Kuppan T. Heat Exchanger Design Handbook

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314

Chapter

2.6 Comparison of Recuperators and Regenerators

A recuperator is easier to build and rugged in design. For a given size, the recuperator

less effective than the regenerator due to lower overall mean temperature difference. The

regenerator, on the other hand, is smaller and, for its size, a much more efficient heat

exchanger. Much higher surface area, higher heat-transfer coefficients because of random

nature of flow through the packing, and a higher oveall temperature difference as the top

of the packing is heated to the exhaust gas temperature

[7]

are found.

Because a recuperator is not rotating and is at a constant temperature, there is less thermal

shock and many normal materials can be used. Because of periodic flow, regenerators are

subjected to thermal shock.

A recuperator does not have the problem of sealing between the hot and cold gas streams.

3 CONSIDERATIONS IN ESTABLISHING

HEAT RECOVERY SYSTEM

Although the addition of a regenerator is highly attractive from a thermodynamic point of

view, its bulk, shape, mass, or cost may be such as to nullify the thermodynamic advantages.

Optimum design therefore will call for a careful consideration of the following factors

[4]:

Compatibility with the existing process

[8].

Initial capital cost.

Economic benefits.

Life of the equipment.

Maintenance and cleaning requirement.

Controllability and production scheduling.

Other limitations include manufacturing limitations, and weight, space, and shape limitations.

3.1 Compatibility with the Existing Process System

In order for a heat exchanger to be integrated into a process, the system design must be

compatible with the process design parameters. One key area of compatibility is pressure drop.

Many combustion processes are designed to use the natural draft of a stack to remove the

products of combustion from the process. The heat recovery equipment designed for such a

process either must be designed within the pressure drop limitations imposed by natural draft

or must incorporate an educator to overcome these pressure drop restrictions

[8].

3.2 Economic Benefits

Economic considerations in establishing the need for heat exchanger should include initial

capital costs, and fuel savings.

Capital Costs

The capital costs include the heat exchanger costs and the ancillary equipments required for

the functioning

the system. Such ancillary equipment includes the following:

Blowers.

Both the flue gas and the preheat air streams would require blowers to overcome

pressure losses in the system.

Ducting.

Ducting

between the furnace and the heat exchanger to conduit the flue gas and

the preheat air.

Controls. The proposed heat recovery system would be operated in conjunction with the

demand of the furnace. A control mechanism would

established for this purpose.

Regenerators

Energy Savings.

The benefits of energy savings due to the heat recovery system should offset

the capital costs on heat exchanger, blowers, ducting and control mechanisms, and maintenance

cost. A break-even analysis (capital costs vs. fuel savings) will help in this regard. The desired

economic benetifs can be accomplished by designing a heat exchanger to [8]:

1. Maximize the equipment life.

Maximize the energy cost savings.

Minimize the equipment capital costs.

3.3

Life of the Exchanger

The success of waste heat recovery depends on the maximum equipment life against the hostile

environment of exhaust gases. The factors that affect the heat exchanger life are

[8]:

Excessive thermal stress.

2. Creep.

Thermal fatigue and thermal shock.

4. High-temperature gaseous corrosion.

Corrosion and stress cause accelerated failure in both metal and ceramic recuperators, resulting

in leakage, which degrades the performance.

3.4

Maintainability

Ideally, a heat exchanger should provide long service life and the equipment installation should

facilitate easy maintenance. Where necessary, the design should incorporate provisions to iso-

late the heat exchanger from the system

that inspection, maintenance, repairs, and replace-

ment can be made without interrupting the process, and the ability to clean the fouling deposits

from the heat transfer surfaces should be provided for those processes

which fouling will

take place, Ref.

(8).

REGENERATOR CONSTRUCTION MATERIAL

An important requirement of a regenerator for waste heat recovery is life and extended durabil-

ity. Regenerators are to work under hostile environments including

(

1) elevated temperatures,

(2)

fouling particulates,

(3)

corrosive gases and particulates, and (4) thermal cycling [9]. To

achieve this requirement, proper material selection is vital. Much of the waste heat is in the

form of high temperature

(

1900-300OoF), and the exhaust gases are corrosive in nature. There-

fore, the two important considerations for selecting material for heat exchangers of a heat

recovery system are

(1)

strength and stability at the operating temperature, and (2) corrosion

resistance. Other parameters include low cost, formability, and availability.

4.1

Strength and Stability at the Operating Temperature

Metals

are

ideal for recuperator and regenerator construction because of their ductility and ease

fabrication. But the metallic units lack the ability to withstand high temperatures and are

susceptible to corrosion from exhaust gases. Stainless steels and certain nickel- and iron-based

alloys are the conventionally preferred materials. Generally, carbon steel at temperatures above

425°C

(800°F)

and stainless steel at temperatures above 650°C (1200°F) begin to rapidly

oxidize, and if the exhaust stream contains corosive constituents, there will be a severe corro-

sion attack

[

101. Approximate temperature ranges for various heat exchanger materials are

shown in Fig. 7

13. In general, above 1600"F, metal heat exchangers have limitations due to

Chapter

Figure

Approximate temperature range for various heat exchanger materials. (From Ref.

excessive costs from the expensive alloys required, requirements of temperature control devices

or loss of effectiveness due to air dilution, and maintenance problems due to high thermal

stresses [12]. In some cases, the high temperature problem is overcome by diluting the flue

gas with a portion

cold air to be preheated. However, dilution lowers the heat transfer from

the flue gas stream.

4.2

Corrosion Resistance

Materials for high-temperature heat exchangers should exhibit high-temperature gaseous and

liquid corrosion resistance to the carburizing, sulfidizing, oxidizing, etc. effects of combustion

products, and to the coal ash slags and fuel impurities. Regenerators used for heat recovery

from the gases generated by boiler, furnaces, heaters, etc. should be protected against “cold

end corrosion” caused by condensation of sulfuric acid and water on the heat-transfer surface

and the volatiles and corrosive fluxes in the exhaust gas. This problem is overcome either by

ceramic units or with the use of the porcelain enameled exchanger.

4.3

Ceramic Heat Exchangers

Ceramic units can be very cost-effective above 1600°F since they have the potential for greater

resistance to creep and oxidation at very high temperatures, and do not require temperature

controls or air dilution because

their high melting points [12]. At present, a ceramic heat

exchanger is probably the most economical solution for high temperature in excess of 800°C

(1475°F) applications where the specific strength of metallic materials decreases very rapidly.

The ceramic recuperators are available as plate-fin and bayonet tube exchangers. Material

properties that favor ceramic as regenerator materials are:

Moderate strength.

Generally inexpensive.

High thermal shock resistance and lower high-temperature creep.

Regenerators

Good corrosion resistance and excellent erosion resistance properties.

Low thermal expansion characteristics; this simplifies the sealing problem.

About one-fifth the density

steel, high specific heats, and higher thermal conductivity.

Low gas permeability.

The inability to join ceramic shapes reliably, once the parts have been densified, is a

serious impediment to the design of large assemblies such as heat exchangers. Among the

other drawbacks, the application of ceramic materials in recuperators is limited by the inherent

brittleness, the higher fabrication costs associated with producing ceramic heat exchangers, and

the low thermal conductivity of many oxide ceramics [13]. According to McNallan et al. [13],

because of their higher thermal conductivities and corrosion resistance compared with other

ceramics, silicon carbide-based ceramics have received the most attention as heat exchanger

materials.

4.4

Ceramic-Metallic Hybrid Recuperator

To overcome the high-temperature heat recovery problem a ceramic-metallic hybrid recupera-

tor is used. It consists

a ceramic recuperator operating in series with a conventional plate-

fin metallic recuperator. An air diluton system is employed between the two recuperators to

overcome the high-temperature oxidation problem of the metallic recuperator. This system is

capable of handling flue gas temperatures up to

1370°C

(2520°F).

4.5

Regenerator Materials for Other Than Waste Heat Recovery

The regenerator construction materials used for applications other than waste heat recovery are

discussed by Shah [3]. They include the following:

1. In the air-conditioning and industrial process heat recovery applications, rotary regenera-

tors are made from knitted aluminum or stainless steel wire matrix.

For cryogenic applications, ordinary carbon steels become brittle,

materials such as

austenitic stainless steels, copper alloys, certain aluminum alloys, nickel, titanium. and a

few other metals that retain ductility at cryogenic temperatures must be used. Cryogenic

materials are covered in the chapter

material selection and fabrication (Chapter 13).

Plastics, paper, and wool are used for regenerators operating below 65°C (150°F).

THERMAL DESIGN: HYDRAULIC FUNDAMENTALS

5.1

Surface Geometrical Properties

A consistent set of geometry-related symbols

and

factors facilitates comparative studies. The

following factors can be used for all geometries, either bluff or laminar [2].

Porosity,

void volume/total volume.

Area density,

surface aredtotal volume.

Hydraulic radius,

flow aredwetted perimeter

o/p.

Flow area,

porosity

frontal area

oAfr.

Cell density,

number of holes or cells per unit frontal area.

Reference 2 presents these surface geometrical factors for several surface geometries-square,

hexagonal, circular, rectangular, and triangular-which are reproduced in Table

The surface

geometrical properties, Dh (4rh),

(flow length),

and

are the same on both fluid sides.

They related to each other as follows:

318

Chapter

Table

Surface

Geometrical Properties for Rotary Regenerators

[2]

cell

density porosity

area

density

hydraulic

radius

cellsh

pOr

1lm

0.37

0.39

b2 4b

(b+S)'

(b+SI2

2Wb

7 b13

4fl

4b2 24 b

(2b+3SI2 (2b+3S

(2b

+36

the frontal area

not

50%

for each fluid, the disk frontal area, minimum free flow area,

and heat transfer area on each side will not be the same. The method to calculate frontal area

and heat-transfer surface area on the hot and cold sides, area for longitudinal conduction, and

mass

described by Shah

[14],

and

various

parameters are explained as per Shah's method.

If the flow area ratio split for both fluids

in the ratio

where

and if the face

seal and

hub

coverage are specified as

the total face area

AI,,[,

then the frontal areas on

each side, namely,

and

A,r.c,

are given by

AI,,[

(D'

d')

At,

AI,.,(

a/lOO)

Regenerators

319

Table

Surface Geometrical Properties for Triangular

Geometry Glass Ceramic Heat Exchangers

[

161

Core description/Case no.

505A 503A

504A

Passage count,

26 1008 2215

Numbedin’

Porosity,

0.794 0.708 0.644

Hyd. diam.,

Dh,

10-’

2.47 1.675 1.074

Area density,

ft’/ft3

1285 1692 2397

Cell heightlwidth,

0.731 0.709 0.708

UDh

101

149.5 233

where

Afr

Afr,h

A1r.c

the regenerator disk outer diameter at the end of the heat transfer surface

the hub diameter

The effective total volume of the regenerator is given by

(Afr.h

Ar,c)L

(4)

With the known porosity

the minimum free flow area on each side is calculated from

oA,,.

The heat-transfer surface areas on the hot and cold sides are given by

The matrix mass

is calculated from the following equation for

known

matrix material

density,

pr:

PrV

o)Ar,,L

(6)

5.2

Correlation

for

and

For

and

values of commonly used surface geometries, refer to Mondt [2] and Kays and

London [15]. Basic heat transfer and

flow

friction design data are presented for three straight,

triangular-passage, glass ceramic heat exchanger surfaces in London et al.

[

161. These surfaces

have heat-transfer area density ratios ranging from 1300 to 2400 ft?/ft’, corresponding to a

passage count of 526-2215 passagedin’. Table

provides a comparison of the surface geomet-

rical characteristics. Figure

provides a description of the idealized triangular geometry used

Figure

Idealised triangular geometry for glass ceramic heat exchanger. (From Ref.

16.)

320

Chapter

to calculate

and

Glass ceramic heat exchangers are of importance to vehicular gas turbine

technology as they give promise of allowing low mass production costs for the high-effective-

ness rotary regenerator required for most of the vehicular turbine engine concepts now under

development.

If manufacturing tolerances are controlled as specified, the recommended

factor for Re

1000

is given by

3.0

J=E

(7)

This is approximately 10% lower than the theory to allow for some passage nonuniformity

(+20% of flow area).

The recommended

factor for Re

1000 is given by

14.0

J=-

This is

higher than the theory to allow a small margin for the walls and the variation

passage cross section along flow length.

THERMAL DESIGN THEORY

The thermal design theory of recuperators is simple and quite straightforward. The effective-

ness-number of transfer units (E-NTU) method is used to analyze heat transfer in recuperators.

In contrast, the theory of the periodic-flow type regenerator is much more difficult. Despite

the simplicy of the differential equations under classical assumptions, their solution has proved

to be challenging, and performances of counterflow regenerators have been widely investigated

numerically as well as analytically

[

171.

Various solution techniques have been tried for solving

the thermal design problem, and they are discussed here.

6.1

Regenerator Solution Techniques

For the steady-state behaviour of a regenerator, Nusselt

[

181 has given an exact solution, which

conists of an infinite series of integrals. However, this solution is complicated for practical

purposes, and hence several solution techniques were developed. They are:

1. Approximate solution methods by simplifying the parameters defining the regenerator be-

haviour; examples include Hausen’s

[

191

heat pole method, which approximates the inte-

gral equation for the initial temperature distribution of the matrix. Hausen expressed the

performance result in terms of two dimensionless parameter called the

reduced length

and

the

reduced period.

Empirical effectiveness relation correlated by treating the regenerator by an equivalent

recuperator, e.g., that of Coppage and London [20].

Open Methods-Numerical Finite-Difference Method

Prior to the availability of general-purpose digital computers, regenerator thermal behavior was

analyzed by restricting the range of parameters. With the availability of digital computers,

Lamberston [21], Bahnke and Howard [22], Mondt

[23],

and Chung-Hsiung Li

[24],

among

others, used a numerical finite-difference method for the calculation of the regenerator thermal

effectiveness.

this approach, the regenerator and the gas streams are represented by two

separate but dependent heat exchangers with the matrix stream in cross-flow with each

gas

stream as shown in Fig.

Regenerators

321

Hot

Fluid

Cold

Fluid

thli 'h

t C,O

Figure

Regenerator matrix as the third stream. (From Ref.

Closed Methods

In the closed methods, the reversal condition is implicitly incorporated in the mathematical

model for solving the differential equations both for the hot period and cold period. The closed

methods used to solve the Nusselt integral equation are

Collocation method of Nahavandi and Weinstin [25] and Willmott and Duggan [26].

Galerkin method of Baclic

[

171 and Baclic et al. [27].

Successive integral method

(SIM)

of Romie and Baclic

[28].

6.2

Basic Thermal Design Methods

For design purposes, a regenerator is usually considered to have attained regular periodic flow

conditions. The solution to the governing differential equations is presented in terms

the

regenerator effectiveness as a function of the pertinent dimensionless groups. The specific form

of these dimensionless groups is to some extent optional, and the two most common forms are

(1)

the effectiveness and number of transfer units (E-NTU,) method (generally used for rotary

regenerators), whereby

$[NTU,,,

C*,

CT,

(hA)*]

(9)

and

(2)

the reduced length-reduced period

(A-ll)

method (generally used for fixed matrix

regenerators) in which

4Wh,

AC,

ml,

nc1

(10)

These two methods are equivalent as shown in Ref.

(20)

and Shah [29]; that is, the thermal

effectiveness of a single fixed regenerator is equal to that

the rotary regenerator with the

same values

the four parameters. This one-to-one correspondence between the two dimen-

322

Chapter

Table

Equivalence Between the

E-NTU,

and

Design Methods

~~~

E-NTU,

method

A-Il

method

[

(hA)*]

NTU,,

(hA)*]

NTU,,

sionless methodologies, as shown in Table

allows the results obtained in the form of either

Eq.

(9)

or (10) to

used for both types

regenerators.

The E-NTU,, method is mainly used for rotary regenerator design and analysis, and was

first developed by Coppage and London

[20].

Their model is explained next.

6.3

Coppage and Longon

[20]

Model

for

Rotary Regenerator

The E-NTU,, method was used for the rotary regenerator design and analysis by Coppage and

London

[20]

with the following idealizations.

The thermal conductivity of the matrix is zero in the gas and air flow directions, and

infinite in the direction normal to the flow.

The specific heats of the fluids and the matrix material are constant with temperature.

No mixing of the fluids occurs during the switch over from hot to cold flow.

The convective conductances between the fluids and the matrix are constant with flow

length.

The fluids flow

counterflow directions.

Entering fluid temperatures are uniform over the flow cross section and constant with time.

Regular periodic conditions are established for all matrix elements, and heat losses to the

surroundings are negligible.

Fluid carryover during the switching operation and the pressure leakage effects are negli-

gible.

On the basis of these idealizations the following differential equations and boundary conditions

may be expressed. For the hot gas flow, energy balance on the element

as shown in Fig.

10,

given by

Equation 11 represents the energy received by the matrix in terms of its thermal capacitance.

The right-hand side of Eq. 12 represents the energy given up by the hot gas, and

mgL

represents

Regenerators

323

Figure

Regenerator basic heat transfer model. (From Ref.

20.)

the mass of the hot gas retained in a flow length

dx.

The convective heat-transfer rate equa-

tion is

Elimination of

dqh

yields the equation

For

the cold gas

flow,

a similar equation results:

at, m'c

at,

Mc,

-+2A

-=---

MJ,

at,

-h&

(tc

Pcax

The boundary conditions are as follows:

For

interval

hot

flow:

th.

constant at

For

interval of cold flow:

t,,

constant at