Heat Transfer Handbook part 105 pot

The heat exchanger performance is represented by two dependent variables: heat transfer rateQ and pressure drop ∆p orpumping powerP , which can be expressed as ∆p = 2f L d i G2 ρ and P =

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It may be noted that objectives 1, 2, and 4 yield savings in operating (or energy) costs, and objective 3 lends to material savings and reduced capital costs These ob-jective functions and constraints have been described by many different performance evaluation criteria (PEC) in the literature (Bergles et al., 1974a,b; Webb, 1981, 1994;

Bergles, 1998; forexample) It is instructive to considersome of these PEC forthe more common case of applying enhancement techniques to the conventional shell-and-tube heat exchanger

The heat exchanger performance is represented by two dependent variables: heat transfer rateQ and pressure drop ∆p orpumping powerP , which can be expressed as

∆p = 2f L

d i

G2

ρ and P = ∆p

GA c

Here the primary independent operating variables are the approach temperature dif-ference∆T i[∆T m = φ(∆T i )] and the mass flow rate ˙m, and in the case of the tubular

geometry, the design variables (heat transfer surface areaA orexchangersize) are the

diameterd i and lengthL of tubes and numberof tubes N perpass PEC are

estab-lished for the process stream of interest by selecting one of the operational variables for the performance objective and applying the design constraints on the remaining variables

For single-phase flow heat transfer inside enhanced and smooth tubes of the

same envelope diameter, PEC for 12 different cases outlined by Bergles (1998) and Webb (1994) are listed in Table 14.2 They represent criteria for comparing the

TABLE 14.2 Performance Evaluation Criteria for Single-Phase Forced Convection in Enhanced Tubes of Same Envelope Diameter (d i) as the Smooth Tube

Fixed

aThe product ofN and L.

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enhanced performance on the basis of the following three broad exchanger geometry constraints:

1 FG criteria The area of flow cross section ( N and d i) and tube lengthL are

kept constant This would typically be applicable for retrofitting the smooth tubes

of an existing exchangerwith enhanced tubes, thereby maintaining the same basic geometry and size (N, d i , L) The objectives then could be to increase the heat load

capacityQ for the same approach temperature ∆T iand mass flow rate ˙m orpumping

powerP ; ordecrease ∆T iorP forfixed Q and ˙m or P ; orreduce P forfixed Q.

2 FN criteria The flow frontal area or cross section ( N and d i) is kept constant, and the heat exchanger length is allowed to vary Here the objectives are to seek a reduction in either the heat transfer surface area (A → L) orthe pumping powerP

fora fixed heat load

3 VG criteria The numberof tubes and theirlength ( N and L) are kept constant,

but theirdiametercan change A heat exchangeris often sized to meet a specified heat dutyQ for a fixed process fluid flow rate ˙m Because the tube-side velocity reduces

in such cases so as to accommodate the higher friction losses in the enhanced surface tubes, it becomes necessary to increase the flow area to maintain constant ˙m This is

usually accomplished by using a greater number of parallel flow circuits It may also

be noted that with a constant exchanger ˙m, the penalty of operating a higher thermal effectiveness inherent in the FG and FN cases is avoided.

For the quantitative evaluation of these PEC, algebraic expression can be obtained that relate the enhanced surface performance (Nu orj and f · Re) with that of an

equivalent smooth duct Fora specified tube bundle geometry (N, L, d i) in a

shell-and-tube heat exchanger, the heat transfer coefficienth and pumping power P can be

expressed as

h = c p jG

P = f AG3

Thus, the performance of enhanced tubes can be related to that of equivalent smooth tubes (N, L, d isame) as

hA/h o A o (P /P o )1/3 (A/A o )2/3 = j/j o

Given eitherj (orNu) and f data or correlations for both the enhanced and smooth

duct, evaluation of the objectives for the PEC in Table 14.2 is rather straightforward

One of the groupingshA/h o A o , P /P o, andA/A o becomes the objective function,

with the other two set as 1.0 for the corresponding operating constraints, which also provide the mass flux ratioG/G orequired to satisfy eq (14.5) Extended details for

obtaining the requisite relationships are given by Webb (1994), Webb and Bergles

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(1983b), and Nelson and Bergles (1986), and two illustrative examples are outlined briefly below

A common enhancement objective formany batch-processing applications in the chemical and process industry is to increase the thermal performance of a given heat exchanger(fixed geometry) by using enhancement techniques, but without changing the pumping power and approach temperature difference requirements This corre-sponds to the FG-2a criterion of Table 14.2, which can be implemented by expressing the ratio of heat transfer rate for the enhanced and smooth duct, respectively, as

Q

Q o =

Nu

Nuo



N,L,d i ,∆T i ,P

(14.6)

The constraint of fixed pumping power can be expressed as



f · Re3

=f o· Re3

o



(14.7)

to establish the relationship between the Reynolds numbers (or mass fluxesG and G o

forthe enhanced and smooth flow passages Because the enhanced duct geometry has higher friction factors than those of the equivalent smooth passage, this constraint requires that for a given flow rate (Re orG) in the former case, Re o (or G o) must

be higher Typical results for the single-phase flow-enhanced performance of tubes with twisted-tape inserts, evaluated according to the FG-2a criterion expressed in

eq (14.6), are presented in Fig 14.3 As can be seen from this graph, using twisted tapes promotes considerable enhancement; details of their specific thermal–hydraulic performance characteristics are discussed later in the chapter

In designing new enhanced-surface heat exchangers for a specified heat duty, approach temperature difference, and pressure drop, a reduction of the required heat transfer surface area is often the primary objective The consequent FN-1 criterion of Table 14.2 can be stated as

A

A o =

Nuo Nu



N,d i ,Q,∆T i ,∆p

(14.8)

In this case, the Reynolds numbers or mass fluxes in the enhanced and smooth duct geometries are related by the fixed∆p requirements as follows:



f · Re2

=f o· Re2

o



(14.9) Typical surface area savings (FN-1 criterion) due to the enhanced heat transfer in wavy-plate (flow-cross-section aspect ratioα = 0, orparallel wavy plates, with a plate separation to waviness depth ratioβ = 1.0) cores of a compact heat exchanger,

forlaminarliquid flow convection, are depicted in Fig 14.4 As high as 95% reduction

in thermal size is obtainable, depending on the operating conditions and wavy-surface geometry In this case, the reference smooth channel is that of a flat parallel-plate core

of the sameβ, and, once again, Reo orG o would be larger than that in the wavy or

enhanced channel in order to meet the constraints of eq (14.9)

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Figure 14.3 Typical enhanced heat transfer performance (FG-2a criterion) of circular tubes fitted with twisted-tape inserts and uniform wall temperature conditions (From Manglik and Yerra, 2002.)

Some additional considerations and variations of these PEC (Table 14.2) for

single-phase convection, which are based on a systems orcomplete heat exchangerunit

approach, have also been considered Bergles et al (1974b), Nelson and Bergles (1986), and Webb (1994) provide the necessary guidance and details of their algebraic development Furthermore, in a very recent study, Zimparov (2001) has outlined

the application of PEC to compound enhancement that involves use of twisted-tape

inserts in spirally corrugated (rough) tubes

The formulation of appropriate PEC for two-phase flow heat transfer (boiling and

condensation) is a rather complex task The difficulty stems from the dependence of the local heat transfer coefficient on the local temperature difference and/or quality, and that the pressure gradient is also involved (although a simplification is often made

by considering a constant pressure level) A variety of different strategies, which

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Figure 14.4 Typical surface area reductions (FN-1 criterion) in compact heat exchangers with parallel wavy-plate cores maintained at uniform wall temperature conditions

include relating heat transfer, pressure drop or pumping power, and vapor–liquid quality in some fashion, have been used in the literature to evaluate the enhanced performance

In forced-convective boiling, the enhanced critical heat flux (CHF) in tubes with twisted-tape inserts has been related to the pumping power by Gambill et al (1961), and for tubes with brush and mesh inserts by Megerlin et al (1974); in the latter case,

a ratio of the dissipated powerat CHF and pumping powerwas presented Matzner

et al (1965) developed an efficiency index based on the increased exit quality, or critical power, that could be achieved with tube inserts, which in turn can be com-pared with the pumping power Royal and Bergles (1978a) have devised two PEC forenhanced condensation in finned tubes and tubes with twisted-tape inserts: (1) size reduction made possible by replacing plain tubes with enhanced tubes of sim-ilar nominal diameter, assuming constant pressure level, and (2) a measure of the pressure drop consequences of an enhanced surface or insert Kubanek and Miletti

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(1979) have considered heat transfer and pressure drop in the evaluation of refriger-ant evaporators with internally finned tubes Luu and Bergles (1981) have similarly examined refrigerant condensers with internally finned tubes, helically ribbed tubes, and spirally fluted tubes

An extended discussion of enhanced performance evaluation of two-phase sys-tems is given by Webb (1988, 1994) In fact, Webb (1988) has developed the only known analysis of PEC fortwo-phase flows that considers the effect of∆p on the

∆T lm in two-fluid heat exchangers Both work-producing (e.g., Rankine powercycle) and work-absorbing (e.g., vapor-compression refrigeration cycle) systems have been

considered In work-producing systems, enhancement techniques may influence their performance by way of (1) reduced boiler and/or condenser surface area (reduced heat exchangersize) forfixed turbine poweroutput or(2) increased turbine power output with fixed boilerheat input and/orcondenserheat rejection Similarly, the following performance objectives and operating constraints may be considered for work-absorbing systems: (1) reduced heat transfer surface area of evaporator and/or condenser(reduced heat exchangersize) forfixed compressorpower; (2) increased evaporator heat load for pressure difference between condenser and evaporator (com-pressorlift); (3) reduced powerinput to the compressorforfixed evaporatorheat load;

as a consequence, the∆T lmvalue of the evaporatorand/orcondenserwould decrease

Based on this assessment of two-phase flow systems, Webb (1988) modified the PEC

of Table 14.2 for evaporators/boilers and condensers, and these are listed in Table 14.3 Procedures for computing these PEC, which may be applied to both flows inside tubes and outside tube bundles, are also given by Webb (1988, 1994)

TABLE 14.3 Modified Performance Evaluation Criteria for Two-Phase Flow Heat Exchange Systems with Enhanced Tubes of Same Envelope Diameter (d i) as the Smooth Tube

Fixed

aDefined as the temperature difference between the exit boiling fluid and inlet process fluid for vaporizers, and the approach temperature difference between the vapor and coolant streams for condensers.

bPower output (turbine power) for producing systems and power input (compressor power) for work-consuming systems.

cThe product ofN and L.

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14.2 TREATED SURFACES

As indicated earlier, treated surfaces are applicable primarily in two-phase heat trans-fer, and they consist of a variety of structured surfaces (continuous or discontinuous integral surface roughness or alterations) and coatings In the event that this treatment provides a “roughness” to the surface, its size (normal protrusion to the surface) is not large enough to influence single-phase forced convection

The influence of surface finish on nucleate and transition pool boiling has been stud-ied formore than fourdecades now (Bergles, 1998; Webb, 1994; Rohsenow, 1985;

Berenson, 1962; Kurihari and Myers, 1960) A variety of methods have been

em-ployed to alter the surface finish by producing different types of structured surfaces

(Bergles, 1998; Webb, 1994) These include the following types of surfaces, along with a few representative citations of patents and experimental studies that have con-sidered them:

• Machined or grooved surfaces (Bonilla et al., 1965; Kun and Czikk, 1969; Chu

and Moran, 1977; Fujikake, 1980; Hwang and Moran, 1981; Zhong et al., 1992)

• Formed or modified low-fin surfaces (Webb, 1972; Zatell, 1973; Nakayama et

al., 1975; Arai et al., 1977; Pais and Webb, 1991)

• Multilayered surfaces made up of stamped or perforated cover foils and fine-wire

or wire-screen wraps (Ragi, 1972; Hasegawa et al., 1975; Schmittle and Starner, 1978; Asakaviˇcius et al., 1979)

• Coated surfaces, which include nonwetting coatings and particle deposits or

material coatings that form artificial surface porosity (Griffith and Wallis, 1960;

Young and Hummel, 1965; Marto and Rohsenow, 1966; Milton, 1971; Oktay and Schmeckenbecher, 1974; Dahl and Erb, 1976; Warner et al., 1978; Fujii et al., 1979; Nishikawa et al., 1983; Cieslinski, 2002)

An illustrative sampling of machined, formed, and coated surfaces that have been used in practice or tested in the laboratory is given in Fig 14.5 Also, some types of fouling on and oxidation of the boiling surface, which perhaps improves the wetta-bility, have been found to increase pool-boiling CHF

Much of the work on developing structured surfaces for enhanced boiling is fun-damentally driven by the principle of producing a large number of stable vapor traps, or nucleation sites, on the surface that lend to early or reduced∆T incipience.

This is particularly relevant to boiling applications for highly wetting fluids (e.g., refrigerants, organic liquids, cryogens, and alkali liquid metals), where the normal cavities present on the heated surface tend to experience subcooled liquid flooding

By selective surface treatment (machining, forming, and coating or sintering), doubly reentrant cavities may be produced that would ensure vapor trapping in low-surface-tension fluids The phase-change mechanism on such structured surfaces, however, is different from “normal” cavity boiling, and extended discussions of different models

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Figure 14.5 Examples of structured boiling surfaces produced by machining, forming, or

coating: (a) deeply knurled surface; (b) different commercial formed-low-fin surfaces; (c)

sin-tered particle-coated surface

are given by Czikk and O’Neill (1979), Nakayama et al (1980a,b), Kovalev et al

(1990), Webb and Haider(1992), and Webb (1994), among others A study (Kule-novic et al., 2002) using high-speed image-processing techniques provides new infor-mation on bubble departure diameters, bubble generation frequency, and their up-flow velocities in pool boiling of propane over a structured surface with reentrant cavities

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103

104

102

101

⌬Tsat[K]

Experimental data (P-xylene, = 1 atm) Yilmaz et al (1980) p High-Flux (Union Carbide)

Gewa-T (Wieland) Plain

Thermoexcel-E (Hitachi)

Figure 14.6 Experimental data reported by Yilmaz et al (1980) for pool boiling of p-xylene

at 1 atm from smooth and structured (Gewa-T, Thermoexcel-E, and High-Flux) surfaces

Considerable enhancement with an order-of-magnitude reduction in wall super-heat has been reported (Thome, 1990; Webb, 1994; Bergles, 1998) for boiling with some of these structured surfaces Yilmaz et al (1980) and Yilmaz and Westwater (1981) have reported a rather comprehensive comparison of the nucleate boiling performances of several commercially available structured surfaces These involved the Wieland Gewa-T, Hitachi Thermoexcel-E, and Union Carbide High-Flux tubular

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surfaces, among others Their P-xylene boiling performance data for these three en-hanced tubes as well as that for a reference smooth tube are give in Fig 14.6 A shift

in theirboiling curves well to the left of that forthe smooth tube, with a significant re-duction in∆Tsat, is shown clearly Moreover, most of these surfaces have been found

to increase the CHF as well In saturated pool boiling of isopropyl alcohol, Yilmaz and Westwater (1981) have reported up to 40% higher CHF with some configurations

of structured surfaces It may be noted that the heat flux in all these cases is based on the area of the equivalent smooth tube of the same outside diameter

The phenomenon of temperature overshoot or incipience hysteresis, which is com-monly seen in boiling of highly wetting fluids over smooth surfaces and where the boiling curve exhibits different characteristics with increasing and decreasing heat flux, has also been reported with sintered-particle coated surfaces (Bergles and Chyu, 1982; Kim and Bergles, 1985) and multilayered (sintered screens) surfaces (Liu et al., 1987) This starting temperature overshoot and hysteresis are shown in Fig 14.7, where the Bergles and Chyu (1982) data for pool boiling of R-113 on a horizon-tal, electrically heated, sintered surface (High-Flux) tube are presented The boiling data of Ma et al (1986) for methanol with similarly coated surfaces, however, show substantially less hysteresis In any event, this suggests that some commercial equip-ment for boiling applications that use enhanced or structured surfaces may encounter

Figure 14.7 Temperature excursion or startup hysteresis in pool boiling of R-113 on a hori-zontal tube with a sintered (High-Flux) surface (From Bergles and Chyu, 1982.)