as independent variables.
tt
t
tt
vm
vm
mm
m
mm
+
=
Equation 2-33
The finite difference form of the moisture balance equation of the desiccant is therefore written as:
=
++
),()(),(),( ixit
t
Aphixitphixitt
t
A
t vm
mm
vm
mmvgmm
mm
m
m
)],1(),1([ ixitixitttt
Avm
vm
mm
m
mmm
+
Equation 2-34
The partial derivativesm
m
t
andvm
m
are obtained from Equation 2-19 as:
]10*13.2
10*09.4[
)1(
)5196
(5)5196
(9
22
max mm T
vm
m
T
vm
m
m
m
m eT
ec
c
c
tt
+
=
=
Equation 2-35
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- 33 -
)5196
(9
22
max 10*09.4*
)1(
mT
m
vm
m
vm
m eTc
c
c
+
=
=
Equation 2-36
For the desorption section, the inlet building exhaust/regeneration air are known boundary
conditions. In the finite difference analysis, the calculations are also carried out in the direction of
the airflow. The finite difference representations of the governing equation set are similar to those
for the adsorption section, except th
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