100 150 200 250 300

Vopor temperature, °F.

FIG. 11-18 Acceleration losses in boiling flow. °C = (°F - 32)/1.8.

100 150 200 250 300 Vapor temperature, °F.

FIG. 11-19 Friction pressure drop in boiling flow. °C = (°F - 32)/1.8.

100 150 200 250 300 Vapor temperature, °F.

FIG. 11-19 Friction pressure drop in boiling flow. °C = (°F - 32)/1.8.

where b = (2.6)(107)(SI) and 1.0 (U.S. customary) and using r2 from Fig. 11-18. The frictional pressure drop is derived from Fig. 11-19, which shows the ratio of two-phase pressure drop to that of the entering liquid flowing alone.

Pressure drop due to hydrostatic head can be calculated from liquid holdup R1. For nonfoaming dilute aqueous solutions, R1 can be estimated from R1 = 1/[1 + 2.5(V/L)(p1/pv)1/2]. Liquid holdup, which represents the ratio of liquid-only velocity to actual liquid velocity, also appears to be the principal determinant of the convective coefficient in the boiling zone (Dengler, Sc.D. thesis, MIT, 1952). In other words, the convective coefficient is that calculated from Eq. (5-50) by using the liquid-only velocity divided by R1 in the Reynolds number. Nucleate boiling augments convective heat transfer, primarily when AT's are high and the convective coefficient is low [Chen, Ind. Eng. Chem. Process Des. Dev., 5, 322 (1966)].

Film coefficients for the boiling of liquids other than water have been investigated. Coulson and McNelly [Trans. Inst. Chem. Eng., 34, 247 (1956)] derived the following relation, which also correlated the data of Badger and coworkers [Chem. Metall. Eng., 46, 640 (1939); Chem. Eng., 61(2), 183 (1954); and Trans. Am. Inst. Chem. Eng., 33, 392 (1937); 35, 17 (1939); 36, 759 (1940)] on water:

nnu = (1.3 + b D)(NPr)0'9(NRe)0^(NaJg34 J"5 ) (11-30)

where b = 128 (SI) or 39 (U.S. customary), NNu = Nusselt number based on liquid thermal conductivity, D = tube diameter, and the remaining terms are dimensionless groupings of liquid Prandtl number, liquid Reynolds number, vapor Reynolds number, and ratios of densities and viscosities. The Reynolds numbers are calculated on the basis of each fluid flowing by itself in the tube.

Additional corrections must be applied when the fraction of vapor is so high that the remaining liquid does not wet the tube wall or when the velocity of the mixture at the tube exits approaches sonic velocity. McAdams, Woods, and Bryan (Trans. Am. Soc. Mech. Eng., 1940), Dengler and Addoms (loc. cit.), and Stroebe, Baker, and Badger [Ind. Eng. Chem., 31, 200 (1939)] encountered dry-wall conditions and reduced coefficients when the weight fraction of vapor exceeded about 80 percent. Schweppe and Foust [Chem. Eng. Prog., 49, Symp. Ser. 5, 77 (1953)] and Harvey and Foust (ibid., p. 91) found that "sonic choking" occurred at surprisingly low flow rates.

The simplified method of calculation outlined includes no allowance for the effect of surface tension. Stroebe, Baker, and Badger (loc. cit.) found that by adding a small amount of surface-

active agent the boiling-film coefficient varied inversely as the square of the surface tension. Coulson and Mehta [Trans. Inst. Chem. Eng., 31, 208 (1953)] found the exponent to be -1.4. The higher coefficients at low surface tension are offset to some extent by a higher pressure drop, probably because the more intimate mixture existing at low surface tension causes the liquid fraction to be accelerated to a velocity closer to that of the vapor. The pressure drop due to acceleration APa derived from Fig. 11-18 allows for some slippage. In the limiting case, such as might be approached at low surface tension, the acceleration pressure drop in which "fog" flow is assumed (no slippage) can be determined from the equation y(Vg - Vi )G2

where y = fraction vapor by weight Vg, Vi = specific volume gas, liquid G = mass velocity

While the foregoing methods are valuable for detailed evaporator design or for evaluating the effect of changes in conditions on performance, they are cumbersome to use when making preliminary designs or cost estimates. Figure 11-20 gives the general range of overall long-tube vertical- (LTV) evaporator heat-transfer coefficients usually encountered in commercial practice. The higher coefficients are encountered when evaporating dilute solutions and the lower range when evaporating viscous liquids. The dashed curve represents the approximate lower limit, for liquids with viscosities of about 0.1 Pas (100 cP). The LTV evaporator does not work well at low temperature differences, as indicated by the results shown in Fig. 11-21 for seawater in 0.051-m (2-in), 0.0028-m (12-gauge) brass tubes 7.32 m (24 ft) long (W. L. Badger Associates, Inc., U.S. Department of the Interior, Office of Saline Water Rep. 26, December 1959, OTS Publ. PB 161290). The feed was at its boiling point at the vapor-head pressure, and feed rates varied from 0.025 to 0.050 kg/(stube) [200 to 400 lb/(h tube)] at the higher temperature to 0.038 to 0.125 kg/ (stube) [300 to 1000 lb/(htube)] at the lowest temperature.

Falling film evaporators find their widest use at low temperature differences—also at low temperatures. Under most operating conditions encountered, heat transfer is almost all by pure convection, with a negligible contribution from nucleate boiling. Film coefficients on the condensing side may be estimated from Dukler's correlation, [Chem. Eng. Prog. 55, 62 1950]. The same Dukler correlation presents curves covering falling film heat transfer to non-boiling liquids that are equally applicable to the falling film evaporator [Sinek and Young, Chem. Eng. Prog. 58, No. 12, 74 (1962)]. Kunz and Yerazunis [J. Heat Transfer 8, 413 (1969)] have

FIG. 11-20 General range of long-tube vertical- (LTV) evaporator coefficients. °C = (°F - 32)/1.8; to convert British thermal units per hour-square foot-degrees Fahrenheit to joules per square meter-second-kelvins, multiply by 5.6783.
FIG. 11-21 Heat-transfer coefficients in LTV seawater evaporators. °C = (°F - 32)/1.8; to convert British thermal units per hour-square foot-degrees Fahrenheit to joules per square meter-second-kelvins, multiply by 5.6783.

since extended the range of physical properties covered, as shown in Fig. 11-22. The boiling point in the tubes of such an evaporator is higher than in the vapor head because of both frictional-pressure drop and the head needed to accelerate the vapor to the tube-exit velocity. These factors, which can easily be predicted, make the overall apparent coefficients somewhat lower than those for nonboiling conditions. Figure 11-21 shows overall apparent heat-transfer coefficients determined in a falling-film seawater evaporator using the same tubes and flow rates as for the rising-film tests (W. L. Badger Associates, Inc., loc. cit.).

Short-Tube Vertical Evaporators Coefficients can be estimated by the same detailed method described for recirculating LTV evaporators. Performance is primarily a function of temperature level, temperature difference, and viscosity. While liquid level can also have an important influence, this is usually encountered only at levels lower than considered safe in commercial operation. Overall heat-transfer coefficients are shown in Fig. 11-23 for a basket-type evaporator (one with an annular downtake) when boiling water with 0.051-m (2-in) outside-diameter 0.0028-m-wall (12-gauge), 1.22-m-(4-ft-) long steel tubes [Badger and Shepard, Chem. Metali. Eng., 23, 281 (1920)]. Liquid level was maintained at the top tube sheet. Foust, Baker, and Badger [Ind. Eng. Chem., 31, 206 (1939)] measured recirculating velocities and heat-transfer coefficients in the same evaporator except with 0.064-m (2.5-in) 0.0034-m-wall (10-gauge), 1.22-m- (4-ft-) long tubes and temperature differences from 7 to 26°C (12 to 46°F). In the normal range of liquid levels, their results can be expressed as

where b = 153 (SI) or 375 (U.S. customary) and the subscript c refers to true liquid temperature, which under these conditions was about 0.56°C (1°F) above the vapor-head temperature. This work was done with water.

No detailed tests have been reported for the performance of propeller calandrias. Not enough is known regarding the performance of the propellers themselves under the cavitating conditions usually encountered to permit predicting circulation rates. In many cases, it appears that the propeller does no good in accelerating heat transfer over the transfer for natural circulation (Fig. 11-23).

Miscellaneous Evaporator Types Horizontal-tube evaporators operating with partially or fully submerged heating surfaces behave in much the same way as short-tube verticals, and heat-transfer coefficients are of the same order of magnitude. Some test results for water were published by Badger [Trans. Am. Inst. Chem. Eng., 13, 139 (1921)]. When operating unsubmerged, their heat transfer performance is roughly comparable to the falling-film vertical tube evaporator. Condensing coefficients inside the tubes can be derived from Nusselt's theory which, based on a constant-heat flux rather than a constant film AT,gives:

FIG. 11-22 Kunz and Yerazunis Correlation for falling-film heat transfer.

FIG. 11-22 Kunz and Yerazunis Correlation for falling-film heat transfer.

For the boiling side, a correlation based on seawater tests gave h

where r is based on feed-rate per unit length of the top tube in each vertical row of tubes and D is in meters.

Heat-transfer coefficients in clean coiled-tube evaporators for sea-water are shown in Fig. 11-24 [Hillier, Proc. Inst. Mech. Eng. (London), 1B(7), 295 (1953)]. The tubes were of copper.

Heat-transfer coefficients in agitated-film evaporators depend primarily on liquid viscosity. This type is usually justifiable only for very viscous materials. Figure 11-25 shows general ranges of overall coefficients [Hauschild, Chem. Ing. Tech., 25, 573 (1953); Lindsey, Chem. Eng., 60(4), 227 (1953); and Leniger and Veldstra, Chem. Ing. Tech., 31, 493 (1959)]. When used with nonviscous fluids, a wiped-film evaporator having fluted external surfaces can exhibit very high coefficients (Lustenader et al., Trans. Am. Soc. Mech. Eng., Paper 59-SA-30, 1959), although at a probably unwarranted first cost.

Heat Transfer from Various Metal Surfaces In an early work, Pridgeon and Badger [Ind. Eng. Chem., 16, 474 (1924)] published test results on copper and iron tubes in a horizontal-tube evaporator that indicated an extreme effect of surface cleanliness on heat-transfer coefficients. However, the high degree of cleanliness needed for high coefficients was difficult to achieve, and the tube layout and

FIG. 11-23 Heat-transfer coefficients for water in short-tube evaporators. °C = (°F - 32)/1.8; to convert British thermal units per hour-square foot-degrees Fahrenheit to joules per square meter-second-kelvins, multiply by 5.6783.

liquid level were changed during the course of the tests so as to make direct comparison of results difficult. Other workers have found little or no effect of conditions of surface or tube material on boiling-film coefficients in the range of commercial operating conditions [Averin, Izv. Akad. Nauk SSSR Otd. Tekh. Nauk, no. 3, p. 116, 1954; and Coul-son and McNelly, Trans. Inst. Chem. Eng., 34, 247 (1956)].

Work in connection with desalination of seawater has shown that specially modified surfaces can have a profound effect on heat-transfer coefficients in evaporators. Figure 11-26 (Alexander and Hoffman, Oak Ridge National Laboratory TM-2203) compares overall coefficients for some of these surfaces when boiling fresh water in 0.051-m (2-in) tubes 2.44-m (8-ft) long at atmospheric pressure in both upflow and downflow. The area basis used was the nominal outside area. Tube 20 was a smooth 0.0016-m- (0.062-in-) wall aluminum brass tube that had accumulated about 6 years of fouling in seawater service and exhibited a fouling resistance of about (2.6)(10-5) (m2 • s • K)/ J [0.00015 (ft2 • h°F)/Btu]. Tube 23 was a clean aluminum tube with 20 spiral corrugations of 0.0032-m (f-in) radius on a 0.254-m (10-in) pitch indented into the tube. Tube 48 was a clean copper tube that had 50 longitudinal flutes pressed into the wall (General Electric double-flute profile, Diedrich, U.S. Patent 3,244,601, Apr. 5, 1966). Tubes 47 and 39 had a specially patterned porous sintered-metal deposit on the boiling side to promote nucleate boiling (Minton, U.S.

FIG. 11-24 Heat-transfer coefficients for seawater in coil-tube evaporators. °C = (°F - 32)/1.8; to convert British thermal units per hour-square foot-degrees Fahrenheit to joules per square meter-second-kelvins, multiply by 5.6783.
FIG. 11-25 Overall heat-transfer coefficients in agitated-film evaporators. °C = (°F - 32)/I.8; to convert British thermal units per hour-square foot-degrees Fahrenheit to joules per square meter-second-kelvins, multiply by 5.6783; to convert centipoises to pascal-seconds, multiply by I0-3.

Patent 3,384,154, May 21, 1968). Both of these tubes also had steam-side coatings to promote dropwise condensation—parylene for tube 47 and gold plating for tube 39.

Of these special surfaces, only the double-fluted tube has seen extended services. Most of the gain in heat-transfer coefficient is due to the condensing side; the flutes tend to collect the condensate and leave the lands bare [Carnavos, Proc. First Int. Symp. Water Desalination, 2, 205 (1965)]. The condensing-film coefficient (based on the actual outside area, which is 28 percent greater than the nominal area) may be approximated from the equation

FIG. 11-26 Heat-transfer coefficients for enhanced surfaces. °C = (°F - 32) /I.8; to convert British thermal units per hour-square foot-degrees Fahrenheit to joules per square meter-second-kelvins, multiply by 5.6783. (By permission from Oak Ridge National Laboratory TM-2203.)

where b = 2100 (SI) or 1180 (U.S. customary). The boiling-side coefficient (based on actual inside area) for salt water in downflow may be approximated from the equation h = 0.035(k3p2g/|2)1/3(4r/|)1/3 (11-34b)

The boiling-film coefficient is about 30 percent lower for pure water than it is for salt water or seawater. There is as yet no accepted explanation for the superior performance in salt water. This phenomenon is also seen in evaporation from smooth tubes.

Effect of Fluid Properties on Heat Transfer Most of the heat-transfer data reported in the preceding paragraphs were obtained with water or with dilute solutions having properties close to those of water. Heat transfer with other materials will depend on the type of evaporator used. For forced-circulation evaporators, methods have been presented to calculate the effect of changes in fluid properties. For natural-circulation evaporators, viscosity is the most important variable as far as aqueous solutions are concerned. Badger (Heat Transfer and Evaporation, Chemical Catalog, New York, 1926, pp. 133-134) found that, as a rough rule, overall heat-transfer coefficients varied in inverse proportion to viscosity if the boiling film was the main resistance to heat transfer. When handling molasses solutions in a forced-circulation evaporator in which boiling was allowed to occur in the tubes, Coates and Badger [Trans. Am. Inst. Chem. Eng., 32,49 (1936)] found that from 0.005 to 0.03 Pa • s (5 to 30 cP) the overall heat-transfer coefficient could be represented by U = b/| 1f.24, where b = 2.55 (SI) or 7043 (U.S. customary). Fragen and Badger [Ind. Eng. Chem., 28,534 (1936)] correlated overall coefficients on sugar and sulfite liquor in the same evaporator for viscosities to 0.242 Pas (242 cP) and found a relationship that included the viscosity raised only to the 0.25 power.

Little work has been published on the effect of viscosity on heat transfer in the long-tube vertical evaporator. Cessna, Leintz, and Badger [Trans. Am. Inst. Chem. Eng., 36, 759 (1940)] found that the overall coefficient in the nonboiling zone varied inversely as the 0.7 power of viscosity (with sugar solutions). Coulson and Mehta [Trans. Inst. Chem. Eng., 31, 208 (1953)] found the exponent to be -0.44, and Stroebe, Baker, and Badger (loc. cit.) arrived at an exponent of -0.3 for the effect of viscosity on the film coefficient in the boiling zone.

Kerr (Louisiana Agr. Exp. Sta. Bull. 149) obtained plant data shown in Fig. 11-27 on various types of full-sized evaporators for cane sugar. These are invariably forward-feed evaporators concentrating to about 50° Brix, corresponding to a viscosity on the order of 0.005 Pa s (5 cP) in the last effect. In Fig. 11-27 curve A is for short-tube verticals with central downtake, B is for standard horizontal tube evaporators, C is for Lillie evaporators (which were horizontal-tube machines with no liquor level but having recirculating liquor showered over the tubes), and D is for long-tube vertical evaporators. These curves show apparent coefficients, but sugar solutions have boiling-point rises low enough not to affect the results noticeably. Kerr also obtained the data shown in Fig.

FIG. 11-27 Kerr's tests with full-sized sugar evaporators. °C = (°F - 32)/1.8; to convert British thermal units per hour-square foot-degrees Fahrenheit to joules per square meter-second-kelvins, multiply by 5.6783.
FIG. 11-28 Effect of viscosity on heat transfer in short-tube vertical evaporator. To convert centipoises to pascal-seconds, multiply by 10-3; to convert British thermal units per hour-square foot-degrees Fahrenheit to joules per square meter-second-kelvins, multiply by 5.6783.

11-28 on a laboratory short-tube vertical evaporator with 0.44- by 0.61-m (1e- by 24-in) tubes. This work was done with sugar juices boiling at 57°C (135°F) and an 11°C (20°F) temperature difference.

Effect of Noncondensables on Heat Transfer Most of the heat transfer in evaporators does not occur from pure steam but from vapor evolved in a preceding effect. This vapor usually contains inert gases— from air leakage if the preceding effect was under vacuum, from air entrained or dissolved in the feed, or from gases liberated by decomposition reactions. To prevent these inerts from seriously impeding heat transfer, the gases must be channeled past the heating surface and vented from the system while the gas concentration is still quite low. The influence of inert gases on heat transfer is due partially to the effect on A T of lowering the partial pressure and hence condensing temperature of the steam. The primary effect, however, results from the formation at the heating surface of an insulating blanket of gas through which the steam must diffuse before it can condense. The latter effect can be treated as an added resistance or fouling factor equal to 6.5 X 10-5 times the local mole percent inert gas (in J-1sm2K) [Stan-diford, Chem. Eng. Prog., 75, 59-62 (July 1979)]. The effect on AT is readily calculated from Dalton's law. Inert-gas concentrations may vary by a factor of 100 or more between vapor inlet and vent outlet, so these relationships should be integrated through the tube bundle.


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