2008 Phdbpd Zhai Chaoqin

8/10/2019 2008 Phdbpd Zhai Chaoqin

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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


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


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


Effectiveness with Uncertainty Range for the Enthalpy Recovery Wheel during

the Winter Experiment ...................................................................................... 119


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


Bypass Ratio, Regeneration Flowrate 0.189 m3/s............................................... 143


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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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


51/209

- 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


52/209

- 31 -

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:


53/209

- 32 -

),(),()(),( 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


54/209

- 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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2008 Phdbpd Zhai Chaoqin