The CRC Handbook of Mechanical Engineering. Chapter 4. Heat and Mass Transfer (776127), страница 41
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1, 1983; Hewitt et al., 1994)A* =qT U *(MTD)(4.5.88)where MTD is the mean temperature difference for the particular flow conditions and configuration. Thekey assumptions are that there is no significant bypassing of fluid around the heat transfer surface, thatthe overall heat transfer coefficient is constant, and that the specific heats of the two streams are constantover their temperature ranges in the exchanger; isothermal phase transitions, such as vaporizing orcondensing a pure component at constant pressure, are also allowed.If the two streams are in countercurrent flow, i.e., if they flow always in the opposite direction to oneanother,MTD = (LMTD) countercurrent =(Th,i) (- Tc,o - Th,o - Tc,iæ T - Tc,o ölnç h,i÷è Th,o - Tc,i ø)(4.5.89)where (LMTD)countercurrent is the “logarithmic mean temperature difference for countercurrent flow” andthe subscripts i and o indicate “inlet” and “outlet,” respectively.
E shells with a single tube-side passand F shells with two tube-side passes are almost always designed for countercurrent flow. (While theflow between adjacent baffles is basically cross flow, it can be shown that the total shell-side flow patternis equivalent to countercurrent flow if there are more than three or four baffles).Very occasionally, usually when close control of tube wall temperatures is required, cocurrent flowis specified, with the two streams flowing in the same direction through the exchanger. For this case,MTD = (LMTD) cocurrent =(Th,i) (- Tc,i - Th,o - Tc,oæ T - Tc,i ölnç h,i÷è Th,o - Tc,o ø)(4.5.90)where the symbols have the same meaning as before.
(LMTD)countercurrent is always equal to or greaterthan (LMTD)cocurrent, so wherever possible, countercurrent design and operation is preferred.However, most shell-and-tube exchangers have nozzle and tube pass configurations which lead tomixed countercurrent and cocurrent flow regions (as well as cross flow in the X shell).
For these cases,MTD = F(LMTD) countercurrent© 1999 by CRC Press LLC(4.5.91)4-172Section 4where (LMTD)countercurrent is calculated from Equation (4.5.89) and F is the “configuration correctionfactor” for the flow configuration involved. F has been found as a function of dimensionless temperatureratios for most flow configurations of interest and is given in analytical and/or graphical form in theearlier part of this section by Shah and in many heat transfer references (e.g., Schlünder, Vol. 1, 1983).F is equal to unity for pure countercurrent flow and is less than unity for all other cases; practicalconsiderations limit the range of interest to values above 0.7 at the lowest and more comfortably tovalues above 0.8.
Values of zero or below indicate conditions that violate the second law of thermodynamics.The Overall Heat Transfer Coefficient. The overall heat transfer coefficient U*, referenced to the heattransfer area A*, is related to the individual (film) heat transfer coefficients and the fouling resistances byU* =**1A ln(do di )*AA+ R fi+Ai2pNt Lkwhi AiA*A*+ R fo+Ao ho Ao(4.5.92)where hi and ho are, respectively, the tube-side and shell-side film heat transfer coefficients, W/m2K(Btu/hr ft2 °F), each referenced to its corresponding heat transfer area; Rfi and Rfo the correspondingfouling resistances (see below), m2K/W (hr ft2 °F/Btu); Nt the total number of tubes in the heat exchanger;L the effective tube length between the inside surfaces of the tubesheets, m (ft); do and di the outsideand inside tube diameters, m (ft); and kw the thermal conductivity of the tube wall material, W/m K(Btu/hr ft°F).
For the special but important case of plain tubesA* = Ao = Nt (pdo L)(4.5.93)and Equation (4.5.92) reduces toUo =1dodo do ln(do di )1+ R fi++ R fo +hi didiho2 kw(4.5.94)If finned tubes are used, the root diameter dr of the fins replaces do in Equation (4.5.92) and Ao includesthe surface area of the fins as well as the bare tube surface between the fins; it is also necessary toinclude a fin efficiency (typically about 0.8 to 0.95) multiplier in the numerators of the last two termson the right side of Equation (4.5.92) to account for resistance to conduction in the fins.
The treatmentof fin efficiency is fully developed in Kern and Kraus (1972). Efficiencies of some of the importantgeometries are given in the earlier half of this section.Film Heat Transfer Coefficients. Calculation of single-phase tube-side heat transfer coefficients for plaintubes is discussed in Section 4.1; special correlations are required for internally enhanced tubes, seediscussion of enhancement in Section 4.8. Intube condensation and vaporization are covered in thesubsection on boiling and condensation in Section 4.4.Shell-side heat transfer calculations are more complex owing to the large number and range of designvariables and process conditions that can occur.
The most accurate methods are proprietary and computerbased. The best known of these methods are those of Heat Transfer Research, Inc. (HTRI), CollegeStation, TX; Heat Transfer and Fluid Flow Services (HTFS), Harwell, U.K.; and B-JAC, Midlothian,VA. For single-phase flow, the Delaware method appears to be the best in the open literature, and it isfeasible for both had and computer use; various presentations of the method appear in many references,including Schlünder, Vol. 3 (1983) and Hewitt et al. (1994). These references also give methods for© 1999 by CRC Press LLCHeat and Mass Transfer4-173shell-side vaporizing and condensing design.
An approximate design procedure is given in the nextsubsection.Fouling. Fouling is the formation of any undesired deposit on the heat transfer surface, and it presentsan additional resistance to the flow of heat. Several different types of fouling are recognized:Sedimentation: deposition of suspended material on the surface.Crystallization: precipitation of solute from supersaturated solutions.Corrosion: formation of corrosion products on the surface.Thermal degradation/polymerization: formation of insoluble products by oxidation, charring, and/orpolymerization of a process stream.Biofouling: growth of large organisms (e.g., barnacles) that interfere with flow to or past a heat transfersurface (“macrobiofouling”) or small organisms (e.g., algae) that form a fouling layer on thesurface (“microbiofouling”).The effect of fouling on design is twofold: Extra surface must be added to the heat exchanger toovercome the additional thermal resistance, and provision must be made to allow cleaning either bychemical or mechanical means.
The fouling resistances included in Equation (4.5.92) result in requiringextra surface by reducing U* (though they do not properly account for the time-dependent nature offouling) and should be chosen with care. Table 4.5.8, based on the TEMA Standards provides someguidance, but prior experience with a given service is the best source of values. Ranges of typical valuesfor major classes of service are included in Table 4.5.10.Other things being equal, a fouling stream that requires mechanical cleaning should be put in thetubes because it is easier to clean the tube side. If this is not possible or desirable, then a removablebundle with a rotated square tube layout should be chosen to facilitate cleaning.Pressure Drop.
Tube-side pressure drop in plain tubes is discussed in Section 3.4. These calculationsare straightforward and quite accurate as long as the tubes are smooth and clean; however, even a smallamount of roughening due to corrosion or fouling (sometimes with a significant reduction of flow area)can double or triple tube-side pressure drop. Special correlations are required for internally enhancedtubes.Calculation of shell-side pressure drop is implicit in the design methods mentioned above for heattransfer. Roughness has less effect on shell-side pressure drop than on tube side, but fouling still mayhave a very substantial effect if the deposits fill up the clearances between the baffles and the shell andbetween the tubes and the baffles, or if the deposits are thick enough to narrow the clearances betweenadjacent tubes. Existing design methods can predict these effects if the thickness of the fouling layercan be estimated.Limitations of Design.
It should be recognized that even under the best of conditions — new, cleanexchangers with conventional construction features — heat exchanger design is not highly accurate. Thebest methods, when compared with carefully taken test data, show deviations of ±20% on overall heattransfer and ±40% on shell-side pressure drop (Palen and Taborek, 1969). These ranges are considerablyworsened in fouling services. In these cases, the thermal system should be designed for operationalflexibility, including carefully chosen redundancy of key components, and easy maintenance.Approximate Design MethodBecause of the complexity of rigorous design methods, it is useful to have an estimation procedure thatcan quickly give approximate dimensions of a heat exchanger for a specified service.
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