Fouling calculation in heat exchanger

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Particulate Fouling of HVAC Heat Exchangers

by

Jeffrey Alexander Siegel

B.S. (Swarthmore College) 1995

M.S. (University of California, Berkeley) 1999

A dissertation submitted in partial satisfaction of the

requirements for the degree of

Doctor of Philosophy

in

Engineering – Mechanical Engineering

in the

GRADUATE DIVISION

of the

UNIVERSITY OF CALIFORNIA, BERKELEY

Committee in charge:

Professor Van P. Carey, Chair

Professor Ralph Greif

Professor William W. Nazaroff

Fall 2002


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To my mother, father, and sister


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TABLE OF CONTENTS

LIST OF FIGURES ...................................................................................................vi

LIST OF TABLES.....................................................................................................ix

NOMENCLATURE ..................................................................................................xi

ACKNOWLEDGEMENTS.......................................................................................xv

CHAPTER 1: PARTICULATE FOULING OF HVAC HEAT EXCHANGERS ....1

1.1 Introduction........................................................................................1

1.2 Review of Published Fouling Models................................................3

1.3 Scope of Dissertation Research .........................................................6

1.4 Important Non-dimensional Parameters ............................................8

1.5 Outline of Dissertation.......................................................................11

CHAPTER 2: MODELING PARTICLE DEPOSITION ON HVAC HEAT

EXCHANGERS.........................................................................................................13

2.1 Introduction........................................................................................13

2.1.1 Fin-and-tube heat exchangers ................................................14

2.2 Previous Studies.................................................................................15

2.3 Preliminary Deposition Modeling using CFD ...................................17

2.4 Modeling the Mechanisms of Particle Deposition on HVAC HeatExchangers.........................................................................................19

2.4.1 Deposition on leading edge of fins ........................................20

2.4.2 Impaction on refrigerant tubes ...............................................23

2.4.3 Gravitational settling on fin corrugations ..............................25

2.4.4 Deposition by air turbulence in fin channels .........................27

2.4.5 Deposition by Brownian diffusion.........................................31

2.4.6 Combining deposition mechanisms .......................................32


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2.4.7 Particle deposition mechanisms not considered ....................33

2.4.8 Particle reflection...................................................................34

2.5 Non-isothermal Deposition Processes ...............................................36

2.5.1 Thermophoresis to fin walls...................................................36

2.5.2 Thermophoretic deposition on tubes......................................38

2.5.3 Diffusiophoresis to fin walls..................................................39

2.5.4 Presence of condensed water .................................................41

2.6 Modeling Parameters .........................................................................41

2.7 Modeling Results ...............................................................................43

2.7.1 Isothermal conditions.............................................................44

2.7.2 Non-isothermal conditions.....................................................54

2.7.3 Comparison with Muyshondt et al. (1998)............................57

2.8 Conclusions and Implications of Model Results ...............................60

CHAPTER 3: MEASURING PARTICLE DEPOSITION ON HVAC HEATEXCHANGERS.........................................................................................................62

3.1 Introduction........................................................................................62


3.3 Experimental Methods .......................................................................64

3.3.1 Measuring particle deposition fraction ..................................65

3.3.2 Measuring deposition fraction in a non-isothermal system...75

3.3.3 Methods for experiment to determine fouling to pressure-

drop relationship ...................................................................79

3.3.4 Measurement devices, sensors, and uncertainty ....................82

3.4 Experimentally Tested Parameters ....................................................84

3.5 Analysis..............................................................................................85


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3.5.1 Deposition fraction (both isothermal and non-isothermal)....85

3.5.2 Non-isothermal experiments..................................................86

3.5.3 Pressure drop experiments .....................................................87

3.6 Results ................................................................................................89

3.6.1 Isothermal deposition fraction ...............................................89

3.6.2 Non-isothermal deposition fractions......................................93

3.6.3 Dust deposition experiment ...................................................96

3.7 Discussion and Implications of Experimental Results.......................99

CHAPTER 4: BIOAEROSOL DEPOSITION ON HVAC HEAT EXCHANGERS

AND IMPLICATIONS FOR INDOOR AIR QUALITY..........................................104

4.1 Introduction........................................................................................104

4.2 Bioaerosols of concern.......................................................................105

4.2.1 Fungi ......................................................................................106

4.2.2 Bacteria ..................................................................................108

4.3 Bioaerosol Deposition on Heat Exchangers ......................................111

4.4 Viability and Spread of Deposited Bioaerosols .................................114

4.5 Discussion..........................................................................................118

CHAPTER 5: FOULING TIMES AND ENERGY IMPLICATIONS OF HVACHEAT EXCHANGER FOULING.............................................................................122

5.1 Introduction........................................................................................122


5.3 Estimation of Fouling Times and Energy Impacts ............................126

5.3.1 Residential systems................................................................126

5.3.2 Commercial systems ..............................................................147

5.4 Analysis Results.................................................................................150



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5.4.2 Commercial systems .............................................................156

5.5 Discussion..........................................................................................158


5.5.2 Commercial systems ..............................................................160

5.6 Conclusions........................................................................................161

CHAPTER 6: CONCLUSIONS ................................................................................164

REFERENCES ..........................................................................................................169

APPENDIX A: EXPERIMENTAL PROTOCOLS...................................................179

APPENDIX B: TABULATED EXPERIMENTAL RESULTS................................193

APPENDIX C: MICROSCOPY OF MATERIAL ON FOULED COILS................196

APPENDIX D: INDOOR PARTICLE NUMBER CONCENTRATION

DISTRIBUTION FUNCTIONS ................................................................................199


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LIST OF FIGURES

Figure 1.1: Asymptotic fouling (modified from Bott, 1995) ...............................4

Figure 1.2: Analysis and experimental plan .........................................................12

Figure 2.1: Front view of leading edge of fins (left) and side view of heatexchanger and refrigerant tubes (right)..............................................14

Figure 2.2: Unrefined mesh from computational fluid dynamics simulation ......18

Figure 2.3: Top view of fin channel showing particle trajectory because of airturbulence...........................................................................................27

Figure 2.4: Critical velocity for onset of particle bounce (Cheng and Yeh,

1979) ..................................................................................................35

Figure 2.5: Deposition as a function of velocity for fin spacing = 4.7 fin/cm .....45

Figure 2.6: Deposition as a function of fin spacing for U = 2 m/s.......................45

Figure 2.7: Impaction deposition on fin edges as a function of velocity for fin

spacing = 4.7 fin/cm...........................................................................46

Figure 2.8: Impaction deposition on fin edges as a function of fin spacing for

U = 2 m/s............................................................................................47

Figure 2.9: Gravitational, tube impaction, and turbulent penetration fractions

for U = 1 m/s and fin spacing = 4.7 fin/cm........................................48

Figure 2.10: Gravitational, tube impaction, and turbulent penetration fractions

for U = 4 m/s and fin spacing = 4.7 fin/cm........................................48

Figure 2.11: Gravitational, tube impaction, and turbulent penetration fractionsas a function of fin spacing for 2.4 fin/cm and U = 2 m/s .................49

Figure 2.12: Gravitational, tube impaction, and turbulent penetration fractionsas a function of fin spacing for 7.1 fin/cm and U = 2 m/s .................50

Figure 2.13: Uncertainty for fin impaction for U = 2 m/s and fin spacing = 4.7

fin/cm.................................................................................................51

Figure 2.14: Uncertainty for tube impaction for U = 2 m/s and fin spacing = 4.7

fin/cm.................................................................................................51

Figure 2.15: Uncertainty for gravitational settling for U = 2 m/s and fin spacing

= 4.7 fin/cm........................................................................................52


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Figure 2.16: Uncertainty in air turbulence impaction for U = 2 m/s and fin

spacing = 4.7 fin/cm...........................................................................53

Figure 2.17: Overall uncertainty bounds for U = 2 m/s and fin spacing = 4.7

fin/cm.................................................................................................54

Figure 2.18: Comparison of deposition on isothermal coil, cooled coil, andcooled-and-condensing coil for U = 2 m/s and fin spacing = 4.7

fin/cm.................................................................................................55

Figure 2.19: Penetration by thermophoresis as a function of θ for U = 2 m/s and

fin spacing = 4.7 fin/cm.....................................................................56

Figure 2.20: Comparison of present model and the work of Muyshondt et al.

(1998) as a function of fin spacing for U = 1.5 m/s...........................59

Figure 3.1: Schematic of experimental apparatus ................................................65

Figure 3.2: Cross section of duct showing measurement points for pitot tube

air velocity measurement ...................................................................69

Figure 3.3: Sampling locations immediately upstream of duct ............................73

Figure 3.4: Schematic of measurements and sensor locations for cooled and

cooled-and-condensing coil experiments...........................................76

Figure 3.5: SAE coarse dust fractional mass distribution function......................80

Figure 3.6: Apparatus for dust experiment...........................................................81

Figure 3.7: Modeled and measured deposition for 1.5 m/s air velocity ...............90



Figure 3.10: Non-isothermal deposition fraction for 1.5 m/s air velocity..............94

Figure 3.11: Normalized mass deposited vs. relative pressure drop for 2.0 m/sair velocity .........................................................................................97

Figure 3.12: Top view of idealized (left) and real (right) fin channels ..................101

Figure 4.1: Deposition fractions for air velocity of 1.5 m/s and fin spacing of

4.7 fin/cm...........................................................................................113


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Figure 5.1: Duct penetration fractions vs. particle size for residential duct

systems described in Table 5.1 ..........................................................129

Figure 5.2: Filter efficiency curves for parametric analysis.................................130

Figure 5.3: Filter Efficiency curves for spun fiberglass furnace filter from

Hanley and Smith (1993) for U = 1.8 m/s .........................................131

Figure 5.4: Filter Efficiency curves for spun fiberglass furnace filter fromHanley et al. (1994) for U = 1.3 m/s..................................................132

Figure 5.5: Coil deposition fractions as a function of fin spacing for U = 2 m/s.133

Figure 5.6: Wet coil deposition fractions as a function of fin spacing for U = 2m/s......................................................................................................134

Figure 5.7: Fan curve and system curves for clean and fouled coil .....................143

Figure 5.8: Fan curves used to determine flow ....................................................144

Figure 5.9: Performance degradation from reduced flow from Parker et al.

(1997).................................................................................................145

Figure 5.10: Performance degradation from reduced flow from Palani et al. (1992) ................................................................................................146

Figure 5.11: Fouling time ratios (relative to Base Case)........................................152

Figure C.1: Optical Microscopy on Coil 1. .........................................................196

Figure C.2: SEM image from Coil 2.....................................................................197

Figure D.1: Urban submicron indoor air particle number concentration

distributions........................................................................................199

Figure D.2: Urban supermicron particle indoor air number concentration

distributions........................................................................................200

Figure D.3: Rural submicron indoor air particle number concentrationdistributions........................................................................................201

Figure D.4: Rural supermicron indoor air particle number concentration

distributions........................................................................................202


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LIST OF TABLES

Table 1.1: Reynolds numbers and ranges for HVAC heat exchangers...............9

Table 1.2: Non dimensional parameters that govern particle behavior in

HVAC heat exchangers......................................................................11

Table 2.1: Summary of approaches used to estimate model uncertainty............33

Table 2.2: Velocities considered in simulations .................................................42

Table 2.3: Geometric parameters for this study and for Muyshondt et al. (1998) ................................................................................................43

Table 2.4: Diffusiophoretic penetration as a function of air relative humidity,φ , for θ = 0.92, U = 2 m/s and fin spacing = 4.7 fin/cm....................57

Table 3.1: Test heat exchanger geometric parameters ........................................70

Table 3.2: Summary of particle sampling locations............................................73

Table 3.3: Summary of temperature and relative humidity measurement

locations .............................................................................................79

Table 3.4: Measurements, sensors, and uncertainty............................................83

Table 3.5: Temperature conditions for non-isothermal experiments ..................94

Table 3.6: Moisture volumes for non-isothermal experiments ...........................95

Table 3.7: Modeled and measured deposition fractions for cooled-and-condensing experiments.....................................................................96

Table 3.8: Mass balance calculations..................................................................98

Table 4.1: Fungal species in different parts of HVAC systems..........................108

Table 4.2: Bacterial species in different parts of HVAC systems.......................110

Table 5.1: Residential duct systems for parametric analysis ..............................128


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Table 5.2: Parameters varied in the simulation of mass deposition....................141

Table 5.3: Commercial HVAC fans....................................................................149

Table 5.4: Fouling time ratios .............................................................................151

Table 5.5: Contribution to mass deposited by particle size ................................154

Table 5.6: Flow reduction and pressure drop for different fan curves................155

Table 5.7: Fan power for clean and fouled coils.................................................156

Table 5.8: Commercial building fan power increase (W) based on fan typeand flow and pressure conditions.......................................................157

Table B.1: Data from isothermal and non-isothermal deposition fractionexperiments ........................................................................................193

Table B.2: Leading edge fraction for isothermal experiments ............................194

Table B.3: Data from pressure drop experiment..................................................195

Table C.1: Fiber diameter and lengths from two residential coils.......................198


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NOMENCLATURE

Aduct duct cross sectional area

A fin fin surface area

Atube tube outer surface area

Anozzle sampling nozzle entry areab f filter bypass

bc coil bypass cf corrugation factor

c8-c18 psychrometric coefficients from ASHRAE (2001)

C air,down downstream air concentration

C air,up upstream air concentration C b,filter concentration of fluorescein extracted from filter

C b,holder concentration of fluorescein extracted from filter holder

C b,nozzle concentration of fluorescein extracted from nozzleC c Cunningham slip correction factor

C D coefficient of dragC in indoor particle concentrationC m coefficient of momentum slip = 1.14

C out outdoor particle concentration

C s coefficient of slip = 1.14C t coefficient of thermal slip = 2.18

d a particle aerodynamic diameter

d d droplet diameter

d nozz nozzle diameterd p particle diameter

d tube tube diameter

D Brownian diffusion coefficient D12 diffusivity of water in air

DC duty cycle of the air handler fan

e coefficient of restitution f friction factor, frequency (of VOAG)

f IPA fraction of isopropyl alcohol in particle solution

g acceleration due to gravity = 9.8 m/s2

h average height of fin corrugations

T fl Lagrangian integral scale of time

k Boltzmann constant = 1.38x10-23

J/K

k g thermal conductivity of the gas

k p thermal conductivity of the particle Kn particle Knudsen number

m mass of deposit per unit area M mass of dust on coil for each insertion

M c mass concentration that deposits on coil M coil mass of fluorescein or test dust on heat exchanger

M duct,up mass of dust on the floor of the duct upstream

M duct,down mass of dust on the floor of the duct downstream


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M f loaded filter mass

M f,0 clean filter mass M filter,up mass of dust collected on the upstream sampling filters

M foul deposited mass that doubles heat exchanger pressure drop

M insert total mass of dust put into the system

M mound mass of dust that fell directly to the floor of the duct underneath the sifter M sifter mass of dust that remained in the sifter after each dust insertion

n fouling exponent

nm,in indoor particle size mass distribution function nrow number of rows of tubes in direction of flow

n set number of sets of offset tube rows

noffset number of offset tube rows per set p penetration fraction through cracks in the building envelope

p1 partial pressure of water

p2 partial pressure of gas P velocity pressure

P duct,r penetration through the return duct system P duct,s penetration through the supply duct system

P D penetration by Brownian diffusion P df penetration by diffusiophoresis

P G penetration by gravitational settling

P fin penetration by fin impaction P H 2O partial pressure of water vapor P H 2O, sat saturated partial pressure of water vapor

P tube penetration by tube impaction P T penetration by air turbulence impaction

P Th penetration by thermophoresis Pr Prandtl number

Q air flow rate through the HVAC system

Qcondensate volumetric flow of condensateQ L VOAG liquid flow rate

Q s air sampling flow rate

Q s,iso isokinetic sampling flow rate

Re p particle Reynolds number Retube tube Reynolds number

R f fouling resistance

R f ∞ asymptotic fouling resistanceSt Stanton number Stk eff,fin particle effective Stokes number based on t

Stk etf,tube particle effective Stokes number based on d tube Stk nozz particle Stokes number based on d nozz t time, experimental duration

t fin fin thickness

T average air temperature

T down average downstream air temperature

T dp air dew point temperature


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T up average upstream air temperature

T wall heat exchanger temperature u air velocity in bulk flow direction

u fin bulk air velocity in fin channels

u’ turbulent fluctuating air velocity in bulk flow direction

u p particle velocity in bulk flow directionu p’ turbulent fluctuating particle velocity in bulk flow direction

U air bulk velocity, instantaneous velocity

U p instantaneous particle velocityv air velocity in vertical direction

vc critical velocity for onset of particle bounce

vi impact velocity v p particle velocity in vertical direction

vr reflection velocity

V b,filter volume of buffer used to extract filterV b,holder volume of buffer used to extract filter holder

V b,nozzle volume of buffer used to extract nozzleV condensate volume of condensate

V H2O volume of condensed water on the coilV s particle settling velocity

w center-to-center fin spacing, wall normal air velocity (Muyshondt et al., 1988)

w’ turbulent fluctuating component of air velocity in wall normal directionw p particle velocity in wall-normal direction

w p’ turbulent fluctuating component of particle velocity in wall normal direction

wtube center-to-center tube spacing in vertical directionW Df overall diffusiophoretic velocity

W Df’ diffusiophoretic velocityW

SfStefan flow velocity

W up humidity ratio upstream of the duct

W down humidity ratio downstream of the duct y peak to trough width of fin corrugations

yT particle entering location

z heat exchanger depth in direction of flow

z tube center-to-center tube spacing in direction of flow

β particle deposition loss rate to building surfaces, fouling constant, coefficient

in Equation (2.22)

∆ turbulent thermal boundary layer thickness

∆ P pressure drop of fouled coil∆ P external static pressure drop of the system

∆ P initial pressure drop of cleaned coil

∆ P / z pressure drop per unit length of the duct

є eddy viscosity

φ air relative humidity

φ D deposition flux to heat exchanger surface

φ R removal flux from heat exchanger surface


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γ 1 mole fraction of water vapor

γ 2 mole fraction of dry air

η deposition fraction

η asp aspiration efficiency

η c coil deposition fraction

η f filter efficiencyη fan fan efficiency

η motor fan motor efficiency

η r HVAC filter efficiency (from Riley et al., 2000)

κ thermophoretic coefficient

λ air mean free path

λ i

envelope infiltration rate

λ r HVAC air exchange rate, µ air dynamic viscosity

ν air kinematic viscosityθ temperature ratio

ρ * unit density = 1 g/cm3

ρ air air density

ρ p particle density

τ shear stress

τ w wall shear stress

τ imp characteristic time for a particle impaction by air turbulence

τ p particle relaxation time


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ACKNOWLEDGEMENTS

I would like to acknowledge the contributions of my advisors: Van Carey, Bill

Nazaroff, and Ralph Greif. Their comments and guidance were crucial in shaping and

improving this dissertation. Van Carey and Bill Nazaroff guided me throughout my

graduate school career and Bill Nazaroff’s extensive comments on a draft of this

dissertation were particularly helpful. Iain Walker and Max Sherman at Lawrence

Berkeley National Laboratory were instrumental in obtaining funding and guiding this

project. John Proctor made many valuable suggestions over the course of this work,

Mark Sippola and De-Ling Liu, my colleagues in the Department of Environmental

Engineering, contributed to this work by reviewing papers, sharing information about

equipment, and assisting with the issues that arose in conducting the experiments.

Fabienne Boulieu from INSA Lyon assisted with data collection. Shana Bernstein and

Laura Siegel edited portions of this document and found many errors – the errors that

remain are mine, not theirs. Adam Lewinberg and Anna Greenberg, among many others,

contributed moral support over the years of dissertation research and writing.

Much of the work in this dissertation was sponsored by the California Institute for

Energy Efficiency (CIEE), a research unit of the University of California (Award No.

BG-90-73). Publication of research results does not imply CIEE endorsement of or

agreement with these findings, nor that of any CIEE sponsor. Support was also provided

by the Office of Research and Development, Office of Nonproliferation and National

Security, and the Office of Building Technology, State, and Community Programs,

Office of Building Research and Standards, US Department of Energy under contract

DE-AC03-76SF00098.


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CHAPTER 1: PARTICULATE FOULING OF HVAC HEAT

EXCHANGERS

1.1 Introduction

Heat exchangers are a significant part of many industrial processes that involve

energy exchange. Most of these heat exchangers become fouled with use. The United

Engineering Foundation, which hosts a conference every three years on the fouling

problem, estimates that the cost of heat exchanger fouling is 0.4 % of global Gross

Domestic Product (UEF, 2001). This high cost has lead to frequent study of the fouling

problem, including numerous books and conferences on the subject (Somerscales and

Knudsen, 1981; Melo et al., 1988; Bott, 1995). Much of this work has focused on

particular industries. Crude oil processing, dairy and food processing, and nuclear

reactor cooling are all industries that have conducted a large amount of research aimed at

understanding and mitigating fouling.

One of the most common uses of heat exchangers is the heating and cooling of

buildings. There are 107 - 10

9 heat exchangers installed in heating, ventilating, and air

conditioning (HVAC) systems in buildings in the United States. Building energy use

represents about one third of total worldwide energy use. Of that total, about one third is

for heating and cooling (EIA, 2002). Heat exchangers are a central part of most heating

and cooling systems, thus even small fractional performance degradations owing to

fouling have the potential to cause large societal energy consequences. Furthermore,

many heat exchangers used in HVAC systems are directly in the indoor air stream. Any

material that deposits on these heat exchangers can react with other deposited or airborne

contaminants and produce odorous compounds. If the deposited material is biological in


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nature, it can grow and contaminate other parts of the HVAC system and spread to indoor

spaces.

The heat exchangers used on the air side of most HVAC systems are extended

surfaces. They are typically a fin-and-tube configuration, which consist of tubes that

carry a refrigerant and fins that facilitate energy exchange between the refrigerant and the

air. Fin-and-tube heat exchangers consist of refrigerant tubes that run perpendicular (and

almost always horizontal) to the flow, and fins that run parallel (and almost always

vertical) to the direction of flow. The fins are often corrugated or have other extensions

from the surface to further promote energy exchange between the refrigerant and the air.

Important parameters in the design of fin-and-tube heat exchangers are the

number and spacing of tubes and the number of fins (usually expressed as a fin pitch, i.e.

the number of fins per unit length). Energy efficiency and performance requirements

often lead to higher fin pitches which increases the heat transfer between the refrigerant

and the air. Pressure drop considerations and cost limitations lead to lower fin pitches.

It is well known to technicians and designers that HVAC fin-and-tube heat

exchangers become fouled with use (RSC, 1987; Neal, 1992; Turpin, 2001). Common

contaminants include airborne particulate matter and dusts. Corrosion, both from

chemical reactions between deposited material on the (often moist) heat exchanger

surface, and from acidic air contaminants is also reported (Proctor, 1998b). Cleaning of

the heat exchangers, usually with strong acids, bases or detergents and mechanical

scrubbing with wire brushes, is a standard part of maintenance and commissioning

procedures (Turpin, 2001). Biological contamination issues are also well known:

textbooks typically recommend the use of biocide coatings or fungicide applications on

and around HVAC heat exchangers (Kuehn et al., 1998).


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Despite the documented occurrence of fouling of HVAC heat exchangers by

particulate matter, there has been relatively little study of the way in which particles are

transported to and deposit on heat exchanger surfaces. There are studies that document

biological growth on heat exchanger surfaces (Hugenholtz and Fuerst, 1992; Morey,

1988) and others that examine the role of HVAC heat exchanger surfaces as sources and

sinks of contaminants (Muyshondt et al. 1998). Others have explored aspects of the

energy consequences of heat exchanger fouling (Krafthefter and Bonne, 1986;

Krafthefter et al., 1987). In summary, despite the importance of HVAC heat exchangers

and anecdotal and scientific evidence that they foul, there has been relatively little study

of the mechanisms and processes that cause fouling of these systems.

The goals of the research reported on here are to improve our understanding of the

processes and rates of fouling by airborne particulate matter and to predict the impacts of

fouling. The structure of this chapter is to review the relevant fouling literature, to

present a scope for this study, to describe non-dimensional parameters that are useful in

characterizing HVAC heat exchangers and particle deposition, and to outline this

research project and dissertation.

1.2 Review of Published Fouling Models

The most widespread general model for heat exchanger fouling is described by

Bott (1995). A summary of the predictions of this model appears in Figure 1.1. The

amount of deposited material initially remains small during the induction period because

adhesive forces are small until sufficient material deposits to condition the surface for

future deposition. The length of the induction period can vary greatly for different

systems (Bott, 1995). The steady growth of the layer occurs as surface conditions permit

a constant increase in fouling. Finally, the deposit layer reaches a maximum and


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asymptotes. This asymptotic behavior, although not universal, is caused by a balance

between deposition and removal of the fouling agent. The y-axis in Figure 1.1 can also

be interpreted as the fouling heat transfer resistance or the friction factor for the heat

exchanger.

Time

D e p o s t T

c

n e s s

Induction or

Initiation

Steady

Growth

Asymptotic Limit

Figure 1.1: Asymptotic fouling (modified from Bott, 1995).

The asymptotic model has been experimentally verified for numerous fouling

problems (Bott and Bemrose, 1983; Epstein, 1981). Mathematically, the generalized

fouling process can be described as (follows Bott, 1995):

d

d D R

m

t φ φ = − (1.1)

Where m is the mass of deposit per unit area, φ D is the deposition flux to the heat

exchanger surfaces, and φ R is the removal flux of fouling agent from the surface.

Experiments need to be done for each system and flow condition to determine the

functional forms of φ D and φ R.

Kern and Seaton (1959) provided the first detailed functional form for asymptotic

fouling:


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( )1 e t f f R ( t ) R β −∞= − (1.2)

Where R f is the heat transfer resistance of the fouled heat exchanger as a function

of time, R f ∞ is the asymptotic limit of fouling resistance and β is a constant that is

dependent on the system. Fouling resistances span a very large range. Some reported

values in the literature include 10-5

– 10-4

°C/W⋅m2 for a cooling water system (Merry

and Polley, 1981) and 10-3

– 10-2

°C/W⋅m2 (Bott, 1981) for paraffin in an industrial heat

exchanger. Mills (1992) tabulates design values for fouling resistances for a wide range

of fluids that range from 10-4 – 10-2 °C/W⋅m2.

The Kern and Seaton expression is by far the most common functional form for

asymptotic fouling and is still used for a wide variety of fluids and heat exchanger

geometries. Other functional forms for asymptotic fouling have been proposed, including

a driving force model (Konak, 1976):

( )d

d

n f f f

R ( t ) K R R ( t )

t ∞

= − (1.3)

Where K and n are constants (note that Equation (1.3) and Equation (1.2) are equal for n

= 1 and K = β ). Epstein (1988) assumed a constant temperature difference between the

heat exchanger and the fluid and that the heat flux follows a power law relationship. He

proposed the following model:

( )

d

d

f

n f f

R ( t ) K

t R R ( t )∞

=

−

(1.4)

The models proposed in Equations (1.2) - (1.4) are all useful for conceptualizing

fouling, but all require extensive testing at all possible system conditions to obtain the

correct functional form and values of the coefficients. Most fouling research consists of

experiments to determine these parameters for a particular system. Very little research


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has been done to determine fouling resistances and their functional form for HVAC heat

exchangers.

Equations (1.2) - (1.4) all focus on an increased resistance to heat transfer caused

by fouling. Bott (1995) points out that the pressure drop increases that result from

fouling can also have a significant effect on heat exchanger performance. This is true for

HVAC heat exchangers and is discussed in more detail in Chapter 5.

1.3 Scope of Dissertation Research

There are many different kinds of heat exchangers used in HVAC systems. In

order to focus the investigation, the following limits are put on this investigation. In this

study, I am primary interested in particulate fouling of air-side indoor fin-and-tube heat

exchangers used for cooling. Corrosion fouling, in addition to particulate fouling, can

occur in HVAC heat exchangers, but is often related to a particular airborne chemical

contaminant (Proctor, 1998b) or is caused by the more extreme temperatures that occur

from the development of a thick fouling layer (Bott, 1995) . Although there are many

water-side heat exchangers in HVAC systems, the fouling that occurs in these liquid

systems is typically one of scaling and precipitation (Somerscales and Knudsen, 1981),

not particle deposition. Outdoor heat HVAC exchangers, which reject/absorb heat that

the refrigerant acquires/loses at the indoor heat exchangers, also foul, but the fouling

mechanism is of a different nature than considered here. Large scale debris, such as

leaves, and wind-blown soil, as well as algal growth in evaporative condensers and

cooling towers are typical fouling agents for outdoor HVAC heat exchangers (RSC,

1987; Neal, 1992). Other designs, such as unextended tube bundles (no fins), are used as

heat exchangers in some larger HVAC systems, but by far the most predominant type are

fin-and-tube. The focus on heat exchangers used for cooling is because the effects of


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fouling are more severe than for heating. Air conditioning systems are more sensitive to

flow reduction (Palani et al., 1992; Parker et al., 1997; Proctor, 1998a) than heating heat

exchangers. Also, cooling heat exchangers (evaporators) serve to dehumidify the air

stream which provides bulk water for microbiological growth and can accelerate the rate

of fouling.

The focus on particulate fouling means that the range of particle diameters being

considered is crucially important, as particle size determines most particle properties.

Previous work on heat exchanger fouling has typically considered supermicron particles

as these particles are sufficiently large to cause a significant fouling layer when they

deposit (Bott and Bemrose, 1983; Muyshondt et al., 1998). However, submicron

particles exist at much higher concentrations in typical indoor environments, so this study

will consider particles as small as 0.01 µm in diameter. Particles in the size range of 0.01

to 1 µm exist in indoor environments as the result of combustion (including tobacco

smoke), penetration from outdoor sources, and gas-to-particle conversion processes

(Hinds, 1999). Particles in the range of 1 - 10 µm include some soil grains, certain

bioaerosols, and particles from cooking and other household activities. Very large

particles, with diameters from 10 – 100 µm, are those found in indoor dusts (Hinds,

1999). It is important to note that smaller particles (i.e. those with a characteristic

dimension of 10 nm or even smaller) do exist in indoor environments. However, because

mass goes with the cube of particle diameter (for spherical particles), these very small

particles are unlikely to contribute significantly to pressure drop or deposited mass. Also,

certain particles, particularly dust fibers, exist in indoor air at sizes larger than 100 µm.

However, there are very limited data on the concentration of these particles in indoor

environments. They are typically non-spherical and thus have poorly understood

behavior in indoor air flows. Their large inertia leads to deviation from fluid streamlines

and makes them difficult to sample, which, combined with very limited regulatory


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8

interest, explains the lack of data. Some analysis of larger dust fibers is included in

Chapter 5, but most of the analysis is limited to 0.01 to 100 µm spherical particles.

1.4 Important Non-dimensional Parameters

In addition to the particle diameter, there are also many non-dimensional

parameters that are relevant for the study of heat exchanger fouling. Table 1.1 lists

important air Reynolds numbers. The ranges of values in the table are based on flow

rates, dimensions, and heat exchanger geometries typical of residential and commercial

systems. The first parameter is the Reynolds number in the duct leading up to a heat

exchanger, Reduct . These flows are always turbulent and frequently are developing

because of bends, constrictions, and other geometric changes to the flow near the heat

exchangers. Another duct Reynolds number, Reτ ,duct is based on the friction velocity, u*,

which is a parameter with dimensions of velocity ( * w air u / τ ρ = , where τ w is the wall

shear stress and ρ air is the air density) that is often used to characterize turbulent flow.

When flow enters the heat exchanger, the Reynolds numbers in the fin channels, Re fin

,

drops two to three orders of magnitude from Reduct because the characteristic dimensions

becomes the much smaller fin spacing. Even though the low values for Re fin in Table 1.2

suggest laminar flow, the upstream turbulence in the duct and enhanced surfaces typically

lead to a transition flow in the heat exchanger core. The Reynolds number based on the

tube diameter, Retube, is used to describe flow around and the heat exchanger tubes, an

important geometric feature in HVAC heat exchangers.


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Table 1.1: Reynolds numbers and ranges for HVAC heat exchangers.

Typical Ranges

Parameter Formulaa Residential Commercial

Reynolds number based

on duct dimensionduct

duct d u

Reν

= 104 - 10

52⋅10

4 - 3⋅10

5

Reynolds number based

on duct dimension and

friction velocity

*duct

,duct d u

Reτ ν

= 6⋅102 - 5⋅10

3 103 - 10

4

Reynolds number in finchannels

fin fin

w u Re

ν

⋅

= 102 – 9⋅10

2 10

2 - 2⋅10

3

Reynolds number basedon tube diameter

tube fintube d u Re

ν

⋅

= 6⋅102 - 5⋅103 6⋅102 - 104

aIn these expressions, d duct is characteristic dimension of duct, u is bulk air velocity, ν is kinematic viscosity

of air, u* is the friction velocity ( 8*u / u f / w air τ ρ = = where f=2d duct ∆ P/ ρ air zu2 where ∆ P/z is the

pressure drop per length of the duct in the direction of flow and ρ air is the air density), u fin is the bulk

velocity in the fin channels (u fin = u(1+t fin/w) where t fin is the fin thickness and w is the center to center fin

spacing), and d tube is the tube diameter.

The Reynolds numbers in Table 1.1 are important when describing and relating

different systems. Although the face area of heat exchangers varies over a large range,

from less than 0.1 m2 to over 4 m

2, the parameters in Table 1.1 and the reduction of a heat

exchanger to the simplest unit of a fin channel allow conclusions to be generalized.

There are also several non-dimensional parameters that govern particle dynamics

and deposition in the system. Particle Reynolds number, Stokes numbers, and relaxation

times for spherical particles of the size range 0.01 – 100 µm and typical HVAC velocities

and geometric parameters are listed in Table 1.2. The particle Reynolds number, Re p is

used to calculate the coefficient of drag, C D, which appears in the other dimensional

parameters in Table 1.2. Stk fin is the particle Stokes number that governs deposition by


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impaction on fin edges. The Stokes numbers in Table 1.2 are in a general form. Stokes

numbers are most commonly reported assuming that Re p < 0.1, for which spherical

particles are in the Stokesian range, and assuming that C D = 24/ Re p. A similar parameter

that governs deposition on the refrigerant tubes is Stk tube. Note that both Stokes numbers

vary by nine orders of magnitude in HVAC systems. This is mostly due to the

dependence of the Stokes numbers on d p2 (for Stokesian behavior, Re p < 0.1). Particle

diameter varies over four orders of magnitude for particles that we are relevant for

present purposes. The last parameter in Table 1.2, the particle relaxation time, is shown

in its dimensionless form as commonly used for particles in turbulent flow. This

parameter governs how rapidly a particle responds to changes in the fluid velocity.

The parameters in Tables 1.1 and 1.2 influence the different mechanisms by

which particles of various sizes are likely to deposit. Deposition mechanisms are

discussed in more detail in the modeling work in Chapters 2 and the experimental work

in Chapter 3.


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Table 1.2: Non-dimensional parameters that govern particle behavior in HVAC heat

exchangers.

Parameter Formula

a

Typical Range

In HVAC Heat

Exchangers

Particle Reynolds number p p p

d u u Re

ν

−

= 10-4 - 4⋅10

1

Particle Stokes number

based on fin thickness

c

D

4C

3C

p p fin

air fin

d Stk

t

ρ

ρ = 5⋅10

-6 - 10

3

Particle Stokes number based on tube diameter

c

D

4C

3C

p ptube

air tube

d Stk

d

ρ

ρ = 2⋅10

-8 - 2⋅101

Particle relaxation time

(dimensionless)( )

2

c

D

4C

3C

* p p

pair

ud

u

ρ τ

ρ ν

+= 8⋅10

-8 – 10

2

aIn these expressions, d p is particle diameter, u p is the particle velocity, C c is the Cunningham slip

correction factor (C c is calculated from Hinds (1999); C c>>1 for d p < the mean free path of air, λ , and C c ~

1 for particles > 1 µm), C D = f( Re p) is the coefficient of drag for the assumed spherical particle calculated

from Seinfeld and Pandis (1998), ρ p is the particle density.

1.5 Outline of Dissertation

The overall outline for this work is presented below in Figure 1.2. The integrated

structure of this investigation is to first determine what particulate contaminants are

present in indoor and in outdoor air and how they are transported through a duct system

to the heat exchanger. Some of these particles are filtered, the rest are available to

deposit on the heat exchanger. Simulation and experimental results are used to determine

what fraction of particles actually deposit in the heat exchanger. The model and

experiments are detailed in Chapters 2 and 3. Chapter 4 applies these results, combined


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with data on bioaerosol concentrations, environmental requirements, and health effects,

to determine the indoor air quality implications of biological fouling (depicted in the

lower branch of Figure 1.2). Chapter 5 uses deposition fraction experimental and

simulation results, as well as results from an additional experiment relating pressure drop

to the mass of material deposited to determine the pressure drop that results from fouling

and the rate of fouling in typical HVAC heat exchangers. This information, combined

with research about fans and the impact of airflow on capacity, is used to estimate the

energy consequences of fouling.

Size Resolved

Particles Presented

to Evaporator Coil

Particles

Deposited on

Evaporator and

Mass

Indoor Air

Particle

Concentrations

Outdoor Air

Particle

Concentrations

Duct

Leakage and

HVAC Air

Flow Data

Filtration,

Filter Bypass,

Coil Bypass

Experimental andSimulated Particle

Deposition

Data

Increased

Pressure Drop

Through Coil

Due to Fouling

Reduced Airflow

Due to Fouling

Energy Impacts

of Coil Fouling

Experimental Foulingvs. Pressure Drop

Data Typical Fan

Curves

Reduced Air

Flow Energy

Consequences

Existing AC

Flow Data

Bioaerosol

Concentrations

Bioaersol

Deposition

Growth and

Amplification

Indoor Air

Quality Impacts

of Biological

Coil Fouling

Environmental

Conditions

Spread to

Indoor

Spaces

Figure 1.2: Analysis and experimental plan.


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CHAPTER 2: MODELING PARTICLE DEPOSITION ON HVAC

HEAT EXCHANGERS

2.1 Introduction

One purpose of this dissertation is to create a simple, robust, and widely

applicable model of particle deposition on fin-and-tube heat exchangers. Particulate

fouling of air-side heat exchangers has been modeled by other researchers, mostly

because of its importance to industrial processes. Significant strides have been made in

the modeling of heat exchanger fouling processes in dairy processing (e.g. Lalande and

Rene, 1988), nuclear reactor cooling systems (e.g. Watkinson, 1988), crude oil

distillation (e.g. Marshall et al., 1988), and other process and industrial heat exchangers.

This body of work is important and has improved many of the processes that use heat

exchangers, but there are several limitations that prevent its application to the specific

problem of HVAC heat exchanger fouling. The first limitation is one of geometry. The

fin-and-tube heat exchangers that are typical of HVAC systems are not widely used in

industrial processes, and the existing models are not typically adaptable to new

geometries. The second limitation is one of medium. Many of the problems discussed in

the literature involve fouling of the liquid side of a heat exchanger. Although the physics

do not change as the medium changes, the limiting mechanisms for fouling of liquid

systems are often crystallization or precipitation reactions. These reactions are less

important in HVAC heat exchanger fouling and other low temperature particulate and gas

fouling problems. The third limitation has to do with the purpose of process heat

exchanger fouling work. In many studies, it is often less important to understand the

mechanisms than it is to find solutions. The purpose of this chapter is to develop a

mechanistic model of particle deposition on HVAC heat exchangers and to understand

the important parameters in the fouling process.


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2.1.1 Fin-and-tube heat exchangers

Before describing different approaches to the problem, it is important to clearly

describe the system being studied. For the purposes of modeling, the fin-and-tube heat

exchanger geometry is reduced to a series of straight channels created by the fins with

cylindrical refrigerant tubes that run horizontally perpendicular to the fins. The fins are

often corrugated to increase area for heat transfer. A schematic of typical fin-and-tube

heat exchanger geometry appears in Figure 2.1.

h

ytfin w

dtube

wtube

z

Air flow

direction

Air flow

into page

Figure 2.1: Front view of leading edge of fins (left) and side view of heat exchanger and

refrigerant tubes (right) where w is the center-to-center fin spacing, h is the averageheight of fin corrugations, t fin is the fin thickness, y is the peak to trough width of fin

corrugations, d tube is the tube diameter, wtube is the tube spacing, z is the heat exchanger

depth.

The tube geometry of HVAC heat exchangers can vary over a wide range of

diameters and configurations. To improve heat transfer, a typical heat exchanger will

have multiple rows of offset tubes. The heat exchanger depicted in Figure 2.1 has two

sets of offset tubes, for a total of four tube rows. This is typical of many HVAC heat

exchangers and matches the test coil used for the experiments described in Chapter 3.


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The notation that is used to describe the heat exchanger in Figure 2.1 is noffset = 2, n set = 2,

and nrow = noffset n set = 4.

2.2 Previous Studies

A general model of fouling by gas-side particulate matter is presented by Bott

(1988). He divides particle fouling into three distinct processes: (1) transport and

deposition of particles to surfaces, (2) adhesion of deposited particles, and (3)

reentrainment of adhered particles. He further subdivides the transport and deposition

portion into transport through the bulk flow to the boundary region (typically caused by

advection, Brownian and eddy diffusion, thermophoresis and gravity) and transport

across the boundary layer (typically caused by the same mechanisms, without advection,

but with the addition of inertial impaction). Although it lacks complete detail, this was

among the first mechanistic examinations of particle deposition in heat exchangers. The

adhesion and potential resuspension of particles are described as “complicated

phenomena” that depend on surface roughness, amount and properties of previously

deposited materials, the presence of a liquid, and turbulent bursts. This work is useful in

outlining a general model and presenting important terms and possible deposition

mechanisms. It stresses the need for experimental data to both verify mathematical

models and provide input data for particular heat exchanger geometries.

In the same volume as Bott (1988), Epstein (1988) presents an overview of the

mechanisms that can cause particle deposition in heat exchangers. He reviews the work

of several authors on particle deposition and discusses the applicably of this work to

particulate fouling problems. He discusses the potential role of and governing equations

for deposition by means of Brownian diffusion, inertial impaction, gravitational settling,

and thermophoresis. He also describes the mechanisms of particle bounce, adhesion and


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re-entrainment. The work also suggests that individual deposition mechanisms can be

assumed to operate independently in many heat exchanger geometries.

Muyshondt et al. (1998) used a very different approach to model the specific

problem of particle deposition on typical fin-and-tube HVAC heat exchangers. They

used a computational fluid dynamics (CFD) package and a Lagrangian approach. The

CFD software solves approximations to the continuity, momentum, and energy equations

for the airflow through a system and then uses this solution in a force balance to track

particle motion through the system. The three-dimensional equations for particle

velocity, for particles of the diameter range of 1- 100 µm, are as follows: (note,

typographical errors in Muyshondt et al. are corrected here):

( )D3 C

4

p air p p

p p

duu u U U

dt d

ρ

ρ = − −

(2.1)

( )D3 C

4

p air p p

p p

dvv v U U g

dt d

ρ

ρ = − − +

(2.2)

( )D3 C

4

p air p p

p p

dww w U U

dt d

ρ

ρ = − −

(2.3)

where u p, v p, and w p are the Cartesian components of the particle velocity, ρ air is the air

density, C D is the coefficient of drag on the (assumed spherical) particle, ρ p is the particle

density, d p is the particle diameter, u, v and w are the components of the air velocity and

U and U p are total air and particle instantaneous velocities (2 2 2U u v w= + + and

2 2 2 p p p pU u v w= + + ), and g is the acceleration due to gravity.

Muyshondt et al. approximated air turbulence with a Reynolds stress turbulence

model with an assumed turbulence intensity of 5%. The turbulence intensity is typically

defined as u´/u where u´ is the standard deviation of the normally distributed fluctuating

component of the air velocity. The turbulence introduced randomness into the model and


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thus a Monte Carlo simulation for several thousand particles was done for each particle

size considered. The resulting collection efficiency curves for a simple HVAC heat

exchanger are presented at three fin spacings (3.9, 4.7 and 5.5 fin/cm), two air velocities

(1.5 and 2.3 m/s), and vertical and horizontal fin orientation. (It is not clear why

Muyshondt et al. varied this last parameter. HVAC heat exchangers are almost always

installed with vertical fins to limit gravitational settling, provide for condensation

drainage, and to facilitate cleaning.) The results of Muyshondt et al. suggest increasing

collection efficiency with particle size, moderate deposition (< 10 %) for all vertical fin

cases for particles of 1 – 10 µm aerodynamic diameter, and sharply increasing deposition

for particles >10 µm. Their reported collection efficiencies asymptote at ~70 - 80 % for

70 µm and larger particles. Their results are discussed later in a comparison with the

modeling work of this chapter.

Although the Muyshondt et al. (1998) simulation work provides estimates of

particle deposition on HVAC heat exchangers, it presents little information on the

physics of the deposition processes. Furthermore, gravitational settling on fin

corrugations was excluded from their analysis, as was deposition on the leading edge of

the fins. My field work indicates that this is an important deposition location.

2.3 Preliminary Deposition Modeling using CFD

A primary purpose of my study was to mechanistically model deposition

processes on HVAC heat exchangers. To this end, initial runs were made with a

commercial CFD package, Fluent™. The initial approach was to construct a 17 × 65, 2-

dimensional grid (see Figure 2.2) and then calculate the velocity flow field through the

system. The original runs were conducted for isothermal conditions (no cooling of the

heat exchanger) and the flow was assumed to be laminar. For simplicity, the fins were


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initially assumed to be infinitely thin and uncorrugated. The grid was refined eight times

until there was less than 2% average difference in the velocity fields between successive

runs.

Figure 2.2: Unrefined mesh from computational fluid dynamics simulation.

A significant challenge occurred when turbulence was introduced into the system.

Typical CFD models have two basic turbulence models: the k-ε model and the Reynolds

stress model. Both of these models approximate turbulence and require unmeasurable

parameters as input. Initial runs were completed with a k-ε model using, initially,

standard turbulence coefficients of C µ = 0.09, C 1 = 1.44, C 2 = 1.92, σ k = 1.0, and σ ε = 1.3.

(Mandrusiak (1988) presents complete equations and descriptions of the coefficients and

their importance in his Appendix A.) There is no clear way to determine these

parameters as they are geometry and flow specific and the transition flow in HVAC heat

exchangers is particularly poorly understood. Successive runs of the flow field

generation and particle tracking software, which solves approximations to Equations (2.1)

- (2.3), produced deposition rates that, although roughly consistent with the results of

Muyshondt et al. (1998), had variations of 30 – 50% in deposition fraction for 15 µm

particles depending on the turbulence model inputs. Even small changes in the

turbulence model parameters resulted in significant changes in the flow field. A

particular area of concern was the boundary layer flows near fin walls and refrigerant


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tubes, as their structure was very sensitive to model parameters and they are crucial to

correctly assessing particle deposition (Bott, 1988). It should be pointed out that the

transition flows (from turbulent duct flow to laminar or to low Reynolds number

turbulent channel flow) that are prevalent in HVAC heat exchangers are particularly

difficult to model numerically with existing models (Versteeg and Malalasekera, 1995).

Given the limitations associated with the CFD approach, even for the 2-D case,

this approach was deemed to be too computationally intensive and too dependent on

unknown turbulence model parameters. Although CFD has applications in the study of

particle deposition problems, the complex geometry and unknown turbulence model

parameters would require a significant effort to produce reasonable results for the system

of interest.

2.4 Modeling the Mechanisms of Particle Deposition on HVAC Heat

Exchangers

Instead of using CFD, I developed a different approach, one that considers

deposition of particles by individual mechanisms. This approach also has many

limitations – it ignores details of boundary layer development, requires some empirical

calculations, involves many assumptions about the nature of the air flow and turbulence,

assumes independent interactions among deposition mechanisms, and makes

idealizations about the geometry. The limitations are discussed in more detail throughout

this chapter. The strengths of this approach are that it is computationally simple, it

allows for clear indication of the importance of various deposition mechanisms, it permits

straightforward investigation of important parameters that lead to particle deposition in

HVAC heat exchangers, and it can be adjusted to new geometries easily.


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The particle deposition model accounts for impaction on refrigerant tubes and fin

leading edges, Brownian diffusion in fin channels, gravitational settling on fin

corrugations, and air turbulence effects. When the heat exchanger is cooled,

thermophoresis to the fins and tubes is also considered. When cooled below the

dewpoint, the effect of condensed moisture, both through the mechanism of

diffusiophoresis and owing to increased tube diameter and fin thickness from condensed

moisture, is also included. Each deposition mechanism is defined and described below.

2.4.1 Deposition on leading edge of fins

My field examination of fouled heat exchangers suggested that impaction on the

leading edge of the fins is an important deposition mechanism. For this analysis, I

assume that the fin edge is a blunt body and use Hinds’ (1999) analysis for rectangular

slit cascade impactors with a modification to account for the fraction of face area of the

coil that is occupied up by fin edges. This analysis assumes that the air approaching the

fin edge makes a 90° bend. All particles that impact on the surface are assumed to stick.

The penetration fraction accounting only for losses because of impaction on fin edges,

P fin, is estimated as follows:

12

fint fin eff , fin

t P S k cf

w

π = −

(2.4)

where Stk eff,fin is the particle Stokes number based on the duct air velocity and the fin

thickness, corrected for particles having particle Reynolds numbers > 0.1 (Israel and

Rosner, 1983; Seinfeld and Pandis, 1998),t fin is the fin thickness, w is the center-to-center

fin spacing, and cf is the corrugation factor. The corrugation factor takes into account the

fact that a corrugated fin is longer than a straight fin and thus has more area for particle

impaction. The corrugation factor is defined as 2 2 y h / h+ where h is the average


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height of the fin corrugations and y is the peak-to-trough corrugation width (see Figure

2.1 for a schematic of the geometry). The term in the parentheses in Equation (2.4) is

limited to a maximum value of one to limit deposition only to the fraction of particles that

are directly in front of each fin.

Hinds (1999) estimates a 10% uncertainty bound on deposition (1- P fin) when

using the formulation of Equation (2.4) for cascade impactors. Although seemingly quite

crude, this uncertainty is adequate for this situation, because of the addition of the t fin /w

factor which, for the most extreme case (corresponding to a dense fin spacing) is 10%.

Thus the actual error in P fin is at most 1% from using this analysis. This contribution to

uncertainty also is likely considerably smaller than that which results from the adaptation

of Equation (2.4) from cascade impactor geometry to analysis of deposition on the

leading edge of heat-exchanger fins.

Equation (2.4) predicts the penetration fraction for cascade impactor plates.

There is some question about how appropriate the analysis is for deposition on a fin edge

because fin edges are much thinner that cascade impactor plates and thus cause less

disturbance to fluid streamlines. The thinner fin edges would cause Equation (2.4) to

underpredict the penetration associated with fin edge-impaction. An alternative estimate

of the penetration fraction for this mechanism was calculated assuming that the fin edges

were vertical half-cylinders with diameter equal to the fin thickness. A modification of

the work of Wang (1986) for deposition of particles from turbulent flow onto circular

cylinders was used:

0 802 1

1 arctan 0 808

. fin

fin,round eff , fin

t P . Stk cf

wπ

= − −

(2.5)

Equation (2.5) is discussed in more detail below, in the section about particle impaction

on refrigerant tubes.


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Equations (2.4) and (2.5) require knowledge of the particle Reynolds number for

the calculation of the Stokes’ numbers. The particle Reynolds number (see Table 1.2)

requires calculation of both the gas and the particle velocity. Without a detailed flow

field, this difference is unknown. The particle Reynolds number is required for

calculating the drag coefficent (C D), which in turn is used to calculated Stk eff,fin. To

explore the effects of Re p on the results, an assumption was made that the difference

between the particle and the gas velocity was equal to the gas velocity for calculating P fin.

The implications of this decision are discussed in the presentation of the simulation

results. For comparison purposes, P fin was also calculated assuming that all particles

obeyed Stokes law for drag on a sphere.

There is reason to believe that Equation (2.4) is a more appropriate predictor of

fin-edge impaction than Equation (2.5). The geometry of a fin edge is more similar to a

blunt impactor plate than it is to the smoothly rounded edge assumed in Equation (2.5).

Also, although the fin edges represent a smaller collection area than impactor plates, the

details of how the air streamlines deviate around the fin edges is also important.

According to the analysis of Panton (1996), for appropriate Reynolds numbers ( Re fin), the

streamlines would deviate from their straight-through orientation much closer to the fin

edge than they would for a cascade impactor plate. This would cause more particles to

impact than if the streamlines curved further back from the fin edge.

Additional attempts to refine the calculations of the fin edge-impaction could be

done by using the flow field from the flow into cascading plates presented by Panton

(1996) and using a Lagrangian approach to track particles. In preliminary simulations

with 15 µm particles, a 2 m/s air velocity, and a fin spacing of 4.7 fin/cm ( Re fin ≅ 200),

this approach yielded similar results to Equation (2.4). This potentially more accurate

and computationally intensive avenue could be explored if greater accuracy was required


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for the leading edge impaction calculation. However, because impaction on fin edges

accounts for, at most, 10% removal of particles (corresponding to complete removal of

particles in front of each fin edge), this deposition mechanism does not warrant these

more sophisticated calculations for my present purposes.

2.4.2 Impaction on refrigerant tubes

Particles may also impact on the refrigerant tubes that run perpendicular to the

airflow direction and the fins. There are several theoretical and experimental studies of

particle impaction on tubes. An extension of the analysis of Israel and Rosner (1983)

suggests the following formula for estimating penetration for flow past a network of

tubes:

14

2 3

1 1 11 1 1 25 0 014 0 508 10

set n

tubetube offset

tube

d P . . . n

a wa a

−−

= − + − + ×

(2.6)

where a = (Stk etf,tube – 1/8) where Stk eff,tube is the particle Stokes number based on the air

velocity in the heat exchanger and the tube diameter, n set is the number of tube sets in the

direction of flow d tube is the refrigerant tube diameter, wtube is the center-to-center tube

spacing, and noffset is the number of offset tube rows in each tube set. The term in the

innermost parentheses is limited to value of less than or equal to one and the

d tube /wtubenoffset factor is added to limit the deposition to particles in the volume of air

directly in front of the tubes. The assumption that a given particle will not deposit if their

Stokes number is less than 1/8 was first proposed by Taylor and has been verified by

other researchers (e.g. Bott, 1988). Israel and Rosner (1983) report that single tube

impaction deposition calculated with this formulation is good to 10% root mean square

(RMS) error for isolated horizontal tubes.

For improved accuracy, the following fit from Wang (1986) was used:


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( )0 8021 arctan 0 80

set n

. tubetube offset

tube

d P . a n

wπ

= −

(2.7)

The difference between Equations (2.6) and (2.7) is very small (< 2%) for Stk eff,tube > 5,

although it is much greater for Stk eff,tube < 1. Given the importance of relatively low

particle Stokes numbers in the fouling problem, Equation (2.7) was used for all modeling.

In all cases, P tube was limited to a minimum value of 1 - d tube /wtubenoffset to only allow for

removal of particles directly in front of the tubes.

There are several important assumptions that must be made to allow the use of

Equation (2.7). The first is that each tube can be considered to be independent of the

other tubes in the system. The simulations and experimental work of Ilias and Douglas

(1989) suggest that this is a good assumption for tubes in a vertical plane with tube

spacings typical of those in HVAC heat exchangers. However, the wake of upstream

tubes can alter deposition for downstream rows of tubes. Braun and Kudriavtsev (1995)

conducted numerical flow simulations for flow past a tube network with d tube = wtube =

z tube, where z tube is the tube spacing in the direction of flow. The flow fields in their work

suggest that the wake effect can lead to greatly increased turbulence on downstream tubes

at Retube typical of HVAC heat exchangers. This greater turbulence would in turn lead to

increased particle deposition, although the magnitude of this effect is unclear. The

narrow fin channels tend to decrease the air turbulence, and geometric features that are

designed to restart the boundary layers and promote turbulence tend to increase air

turbulence. The effect of tube wake was not quantified because of lack of data on

turbulence characteristics in a representative geometry.

The second assumption is that the particles are uniformly mixed as they approach

each tube. Although the tube wakes promote mixing, the short characteristic time that it

takes particles to travel between the sets of tubes [O(10 ms)] means that the assumed


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25

uniform particle concentration, particularly at high enough Stk eff,tube to cause significant

deposition (Stk eff,tube > ~1), is unlikely to be correct for downstream tube rows. Bouris

and Bergeles (1996) document this shielding effect for a very high flow system ( Retube =

1.3 ×104) with very large particles (45 - 700 µm). Their experimental work in a

combustion boiler heat exchanger, suggests about 80% less deposition on the second row

of aligned tubes. Their work is not directly applicable (because of the high flows and

large particle sizes), but it does suggest that the shielding effect can be significant. This

would then lead to Equation (2.7) overestimating deposition. To establish the lower

bound on uncertainty resulting from the shielding effects, calculations were done

assuming complete shielding (i.e. only considering deposition on the first two vertical

row of tubes in Figure 2.1 by setting n set = 1 in Equation (2.7)).

Similar to the calculation of P fin, the difference between particle and gas velocity

is not explicitly known. As in the fin impaction case, assumption of this difference being

equal to the air velocity was made for impaction on tubes. This is more clearly a good

assumption for impaction deposition on tubes than it is for fins because, as a consequence

of the larger tube diameter, deposition only occurs for much larger particles than impact

on the fin edges. Larger particles have significant inertia and larger relaxation times and

are less likely to quickly adjust to changes in air velocity near the tubes. Thus, the

assumption of non-Stokesian drag (i.e. using the Seinfeld and Pandis (1998) equations for

C D) is more appropriate and was used for all calculations.

2.4.3 Gravitational settling on fin corrugations

To increase heat transfer, manufacturers often corrugate fins. Large particles can

deposit by gravitational settling on the corrugation ridges. The penetration fraction

accounting for losses only from gravitational settling, P G, is estimated as follows (Fuchs,

1964):


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( )1

V z y s P GhU w t fin

= −

− (2.8)

where V s is the particle settling velocity, z is the heat exchanger depth in the direction of

bulk air flow, h is the average height of the fin corrugations, U is the bulk air velocity in

the heat exchanger, and y is the peak-to-trough corrugation width (see Figure 2.1 for

geometric description). The ratio in the parentheses is limited to a value of one. Particles

are not assumed to be Stokesian for the calculation of V s, for which this equation is used:

( )cD

4C

3C

p air p s

air

d g V

ρ ρ

ρ

−=

(2.9)

where C c is the Cunningham slip correction factor (Hinds, 1999), ρ p is the particle

density, ρ air is the air density, d p is the particle diameter, g is acceleration due to gravity,

and C D is the coefficient of drag on the particle calculated assuming the particle is a

sphere and using the formulation presented in Seinfeld and Pandis (1998). Because C D

is a function of particle Reynolds number, which is a function of V s, an iterative scheme

was used to determine V s.

The largest uncertainty connected to deposition associated with gravitational

settling is that the channel geometry that Fuchs (1964) considered is significantly

different than the sloped wall and ceiling geometry that occurs in the fin corrugations.

Furthermore Fuchs’ analysis was limited to laminar flow, rather than the transition flow

in heat exchangers. Several researchers have considered gravitational settling in

horizontal tubes (e.g. Pich, 1972) and inclined tubes (e.g. Lipatov et al., 1988; Anand et

al., 1992), but these geometries are even less applicable because of their circular cross

section or the fact that they slope in the direction of flow, rather than across the channel

as occurs in a fin corrugation. To assess the variation in deposition by gravitational

settling, an upper bound on the penetration fraction associated with this mechanism was


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made by doubling the average height of the fin corrugation. Similarly, a lower bound

was estimated by halving the average height of the fin corrugation.

2.4.4 Deposition by air turbulence in fin channels

Air turbulence in the duct leading up to a heat exchanger can also induce

deposition on heat-exchanger surfaces. The fluctuating components of velocity can

impart an angled trajectory to particles as they enter the heat exchanger (see Figure 2.3).

If the particle has a sufficiently large relaxation time and a sufficient deviation in velocity

direction from the bulk flow, it will impact on a fin and not penetrate the coil.

w p'

wT

u p'U

z

Figure 2.3: Top view of fin channel showing particle trajectory because of air turbulencewhere wT is the particle entering location, w p´ is the fluctuating particle velocity

component perpendicular to fin channel, U is the bulk air velocity, u p´ is the fluctuating

particle velocity component in the direction of airflow, and z is the heat exchanger depth

Mathematically, I estimate the penetration associated with losses owing to

turbulent deposition as:

Prob 1imp

T

p

P τ

τ

= >

(2.10)

where τ imp is the characteristic time for a particle to impact on the wall and τ p is the

particle relaxation time. The impaction time scale, τ imp is calculated from geometry and

trigonometry as follows:


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T

imp p

w

w ' τ =

(2.11)

where wT is the distance from the nearest fin when the particle enters the channel and w p´

is the particle turbulence fluctuating velocity component perpendicular to the fin channel

at a given particle entering location. The particle relaxation time, τ p, was computed

according to the following expression, which does not assume Re p < 0.1 Hinds (1999).

( )c

D

4C

3C

p p p '

air p

d

U u

ρ τ

ρ =

+ (2.12)

where u p´ is the particle turbulence fluctuating velocity component in the streamwise

direction at a given particle entering location

A Monte Carlo simulation was used to estimate P T . For a given particle size, 107

simulations were completed to minimize any numerical uncertainty. In the analysis,

particles were assumed to enter the channel uniformly distributed between the fins, by

selecting wT from a uniform distribution with maximum value of (w-t fin )/2. The

fluctuating components of the air velocity were assumed to be independent Gaussian

distributions whose shape, as a (weak) function of bulk velocity in the duct, comes from

direct numerical simulation (DNS) data presented by Moser et al. (1999). Although we

are considering impaction by air turbulence as a two-dimensional phenomenon (because

the vertical component of fluctuating velocity will not lead to significant increased

deposition), the Moser et al. (1999) simulations consider all three dimensions.

The Moser et al. (1999) data provide the fluctuating components of the air

velocity. Caporaloni et al. (1975) present a multi-step formulation for relating fluid

fluctuating velocity components to those of particles in the turbulent flow:

pu ' Ku' = (2.13)


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2

1

fl

fl

aT b K

aT

+=

+ (2.14)

( )2

36

2 p air p

µa

d ρ ρ =

+ (2.15)

3

2air

p air

b ρ

ρ ρ =

+ (2.16)

where T fl is the Lagrangian integral scale of time which is assumed to be equal to є /u´ 2

where є is the eddy viscosity determined from the Moser et al. (1999) data and µ is the

dynamic viscos

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Fouling calculation in heat exchanger

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