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

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TUBE-IN-TUBE HEAT EXCHANGERS WITH HEAT TRANSFER ENHANCEMENT IN THE ANNULUS

by

Ventsislav D. ZIMPAROV, Plamen J. PENCHEV, and Joshua P. MEYER

Original scientific paper UDC: 66.045.1:519.876.5 BIBLID: 0354-9836, 10 (2006), 1, 45-56

Dif fer 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 fer in the an nu lus of tube-in-tube heat exchangers. The heat trans fer en hance ment in the shell can be sup ple mented by heat trans fer aug men ta tion in tubes us ing twisted tape in serts or mi cro-finned tubes. The ef fect of the ther mal re sis tance of the con dens ing re frig er ant could also be taken into con sid er ation. To as sess the ben e fit of us ing these tech niques ex - tended per for mance eval u a tion cri te ria have been im ple mented at dif fer ent con straints. The de crease of the en tropy gen er a tion can be com bined with the rel a tive in crease of the heat trans fer rate or the rel a tive re duc tion of the heat trans fer area to find out the geo met ri cal pa ram e ters of the tubes for op - ti mal ther mo dy nam ics per for mance. The re sults show that in most of the cases con sid ered, the an gled spi ral ing tube in sert tech nique is the most ef fi - cient.

Key words: enhanced heat transfer in annulus, spiraling tape insert, spiraled tube, performance evaluation criteria

Introduction

The per for mance of con ven tional 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 fer en hance ment de vices are com monly em ployed to im prove the per for mance of an ex ist ing heat exchanger or to re duce the size and cost of 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 ef fi ciency, which al lows to re duce the op er at ing cost. A clas si fi ca tion of en hance ment tech niques can be found in [1-3].

The sur face meth ods in clude any tech nique which di rectly in volves the heat exchanger sur face. They are used on the side of the sur face that co mes into con tact with a fluid of low heat trans fer co ef fi cient in or der to re duce the thick ness of the bound ary layer and to in tro duce better fluid mix ing. Some of the ex ist ing meth ods for en hanc ing heat trans fer in a sin gle-phase, fully de vel oped tur bu lent flow are one of the two types: (a) meth - ods in which the sur face is rough ened, e. g. with re peated or he li cal rib bing, by sand ing, or

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with fins, and (b) meth ods in which a heat trans fer pro moter, e. g., a twisted tape, disk or stream lined shape is in serted into the chan nel.

In many cases heat trans fer en hance ment in tubes can be sup ple mented by heat trans fer en hance ment on the out side wall of tubes, as for tube-in-tube heat exchangers. An ap pli ca tion is in va por com pres sion hot-wa ter heat pumps. The con dens ing re frig er ant may typ i cally flow in the in ner tube and the wa ter to be heated in a coun ter flow di rec tion in the an nu lus. In this case, heat trans fer en hance ment on the outer wall is also im por tant. Heat trans fer en hance ment on the in ner or outer tube de creases the tem per a ture dif fer ence be - tween the con dens ing re frig er ant and wa ter to be heated, which is an ad van tage as higher tem per a ture can be reached.

Re cently, sev eral stud ies have been done to im prove the heat trans fer co ef fi cient in annuli [4-6]. The pur pose of these stud ies was to in ves ti gate the po ten tials of some very sim ple and in ex pen sive meth ods of heat trans fer aug men ta tion that could be used by small man u fac tur ing com pa nies. 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 fer co ef fi cient by up to 50%. At the same time the fric tion fac 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 of a tube-in-tube heat exchanger. Three tubes were thus used. Ex cept for the in - ner and outer tube, the third tube was spi raled in the an nu lus of the other two and also formed a flow pas sage. The aim was not only to in crease the heat trans fer in the an nu lus by swirl flow but also to in crease the cross flow area, since some of the flow will not only be through the an nu lus but also through the spi raled tube. The ad van tage of this method when com pared to spi raled thin wires is that no flow can oc cur through a wire since it blocks the flow.

The third method that makes use of 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, fig. 1. Three tube-in-tube heat exchangers were tested with an gled spi ral ing tape in the an nu lus with dif - fer ent pitches. It was de ter mined that the heat exchanger with the small est pitch of the an - gled spi ral ing tape and with flow against the cur va ture of the tape re sulted in the high est in - crease in the Nusselt num ber of 206%. As pen alty this heat exchanger also had the high est in crease of the pres sure drop of 203%.

Figure 1. Schematic representation of angled spiraling tape heat exchanger [6]

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Be ing fa mil iar with these in ves ti ga tions [4-6] one faces a ques tion, “Which sur - face is the best?” The de signer may feel frus trated, since the per for mance char ac ter is tic of each of the sur faces tested has not been eval u ated on any com mon ba sis.

In this pa per we at tempt to iden tify the pre ferred en hance ment ge om e try on the ba sis of its ther mo dy namic per for mance. The eval u a tion of the per for mance will be made on the ba sis of the first and the sec ond law anal y sis, tak ing into ac count some de sign or op - er a tional con straints.

Performance evaluation criteria

The ex tended per for mance eval u a tion cri te ria (PEC) equa tions have been used to as sess the ther mo dy namic ef fi ciency of the tubes in ves ti gated. The equa tions are de vel - oped for tubes of dif fer ent di am e ters and heat trans fer and fric tion fac tors based on the pre - sen ta tion for mat of per for mance data for en hanced tubes [8]. The rel a tive equa tions for sin - gle-phase flow in side enhanced tubes or channels are [9]:

A_* = N_*L_*D_* (1)

P W p f

f D L N u

W L N D

f

* * * f

* * * *

* *

= D = ^R =

S m

R 3 S

3

2 5 (2)

Q_* =W_{* *}e DT_i^* (3)

W_* u _*D N_* _* Re D N_* _*

= _m =Re^R

S

2 (4)

Dp f

f L

D u f

f L

* * D

*

* *

*

Re Re

= ^R =

S

m R

S

R S 2

3 2

2 (5)

( )

* * *

UA UA

R f

f P A R

A

iR iS

S S

R R S

R

St St

= +

+ 1

1 1 1

3 2

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where R is a sum of resistances (defined in [9]).

The ef fect of the ther mal re sis tance ex ter nal to the sur face un der con sid er ation could also be taken into ac count by in clud ing the ex ter nal heat trans fer co ef fi cient h_oS. 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 face E_o = h_oR/h_oS. The foul ing resistances on both sides of 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

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con di tion con stant wall tem per a ture. It should be pointed out that be fore this the cor re lated fric tion fac tors and heat trans fer co ef fi cients have been re cal cu lated with re spect to the hy - drau lic di am e ter of the smooth tube-in-tube heat exchanger as a com mon ba sis for com par i - son.

The eval u a tion and com par i son of the heat trans fer aug men ta tion tech niques [4-6]

have been made on the ba sis of both first and sec ond law anal y sis. Thus it is pos si ble to de - ter mine the ther mo dy namic op ti mum in a heat exchanger by min i miz ing the aug men ta tion en tropy gen er a tion num ber com pared with the rel a tive in crease of heat trans fer rate Q_* > 1, or rel a tive re duc tion of heat trans fer area A_* < 1 or pump ing power P_* < 1. Con se quently, a ra tio N_S/Q_* and a group N_SA_* = f(Re_R) might be de fined to con nect the two ob jec tives pur - sued by the first and sec ond law anal y sis and as a ba sis for ther mo dy namic op ti mi za tion.

The heat trans fer ef fi ciency of the tubes in ves ti gated has been eval u ated for the fol low ing cases.

Fixed geometry criteria (FG)

These cri te ria in volve a one-for-one re place ment of the in ner smooth tubes of shell-and-tube heat exchanger by aug mented ones of the same ba sic ge om e try, e. g., shell di am e ter, tube length, and num ber of tubes. The FG-1 cases [9] seek in creased heat duty or over all con duc tance UA for con stant exchanger flow rate. The pump ing power of the en - hanced shell-and-tube heat exchanger will in crease due to the in creased fluid fric tion char - ac ter is tics of the aug mented sur face. 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_S, [10] is:

N Q B D T

T Q

S =

+ æ -

èçç ö

ø÷÷

é ë ê

ù û

ú +

1 -

1 1 ^{0 8}

f_o

R S

iS oS

St

* St *

exp . _*

*

1 .

1

- 4 75

æ

èçç ö

ø÷÷

é ë ê

ù û

ú +

ì í ï ï

î ï ï

ü ý ï ï

þ T -

T

f f D

iS oS

o R

f S

ï ï

= f(Re ) _R

(7) The ra tio N_S/Q_* vs. Reynolds num ber, for the chan nels in ves ti gated in [4-6] is shown in figs. 2-4. As can be seen, in the range Re < 1.4·10⁴, the best char ac ter is tics have the chan nels with tubes 1, 2 [6] (y = 0.731, the small est pitch of the an gled spi ral ing tape), whereas for Re > 2.5·10⁴, 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 for mance, whereas for Re > 1.3·10⁴, the tubes 3-6 [6] im prove their char ac ter is tics di min ish ing the en - tropy gen er a tion.

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 ref 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

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thus the exchanger flow rate. The con straints are: N_* = 1, L_* = 1, and P_* = 1 re quir ing W_* <

< 1, and Re_R < Re_S. In the case FG-2a the goal is in creased heat trans fer rate Q_*> 1. The aug men ta tion en tropy gen er a tion num ber N_S [10] is:

N Q B D f

S f

o

= + - æ

èçç ö ø÷÷

æ è

ç ^-

1

1 1 ^{1 145}

0 073

f ^* ^*

.

exp St

St

R S

R

ç S

ö ø

÷

÷ é

ë ê ê

ù û ú ú ì

íï îï

×

× + æ

èçç ö ø÷÷ ^- T

T Q f

f D

iS oS

R S

*

.

* 0 364

1.⁷²⁷ (Re )

1

æ1-

èçç ö

ø÷÷

é ë ê ê

ù û ú ú

+ ü ýï þï

=

-

T T

iS oS

o f R

f (8)

Figure 2. The performance ratio NS/Q* vs. Reynolds number, [6]

1 – y = 0.731 – against; 2 – y = 0.731 – along; 3 – y = 1.799 – against; 4 – y = 1.799 – along; 5 – y = 2.878 – against;

6 – y = 2.878 – along

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The re sults for the case FG-2a are pre - sented in figs. 5-7 and they are nearly the same as those for the case FG-1a.

Figure 3. The performance ratio Ns/Q* vs.

Reynolds number, [4]

1 – 45ô; 2 – 60ô; 3 – 90ô; 4 – 105ô twist

Figure 4. The performance ratio N_s/Q_* vs.

Figure 5. The performance ratio Ns/Q* vs.

1 – y = 0.731 – against, 2 – y = 0.731 – along;

3 – y = 1.799 – against; 4 – y = 1.799 – along;

5 – y = 2.878 – against; 6 – y = 2.878 – along

Figure 6. The performance ratio N_s/Q_* vs.

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Variable geometry criteria (VG)

In most cases a heat exchanger is de signed for a re quired ther mal duty with a spec i fied flow rate. Since the shell-side ve loc ity must be re duced to ac com mo date the higher fric tion char - ac ter is tics of the aug mented sur face, it is nec es sary to in crease the flow area to main tain W_* = 1 and to per mit the exchanger flow fron tal area to vary in or der to meet the pump ing power con - straint: N_* > 1, L_* < 1, Re_R < Re_S.

In the case VG-1 [9] the ob jec tive is to re duce sur face area A_* < 1 with W_* = 1 for Q_* = P_* = 1.

The en tropy gen er a tion num ber is cal cu lated from [10]:

N f

f A

D B

S = +

æ

èçç ö

ø÷÷ × ì

íï îï

× -

1 -

1

0 364

2 091

f_o

R S

St

* .

*

. exp ^R

S R

St S

f

f A D

æ èçç ö

ø÷÷

æ è ç ç

ö ø

÷

÷ é

ë ê ê

- ù

- 0 291

0 709 0 127 .

* .

û ú ú+

ü ýï þï f_o =

f R

N_* (Re ) (9)

The group A_*N_S vs. Reynolds num ber, for the chan nels in ves ti gated in [4-6] is shown in figs. 8-10. For this case the best per for mance has a tube 4 [5], whereas the tubes 1, 2 [6] have worse per for mances even than tube 2 [5].

The cases VG-2 [9] aim at in creased ther mal per for mance (U_RA_R/U_SA_Sor Q_* >1) for 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 for W_* = 1 and A_* = P_* = 1. The val ues of N_S are cal cu - lated fol low ing [10]:

N Q f

f

D B

S = +

æ èçç ö

ø÷÷ × ì

íï îï

× -

1 -

1

0 364

2 091

f_o

R S

St

*

.

*

. exp ^R

S R S

iS

St f

f D T

T æ

èçç ö ø÷÷

æ è ç ç

ö ø

÷

÷ é

ë ê ê

ù û ú ú

- - 0 291

0 127 .

* .

oS

iS oS

o

f R

+ æ -

èçç ö

ø÷÷

é ë ê

ù û

ú +

ü ýï þï

=

-

Q T

T N

*

(Re ) 1

1

f

(10) Figure 7. The performance ratio N_S/Q_* vs.

mm1 – 45°; 2 – 60°; 3 – 90°; 4 – 105° twist

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For this case, in the range Re < 10⁴, the best per for mance has tube 4 [5], but for Re > 10⁴ the best one is tube 1 [6]. The re sults pre sented in figs. 2-13 have been ob tained as sum ing that the in ter nal heat trans fer co ef fi cient of the in ner tube is rel a tively large in com par i son with the heat trans fer co ef fi cient in the an nu lus. Con se quently, in this case of wa ter through the an nu lus heat ing with re frig er ants flow ing in the in side of a tube, the

Figure 9. The performance group A_*N_S vs.

Figure 10. The performance group A*NS vs.

1 – 45 °; 2 – 60°; 3 – 90°; 4 – 105° twist Figure 8. The performance group A_*N_S vs.

1 – y = 0.731 – against; 2 – y = 0.731 – along;

3 – y = 1.799 – against; 4 – y = 1.799 – along;

5 – y = 2.878 – against; 6 – y = 2.878 – along

Figure 11. The performance ratio N_S/Q_* vs.

1 – y = 0.731 – against; 2 – y = 0.731 – along;

3 – y = 1.799 – against; 4 – y = 1.799 – along;

5 – y = 2.878 – against; 6 – y = 2.878 – along

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heat trans fer co ef fi cient of con dens ing re frig er ant is as sumed rel a tively large h_i = 4 and the ther mal re sis tance on the an nu lus side is the high est. But, in many cases, for intube boil ing or con den sa tion of re frig er ants, the in side heat trans fer co ef fi cient is rel a tively small, and has to be aug mented.

Figure 12. The performance ratio NS/Q* vs.

1 – 45 °; 2 – 60°; 3 – 90°; 4 – 105° twist Figure 13. The performance ratio N_S/Q_* vs.

1 – y = 0.731 –, 2 – y = 0.731 – along;

3 – y = 1.799 – against; 4 – y = 1.799 – along;

5 – y = 2.878 – against; 6 – y = 2.878 – along

1 – y = 0.731 –, 2 – y = 0.731 – along;

3 – y = 1.799 – against; 4 – y = 1.799 – along;

5 – y = 2.878 – against; 6 – y = 2.878 – along

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Fig ures 8, 14, and 15 show in flu ence of the in side heat trans fer co ef fi cient on the per for mance of the tubes [6] for the case VG-1. The val ues of the in side heat trans - fer co ef fi cient are as fol lows: h_i = µ (fig. 8); h_i = 2127 W/m²K (plain tube – fig. 14), and h_i = 5290 W/m²K (Microfin #3 – fig. 15), Thome [11]. When the in side wall of the in ner tube is smooth or mi cro-finned, the best per for mance has tube 1, but when the in side heat trans fer co ef fi cient be comes large and the in ter nal ther mal re sis tance is neg li gi ble, the best per for mance has tube 2.

Conclusions

Ex tended per for mance eval u a tion cri te ria equa tions have been used to as sess the ther mo dy namic ef fi ciency of some tech niques to en hance heat trans fer in the an nu lus of 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 fer en hance ment in the shell can be sup ple mented by heat trans fer aug men ta tion in tubes us ing twisted tape in - serts or mi cro-finned tubes. The ef fect of the ther mal re sis tance of the con dens ing re frig er - ant could also be taken into con sid er ation. The eval u a tion of the per for mance of each tech - nique has been made on the ba sis of the first 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 of the cases con sid - ered, the an gled spi ral ing tube in sert tech nique is the most ef fi cient.

Nomenclature

A – heat transfer surface area, [m²]

A* – non-dimensional heat transfer surface (=AR/AS), [–]

B – constant, [–]

D – tube diameter, [m]

D* – non-dimensional tube diameter (=DR/DS), [–]

f – Fanning friction factor, [–]

h – heat transfer coefficient, [W/m² K]

L – tube length, [m]

L_* – non-dimensional tube length, (=LR/LS), [–]

Nt – number of tubes, [–]

NS – augmentation entropy generation number, [–]

N* – ratio of number of tubes (=NtR/NtS) P – pumping power, [W]

P* – non-dimensional pumping power (=PR/PS) Dp – pressure drop, [Pa]

&

Q – heat transfer rate, [W]

Q* – non-dimensional heat transfer rate (=Q& / & )_R Q_S Re – Reynolds number, [–]

St – Stanton number, [–]

T – temperature, [K]

DT – temperature difference, [K]

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DT_i^* – non-dimensional inlet temperature difference between hot and cold streams (=DTiR/DTiS) U – overall heat transfer coefficient, [W/m²K]

u – flow velocity, [m/s]

u_m* – non-dimensional flow velocity (=umR/umS) W – mass flow rate in heat exchanger, [kg/s]

W* – non-dimensional mass flow rate (=WR/WS) y – twist ratio (=z/2Di), [–]

z – pitch of the angled spiraling tape, [m]

Greek Letters

a – helix angle of tape (fig. 1), [°]

e_* – ratio of heat exchanger effectiveness (=eR/eS), [–]

q – tape angle (fig. 1), [°]

f_o – irreversibility distribution ratio, [–]

Subscripts

i – inside, or value at x = 0 m – mean value

R – rough tube S – smooth tube

o – outside, or value x = L

References

[1] Bergles, A. E., Tech niques to Aug ment Heat Trans fer, in: Hand book of Heat Trans fer Ap pli - ca tion, (Chap ter 3), McGraw-Hill, New York, USA, 1985

[2] Bergles, A. E., Some Per spec tives on En hanced Heat Trans fer Sec ond Gen er a tion Heat Trans fer Tech nol ogy, ASME Jour nal of Heat Trans fer, (1988), 110, pp. 1082-1096 [3] Bergles, A. E., Heat Trans fer En hance ment – the En cour age ment and Ac com mo da tion of

High Heat Fluxes, ASME Jour nal of Heat Trans fer, (1997), 119, pp. 8-19

[4] Van der Vyver, S., Meyer, J. P., Heat Trans fer Aug men ta tion in the An nu lus of a Heat Exchanger Con sist ing of a Round Tube in side a Twisted Square Tube, R&D Jour nal, 13 (1997), 3, pp. 77-82

[5] Herman, H., Meyer, J. P., Heat Trans fer Aug men ta tion of a Spi ralled Tube in side the An nu lus of a Tube-in-Tube Heat Exchanger, R&D Jour nal, 14 (1998), 3, pp. 43-48

[6] Coetzee, H., Heat Trans fer and Pres sure Drop Char ac ter is tics of An gled Spill ing Tape In serts in a Heat Exchanger An nu lus, M. Sc. the sis, Rand Af ri kaans Uni ver sity, Jo han nes burg, South Af rica, 2001

[7] Meyer, J. P., Coetzee, H., Tube-in-Tube Heat Exchanger with En hanced Heat Trans fer, Pat - ent no. 99/5561 (1999), South Af rica

[8] Marner, W. J., Bergles, A. E., Chenoweth, J. M., On the Pre sen ta tion of Per for mance Data for En hanced Tubes Used in Shell-in-Tube Heat Exchangers, ASME Jour nal of Heat Trans fer, (1983), 105, pp. 358-365

[9] Webb, R. L., Per for mance Eval u a tion Cri te ria for Use of En hanced Heat Trans fer Sur faces in Heat Exchanger De sign, In ter na tional Jour nal of Heat and Mass Trans fer, (1981), 24, pp.

715-726

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[10] Zimparov, V. D., Ex tended Per for mance Eval u a tion Cri te ria for En hanced Heat Trans fer Sur faces: Heat Trans fer through Ducts with Con stant Wall Tem per a ture, In ter na tional Jour - nal of Heat and Mass Trans fer, 43 (2000), 17, pp. 3137-3155

[11] Thome, J. R., High Per for mance Aug men ta tions for Re frig er a tion Sys tem Evap o ra tors and Con dens ers, Jour nal En hanced Heat Trans fer, 1 (1994), 3, pp. 275-285

Authors' addresses:

V. D. Zimparov, P. J. Penchev

Department of Mechanical Engineering Gabrovo Technical University

4, Hadji Dimitar Str.

5300 Gabrovo, Bulgaria J. P. Meyer

Department of Mechanical and Aeronautical Engineering University of Pretoria

Pretoria 0002 South Africa

Corresponding author (V. Zimparov):

E-mail: vdzim@tugab.bg

Paper submitted: Decembar 2, 2004 Paper revised: February 4, 2005 Paper accepted: February 13, 2006