BOOKCOMP, Inc. — John Wiley & Sons / Page 1077 / 2nd Proofs / Heat Transfer Handbook / Bejan SWIRL FLOW DEVICES 1077 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 [1077], (49) Lines: 946 to 953 ——— 2.927pt PgVar ——— Normal Page PgEnds: T E X [1077], (49) exchanger for a specified heat duty, significant reduction in size can be achieved. The ease of fitting multitube bundles with tape inserts and their removal, as depicted in Fig. 14.30a, makes them particularly useful in fouling situations, where frequent tube-side cleaning may be required. The characteristic geometrical features of a twisted tape, as shown in Fig. 14.30b, include the 180° twist pitch H , tape thickness δ, and tape width w (which is usu- ally about the same as the tube inside diameter d in snug- to tight-fitting tapes). The severity of tape twist is described by the dimensionless twist ratio y(= H/d), and depending on the tube diameter and tape material, inserts with a very small twist ratio can be employed. When placed inside a circular tube, the flow field gets altered in sev- eral different ways: increased axial velocity and wetted perimeter due to the blockage and partitioning of the flow cross section, longer effective flow length in the helically twisting partitioned duct, and tape’s helical curvature–induced secondary fluid circu- lation or swirl. Of these, the most dominant mechanism is swirl generation, which effects transverse fluid transport across the tape-partitioned duct, thereby promoting greater fluid mixing and higher heat transfer coefficients. The growth and structure of this tape-induced swirl in the laminar flow regime, as characterized by experimental flow visualization (Manglik and Ranganathan, 1997) and computational simulations Figure 14.30 Twisted-tape inserts: (a) typical application in a shell-and-tube heat exchanger (courtesy of Brown Fintube Company); (b) characteristic geometrical features. BOOKCOMP, Inc. — John Wiley & Sons / Page 1078 / 2nd Proofs / Heat Transfer Handbook / Bejan 1078 HEAT TRANSFER ENHANCEMENT 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 [1078], (50) Lines: 953 to 975 ——— 9.56053pt PgVar ——— Normal Page PgEnds: T E X [1078], (50) (Manglik and You, 2002), are depicted in Fig. 14.31. The fully developed laminar swirl flows, which consist of two asymmetrical counter-rotating helical vortices, have been shown (Manglik and Bergles, 1993a; Manglik et al., 2001a) to scale by a dimen- sionless swirl parameter defined on the basis of a primary force balance as Sw = Re s √ y (14.31a) where Re s = ρV s d µ V s = G ρ 1 + π 2y 2 1/2 (14.31b) Figure 14.31 Structure of swirl produced by twisted-tape inserts in laminar flows in circu- lar tubes: (a) experimental visualization of secondary flow patterns (from Manglik and Ran- ganathan, 1997); (b) results of numerical simulations (From Manglik and You, 2002). BOOKCOMP, Inc. — John Wiley & Sons / Page 1079 / 2nd Proofs / Heat Transfer Handbook / Bejan SWIRL FLOW DEVICES 1079 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 [1079], (51) Lines: 975 to 1024 ——— 0.15529pt PgVar ——— Normal Page PgEnds: T E X [1079], (51) Based on this scaling of the swirl behavior in the laminar flow regime, the follow- ing correlation for predicting the isothermal Fanning friction factor has been proposed (Manglik and Bergles, 1993a): f s = 15.767 Re s π +2 − 2(δ/d) π −4(δ/d) 2 1 +10 −6 Sw 2.55 1/6 (14.32) where f s is based on the effective swirl velocity and swirl flow length, or f s = ∆pd 2ρV 2 s L s L s = L 1 + π 2y 2 1/2 (14.33) Equation (14.32) has been shown to predict within ±10% a fairly large set of exper- imental data for a very wide range of flow conditions and tape geometry: 0 ≤ Sw ≤ 2000, 1.5 ≤ y ≤∞, 0.02 ≤ (δ/d) ≤ 0.12 (Manglik and Bergles, 1993a; Manglik et al., 2001a). For laminar flow heat transfer in tubes maintained at a uniform wall temperature (UWT), the following correlation developed by Manglik and Bergles (1993a) is recommended: Nu m = 4.612(µ b /µ w ) 0.14 fully developed flow (1 +0.0951Gz 0.894 ) 2.5 thermal entrance +6.413 ×10 −9 (Sw ·Pr 0.391 ) 3.835 swirl flows 2 + 2.132 ×10 −14 (Re a · Ra) 2.23 free convection 0.1 (14.34) Here each of the terms that account for various convection effects is highlighted, and the interplay between thermal entrance effects and fully developed tape-induced swirl flows is depicted in Fig. 14.32. With Ra ∼ 0, their respective asymptotes are represented by Sw → 0, Gz →∞(entrance effects), and Sw →∞, Gz → 0 (swirl-dominated flows). Similarly, in flows where Gr > Sw 2 , free convection effects dominate and they are scaled by the grouping (Re a · Ra), as shown in Fig. 14.33. For tubes with the uniform heat flux (UHF) condition, the correlation devised by Hong and Bergles (1976) for fully developed swirl flows may be considered after incorporating the classical viscosity-ratio correction factor to account for viscous property variations as follows: Nu z = 5.172 1 +5.484 ×10 −3 Pr 0.7 Re a y 1.25 0.5 µ b µ w 0.14 (14.35) Furthermore, to account for the influence of free convection on swirl flows in UHF tubes, Bandyopadhyay et al. (1991) have extended the Hong and Bergles correlations to include mixed convection as BOOKCOMP, Inc. — John Wiley & Sons / Page 1080 / 2nd Proofs / Heat Transfer Handbook / Bejan 1080 HEAT TRANSFER ENHANCEMENT 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 [1080], (52) Lines: 1024 to 1053 ——— -0.67392pt PgVar ——— Normal Page PgEnds: T E X [1080], (52) Figure 14.32 Influence of twisted-tape-generated swirl and tube partitioning on the average Nusselt number in thermal developing and fully developoed laminar flows in circular tubes with uniform wall temperature. (From Manglik and Bergles, 1993a.) Nu z = Nu 9 z,HB + 1.17 Ra ∗0.181 9 1/9 (14.36) For predicting friction factors under the more practical diabatic (heating or cooling) conditions, based on the theoretical results of Harms et al. (1998) for the limiting case of a straight-tape insert (y =∞, δ = 0) for liquids and the experimental results of Watanabe et al. (1983), a first-order correction to the isothermal results of eq. (14.32) can be made as f f iso = µ b µ w m for liquids T b T w 0.1 for gases (14.37a) where m(UWT) = 0.65 heating 0.58 cooling or m(UHF) = 0.61 heating 0.54 cooling (14.37b) In the turbulent flow regime, which is characterized inherently by fluctuating velocities, a well-mixed cross-stream eddy structure, and flow instabilities in the transition process, the scaling of swirl flows due to twisted-tape inserts with Sw is BOOKCOMP, Inc. — John Wiley & Sons / Page 1081 / 2nd Proofs / Heat Transfer Handbook / Bejan SWIRL FLOW DEVICES 1081 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 [1081], (53) Lines: 1053 to 1069 ——— 0.44505pt PgVar ——— Normal Page * PgEnds: Eject [1081], (53) Figure 14.33 Mixed convection effects in laminar fully developed twisted-tape-induced swirl-flow heat transfer in circular tubes with uniform wall temperature. (From Manglik and Bergles, 1993a.) found to be inapplicable (Manglik and Bergles, 1993b). Instead, the friction factor correlates with a power law reciprocal of the twist ratio as f = 0.0791 Re 0.25 1 + 2.752 y 1.29 π π −(4δ/d) 1.75 π +2 − (2δ/d) π −(4δ/d) 1.25 (14.38) and it describes the available experimental data within ±5% (Manglik and Bergles, 1993b; Tong et al., 1996; Manglik and Bergles, 2002a). Again, to correct for heating and cooling conditions in predicting the friction factors, the following recommenda- tions given by Lopina and Bergles (1969) for liquids, and by Watanabe et al. (1983) for gases, may be adopted: f f iso = µ b µ w 0.35(d h /d) for liquids T b T w 0.1 for gases (14.39) BOOKCOMP, Inc. — John Wiley & Sons / Page 1082 / 2nd Proofs / Heat Transfer Handbook / Bejan 1082 HEAT TRANSFER ENHANCEMENT 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 [1082], (54) Lines: 1069 to 1113 ——— 3.93306pt PgVar ——— Normal Page * PgEnds: Eject [1082], (54) For turbulent flow heat transfer with Re ≥ 10 4 , Manglik and Bergles (1993b) have proposed a Nusselt number correlation that is expressed as Nu = 0.023Re 0.8 · Pr 0.4 1 + 0.769 y π +2 − (2δ/d) π −(4δ/d) 0.2 π π −(4δ/d) 0.8 φ (14.40a) where the property correction factor φ is given by φ = µ b µ w n or T b T w m (14.40b) where n = 0.18 liquid heating 0.30 liquid cooling and m = 0.45 gas heating 0.15 gas cooling (14.40c) The predictions of eq. (14.40) have been found (Manglik and Bergles, 1993b; 2002a) to describe within ±10% the majority of experimental data for a very wide range of tape-twist ratios (2 ≤ y ≤∞) reported in the literature for both gas and liquid turbulent flows in circular tubes with twisted-tape inserts. 14.6.2 Boiling Of all the swirl flow devices, twisted tapes have also found extensive use in boiling applications. Two recent reviews (Shatto and Peterson, 1996; Manglik and Bergles, 2002a) have covered most aspects of their thermal–hydraulic performance, which includes bulk boiling with net vapor generation, subcooled boiling, and critical heat flux. A schematic synopsis of the effects of twisted-tape inserts on the heat transfer in a uniformly heated tube with once-through boiling (typically encountered in power boilers and refrigerant evaporators) is given in the bulk fluid and tube wall tempera- ture map of Fig. 14.34. Variations in the wall temperature of an empty smooth tube and one fitted with a twisted tape and in the bulk fluid temperature are depicted for a typical case of fixed mass flux, inlet temperature, and pressure level in a uniformly heated tube. The heat transfer enhancement due to the tape insert is reflected in the reduced wall temperature along the tube length in the single-phase liquid, subcooled boiling, bulk boiling, dispersed-flow film boiling, and post-dryout single-phase va- por regimes. Also, dryout is delayed to significantly higher quality. The primary en- hancement mechanism is perhaps tape-induced swirl, which tends to improve vapor removal and wetting of the heated surface. Enhancement of subcooled boiling is of particular interest for cooling and ther- mal management of high-heat-flux devices (e.g., electrical machines, electronic and microelectronic devices, and nuclear reactors cores). Gambill et al. (1961), Feinstein and Lundberg (1963), and Lopina and Bergles (1973) have reported a limited set of experimental data, and the typical boiling curves for the influence of a tape-twist BOOKCOMP, Inc. — John Wiley & Sons / Page 1083 / 2nd Proofs / Heat Transfer Handbook / Bejan 1083 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 [1083], (55) Lines: 1113 to 1122 ——— * 528.0pt PgVar ——— Normal Page * PgEnds: PageBreak [1083], (55) Figure 14.34 Characteristic axial evolution of tube wall and bulk fluid temperatures in forced convection boiling in a uniformly heated circular tube with and without a twisted-tape insert. (From Manglik and Bergles, 2002a.) BOOKCOMP, Inc. — John Wiley & Sons / Page 1084 / 2nd Proofs / Heat Transfer Handbook / Bejan 1084 HEAT TRANSFER ENHANCEMENT 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 [1084], (56) Lines: 1122 to 1140 ——— 0.927pt PgVar ——— Normal Page PgEnds: T E X [1084], (56) 6 7 8 9 20 30 40 10 10 6 2 3 4 5 6 7 8 9 10 6 ( ) [K]TT w Ϫ sat qЉ [W/m ] 2 y = 2.48 y = 3.15 y = 5.26 y = 9.20 Empty tube Degassed, demineralized water L Nickel tubes, Inconel tapes Swirl tubes = 4.915 mm Empty tube = 5.029 mm d d i i ( ) 3.10.93 K = 344.73 kPa = 2.743 7.925 m/s TT p V sat exit in Ϫ ϳ ϳ Ϫ b Figure 14.35 Boiling curves for fully developed subcooled flow boiling heat transfer in a tube with twisted-tape inserts of different twist severity. (From Lopina and Bergles, 1973.) ratio, as characterized by the results of Lopina and Bergles (1973), are depicted in Fig. 14.35. The slight leftward shift of the swirl flow boiling curves relative to that for an empty tube suggests some heat transfer enhancement, although the change in the y values seems to have no significant effect. A more effective use of twisted tapes in subcooled boiling has been shown for increasing the critical heat flux (Bergles, 1998; Manglik and Bergles, 2002a). Higher wall heat fluxes are essentially sustained because swirl-induced radial pressure gradi- ents promote greater vapor removal from and transport of liquid droplets to the heated BOOKCOMP, Inc. — John Wiley & Sons / Page 1085 / 2nd Proofs / Heat Transfer Handbook / Bejan SWIRL FLOW DEVICES 1085 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 [1085], (57) Lines: 1140 to 1140 ——— 0.42099pt PgVar ——— Normal Page PgEnds: T E X [1085], (57) Figure 14.36 Enhanced CHF in subcooled boiling due to twisted-tape-induced swirl flows. (From Gambill et al., 1961.) surface. This enhancement is seen in the experimental data of Gambill et al. (1961) in Fig. 14.36, where increase in CHF of up to 100% is seen. In fact, Gambill et al. (1961) have shown that the CHF is higher by a factor of 2 in tubes with twisted-tape inserts compared to that in smooth empty tubes for the same pumping power. Dri ˇ zius et al. (1978) measured CHF in a 1.6-mm-diameter tube fitted with 2 ≤ y ≤ 10 tapes, and found the data to be independent of subcooling but dependent on mass flux y and heated length. In a more recent study, Gaspari and Cattadori (1994) reconfirmed the BOOKCOMP, Inc. — John Wiley & Sons / Page 1086 / 2nd Proofs / Heat Transfer Handbook / Bejan 1086 HEAT TRANSFER ENHANCEMENT 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 [1086], (58) Lines: 1140 to 1168 ——— 0.98206pt PgVar ——— Long Page PgEnds: T E X [1086], (58) enhanced performance of twisted tapes with their CHF data, which is 1.4 to 2.1 times higher with twist ratios of y = 2.0 and 1.0, respectively. Similarly, in their experi- ments with small-diameter (2.44 ≤ d ≤ 6.54 mm) stainless steel tubes and different twist ratio (1.9 ≤ y ≤∞) tapes, Tong et al. (1996) found the CHF enhanced by a factor of 1.5 with the tightest twisted tape and a mass flux of 15,000 kg/m 2 ·s. They also deduced that CHF was inversely proportional to y,d,T i , and l/d, but directly proportional to G and p e . Based on this parametric analysis, the following empirical correlation has been proposed: q cr = 31.554 ( G/G o ) 0.6657 (p e /p e,o ) 0.2787 (y/y o ) 0.2412 (d/d o ) 0.0735 (L h /d) o (L h /d) 0.2191 T sub,e − T i T sat,e − T i,o 1.041 (14.41) Here the variables with the subscript o pertain to a reference condition (see Tong et al. for details), and the predictions of eq. (14.41) have been shown to describe within ±25% most of their own experimental data as well as those of Gambill et al. (1961), Dri ˇ zius et al. (1978), Inasaka et al. (1991), and Gaspari and Cattadori (1994). For the pressure drop in subcooled flow boiling, needed to size the pumping system, determine the exit pressure, and assess the thermal–hydraulic stability of the system (Manglik and Bergles, 2002a), Pabisz and Bergles (1997) have devised an empirical correlation. Their equation is based on the Tong et al. (1996) data, where any gravitational component has been subtracted from the measured pressure drop and is expressed as ∆p = (∆p fluid only + ∆p subcooled boiling ) 1/n (14.42) The details of procedures for calculating the single-phase fluid only and subcooled boiling contributions can be found in Pabisz and Bergles (1997), and the predic- tions of this correlation have been shown to describe most of the experimental data within ±15%. In bulk or saturated boiling conditions, twisted-tape inserts have been shown to en- hance the heat transfer coefficient throughout the entire quality region (0 ≤ x ≤ 1), as well as to increase the CHF (or dryout quality) and the heat transfer coefficients in the post-dryout dispersed-flow film boiling region (Shatto and Peterson, 1996; Manglik and Bergles, 2002a). Enhanced performance data have been reported for a variety of fluids, including water, refrigerants, cryogenic fluids, and liquid metals (Bergles et al., 1995; Manglik and Bergles, 2002a). As reviewed by Shatto and Peterson (1996), several different correlations have been proposed by different investigators (Gambill et al., 1961; Blatt and Adt, 1963; Jensen and Bensler, 1986; Agarwal et al., 1986; Kedzierski and Kim, 1997). For predicting the CHF, Jensen (1984) provides an em- pirical correlation based on data for water and R-22 that describes the experimental results within an average deviation of ±10%. Bergles et al.(1971)have considered the dispersed flow (post-dryout) regime and have devised a rather elaborate correlation. Their equation is based on several variables that affect and describe swirl flow behav- ior and on the assumption that the vapor remains at saturated conditions. Blatt and Adt (1963), and Agarwal et al. (1982) have also given correlations for the two-phase flow pressure drop in bulk boiling that are based on their respective data for R-11 and R-12. . and heated length. In a more recent study, Gaspari and Cattadori (1994) reconfirmed the BOOKCOMP, Inc. — John Wiley & Sons / Page 1086 / 2nd Proofs / Heat Transfer Handbook / Bejan 1086 HEAT TRANSFER. gases (14.39) BOOKCOMP, Inc. — John Wiley & Sons / Page 1082 / 2nd Proofs / Heat Transfer Handbook / Bejan 1082 HEAT TRANSFER ENHANCEMENT 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 [1082],. convection as BOOKCOMP, Inc. — John Wiley & Sons / Page 1080 / 2nd Proofs / Heat Transfer Handbook / Bejan 1080 HEAT TRANSFER ENHANCEMENT 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 [1080],