Kuppan T. Heat Exchanger Design Handbook

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144

Chapter

4xVeloci

Pressure Drop in the Nozzles

Pressure drop in the inlet nozzle,

-pnSi,

is given by

1.0xVelocity head

Pressure drop in the outlet nozzle,

AP~,~,

is given by

0.5Gi

Pn,e

gcPt

OSxVelocity head

Total pressure

drop

associated with the inlet and outlet nozzles,

Apn,

is given

1.5xVelocity head

where

is mass velocity through nozzle.

6.2

Temperature-Dependent Fluid Properties Correction

One of the basic idealizations made in the theoretical solutions for

and

is that the fluid

properties are constant. Most of the experimental

and

data obtained involve small tempera-

ture differences

that the fluid properties do not

vary

significantly. For those problems that

involve large temperature differences, the constant-property results would deviate substantially

and need to be modified

[2,5].

Two schemes for such correction commonly used are:

The property ratio method, which is extensively used for the internal flow problem

The reference temperature method, which is most common for the external flow problem

One of the two methods, the property ratio method, is described next. In the property ratio

method,

all

properties are evaluated at the bulk mean temperature, and then all

the variable

properties effects are lumped into a function. Shah’s approach

[5]

to temperature-dependent

fluid properties correction via the property ratio method is discussed here.

Gases

For gases, the viscosity, thermal conductivity, and density are functions of the absolute temper-

ature

they generally increase with temperature. The temperature-dependent property effects

for

gases are correlated by the following equations:

145

Heat Exchanger Thermal

Design

where the subscript cp refers to the constant property variable and all temperatures are absolute.

All of the properties in dimensionless groups of Eqs. 15 and 16 are evaluated at the bulk mean

temperature. The values of the exponents

and

depend upon the

flow

regime, namely,

laminar or turbulent.

Larninar Flow.

For laminar

flow,

the exponents

and

are given by

[

161:

0.0,

.OO

for 1

(heating)

(17)

0.0,

0.81 for

0.5

Trn

(cooling)

(18)

Turbulent

Flow.

Gas Heating.

For gas heating, Sleicher and Rouse

[

171 recommend the following correla-

tions:

0.012 (Pr

0.29)(T,/Tm)”

(19)

where

-[l~glo(TJTrn)]~.~’

0.3

(20)

Equations

and 20 are valid for

0.6

0.9,

104

106, 1

TJT,

WDh

40. All

the fluid properties in

Nu,

Re, and

are evaluated at the bulk mean temperature.

Further,

-0.10 for 1

Tw/Trn

2.4.

Gas Cooling.

Kays and Crawford

[

181 recommend

0.0

and

-0.10.

Liquids

For liquids, only the viscosity varies greatly with temperature.

Thus,

the temperature-dependent

effects for liquids are correlated by the following equations:

Larninar Flow.

For laminar flow through a circular tube, the exponents

and

are given by

Deissler

[

191 for heating and by Shannon and Depew [20] for cooling as

-0.14,

0.58

for

1 (heating)

-0.14,

+0.54 for

1 (cooling)

(24)

CLm

Turbulent Flow.

Petukhov [21] recommends the following values for the exponents

and

rn:

-0.11 for 0.08

L/pm

1 (heating)

-0.25

for 40

uprn

1 (cooling)

which are valid for 2

140, 104

1.25

10’. Also,

0.25 for

0.35

pw/p,,,

1 (heating)

0.24 for 2

&/pm

1 (cooling)

which are valid for 1.3

10, 104

2.3

10’.

146

Chapter

For liquid heating, Petukhov [21] correlates the variable property friction data in the fol-

lowing forms:

Equation 29 is based on the following data:

1.3

10,

10'

Re 22.3

lO', and 0.35-2 for

pwlpm.

Tables 6a and 6b show property ratio method exponents of Equations

(IS),

(16) or

Equations

(21)

and (22) for laminar flow and turbulent flow, respectively, both for gases and

liquids.

6.3

Performance Failures

Satisfactory performance of heat exchangers can be obtained only from units that are properly

designed and have built-in quality. Correct installation and preventive maintenance are user

responsibilities. The failure

heat exchanger equipment to perform satisfactorily may

caused by one or more factors:

Improper thermal design

Operating conditions differing from design conditions

Uncertainties in the design parameters

Excessive fouling

Air

gas blanketing

Flow maldistribution

Deterioration

the geometrical parameters that cause bypassing the main fluids

6.4

Maldistribution

A serious deterioration in performance results for a heat exchanger when the flow through

the

core is

not

uniformly distributed. This is known as maldistribution. Maldistribution of flow

takes place when the flow is not uniformly distributed over the frontal area of the core. This

is due to inherent design constraints in accommodating the distributor. Due to maldistribution,

the flow passages nearer to the distributor will be flush with more fluids, whereas the passages

further away will have lean flow or starve for want of fluids. Maldistribution causes the

fol-

lowing:

Thermal performance deterioration

Enhanced pressure drop

Erosive wear of flow passages with high mass velocity

Typical causes of maldistribution are

Poor header design; for example, too small header or distributor located in one end

the

core; flow commences from one end of the core and flows perpendicular to the core.

Blocking of fin passages due to fouling, mechanical damage of core passages.

Damage of flow passages either at the entrance

at the exit.

Maldistribution due to unfavorable nozzle location can

corrected either by relocating

the nozzles (Fig.

or using deflecting vanes (for side entry nozzle), or baffle plates or perfora-

ted plates

the header to direct the fluid uniformly through the tubes [22]. The baffle plate/

perforated plate should be installed parallel to the tubesheet.

---

Heat Exchanger Thermal

Design

147

GEOMETRY

ERROR

MESSAGES

Figure

Overall structure of a thermal design computer program for a compact heat exchanger. From

Low

Reynolds

Number

Flow

Heat Exchangers, 1983, pp. 983-998, Shah,

K.,

Hemisphere Publishing

Corporation, Washington,

D.C.

6.5

Fouling

Fouling of the shell-side heat-transfer surfaces is common. Generally the effects of fouling are

to reduce the leakage of fluid between baffles and tubes by blocking these gaps, and it

also

results in less leakage paths

[23].

Industrial practice is generally to evaluate the heat transfer

in the clean condition and apply appropriate fouling resistances (Table

of Chapter

gives

partial list) to arrive at the heat-transfer surface area required in the fouled condition. Pressure

drop is lower during commissioning and startup after cleaning and gradually increases to values

those predicted in the fouled condition.

I48

Chapter

Table 6a

Property Ratio Method Exponents of

Eqs.

(15) and (16), or of

Eqs.

(21) and

(22) for Laminar

Flow

~ ~~ ~

Fluid Heating Cooling

Gases

=O.O,

1.00

for

<TJT,

[16] n=0.0, m=0.81 for

0.5

TJT,,

[16]

Liquids

-0.14,

0.58 for

pu/pm

1 [20]

[19] n

-0.14,

0.54 for

pu/pm

Table 6b

Property Ratio Method Correlations Or Exponents of

Eqs.

(15)

and (16),

or of Eqs. (21) and (22) for Turbulent

Flow

Fluid Heating Cooling

Gases

0.012

Re""

(Pr

0.29) (TJT,)"

n=O

[18]

-[10g,,,(T,,/T,)1"~

0.3

for 1

TJT,

0.6

0.9,

10'

106

and

L/Dh

[

171

-0.1

for

TJT,,

2.4

-0.1

(tentative)

[

181

Liquids [2

-0.1

for

0.08

pH/pm

-0.25t for

h/pm

f/f,,

pJp,)/6$

0.25 for

0.35

p,/p,,,

0.24$ for

~,,/p,,,

~~ ~~ ~~~~~~~~~

?Valid

for 2

140,

10'

1.25

10'

$Valid

for

1.3

10,

10'

2.3

10'

6.6

Corrosion Allowance

Corrosion allowances are required for the various heat exchanger components to allow for the

material loss due

corrosion in service. Corrosion allowances are specified according to the

severity of corrosion and the corrosion resistance property

the material. Corrosion allowance

usually specified by the purchaser and goes hand-in-hand with the material selection.

COOPERATIVE RESEARCH PROGRAMS ON HEAT EXCHANGER

DESIGN

text on thermal design of heat exchangers would not be considered complete unless mention

is made about HTRI and HTFS.

7.1

HTRI

Heat Transfer Research, Inc. (HTRI), Alhambra, CA, is a cooperative research organization

whose membership includes many of the leading users

heat exchangers, engineering contrac-

tors, and heat exchanger manufacturers. One

the major activities of HTRI is the development

computer programs that enable its members to design and rate heat exchangers.

7.2

HTFS

Heat Transfer and Fluid Flow Service (HTFS) is a cooperative venture between industry and

the United Kingdom and Canadian governments.

HTFS

carries

out

its work at three facilities:

Harwell Laboratory (its headquarters) in England, NEL (formerly the National Engineering

Laboratory) in Scotland, and Chalk River Laboratories in Ontario, Canada. HTFS has over

200

members worldwide, in over

countries. Industries covered include chemical processing,

engineering contracting, heat exchanger fabrication, petroleum refining, pharmaceuticals, elec-

tric

and gas utilities, petrochemicals, and plastics. HTFS products and services such as com-

Heat Exchanger Them1 Design

149

puter programs, design handbook, and research papers are available only to members. HTFS

also provides technical advice and consultancy and other information services, including educa-

tional courses. For more information, contact Marketing Manager, Heat Transfer and Fluid

Flow Service, Chalk River Laboratories, Chalk River, Ontario, Canada,

KOJ

JO.

UNCERTAINTIES IN THERMAL DESIGN

HEAT EXCHANGERS

A major problem constantly faced by heat exchanger designers is to predict accurately the

performance of a given heat exchanger or a system of heat exchangers for a given set of

service conditions. The problem is complicated by the fact that uncertainties exist in most of

the design parameters and in the design procedures themselves [24]. The design parameters

that are used

the basic thermal design calculations

a heat exchanger include process

parameters, heat-transfer coefficients, tube dimensions (e.g., tube diameter, wall thickness),

thermal conductivity

the tube material, and thermophysical properties

the fluids. Nominal

or mean values

these parameters are used in the design calculations. However, uncertainties

in these parameters prevent us from predicting the exact performance of the unit. The effect

of the uncertainties is mostly in the performance degradation in service. Hence, there is an

imperative need to consider all the uncertainties and to critically evaluate them and correctly

predict the thermal performance of a heat exchanger. This is particularly true for critical appli-

cations. In this section, various uncertainties that influence the thermal performance and a

method to account for these uncertainties in the design calculations are presented.

8.1

Uncertainties in Heat Exchanger Design

Uncertainties in the design parameters are summarised by Al-Zakri et al. [24], Cho [25], and

Mahbub Uddin and Bell 1261. Various uncertainties and their reasons are:

Fluid flow rates, temperatures, pressures, and compositions

vary

from the design condi-

tions.

2. Temperatures of cooling water and air used to cool process fluids vary with seasonal

temperature changes.

Physical properties of the process fluids are often poorly known, especially for mixtures.

Heat-transfer and pressure-drop correlations from which one computes convective heat-

transfer coefficients and pressure drop have data spreads around the mean values.

Manufacturing of heat-transfer tubes and other component dimensions influencing thermal

performance does not produce precise tube dimensions.

Manufacturing tolerances in equipment lead to significant differences in thermohydraulic

performance between nominally identical units.

Fouling of heat-transfer surface is poorly predictable.

Miscellaneous factors influence the thermal performance.

In this section, the following uncertainties

are

discussed.

Uncertainty in process conditions

Uncertainty in the physical properties of the process fluids

Flow nonuniformity

Nonuniform flow passages

Uncertainty in the basic design correlations

Uncertainty due to thermodynamically defined mixed or unmixed flows for crossflow

heat exchangers

Bypass path on the air side of compact fin-tube exchangers

150

Chapter

Nonuniform heat-transfer coefficient

Uncertainties in fouling

10.

Miscellaneous effects

Items 1-3,

and 8-10 are common both for shell and tube exchangers and compact heat

exchangers. Items

and 7 pertain to compact heat exchangers only.

Uncertainty in Process Conditions

Heat exchangers are designed for a nominal set of operating conditions chosen to represent

relatively ideal state of a system. In general, a heat exchanger will not operate under the ideal

design conditions. Process stream flow rates, compositions, and temperatures can all be ex-

pected to vary during the lifetime of the exchanger, and seasonal changes in weather constantly

change cooling water and air temperatures.

Uncertainty

the Physical Properties of the Process Fluids

Correlations for heat-transfer coefficients and pressure drops, and the heat-transfer rate equa-

tion, require values of one or more of the following physical properties: density, specific heat,

viscosity, thermal conductivity, latent heat, etc. There are substantial uncertainties in the physi-

cal properties of all but a few fluids. Uncertainties

these physical properties are due to

the

following reasons [27]:

1. Measure error.

Extrapolation and interpolation errors-interpolation errors may be very small, whereas

extrapolation errors may substantial.

3. Estimation errors.

Errors

estimated temperatures and pressures.

Mixture properties calculated from component properties.

Physical properties closer to the critical temperature and pressure change rapidly and

sig-

nificantly. Any attempt to get mixture properties via individual properties of components

around their critical points needs great care.

the fluid

a mixture, the uncertainties will normally be larger than those for a pure

component.

Flow Nonuniformity

obtain maximum thermal performance, the flow should be uniform across the entire frontal

area of the core. However, the flow may not be uniform due to unfavorable header design,

nozzle location, and nonuniform flow passages in the case of tube-fin and plate-fin heat ex-

changers. For example, automobile radiators are usually designed with the assumptions that

the cooling air

uniformly distributed over the radiator core, and the cooling water is uni-

formly distributed over the radiator tubes

[28].

According to Chiou [28], these assumptions are

normally not met due to these reasons: Flow nonuniformity on the cooling airside is usually

due to unfavorable location

fan with respect to the radiators and due to crowded radiator

compartment. The flow nonuniformity on the engine coolant side is the result of the unfavor-

able arrangement and configuration

the inlet manifold of the coolant to the radiator. Nonuni-

form flow distribution adversely affects the thermal performance and also could produce high-

velocity regions leading to erosion-corrosion of flow passages. Chiou presents a mathematical

method to determine the thermal effectiveness

the engine radiator accounting for two-dimen-

sional nonuniform fluid flow distribution on both cooling air and engine coolant sides. Flow

nonuniformity due to header design and due to unfavorable location

radiator fan of a diesel

electric locomotive are discussed next.

Flow

Nonuniformity

Due

Header Design.

Normally the frontal area of a compact heat

exchanger is very large compared to the dimensions of the nozzles and the core depth. The

151

Heat Exchanger The

rma

Design

large frontal area requires turning the streams in a system of headers. The turnings have marked

area changes through the headers, leading to nonuniform flow through the core (Fig.

9),

even

though there may be uniform flow passages. Therefore, the header design has a profound effect

on the thermal performance of the core. The main objective

designing the header is to ensure

uniform distribution of fluids over the entire frontal area of the core and to have minimum

pressure drop due to flow turning. Maldistribution due to unfavorable nozzle location can be

corrected as discussed earlier, The thermal performance degradation due to unfavorable nozzle

location on the tubeside can be evaluated as discussed by Muller

[29].

If the tube-side film

coefficient is not controlling the overall thermal resistance, the effect of maldistribution on the

overall heat-transfer coefficient will be negligible.

Maldistribution Due to Unfavorable Location

Radiator Fan in a Diesel Electric Locomotir*e.

Flow nonuniformity on diesel locomotive radiators is usually due to inherent problems on the

air side due to unfavorable location

the fan with respect to the radiators. In diesel locomo-

tives, the left and right radiators are mounted vertically; the radiator fan

mounted at the top

but at the center

the radiators, which results in nonuniform flow distribution over the radia-

tors. Other reason for flow nonuniformity are crowded radiator compartment fitted with lube

oil cooler and filter, and radiator fan drives.

Nonuniform Flow Passages

For high-surface-density compact heat exchangers like tube-fin and plate-fin units with parallel

fins, the identified nonuniform flow passages are due to

[30]

(1)

nonuniform

fin

spacing,

(2)

recurved fin, and

(3)

open fin. For mechanically bonded tube-fin cores, there

ample scope

for bunching of fins due to deficiency in bullet expansion, thermal fatigue, and cracking of

fin

collars. Maldistribution due

nonuniform flow passages as shown

Fig.

does not ad-

versely affect the thermal performance in the case of either turbulent flow or highly interrupted

laminar flow surfaces like offset strip fins and louvred fins, but can have a marked effect in

fully developed laminar flow in continuous cylindrical passage geometries, such as those em-

ployed in disk-type rotary regenerators

[31].

a result, the reduction in Colburn

factor is

substantial, with a slight reduction in friction factor

The theoretical analysis of this problem

\’

-f

I 1

Figure

Pressure drop through

heat exchanger on one side (schematic representation). From Low

Reynolds Number

Flow

Heat Exchangers,

1983,

pp. 21-71, Shah, R.

K.,

Hemisphere Publishing Corpora-

tion, Washington,

D.C.

Reproduced with permission.

All

rights reserved.

Figure

Entrance and exit pressure loss coefficients for (a) a multiple circular tube core, (b) multiple

flat tube core,

(c)

a multiple square tube core, and (d)

multiple triangular tube core,

Kays".

152

153

Heat Exchanger Thermal Design

for low Reynolds number laminar flow surfaces is discussed in Refs. 30a, 30b, and 31. To a

certain extent, nonuniform flow passages due to fin bunching of mechanically bonded cores or

soldered radiator cores can

overcome by combing of fins during maintenance schedules.

Uncertainty in the Basic Design Correlations

All of the correlations for the basic fluid flow and heat-transfer mechanisms in heat exchangers

show scatter when compared to experimental data. Some processes, such as, nucleate boiling,

are only very crudely predictable a priori

[24].

Uncertainty Due to Thermodynamically Defined Mixed or Unmixed Flows for

Crossflow Heat Exchangers, After Digiovanni and Webb

[32]

The thermal effectiveness of cross-flow heat exchangers is evaluated for known values of NTU

and capacity rate ratio

C*,

from the thermodynamically defined fluid mixedness and unmixed-

ness and/or both through the core. The typical patterns of flow mixedness across the core are:

1. Unmixed-unmixed; e.g., brazed plate-fin exchanger with plain fins and continuously

finned tube compact heat exchanger

Unmixed-mixed

3. Mixed-mixed

However, the thermodynamic definitions

not tell whether a specific geometry will

provide mixed or unmixed flow. For any values of NTU and

C*,

the unmixed-unmixed ar-

rangement yields the highest thermal effectiveness and the mixed-mixed arrangement has the

lowest, and the unmixed-mixed case offers the intermediate values.

Generally there is always some mixedness on the air side in the cases of individually

finned tube banks and offset strip fins. During the design stage if these cases are assumed to

act

a thermodynamically unmixed case, the actual thermal effectiveness will be less than

the predicted value. For a tube bank, the level

mixedness depends on the tube layout pat-

terns, pitch ratios, Reynolds number, size of the eddies in the transverse direction, etc.

Correction

for

Partial

Mixing.

Digiovanni and Webb [32] developed a procedure to calculate

the effectiveness of cross flow heat exchangers for partially mixed flow. To calculate the

correction factor, it is necessary to provide a quantitative definition of the “percent mixing,”

which is designated

1OOy.

The partially mixed condition is defined by linear interpolation

between the unmixed and the mixed flow effectiveness values. If

y=O,

the flow stream is

unmixed, and

represents the fully mixed stream. There are three possible cases of interest

for the partially mixed condition:

Partially mixed flow on one stream and unmixed in the other stream

One stream partially mixed and the other stream mixed

Both streams partially mixed

They presented equations to define

for the three cases of interest. For case

has been

defined; for the other two cases refer to Ref. 32.

Case 1.

If the measured effectiveness of the partially mixed exchangers is

then

From the above equation, for

mixedness,

is given by

~pm,u

&u,u

(~,u

ErnJ

(31)

Nonuniform Heat-Transfer Coefficient

The idealization that the heat transfer coefficient,

is constant throughout its flow length is

not correct. It varies with location, the entrance length effect (due to the boundary layer devel-