PERFORMANCE EVALUATION OF TUBE-IN-TUBE HEAT EXCHANGERS WITH HEAT TRANSFER ENHANCEMENT IN THE ANNULUS

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1 PEFOMANCE EVALUATION OF TUBE-IN-TUBE HEAT EXCHANGE WITH HEAT TANFE ENHANCEMENT IN THE ANNULU by Ventsislav D. ZIMPAOV, Plamen J. PENCHEV, and Joshua P. MEYE Original scientiic paper UDC: : BIBLID: , 10 (2006), 1, Di er ent tech niques as an gled spi ral ing tape in serts, a round tube in side a twisted square tube and spi raled tube in side the an nu lus have been used to en hance heat trans er in the an nu lus o tube-in-tube heat exchangers. The heat trans er en hance ment in the shell can be sup ple mented by heat trans er aug men ta tion in tubes us ing twisted tape in serts or mi cro-inned tubes. The e ect o the ther mal re sis tance o the con dens ing re rig er ant could also be taken into con sid er ation. To as sess the ben e it o us ing these tech niques ex - tended per or mance eval u a tion cri te ria have been im ple mented at di er ent con straints. The de crease o the en tropy gen er a tion can be com bined with the rel a tive in crease o the heat trans er rate or the rel a tive re duc tion o the heat trans er area to ind out the geo met ri cal pa ram e ters o the tubes or op - ti mal ther mo dy nam ics per or mance. The re sults show that in most o the cases con sid ered, the an gled spi ral ing tube in sert tech nique is the most e i - cient. Key words: enhanced heat transer in annulus, spiraling tape insert, spiraled tube, perormance evaluation criteria Introduction The perormance o conventional heat exchangers can be sub stan tially im proved by many aug men ta tion tech niques ap plied to de sign sys tems. Heat trans er en hance ment de vices are com monly em ployed to im prove the per or mance o an ex ist ing heat exchanger or to re duce the size and cost o a pro posed heat exchanger. An al ter na tive goal is to use such tech niques to in crease the sys tem ther mo dy namic e i ciency, which al lows to re duce the op er at ing cost. A clas si i ca tion o en hance ment tech niques can be ound in [1-3]. The sur ace meth ods in clude any tech nique which di rectly in volves the heat exchanger sur ace. They are used on the side o the sur ace that co mes into con tact with a luid o low heat trans er co e i cient in or der to re duce the thick ness o the bound ary layer and to in tro duce better luid mix ing. ome o the ex ist ing meth ods or en hanc ing heat trans er in a sin gle-phase, ully de vel oped tur bu lent low are one o the two types: (a) meth - ods in which the sur ace is rough ened, e. g. with re peated or he li cal rib bing, by sand ing, or 45

2 THEMAL CIENCE: Vol. 10 (2006), No. 1, pp with ins, and (b) meth ods in which a heat trans er pro moter, e. g., a twisted tape, disk or stream lined shape is in serted into the chan nel. In many cases heat trans er en hance ment in tubes can be sup ple mented by heat trans er en hance ment on the out side wall o tubes, as or tube-in-tube heat exchangers. An application is in vapor compression hot-water heat pumps. The condensing rerigerant may typ i cally low in the in ner tube and the wa ter to be heated in a coun ter low di rec tion in the an nu lus. In this case, heat trans er en hance ment on the outer wall is also im por tant. Heat trans er en hance ment on the in ner or outer tube de creases the tem per a ture di er ence be - tween the con dens ing re rig er ant and wa ter to be heated, which is an ad van tage as higher temperature can be reached. e cently, sev eral stud ies have been done to im prove the heat trans er co e i cient in annuli [4-6]. The pur pose o these stud ies was to in ves ti gate the po ten tials o some very sim ple and in ex pen sive meth ods o heat trans er aug men ta tion that could be used by small manuacturing companies. Van der Vyver and Meyer [4] used a round tube in side a twisted square tube to en hance the ro ta tion com po nent in the an nu lus which in creased the heat trans er co e i cient by up to 50%. At the same time the ric tion ac tor in creased by up to 9%. An other method used by Herman and Meyer [5] was to use a spi ral ing tube in side the an nu lus o a tube-in-tube heat exchanger. Three tubes were thus used. Ex cept or the in - ner and outer tube, the third tube was spi raled in the an nu lus o the other two and also ormed a low pas sage. The aim was not only to in crease the heat trans er in the an nu lus by swirl low but also to in crease the cross low area, since some o the low will not only be through the an nu lus but also through the spi raled tube. The ad van tage o this method when com pared to spi raled thin wires is that no low can oc cur through a wire since it blocks the low. The third method that makes use o this prin ci ple was pat ented by Meyer and Coetzee [7]. An an gled spi ral ing tape is used in the an nu lus to in duce swirl, ig. 1. Three tube-in-tube heat exchangers were tested with an gled spi ral ing tape in the an nu lus with di - er ent pitches. It was de ter mined that the heat exchanger with the small est pitch o the an - gled spi ral ing tape and with low against the cur va ture o the tape re sulted in the high est in - crease in the Nusselt num ber o 206%. As pen alty this heat exchanger also had the high est in crease o the pres sure drop o 203%. Figure 1. chematic representation o angled spiraling tape heat exchanger [6] 46

3 Zimparov, V. D., Penchev, P. J., Meyer, J. P.: Perormance Evaluation o Tube-in-Tube... Be ing a mil iar with these in ves ti ga tions [4-6] one aces a ques tion, Which sur - ace is the best? The de signer may eel rus trated, since the per or mance char ac ter is tic o each o the sur aces tested has not been eval u ated on any com mon ba sis. In this pa per we at tempt to iden tiy the pre erred en hance ment ge om e try on the ba sis o its ther mo dy namic per or mance. The eval u a tion o the per or mance will be made on the ba sis o the irst and the sec ond law anal y sis, tak ing into ac count some de sign or op - erational constraints. Perormance evaluation criteria The extended perormance evaluation criteria (PEC) equa tions have been used to as sess the ther mo dy namic e i ciency o the tubes in ves ti gated. The equa tions are de vel - oped or tubes o di er ent di am e ters and heat trans er and ric tion ac tors based on the pre - sen ta tion or mat o per or mance data or en hanced tubes [8]. The rel a tive equa tions or sin - gle-phase low in side enhanced tubes or channels are [9]: A = N L D (1) W L P W Dp 3 D L N u N D m (2) Q W e DT i (3) 2 e W um D N D N e Dp L D u 2 m L D 3 e e 2 2 (4) (5) ( UA) ( UA) i i t t P A 2 A (6) where is a sum o resistances (deined in [9]). The e ect o the ther mal re sis tance ex ter nal to the sur ace un der con sid er ation could also be taken into ac count by in clud ing the ex ter nal heat trans er co e i cient h o. The anal y sis in cludes the pos si bil ity that the en hanced heat exchanger may have an en hanced outer tube sur ace E o = h o /h o. The oul ing resistances on both sides o the tube wall could also be put into con sid er ation. In this study all the tubes have been eval u ated at bound ary 47

4 THEMAL CIENCE: Vol. 10 (2006), No. 1, pp con di tion con stant wall tem per a ture. It should be pointed out that be ore this the cor re lated ric tion ac tors and heat trans er co e i cients have been re cal cu lated with re spect to the hy - drau lic di am e ter o the smooth tube-in-tube heat exchanger as a com mon ba sis or com par i - son. The evaluation and comparison o the heat transer augmentation techniques [4-6] have been made on the ba sis o both irst and sec ond law anal y sis. Thus it is pos si ble to de - termine the thermodynamic optimum in a heat exchanger by minimizing the augmentation en tropy gen er a tion num ber com pared with the rel a tive in crease o heat trans er rate Q > 1, or rel a tive re duc tion o heat trans er area A < 1 or pump ing power P < 1. Con se quently, a ratio N /Q and a group N A = (e ) might be de ined to con nect the two ob jec tives pur - sued by the irst and sec ond law anal y sis and as a ba sis or ther mo dy namic op ti mi za tion. The heat trans er e i ciency o the tubes in ves ti gated has been eval u ated or the ol low ing cases. Fixed geometry criteria (FG) These cri te ria in volve a one-or-one re place ment o the in ner smooth tubes o shell-and-tube heat exchanger by aug mented ones o the same ba sic ge om e try, e. g., shell di am e ter, tube length, and num ber o tubes. The FG-1 cases [9] seek in creased heat duty or overall conductance UA or con stant exchanger low rate. The pump ing power o the en - hanced shell-and-tube heat exchanger will in crease due to the in creased luid ric tion char - ac ter is tics o the aug mented sur ace. For these cases the con straints, DT i 1, W = 1, N = = 1, and L = 1 re quire P > 1. When the ob jec tive is in creased heat duty Q > 1, this cor re - sponds to the case FG-1a, [9]. The aug men ta tion en tropy gen er a tion num ber N, [10] is: 1 t 0 8 Ti N Q B D Q 1. T exp 1 1 o t T o T i o 1 o D (e ) (7) The ra tio N /Q vs. eynolds num ber, or the chan nels in ves ti gated in [4-6] is shown in igs As can be seen, in the range e < , the best characteristics have the chan nels with tubes 1, 2 [6] (y = 0.731, the small est pitch o the an gled spi ral ing tape), whereas or e > , the tube N5 [6] have a ten dency to be the best. Fur ther more, all the tubes in [4, 5] and tubes 1, 2 [6] con tin u ously have a deg ra da tion in their per or mance, whereas or e > , the tubes 3-6 [6] im prove their char ac ter is tics di min ish ing the en - tropy generation. The FG-2 [9] cri te ria have the same ob jec tives as FG-1, but re quire that the aug - mented tube unit should op er ate at the same pump ing power as the re er ence smooth tube unit. The pump ing power is main tained con stant by re duc ing the shell-side ve loc ity and 48

5 Zimparov, V. D., Penchev, P. J., Meyer, J. P.: Perormance Evaluation o Tube-in-Tube... Figure 2. The perormance ratio N /Q vs. eynolds number, [6] 1 y = against; 2 y = along; 3 y = against; 4 y = along; 5 y = against; 6 y = along thus the exchanger low rate. The con straints are: N = 1, L = 1, and P = 1 re quir ing W < < 1, and e < e. In the case FG-2a the goal is in creased heat trans er rate Q > 1. The augmentation entropy generation number N [10] is: T T 1 N Q B t exp 1 D 1 o t i o Q D T 1 T i o o (e ) (8) 49

6 THEMAL CIENCE: Vol. 10 (2006), No. 1, pp Figure 3. The perormance ratio N s /Q vs. eynolds number, [4] 1 45 o ; 2 60 o ; 3 90 o ; o twist Figure 4. The perormance ratio N s /Q vs. eynolds number, [5] Figure 5. The perormance ratio N s /Q vs. eynolds number, [6] 1 y = against, 2 y = along; 3 y = against; 4 y = along; 5 y = against; 6 y = along Figure 6. The perormance ratio N s /Q vs. eynolds number, [5] The re sults or the case FG-2a are pre - sented in igs. 5-7 and they are nearly the same as those or the case FG-1a. 50

7 Zimparov, V. D., Penchev, P. J., Meyer, J. P.: Perormance Evaluation o Tube-in-Tube... Variable geometry criteria (VG) In most cases a heat exchanger is de signed or a re quired ther mal duty with a spec i ied low rate. ince the shell-side ve loc ity must be re duced to ac com mo date the higher ric tion char - ac ter is tics o the aug mented sur ace, it is nec es sary to in crease the low area to main tain W = 1 and to per mit the exchanger low ron tal area to vary in or der to meet the pump ing power con - straint: N > 1, L < 1, e < e. In the case VG-1 [9] the ob jec tive is to re duce sur ace area A < 1 with W = 1 or Q = P = 1. The en tropy gen er a tion num ber is cal cu lated rom [10]: N t D. expb1 t o Figure 7. The perormance ratio N /Q vs. eynolds number, [4] mm1 45 ; 2 60 ; 3 90 ; twist A A D. o (e ) (9) N The group A N vs. eynolds num ber, or the chan nels in ves ti gated in [4-6] is shown in igs For this case the best per or mance has a tube 4 [5], whereas the tubes 1, 2 [6] have worse per or mances even than tube 2 [5]. The cases VG-2 [9] aim at in creased ther mal per or mance (U A /U A or Q >1) or A = 1 and P = 1. They are sim i lar to the cases FG-2. When the ob jec tive is Q > 1, case VG-2a [9], an ad di tional con straint is DT i. The last case con sid ered is VG-2a where the ob jec tive is in creased heat rate Q > 1 or W = 1 and A = P = 1. The val ues o N are cal cu - lated ollowing [10]: t D. expb1 t N Q 1 1 o T D T i. o Q T 1 T i o 1 N o (e ) (10) 51

8 THEMAL CIENCE: Vol. 10 (2006), No. 1, pp Figure 8. The perormance group A N vs. eynolds number, [6] 1 y = against; 2 y = along; 3 y = against; 4 y = along; 5 y = against; 6 y = along Figure 9. The perormance group A N vs. eynolds number, [5] Figure 10. The perormance group A N vs. eynolds number, [4] 1 45 ; 2 60 ; 3 90 ; twist Figure 11. The perormance ratio N /Q vs. eynolds number, [6] 1 y = against; 2 y = along; 3 y = against; 4 y = along; 5 y = against; 6 y = along For this case, in the range e < 10 4, the best per or mance has tube 4 [5], but or e > 10 4 the best one is tube 1 [6]. The re sults pre sented in igs have been ob tained as sum ing that the in ter nal heat trans er co e i cient o the in ner tube is rel a tively large in com par i son with the heat trans er co e i cient in the an nu lus. Con se quently, in this case o wa ter through the an nu lus heat ing with re rig er ants low ing in the in side o a tube, the 52

9 Zimparov, V. D., Penchev, P. J., Meyer, J. P.: Perormance Evaluation o Tube-in-Tube... Figure 12. The perormance ratio N /Q vs. eynolds number, [4] 1 45 ; 2 60 ; 3 90 ; twist Figure 13. The perormance ratio N /Q vs. eynolds number, [5] Figure 14. The perormance group A N vs. eynolds number, [6] 1 y = 0.731, 2 y = along; 3 y = against; 4 y = along; 5 y = against; 6 y = along Figure 15. The perormance group A N vs. eynolds number, [6] 1 y = 0.731, 2 y = along; 3 y = against; 4 y = along; 5 y = against; 6 y = along heat trans er co e i cient o con dens ing re rig er ant is as sumed rel a tively large h i = and the ther mal re sis tance on the an nu lus side is the high est. But, in many cases, or intube boil ing or con den sa tion o re rig er ants, the in side heat trans er co e i cient is rel a tively small, and has to be aug mented. 53

10 THEMAL CIENCE: Vol. 10 (2006), No. 1, pp Fig ures 8, 14, and 15 show in lu ence o the in side heat trans er co e i cient on the per or mance o the tubes [6] or the case VG-1. The val ues o the in side heat trans - er co e i cient are as ol lows: h i = µ (ig. 8); h i = 2127 W/m 2 K (plain tube ig. 14), and h i = 5290 W/m 2 K (Microin #3 ig. 15), Thome [11]. When the in side wall o the in ner tube is smooth or mi cro-inned, the best per or mance has tube 1, but when the in side heat trans er co e i cient be comes large and the in ter nal ther mal re sis tance is neg li gi ble, the best per or mance has tube 2. Conclusions Extended perormance evaluation criteria equations have been used to assess the ther mo dy namic e i ciency o some tech niques to en hance heat trans er in the an nu lus o tube-in-tube heat exchangers, such as: an gled spi ral ing tape in serts, a round tube in side a twisted square tube and spi raled tube in side the an nu lus. The heat trans er en hance ment in the shell can be sup ple mented by heat trans er aug men ta tion in tubes us ing twisted tape in - serts or mi cro-inned tubes. The e ect o the ther mal re sis tance o the con dens ing re rig er - ant could also be taken into con sid er ation. The eval u a tion o the per or mance o each tech - nique has been made on the ba sis o the irst and sec ond law anal y ses, tak ing into ac count some de sign or op er a tional con straints. The re sults show that in most o the cases con sid - ered, the an gled spi ral ing tube in sert tech nique is the most e i cient. Nomenclature A heat transer surace area, [m 2 ] A non-dimensional heat transer surace (=A /A ), [ ] B constant, [ ] D tube diameter, [m] D non-dimensional tube diameter (=D /D ), [ ] Fanning riction actor, [ ] h heat transer coeicient, [W/m 2 K] L tube length, [m] L non-dimensional tube length, (=L /L ), [ ] N t number o tubes, [ ] N augmentation entropy generation number, [ ] N ratio o number o tubes (=N t /N t ) P pumping power, [W] P non-dimensional pumping power (=P /P ) Dp pressure drop, [Pa] Q heat transer rate, [W] Q non-dimensional heat transer rate ( Q / Q ) e eynolds number, [ ] t tanton number, [ ] T temperature, [K] T temperature dierence, [K] 54

11 Zimparov, V. D., Penchev, P. J., Meyer, J. P.: Perormance Evaluation o Tube-in-Tube... DT i non-dimensional inlet temperature dierence between hot and cold streams (=DT i /DT i ) U overall heat transer coeicient, [W/m 2 K] u low velocity, [m/s] u m non-dimensional low velocity (=u m /u m ) W mass low rate in heat exchanger, [kg/s] W non-dimensional mass low rate (=W /W ) y twist ratio (=z/2d i ), [ ] z pitch o the angled spiraling tape, [m] Greek Letters a helix angle o tape (ig. 1), [ ] e ratio o heat exchanger eectiveness (=e /e ), [ ] q tape angle (ig. 1), [ ] o irreversibility distribution ratio, [ ] ubscripts i inside, or value at x = 0 m mean value rough tube smooth tube o outside, or value x = L eerences [1] Bergles, A. E., Tech niques to Aug ment Heat Trans er, in: Hand book o Heat Trans er Ap pli - cation, (Chap ter 3), McGraw-Hill, New York, UA, 1985 [2] Bergles, A. E., ome Per spec tives on En hanced Heat Trans er ec ond Gen er a tion Heat Trans er Tech nol ogy, AME Jour nal o Heat Trans er, (1988), 110, pp [3] Bergles, A. E., Heat Trans er En hance ment the En cour age ment and Ac com mo da tion o High Heat Fluxes, AME Jour nal o Heat Trans er, (1997), 119, pp [4] Van der Vyver,., Meyer, J. P., Heat Trans er Aug men ta tion in the An nu lus o a Heat Exchanger Con sist ing o a ound Tube in side a Twisted quare Tube, &D Jour nal, 13 (1997), 3, pp [5] Herman, H., Meyer, J. P., Heat Trans er Aug men ta tion o a pi ralled Tube in side the An nu lus o a Tube-in-Tube Heat Exchanger, &D Jour nal, 14 (1998), 3, pp [6] Coetzee, H., Heat Trans er and Pres sure Drop Char ac ter is tics o An gled pill ing Tape In serts in a Heat Exchanger An nu lus, M. c. the sis, and A ri kaans Uni ver sity, Jo han nes burg, outh A rica, 2001 [7] Meyer, J. P., Coetzee, H., Tube-in-Tube Heat Exchanger with En hanced Heat Trans er, Pat - ent no. 99/5561 (1999), outh A rica [8] Marner, W. J., Bergles, A. E., Chenoweth, J. M., On the Pre sen ta tion o Per or mance Data or En hanced Tubes Used in hell-in-tube Heat Exchangers, AME Jour nal o Heat Trans er, (1983), 105, pp [9] Webb,. L., Per or mance Eval u a tion Cri te ria or Use o En hanced Heat Trans er ur aces in Heat Exchanger De sign, In ter na tional Jour nal o Heat and Mass Trans er, (1981), 24, pp

12 THEMAL CIENCE: Vol. 10 (2006), No. 1, pp [10] Zimparov, V. D., Ex tended Per or mance Eval u a tion Cri te ria or En hanced Heat Trans er ur aces: Heat Trans er through Ducts with Con stant Wall Tem per a ture, In ter na tional Jour - nal o Heat and Mass Trans er, 43 (2000), 17, pp [11] Thome, J.., High Per or mance Aug men ta tions or e rig er a tion ys tem Evap o ra tors and Con dens ers, Jour nal En hanced Heat Trans er, 1 (1994), 3, pp Authors' addresses: V. D. Zimparov, P. J. Penchev Department o Mechanical Engineering Gabrovo Technical University 4, Hadji Dimitar tr Gabrovo, Bulgaria J. P. Meyer Department o Mechanical and Aeronautical Engineering University o Pretoria Pretoria 0002 outh Arica Corresponding author (V. Zimparov): Paper submitted: Decembar 2, 2004 Paper revised: February 4, 2005 Paper accepted: February 13,

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