BOOKCOMP, Inc. — John Wiley & Sons / Page 775 / 2nd Proofs / Heat Transfer Handbook / Bejan FILM CONDENSATION ON TUBE BUNDLES 775 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [775], (57) Lines: 1567 to 1583 ——— 0.04703pt PgVar ——— Normal Page PgEnds: T E X [775], (57) minimize or almost eliminate this type of noncondensable gas buildup or pockets. The important design concept is that the pressure drop from the top of the bundle to the air vent manifold is identical for all possible vapor paths. Figure 10.18 shows a good layout. Note that the vent manifold is not in the geometric center because of the difference between the two-phase pressure drop in countercurrent upflow and co- current downflow. A two-dimensional flow-field code is the most precise method to locate the true low-pressure point—the location of the vent manifold. pockets caused by the longitudinal heat flux maldistribution As shown in Fig. 10.16, the vapor is forced to flow nearly perpendicular to the tubes in each bay in a series of parallel flow paths. However, the vapor flow rate in each of the bays is different and is controlled by two common boundary conditions: (1) the outlet tube- side fluid temperature is the inlet temperature to the adjacent upstream bay, and (2) the shell-side pressure from the vapor inlet to the vent off-take is the same for all the bays. Because of the first, the condensing capability of each bay is different, due to the temperature rise along the length of the condenser. Because of the second, the pressure drops from the vapor inlet to the vent location for all the bays must be the same or balanced. The inlet vapor flow rates into each bay are controlled by these two boundary conditions and must decrease from the cold to the hot end of the condenser. This longitudinal heat flux maldistribution cannot be avoided because of the reduced temperature difference due to the rise in each successive bay. Tinker (1933) presented the first and one of the best explanations for the longitu- dinal maldistribution problem. Figure 10.19 shows air pockets at the bottom of the three cold-end bays of a single-pass condenser with a single air removal vent. Because of the unequal heat flux and the uniform pressure-drop constraint, the cold-end bays “run out of steam” and air pockets will form on the remaining and inactive surface in each. These pockets can have a major impact on the performance because their size is somewhat controlled by the air in-leakage, vent location, and/or vent capacity. Figure 10.19 Air pockets due to longitudinal heat flux maldistribution. (From Tinker, 1933.) BOOKCOMP, Inc. — John Wiley & Sons / Page 776 / 2nd Proofs / Heat Transfer Handbook / Bejan 776 CONDENSATION 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [776], (58) Lines: 1583 to 1587 ——— 0.15701pt PgVar ——— Normal Page PgEnds: T E X [776], (58) Figure 10.20 Relative pressure variations in each bay for air pocket removal with bay vent- ing. (From Tinker, 1933.) The longitudinal gas pockets can only be completely eliminated with unrealistic vent flow rates. Figure 10.20 shows that the pressure drop is increased by a factor of 5.7 in the cold-end bay if all the pockets are eliminated by venting each bay separately. It would not be practical and certainly not cost-effective to vent each bay separately because anywhere from about five to 15 separate, noncondensable gas- removal systems would be required for typical condenser applications. In addition, there would be a significant increase in the saturation temperature depression in the cold-end bays. The negative impact of the gas pockets can be minimized or controlled by forcing more vapor into the cold-end bays by (1) orificing the vent manifold, (2) longitudinal vent flow cascading, (3) increasing the number of tube-side passes, and (4) increasing the vent flow rate. To force more vapor to the cold-end bay shown in Fig. 10.20, pressure drops must be introduced into the flow paths (blocking plates with different- sized openings or orifices) of theotherthree bays toobtainsimilarpressure-drop value for all four flow paths. Barsness (1963), Andrews (1974), Rabas (1985b), and Spencer and Hewitt (1990) discussed this concept in depth. Cascading, another concept used to minimize the size of cold-end pockets, was first proposed by Tinker (1933). The basis for this simple concept is to permit vapor to pass from a higher temperature bay to the lower temperature bay through the tube supports. This can be done for all the tube supports, a selected number, or just for the cold-end bay. Another approach is to increase the number of tube-side passes; however, this is not always feasible because of pumping limitations. Increasing the vent flow rate is discussed in the next section. Noncondensable gas pockets will always exist even if the inlet gas concentration is small, or less than the 1000 rule mentioned above. With good design, the performance reduction due to the pockets can be limited to a couple of percent when based on the condition that all the heat transfer surface is active or not blanketed (Rabas and Kassem, 1985). It is interesting to note that these same two constraints are also BOOKCOMP, Inc. — John Wiley & Sons / Page 777 / 2nd Proofs / Heat Transfer Handbook / Bejan FILM CONDENSATION ON TUBE BUNDLES 777 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [777], (59) Lines: 1587 to 1598 ——— 1.227pt PgVar ——— Normal Page PgEnds: T E X [777], (59) responsible for the formation of noncondensable pockets with in-tube condensers and will be discussed later. Proper Venting Proper venting is necessary to minimize the adverse effect of non- condensable pockets. The first issue is the vent location. For single-pass X-shell con- densers, this is at or near the center of the cold-end bay. A more general statement of Butterworth (1991) is that “the vent should be located as near as possible to the coldest part of the condenser, which, of course, is where the coolant enters.” Note that these statements are essentially the same. For a two-pass unit, the recommended ap- proach is to vent each pass separately: If this is not feasible, care should be exercised to route the vapor-gas vent flow from the higher-temperature passes to the cold-end of the coldest pass. The second issue is the vent flow rate. The condenser performance is always im- proved with an increasing rate, but the extent may or may not be significant. Figure 10.21 shows the predicted performance improvements (Rabas, 1985b) with increas- ing vent flow for two evaporator condensers used in multistage flash evaporators that are operating at different temperature levels. The important point is that the perfor- mance improvement of the low-temperature unit is limited by the saturation tem- perature depression. Another important consideration is the increased capital cost of the vacuum system and the increased quantity of vapor rejected to the environment. The desired goal is to vent the minimum amount of vapor, yet maintain reasonable condenser performance. Another issue that may override these considerations, the oxygen concentration in the condensate, is not addressed here. 0.2 0.5 1.0 2.0 5.0 0.90 0.92 0.94 0.96 0.98 1.00 Heat Duty Reduction Ratio Percent Vent Flow Based on Inlet Steam Flow 220°F 90°F Parameter: Inlet recycle temperature Figure 10.21 Effect of the vent flow rate on condenser performance. BOOKCOMP, Inc. — John Wiley & Sons / Page 778 / 2nd Proofs / Heat Transfer Handbook / Bejan 778 CONDENSATION 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [778], (60) Lines: 1598 to 1610 ——— 0.30911pt PgVar ——— Normal Page PgEnds: T E X [778], (60) Two methods are used by industry to select the vent flow rate. The first is simply to size the venting system for a percentage of the inlet vapor flow rate, the magnitude being based on experience. The second method is to select the vent flow rate based on estimates of the inlet gas flow rate and of the exit vapor/gas mass ratio. This ratio is calculated as follows: m g,o m a,i = M g M a P g,o P total,i − P g,o (10.94) where P g,o is the saturation pressure at an assumed subcooled mixture outlet tempera- ture and T total,i is the vapor pressure at the condenser inlet. The total vent flow is equal to the sum of m a,i and m g,o . For example, the Heat Exchange Institute (1984) recom- mends 7.5°F subcooling and an air in-leakage rate based on the condenser volume. Figure 10.22 Effect of the vent flow rate on condenser performance. BOOKCOMP, Inc. — John Wiley & Sons / Page 779 / 2nd Proofs / Heat Transfer Handbook / Bejan FILM CONDENSATION ON TUBE BUNDLES 779 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [779], (61) Lines: 1610 to 1620 ——— 0.0pt PgVar ——— Normal Page PgEnds: T E X [779], (61) Rabas and Mueller (1986) recommended an exit vapor/gas ratio that is about twice the minimum value calculated with eq. (10.94) with P g,o based on the inlet coolant temperature or the maximum subcooling. Figure 10.22 shows the effect of the vent flow rate on the heat duty reduction for a typical brine heater, the thermal performance now being evaluated with a pointwise method that contains a Colburn–Hougen anal- ysis (Colburn and Hougen, 1933) to calculate the effect of the noncondensable gases (Rabas and Mueller, 1986). Note the very sharp drop in the performance when the vent flow rate approaches the minimum value for either air or carbon dioxide as the inlet noncondensable gas. 10.8.2 In-Tube Condensers Most in-tube condensing applications use a crossflow arrangement with horizontal or slightly downward-sloping tubes. Similar bundle effects—maldistribution, noncon- densable gas, and saturation temperature depression—also have a negative impact on the thermal performance. Only the effects of outside maldistribution and noncon- densable gas pockets are discussed because the prediction of the in-tube condensing pressure drop has already been addressed. Nonuniform Outside Inlet Flow and Temperature Distributions Standard design practice is to assume that the flow and temperature distributions are uniform at the exchanger face. However, these profiles can be very nonuniform and depend on the fan arrangement (induced or forced draft), the fan characteristics, the fan plenum design, and side obstructions. Of interest is to what extent these nonuniform flow distributions affect condenser thermal performance. The first investigations addressed only inlet flow variations and restricted the analysis to one dimension. Two later in- vestigations removed these restrictions. Rabas (1987b) considered condensers with a constant saturation temperature, and later, Beiler and Kr ¨ oger (1996) extended the analysis to condensers with a varying saturation temperature (the situation with a temperature drop due to the pressure drop, the presence of noncondensable gases, or multicomponent condensation). Both investigations showed that there is a heat load reduction with an increase departure from uniform distributions. However, the performance reduction was only about 7% with severe nonuniform distributions. The maldistribution occurring in well-designed cross-cooled heat exchangers reduces the thermal performance by only a few percent. In other words, be concerned about shell-side maldistributions only when very nonuniform flow distributions exist. Se- vere shell-side maldistributions are characterized with forced-draft fan arrangement, shallow tube banks, and a marginal fan plenum design. Noncondensable Gas Pockets Berg and Berg (1980) stated that customary design practice is to assume that the inlet flow rates are the same for each tube and that all the vapor is condensed at the exit with condensate filling the tube. They and others—Breber et al. (1982) and Fabbri (1987)—clearly demonstrated that this is not the case. The same two reasons responsible for varying inlet flows into each bay and noncondensable pockets therein with shell-side condensation apply again: (1) The BOOKCOMP, Inc. — John Wiley & Sons / Page 780 / 2nd Proofs / Heat Transfer Handbook / Bejan 780 CONDENSATION 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [780], (62) Lines: 1620 to 1643 ——— 1.44205pt PgVar ——— Normal Page PgEnds: T E X [780], (62) approaching shell-side fluid temperature to each transverse tube row is increased be- cause of the temperature rise(s) of the previous row(s), and (2) the tube-side pressure from the vapor inlet to the outlet headers is the same for all tubes. Fabbri (1987) evaluated the percentage of the total tube length that was blanketed with noncon- densables or flooded with condensate with different transverse row numbers and row effectiveness values, the same value assumed for each row. With a row effective value of 0.5, the noncondensing percentages are about 15 and 30% for three and 10 rows, respectively. Manufacturers have developed many different techniques to minimize this ineffective portion of the tube bank. For more details, see Berg and Berg (1980), Henry et al. (1983), and Breber (1987). 10.9 CONDENSATION IN PLATE HEAT EXCHANGERS 10.9.1 Introduction Figure 10.23 shows an isometric, cross-sectional view of a plate heat exchanger. Plate heat exchangers are made by stacking corrugated metal sheets to create channels that alternate between two fluid streams. Fluid paths are made by alternating the orientation of the chevron-shaped bumps as the plates are assembled. Areas where chevrons of adjacent plates touch create obstructions that mix the flow. The chevrons are approximately 62° with respect to the flow direction, as shown in Fig. 10.23. Some plate heat exchangers have chevrons that “point” perpendicularly to the flow direction. The 62° chevron angle (28° from the horizontal) arises from a compromise between increasing heat transfer and increased pressure drop. Gasketed plate heat exchangers use O-rings to seal the edges of the plates, while the edges of compact brazed plate heat exchangers (CBEs) are brazed. The CBE has the advantage of relatively large operating pressures and the gasketed plate heat ex- changer that of dissembling for cleaning. The same plate design can be used for the two heat exchanger types, which leads to similar condensation performance. Milk producers and other food and drink processors satisfied hygiene requirements by dis- assembling and cleaning the gasketed plate heat exchangers periodically (Saunders, 1988). Currently, the compactness of the CBE drives its use as refrigerant evaporators and condensers (Falls et al., 1992; Jonsson, 1985). For example, Saunders (1988) cites a case where one CBE replaced several shell-and-tube exchangers. Unfortu- nately, the available research on plate heat exchangers as condensers is not entirely comprehensive. 10.9.2 Steam Condensation Heat Transfer Wang and Zhao (1993) have developed an expression for steam condensation in a plate heat exchanger where the chevrons point perpendicularly to the flow direction: Nu = 0.00115 Re l · λ(1 +0.68Ja) c p,l (T sat − T w ) 0.983 · Pr 0.33 l ρ l ρ g 0.248 (10.95) BOOKCOMP, Inc. — John Wiley & Sons / Page 781 / 2nd Proofs / Heat Transfer Handbook / Bejan CONDENSATION IN PLATE HEAT EXCHANGERS 781 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [781], (63) Lines: 1643 to 1662 ——— 0.73315pt PgVar ——— Normal Page PgEnds: T E X [781], (63) 0.12 MPa ≤ P s ≤ 0.2MPa 10,000 ≤ Re l = G T (1 − x qo )D e µ l ≤ 45,000 where D e is the equivalent round tube diameter based on the cross-sectional flow area between two plates. All steam transport properties are evaluated at f = 0.00228Re −0.062 lo Φ 0.021 3500 ≤ Re lo = G T D h µ l ≤ 24,000 The latent heat and steam density are evaluated at the average steam temperature. Equation (10.95) is valid for both complete and partial condensation. The x qo is the mass quality of the steam exiting the plate heat exchanger. The quality term in the 30° Fluid stream 1 Fluid stream 2 Figure 10.23 Cross-sectional view of a plate heat exchanger. BOOKCOMP, Inc. — John Wiley & Sons / Page 782 / 2nd Proofs / Heat Transfer Handbook / Bejan 782 CONDENSATION 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [782], (64) Lines: 1662 to 1675 ——— -0.974pt PgVar ——— Normal Page PgEnds: T E X [782], (64) Reynolds number accounts for the partial condensation condition. Equation (10.95) predicted most of the Wang and Zhao (1993) data to within ±15%. 10.9.3 Effect of Inclination on Heat Transfer Performance It may be advantageous to install the CBE skewed in equipment to achieve a lower profile, and consequently, lower-cost unit enclosure. In the event of a redesign, equip- ment manufacturers require the effect of inclination on heat exchanger duty. Accord- ingly, Kedzierski (1997) quantified the change in performance associated with tilting a CBE from the designed vertical position. Detailed measurements of the effect of in- clination on the performance of a CBE are required to weigh the performance change carefully against the production cost savings. Figure 10.24 shows that the measured overall conductance of a CBE for R-22 condensation improved by approximately 17 to 30% by rotating it from the vertical to the horizontal position. Figure 10.24 shows the orientation of the rotation with respect to heat exchanger connections. The overall heat transfer coefficient of the condenser improved nearly linearly with rotation. The results suggest that a compact braze heat exchanger performs best as a condenser when the width is installed in the vertical direction to give the shortest condensing length. The enhancement of the condenser performance in the horizontal orientation is due to shortening of the condensing length. The condensing length was 72 mm Figure 10.24 Normalized overall conductance of CBE as a function of inclination. BOOKCOMP, Inc. — John Wiley & Sons / Page 783 / 2nd Proofs / Heat Transfer Handbook / Bejan CONDENSATION IN PLATE HEAT EXCHANGERS 783 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [783], (65) Lines: 1675 to 1686 ——— -2.243pt PgVar ——— Normal Page * PgEnds: PageBreak [783], (65) and 466 mm long when the condenser is in the horizontal and vertical positions, respectively. The longer condensing length permits the film thickness to increase through inundation. The thin-film region near the leading edge of the condensing length exhibits the most favorable heat transfer. The length of the leading edge for the condenser in the horizontal position is nearly 6.5 times that for the condenser in the vertical position. Consequently, the average condensate film thickness for the condenser in the horizontal position is thinner than that in the vertical position. Thin condensate films induce a greater overall heat transfer coefficient for the condenser in the horizontal position. 10.9.4 Effect of Inclination on Pressure Drop Figure 10.25 shows the refrigerant-side condenser pressure drop (∆P c ) as measured by Kedzierski (1997) for refrigerant downflow plotted against the rotation angle. The mean pressure drop remained within 2% of the vertical value (∆P co ) for all angles of counterclockwise rotation. Gravitational effects were small because most of the volume (height) in the condenser was in the vapor phase. Conversely, gravity influences the pressure drop for the clockwise rotation past 45°. The refrigerant exit port is located near the top of the channel. Consequently, refrigerant must accumulate in the channel before exiting. The greater holdup of liquid in the condenser increased the pressure drop of the condenser for the clockwise rotation. 0 20 40 60 80 100 (degrees) 0.9 1.0 1.1 1.2 1.3 ⌬ ⌬ P P C CO 90 CCW 90 CW 0 R22, = 292.7 K, condenserT s Counter-clockwise = 5.2 kW –– ⌬P CO Clockwise = 4.4 kW –– ⌬P CO } lines are cubic regressions shaded and hatched regions depict 95% confidence intervals on the mean Figure 10.25 Condensation pressure drop of CBE as a function of inclination. BOOKCOMP, Inc. — John Wiley & Sons / Page 784 / 2nd Proofs / Heat Transfer Handbook / Bejan 784 CONDENSATION 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [784], (66) Lines: 1686 to 1738 ——— 0.7054pt PgVar ——— Normal Page PgEnds: T E X [784], (66) APPENDIX A In this appendix we present the equations that describe the K-W fin profiles (Kedzier- ski and Webb (1990) and the constants used in eq. (10.21). The radius of curvature r of the new profile is defined by r = C 1 + C 2 e Zθ + C 3 θ (10.A.1) The constants C 1 ,C 2 ,C 3 , and C 4 are given by C 1 = r o − C 2 (10.A.2) C 2 = 0.5t r (sin θ m − θ m cos θ m ) − e(cos θ m + θ m sin θ m − 1) C 4 − [ 2(1 − cos θ m ) − θ m sin θ m ] + r o − [ θ m sin θ m − 2(1 − cos θ m ) ] C 4 − [ 2(1 − cos θ m ) − θ m sin θ m ] (10.A.3) C 3 = 0.5t r − C 1 sin θ m − C 2 Ze Zθ m cos θ m /(Z 2 + 1) cos θ m + θ m sin θ m − 1 − C 2 (e Zθ m sin θ m − Z)/(Z 2 + 1) cos θ m + θ m sin θ m − 1 (10.A.4) C 4 = e Zθ m [ 1 − cos θ m + Z(sin θ m − θ m ) ] + (Zθ m − 1) cos θ m − (Z +θ m ) sin θ m + 1 Z 2 + 1 (10.A.5) The constants defined by eqs. (10.A.2)–(10.A.5) are obtained by applying the follow- ing boundary conditions to eq. (10.A.1): r = r o at θ = 0 (10.A.6) t r = 2 x/2 0 r cos θ dθ (10.A.7) e = x/2 0 r sin θ dθ (10.A.8) The procedure to solve for the radius of curvature r of the new profile is outlined in the following. First, select e,t r , θ m ,r o , and Z. Then evaluate C 4 given by eq. (10.A.5) and substitute C 4 into eq. (10.A.3) and solve for C 2 . Next, use C 2 to solve eq. (10.A.2) for C 1 . The constants C 1 and C 2 can now be used to solve for the remaining constant, C 3 . N = p − C 1/3 3 2 p 2 − C 1/3 3 p − C 2/3 3 (10.A.9) . performance. BOOKCOMP, Inc. — John Wiley & Sons / Page 779 / 2nd Proofs / Heat Transfer Handbook / Bejan FILM CONDENSATION ON TUBE BUNDLES 779 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [ 779] ,. Air pockets due to longitudinal heat flux maldistribution. (From Tinker, 1933.) BOOKCOMP, Inc. — John Wiley & Sons / Page 776 / 2nd Proofs / Heat Transfer Handbook / Bejan 776 CONDENSATION 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [776],. plate heat exchangers as condensers is not entirely comprehensive. 10.9.2 Steam Condensation Heat Transfer Wang and Zhao (1993) have developed an expression for steam condensation in a plate heat