Selecting Tube Inserts for Shell-and-Tube Heat Exchangers
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Heat Exchanger Design for Engineering Purposes...
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Selecting Tube Tube Inser Inserts ts for Shell-and-Tube Heat Exc Exchangers hangers Richard L. Shilling, P.E. P.E. Heat Transfer Research, Inc.
A tube insert modifies flow stream characteristics to enhance heat transfer. Here’s how to choose the optimal insert to meet process requirements.
W
hen specifying a shell-and-tube heat exchanger, the rst steps are selecting a shell design (1) and (1) and determining the most effective bafe arrangement (2). (2). After the shellside conguration has been established, the focus shifts to tubeside heat transfer. Tube inserts are useful tools that improve tubeside performanc performancee in heat heat exchan exchangers. gers. Insert Insertss are used for for applica applica-tions in which tubeside heat transfer is thermally limiting and an increase in pressure drop is allowed. The best insert type and design for a particular application depends on ow conditions and uid properties. This article describes the most common types of inserts and their principles of operation. Each insert type has one or more means of ow modication, as well as specic advantages and disadvantages. Often, but not always, the benet benet of an an insert insert in two-phase two-phase ow ow is quite different different than the benet obtained by the same insert in single-phase ow. Understanding these concepts tremendously simplies the evaluation and selection of the proper insert for a given application.
Tubeside flow patterns Consider uid owing inside of a tube with a uniform inlet velocity and temperature prole. At the beginning of the ow, a lower-velocity boundary layer is initiated at the tube wall by the no-slip boundary condition, while a highervelocity, velocity, inviscid ow region remains in the core near the center of the tube (Figure 1). Similarly, a thermal boundary layer forms that spans the distance from the wall to the position of the undisturbed inlet temperature (Figure 2). Eventually, ally, both the velocity and thermal boundary layers grow and fully displace the inviscid, isothermal core region. Copyright © 2012 American Institute of Chemical Engineers (AIChE)
Uniform Laminar Velocity Profile Hydrodynamic Boundary Layer
Developing Velocity Profile
Fully Developed Hagen Poissuille Laminar Velocity Profile
r x
Hydrodynamic Entry Length
Fully Developed Hydrodynamic Flow
1. At p Figure 1. At
the start of fluid flow, a lower-velocity hydrodynamic boundary layer forms at the tube wall.
Fully Developed Laminar Velocity Profile
Thermal Boundary Layer
Uniform Temperature Profile
Fully Developed Laminar Temperature Profile
Developing Temperature Profile
r x
Adiabatic Starting Length
Thermal Entry Length
Thermally Fully Developed Flow
2. Likewise, a thermal boundary layer also develops at the p Figure 2. Likewise, tube wall.
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In laminar ow, where mixing is minimal, the growth of the thermal boundary layer is limited by the uid’s thermal conductivity. Fluids with high thermal conductivities (such as liquid metals) have short thermal entry lengths, and uids with low thermal conductivities (such as oils) have long thermal entry lengths. Once the ow is fully thermally developed, laminar heat transfer depends only on thermal conductivity.
able when it is deployed in a ow that is laminarized ( i.e., fully developed laminar ow). A ow becomes laminarized when the thickness of the laminar boundary layer becomes equal to the dimension of the ow channel and there is no free ow stream beyond the boundary layer. In this ow regime, static mixers are the only insert type that will enhance heat transfer. A useful dimensionless number for estimating the onset of this regime is the Graetz number:
Single-phase heat transfer inserts Inserts that augment single-phase heat transfer use one or more of four distinct mechanisms to compensate for boundary layer effects: static mixing, boundary layer interruption, swirl ow, and displaced ow.
Static mixing All inserts produce some mixing when the ow stream possesses enough kinetic energy to induce mixing due to radial displacement in the vicinity of the insert. Static mixing, however, is the physical interchange of uid particles to different locations in the ow stream by mechanical (rather than kinetic) means. The purpose of the static mixer (Figure 3) is to transport, by its mechanical construction, the uid at the tube wall to the center of the tube, to transport the uid at the center of the tube toward the tube wall, and to fold these transported regions of uid into each other. This dramatically improves heat transfer, because it increases the local temperature difference between portions of the bulk (tubeside) uid and the tube wall. A common application for static mixing augmentation is in the cooling of highly viscous polymers where no other method will produce acceptable results. The effect of a static mixer is most pronounced and valu-
Gz = Re # Pr #
` D L j h
^ 1h
where Re is the Reynolds number, Pr is the Prandtl number, Dh is the tube’s hydraulic diameter (m), and L is the uid ow length from the tube’s entrance to the rst boundary layer interruption (m). Laminarization occurs for viscous liquid ow (where natural convection can be neglected) at Graetz numbers less than about 20–200, depending on the shape of the ow channel. Below the Graetz number threshold, there is insufcient energy in the ow for augmentation by any other mechanism. Heat transfer is limited by the thermal conductivity of the liquid. Because design calculations are based on an overall mean temperature difference along the entire tube length, the augmentation provided by static mixing is typically reported in terms of an enhanced tubeside heat-transfer coefcient instead of an increase in the local temperature difference. In reality, the coefcient in the laminarized ow regime is con stant, and all augmentation is due to temperature difference enhancement. In some applications, a static mixing insert can provide a sixfold improvement in heat transfer over that in a tube without an insert. For laminar ow in the thermal entry region, static mixer heat-transfer equations are given in a form similar to the Sieder-Tate equation for laminar ow (3): 0.14 Dh 0.33 n Nu = 1.75 Re # Pr nw L
`
c m
j
(2)
where Nu is the Nusselt number, μ is the uid viscosity (N-s/m2), and μw is the uid viscosity at the inside tube wall’s temperature (N-s/m 2). For static mixers, Eq. 2 can be simplied to:
^
mixers augment tubeside heat transfer by mechanically moving fluid elements to different locations in the flow stream. p Figure 3. Static
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0.14
h c n n m
Nu = A Re # Pr
B
w
^h 3
where A is a correlation constant that includes the mixing efciency as a virtual boundary-layer interruption and B is a constant that is normally equal or very close to 0.33. With
Copyright © 2012 American Institute of Chemical Engineers (AIChE)
B set to 0.33, one measured heat-transfer data point for a specic static mixer can be used to determine a value for A and thus an equation that will closely predict heat transfer performance for that mixer at other laminar owrates.
Boundary-layer interruption At higher Graetz numbers (often at Reynolds numbers between 1 and 1,000), the thickness of the laminar boundary layer can easily be reduced by boundary-layer interruption inserts. These inserts come in a variety of shapes and sizes (Figure 4). The key to their operation is that the interrupting portion of the insert must protrude out of the laminar boundary layer at the tube wall. An interrupter “trips” the boundary layer, causing it to thin to its minimum thickness, which enhances heat transfer. After interruption, the boundary layer begins to thicken until the ow encounters the next interruption. Interruption inserts are commonly used for the augmentation of oil ows (such as lube oil) inside tubes when the ow regime is laminar. Some of these inserts can increase the heat transfer in laminar ows by as much as ve times, depending on the uid’s thermal conductivity. Typically, a threefold increase can be expected for most hydrocarbon streams. The magnitude of the heat transfer increase is inversely proportional to the hydraulic diameter and interrupted ow length. Equation 4 is useful for evaluating the effectiveness of a boundary-layer interrupter relative to a bare tube and for comparing the effectiveness of two different interrupter inserts: h1 h2
=
Dh2 L 2
` D
h1 L 1
1
j
3
^ 4h
where h is the heat-transfer coefcient (W/m2-K), Dh is the tube inside hydraulic diameter (m), L is the interrupted ow length (m), and the subscripts 1 and 2 denote the two inserts or the bare tube and an insert. A boundary-layer interrupter relies on a combination of the interruption height and the spacing between interruptions. If the height/spacing combination permits the bound-
interrupters protrude out of the laminar boundary layer at the tube wall, causing the boundary layer to thin. p Figure 4. Flow
Copyright © 2012 American Institute of Chemical Engineers (AIChE)
ary layer to grow thicker than the interruption height, there will be no heat-transfer augmentation, because the uid in the boundary layer will simply ooze around the protuberance and continue on its path unaffected. In addition, interrupters that are circumferentially symmetrical are more effective than asymmetrical interrupters. The simplest boundary-layer interruption device is a corrugated metal strip whose width matches the tube’s inside diameter. Another common design is a coiled wire with an outside diameter matching the tube’s inside diameter; the wire diameter and the pitch of the coil act as the interruption height and interruption spacing, respectively. Other interruption inserts consist of a series of small, nested wire loops; although the wires are small, these devices effectively balance height and spacing. Remember that most boundary-layer interruption inserts
Nomenclature A
= correlation constant for static mixer heat-transfer equation (Eq. 3) B = exponent for static mixer heat-transfer equation (Eq. 3) = specic heat, J/kg-K C p D = inside tube diameter, m De = equivalent inside tube diameter for turbulent ow heat transfer, m Dh = inside hydraulic tube diameter, m Dh1 = inside hydraulic tube diameter with Insert 1, m Dh2 = inside hydraulic tube diameter with Insert 2, m G = mass velocity of uid, kg/s-m2 Gz = Graetz number (Eq. 1) hcore = heat-transfer coefcient with core insert, W/m2-K htube = heat-transfer coefcient without insert, W/m2-K h1 = heat-transfer coefcient with Insert 1, W/m2-K h2 = heat-transfer coefcient with Insert 2, W/m2-K k = thermal conductivity, W/m-K L = uid ow length inside tube from entrance to rst boundary layer interruption, m = interrupted ow length with Insert 1, m L1 L2 = interrupted ow length with Insert 2, m Nfa = net free area inside tube with or without insert, m 2 Nu = Nusselt number (Eqs. 2 and 3) Pr = Prandtl number = C pμ/k Re = Reynolds number = ρvDh/μ v = velocity of the fluid, m/s Greek Letters μ = uid viscosity, N-s/m 2 μw = fluid viscosity at the inside tube wall temperature, N-s/m2 ρ = fluid density, kg/m 3
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are not considered static mixers because their only means of redirecting ow relies on the kinetic energy of the owing uid (rather than the mechanical movement imparted by the static mixing element). At Graetz numbers below 20, interrupters are ineffective. In addition, if the boundary layer grows too fast for the interruption height and spacing, either due to poor insert design or a change in uid conditions, the device will not augment heat transfer — it will only increase pressure drop. Any tube insert for which there exists a lower threshold owrate where mixing does not occur is not a static mixer.
Swirl flow Swirl-ow augmentation techniques are effective with upper-laminar ows through the transition regime — that is, Reynolds numbers between 200 and 10,000. The most common swirl-ow insert is the twisted tape (Figure 5). It enhances heat transfer up to ve times that of an empty tube, depending on the ow regime in the empty tube. References 4 and 5 provide correlations for modeling twisted-tape heat
transfer under laminar ow and turbulent ow conditions, respectively. Contrary to popular belief, swirl ow is not a boundary-layer interruption technique. Rotational ow has two effects. It imparts a helical ow path along the inside wall of the tube, thereby producing a high velocity along the tube wall that is a function of the helical ow angle. It also imparts a combination of ow rotation and centripetal force away from the center of the tube that, in single-phase ow, increases mixing and turbulence at the tube wall. This creates turbulent ows at Reynolds numbers that would be characteristic of laminar or transition ows in tubes without inserts. Inducing turbulence at a lower Reynolds number enhances heat transfer.
Displaced flow Displaced-ow inserts increase heat transfer by block ing the ow area farthest from the tube wall, which creates higher velocities along the tube wall heat-transfer surface. The simplest type of displaced-ow insert is a round cylinder (or core) that is supported in the center of the tube and extends the entire length of the tube (Figure 6). Displaced-ow inserts can effectively increase heattransfer coefcients by increasing already turbulent tubeside ows. A very simple way to model their heat-transfer effect in single-phase turbulent ow is to calculate a heat-transfer equivalent diameter, De: De =
p Figure 5. Twisted
tapes are the most common type of swirl-flow insert.
4 Nfa
^ 5h
r D
where Nfa is the net free area inside of the tube with or without an insert (m2). De will be smaller than the empty tube diameter by an amount that depends on the diameter of the core; the ratio of D/ De is typically between 1.5 and 3. In turbulent ow, the heat-transfer improvement due to the core can be approximated by multiplying the plain tube heat-transfer coefcient by D/ De: hcore = htube
` D D j
^ 6h
e
long, cylindrical rod, or core, is the simplest type of displaced-flow insert. p Figure 6. A
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where hcore is the heat-transfer coefcient inside a tube with a core insert (W/m2-K) and htube is the heat-transfer coefcient inside a tube without an insert (W/m 2-K). For uids such as water, heat transfer can be increased by more than 2.5 times, depending on the available pressure drop. Although displaced-ow inserts can also enhance some laminar ows, they are typically not as effective as the other methods. In addition, care must be taken to avoid reducing the hydraulic diameter to the point that the ow becomes laminarized, which can lead to very poor heat-transfer performance. Copyright © 2012 American Institute of Chemical Engineers (AIChE)
wire-wrapped core insert combines swirl-flow and displaced-flow augmentation. p Figure 7. A
Flow regime overlap and compound enhancements Flow regime overlap. Usually more than one type of insert can be used to improve heat transfer. (The exception is static mixers operating in the laminarized ow regime.) This ow regime overlap among the various insert types is useful, and can be extended through custom design. For example, static mixers can be designed to augment heat transfer in the entire laminar ow regime and beyond. Flow interrupters can easily augment ows at Reynolds numbers above 2,000. Swirl-ow inserts can augment ows at Reynolds numbers below 20. However, for a given set of uid conditions, there is a preferred range over which each mechanism is most efcient for heat transfer enhancement. Compound enhancements. Every insert type enhances heat transfer not only by the primary mechanism for which it was designed, but also, to a lesser extent, by some of the other mechanisms discussed earlier. For example, although a twisted-tape insert is designed for swirl-ow augmentation, it also provides a slight enhancement due to displaced-ow augmentation because the tape occupies space inside of the tube. Static mixers are able to improve heat transfer outside of the laminarized region because their construction provides interruption augmentation if there is sufcient kinetic energy in the ow. Some inserts are specically designed to take advantage of more than one kind of augmentation technique. For instance, a wire-wrapped core insert combines displacedow and swirl-ow augmentation. The wire-wrapped core (Figure 7) consists of a cylindrical rod or tube around which a smaller-diameter wire has been spirally wrapped. The core and wire diameters are sized to increase the linear velocity to the desired value based on the uid ow characteristics. The wire wrap angle is adjusted to further augment the heat transfer by swirl ow. Under the right circumstances, it is not uncommon to achieve a tenfold augmentation of heat transfer over that in an empty tube.
Two-phase flow inserts The static mixing, boundary-layer interruption, and dis placed-ow mechanisms enhance two-phase ow primarily by increased turbulence or enhanced mixing. In two-phase ow, nonhomogeneous, poorly mixed ow is common. In most cases, nonequilibrium two-phase ow produces lower
Copyright © 2012 American Institute of Chemical Engineers (AIChE)
heat transfer than an equivalent ow whose phases are well mixed. Static mixers and interrupted-ow devices increase this two-phase mixing and can improve heat transfer by a full order of magnitude. However, without proper design, adding these devices can result in an unacceptably high pressure drop. Displaced-ow inserts will enhance two-phase ow only as much as the resulting increased velocity will benet heat transfer. In two-phase ow, the effects of swirl ow inside a tube are different than the effects generated in single-phase ow. Two-phase ow is usually very turbulent, and the relative densities of the liquid and vapor phases often exceed 100:1. Therefore, swirl ow acts as a centrifuge to concentrate the denser liquid phase at the tube wall and the lighter vapor phase near the tube center. In tubeside boiling applications, the accumulation of vapor at the wall of a tube without inserts reduces the normally high convective boiling coefcient. Swirl ow concentrates the liquid phase to be boiled at the tube wall, which improves heat transfer over the entire vapor quality range. For some boiling conditions (such as horizontal tubeside ow), swirl ow is the only means to achieve 100% vapor quality exiting a tube. Because swirl ow is typically a turbulent enhancement device, the pressure drop increase is minimal for most new applications.
Practical considerations when using tube inserts Pressure drop. In the design of new heat exchangers, where the ow length is adjusted based on the duty achieved, most inserts (operating in their optimum regime) can be designed to produce the same tubeside pressure drop that would be experienced by a much longer plain tube. If an insert is added to an existing heat exchanger, pressure drop may signicantly increase if the system was designed for plain-tube conditions. In these cases, for the same ows, the pressure drop can be two to six times the plain-tube pressure drop, which sometimes makes a retrot impractical. Upset conditions. The system design must take into account upset conditions that can change the tubeside operating characteristics. Many inserts are attached to the faces of the tubesheets to permit removal and/or replacement during maintenance. The insert attachment can be designed to withstand a substantial upset pressure drop if the sup plier knows what upset conditions might be experienced. An attachment design based on the steady-state pressure drop with a small margin for condition changes may not be able to withstand a substantially higher load (as produced in an upset). For example, inserts have been found embedded in a downstream pump when upset conditions were not accounted for. Transient operation. Be certain to advise the designer if
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transient operation is anticipated. Inserts can tremendously augment heat transfer in laminar ows, but if the uid ow stops and is allowed to cool to ambient, the start-up pressure drop with the inserts can approach 100 times the pressure drop at normal operating conditions. In these cases, to prevent problems at start-up, it is important to heat the tubeside uid to the approximate operating temperature before attempting to reach the design owrate. Materials compatibility. Make sure that the insert material is compatible with the tube material and the uid. For example, carbon steel inserts in a water service tend to “weld” themselves to the tube wall over a few months of operation, sometimes requiring scrapping of the entire tube bundle to replace them. The use of stainless steel and other corrosion-resistant metallurgies is often the best way to avoid this problem. Fluid condition. Be aware of the conditions of the tubeside uid. For example, when augmenting a laminar ow, the uid should be relatively free of particulates to prevent tube plugging. In laminar ow, an interrupter can act as a particulate dam, and a swirl-ow device may not produce enough turbulence to carry the particles up and around each helical rotation, so these designs should not be used in laminar ow containing particulates. Anticipated fouling. It is important to evaluate the extent and types of fouling expected and determine whether it will be possible to remove the insert for maintenance. If hard, crusty fouling (such as from polymerization) is expected inside the tube, the fouling layer may fuse the insert to the tube wall. Some inserts are strong enough that they can be removed without damage (and draw a great deal of fouling
out of the tubes upon removal as well). If the insert is not robust enough to be withdrawn from the tube without breaking, the fouling layer will need to be chemically dissolved to allow withdrawal of the insert.
Typical application A process stream is preheated using waste heat recovered during the cooling of a light polymer. The polymer stream requires Type 316 stainless steel, whereas carbon steel with a 3-mm corrosion allowance is sufcient for the process stream. Maximum energy recovery involves a temperature cross (i.e., the outlet temperature of the cold stream is higher than the inlet temperature of the hot stream). The required tubular heat exchanger must be either a single counterow heat exchanger or multiple shells in series. For the same reason, the normal practice of increasing the number of tube passes
RICHARD L. SHILLING, P.E., is Senior Engineering Consultant at Heat Transfer Research, Inc. (HTRI; www.htri.net), where he provides technical expertise and research, software, and engineering services for various projects. Previously, he worked for more than 25 years for Koch Heat Transfer Co. (formerly Brown Fin Tube Corp.) in Houston, TX, where as Vice President of Engineering, he directed and managed engineering research projects and oversaw engineering software development. He has developed new heat exchanger enhancement devices and techniques for equipment designs, and is experienced in troubleshooting exchanger problems in a refinery. Shilling holds a BS in mathematics from Grove City College in Pennsylvania and a BEng in mechanical engineering from Youngstown State Univ. in Ohio. He chairs the HTRI Exchanger Design Margin Task Force (EDMTF) and is the editor of the heat transfer equipment section of Perry’s Chemical Engineers’ Handbook. A member of ASME, he is a licensed professional engineer in Texas.
Table 1. Tube inserts augment heat tr ansfer, and require a shorter tube length than a system that uses no inserts. Design No.
Description*
No. of Tube Passes
h-shellside†, W/m2K
h-tubeside‡, W/m2K
dP-tubeside#, kPa
Area¶, m2
MTD**, K
1
(1)-12420 AFU, No Inserts
2
452.7
90.52
1.03
79.9
24.4
2
(1)-12228 AFU, Twisted-Tape Inserts
2
451.3
188.5
2.34
43.8
24.4
3
(1)-12144 AFU, Wire-Wrapped Cores
2
450.0
395.1
12.5
27.9
24.4
4
(1)-08240 AFU, Wire-Wrapped Cores
2
620.4
564.1
72.7
19.1
24.4
5
(2)-12180 AEU, No Inserts
8
332.8
202.3
61.0
52.5
21.2
*The number in parentheses is the number of shells. The first two digits after the dash indicate the shell inside diameter in inches, and the final three digits represent the straight tube length in inches. The letters used in the heat exchanger descriptions are based on the Tubular Exchanger Manufacturers Association (TEMA) nomenclature standards; A designates a removable front channel with cover, F a shell with an axial baffle in the center that creates two shell passes, E a one-pass shell, and U a U-tube bundle. †
h-shellside is the heat-transfer coefficient of the fluid flowing on the outside surface of the tubes.
‡
h-tubeside is the heat-transfer coefficient of the fluid flowing on the inside surface of the tubes.
#
dP-tubeside is the total pressure drop, from inlet to outlet, of the fluid flowing inside the tubes.
¶
Area is the total surface area of all the tubes in the bundle calculated based on the tube outside diameter.
**MTD is the mean temperature difference between the fluids flowing outside and inside the tubes.
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Copyright © 2012 American Institute of Chemical Engineers (AIChE)
to augment the tubeside heat-transfer coefcient requires multiple shells in series. Table 1 summarizes key parameters for ve alternative designs. Adding twisted-tape (Design 2) or wire-wrapped core inserts (Design 3) to the tubes reduces the required ow length while increasing the tubeside heat transfer. This allows for a more compact design than the plain tube exchanger (Design 1). Reducing the shell diameter (Design 4) increases heat transfer, but with a signicant pressure drop penalty. Changing from a single two-pass shell to two single-pass shells and increasing the number of tube passes from two to eight, without adding inserts (Design 5), increases tubeside heat transfer, but noticeably reduces shellside heat transfer and increases pressure drop.
Closing thoughts Of the four inserts types, the best design for a particular application will depend mainly on the specic space and pressure drop limits. The decisions on the use of tube inserts must be balanced with the proper selection of shell type and bafe type in order to design the most efcient heat CEP exchanger for the required conditions.
Literature Cited 1.
Lestina, T. G., “Selecting a Heat Exchanger Shell,” Chem. Eng. Progress, 107 (6), pp. 34–38 (June 2011).
2.
Bouhairie, S., “Selecting Bafes for Shell-and-Tube Heat Exchangers,” Chem. Eng. Progress, 108 (2), pp. 27–33 (Feb. 2012).
3.
Sieder, E. N., and G. E. Tate, “Heat Transfer and Pressure Drop of Liquids in Tubes,” Industrial & Engineering Chemistry, 28, pp. 1429–1435 (1936).
4.
Manglik, R. M., and A. E. Bergles, “Heat Transfer and Pressure Drop Correlations for Twisted-Tape Inserts in Isothermal Tubes: Part I — Laminar Flow,” ASME Journal of Heat Transfer, 115 (4), pp. 881–889 (1993).
5.
Manglik, R. M., and A. E. Bergles, “Heat Transfer and Pressure Drop Correlations for Twisted-Tape Inserts in Isothermal Tubes: Part II — Transition and Turbulent Flows,” ASME Journal of Heat Transfer, 115 (4), pp. 890–896 (1993).
Additional Reading Sununu, J. H., “Heat Transfer with Static Mixer Systems,” Kenics Corp., Danvers, MA (1970).
8 1 1 . o N e l c r i C r o p e c / g r o . e h c i a . w w w
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