ELSEVIER Chemical Engineering and Processing 36 (1997) 149-159

Pressure drop on the shell side of shell-and-tube heat exchangers with segmental baffles1

Edward S. Gaddis a,*, Volker Gnielinski b a Institut fir Thermische Verfuhrenstechnik, Technische UniversitZit ClausthaI, LeibnizsraJe 1.5, 38678 ClausthaI-Zellerfeld, Germany

b Lehrstuhl ldnd Institut fir Then-n&he Verfahrenstechnik, Universitiit h’arlsruhe TH, ICaiserstraJe 12, 76131 Karlsrtlhe, Germany

Received 1 December 1996

Abstract

A procedure is presented for evaluating the shell side pressure drop in shell-and-tube heat exchangers with segmental baffles. The procedure is based on correlations for calculating the pressure drop in an ideal tube bank coupled with correction factors, which take into account the influence of leakage and bypass streams, and on equations for calculating the pressure drop in a window section from the Delaware method. The proposed equations were checked by comparing experimental measurements available in the literature with the theoretical predictions. The ranges of the geometrical and operational parameters, for which the deviations between the experimental measurements and the theoretical predictions were within & 35%, are presented in the paper.

Kurzfassung

Em Verfahren fiir die Berechnung des Druckverlusts im AuSenraum von Rohrbfindel-Warmetibertragern mit Segment-Um- lenkblechen wird dargestellt. Das Verfahren basiert auf Gleichungen fur die Berechnung des Druckverlusts in einem idealen Rohrbiindel gekoppelt mit Korrekturfaktoren, die den EinfluD der Leek- und der Bypassstromungen beriicksichtigen, und auf Gleichungen fur die Berechnung des Druckverlusts in einer Fensterzone nach der Delaware-Methode. Zur Uberprtifung der Gleichungen wurden MeBwerte aus dem Schrifttum herangezogen und mit den theoretischen Berechnungen verglichen. Die Bereiche der geometrischen und der betrieblichen Parameter, fiir die die Abweichungen zwischen den gemessenen und den berechneten Werten innerhalb & 35% lagen, werden angegeben. 0 1997 Elsevier Science S.A.

Keywords: Pressure drop; Segmental baffles; Shell-and-tube heat exchangers

Synopse

Die Striimung im AuJ’enraum von Rohrbiindel- Wiirmeiibertragern mit Segment-Umlenkblechen unter-

scheidet sich von der Striimung quer zu einem Rohrbiindel ohne Umlenkbleche dudurch, daJ die Umlenkbleche eine Strtimung des Fluids bewirken, die teils parallel und teils quer zum Rohrbiindel verlauft. Fertigungsbedingte Spalte zwischen den Rohren und den Bohrungen in den Um- lenkblechen sowie zwischen den Umlenkblechen und dem Mantel fihren zu Leckstriimungen, die den Druckverlust

* Corresponding author. ’ Dedicated to Prof. Dr.-Ing. A. Vogelpohl on the occasion of his

65th birthday.

0255-2701/97/$17.00 Q 1997 Elsevier Science S.A. All rights reserved

PIISO255-2701(96)04194-3

im AuJenraum beeinj&ssen. Dies gilt ebenso fur den Bypass-Strom; denn die Rohre konnen nicht gleichmaJig und dicht am Mantelblech angeordnet werden.

Die in dieser Arbeit angegebene Methode zur Berech- nung des Druckverlustes im AuJenraum hat sich im wesentlichen aus der Delaware-Methode entwickelt, bei der der Auj’enraum in Zonen unterteilt wird. Der Ein@J der Leek- und der Bypass-Stromungen auf den Druck- verlust wird mit Hi&e von Korrekturfaktoren beriick- sichtigt. Gegeniiber der Delaware-Methode werden fir die Berechnung des Druckverlusts im querangestriimten idealen Rohrbiindel nicht Diagramme sondern Gleichun- gen verwendet. Dieses so modtjizierte Berechnungsver- fahren wurde an einer grojen Anzahl von MeJwerten aus dem Schrifttum iiberpriift. Anhand dieses Vergleichs wur

150 ES. Gaddis, V. Gnielinski/ Chemical Engineering and Processing 36 (1997) 149-159

den die Bereiche der geometrischen und der betrieblichen Parameter ermittelt, bei denen die Abweichungen zwis- then den gemessenen und den berechneten Druckverlusten innerhalb & 35% liegen. Dieses Berechnungsverfahren bildet die Grundlage jlir dus in dem deutschen Handbuch ‘VDI- WLirmeatlas’ [15] und in deer englischen obersetzung dieses Handbuchs ‘VDI Heat Atlas’ 1161 angegebene Berechnungs-verfahren.

1. Introduction

The flow in the shell side of a shell-and-tube heat exchanger with segmental baffles is very complex. The baffles lead to a stream inside the shell, as shown in Fig. 1, which is partly perpendicular and partly parallel to the tube bank. The gaps between the tubes and the holes in the baffles and the gap between a baffle and the shell cause leakage streams S,, which may modify the main stream S, significantly. Since the tubes of the heat exchanger can not be placed very near to the shell, bypass streams S, may be formed, which influence also the main stream. The flow direction of the main stream relative to the tubes is different in the window sections created by the baffle cut from that in the cross flow sections existing between the segmental baffles. This necessitates the use of different equations to calculate the pressure drop in the window sections to those used in the cross flow sections. The spacing between the tube plates and the tist and the last baffle, which is mostly dictated by the diameter of the inlet and oulet nozzles, differs in many cases from the spacing between two adjacent baffles and some of the aforementioned streams are not present in the first and in the last heat exchanger sections. This adds to the complexity of the problem.

A lot of publications appeared in the last few decades (e.g. [l-5]), which describe methods to calculate the pressure drop in the shell of a shell-and-tube heat exchanger with baffles. A critical review is given by Palen and Taborek [6]. The different calculation proce-

SH main stream

SL leakage stream

SE bypass stream

Fig. 1. Flow through the shell of a shell-and-tube heat exchanger with segmental baffles.

AP

=

(n,-IlAp,

+

*AbE

+

nu AP,

+

.Aps

Fig. 2. Dividing the shell side of a shell-and-tube heat exchanger into sections.

dures have been checked in [6] against a large number of experimental measurements on small units and on industrial scale heat exchangers. According to [6], the methods of Tinker [3,4] and of Delaware [5] gave the best results compared with the other methods available in the open literature. The method of Tinker [3,4] has been frequently criticized because it is relatively compli- cated. The procedure presented in this paper for calcu- lating the shell side pressure drop is based principally on the Delaware method [5]. However, instead of using diagrams-as in the Delaware method-to calculate the pressure drop in the ideal tube bank, the present authors use equations previously presented in [7,8]. Correction factors are then used-as in the Delaware method-to take into consideration the deviatation of the flow inside the shell of the heat exchanger from that in the ideal case of a tube bank. Pressure drops ob- tained experimentally by different investigators from measurements on a number of shell-and-tube heat ex- changers were compared with those calculated by this procedure. In the paper, the comparison is presented and discussed and the validity ranges of the equations are given. This procedure forms the basis for the com- putational procedure in the German handbook ‘VDI- Wgrmeatlas’ [15] and in the English translation of that handbook ‘VDI Heat Atlas’ [16].

2. Calculation procedure

As seen in Fig. 2, the shell side pressure drop may be calculated from the equation

AP = (nu - l)ApQ + 2ApQE + n&p, + APS (1)

where Ap is the shell side pressure drop, ApQ is the pressure drop in a cross flow section, ApQE is the

ES. Gaddis, V. Gnielinslci / Chemical Engineering and Processing 36 (1997) 149-159 151

pressure drop in an end cross flow section, Ap, is the pressure drop in a window section, Aps is the pressure drop in both inlet and outlet heat exchanger nozzles and n, is the number of segmental baffles.

It is assumed in Eq. (1) that the pressure drop components, are constant in the corresponding sections along the heat exchanger length. The change in the physical properties in the different sections is thus ignored and the mean value can be used. The assump- tion of a constant window pressure drop in all window sections implies that the difference in the length of the Crst and the last window sections as compared with that of the intermediate window sections is not signifi- cant and is thus ignored.

2.1. Pressure drop in a crossJiow section

A cross flow section is that part of the heat exchanger shell, which lies between two adjacent baffles and is bounded from the top and the bottom by the planes that touch the upper and lower edges of the baffle cuts. The pressure drop in a cross flow section may be calculated from the following equation:

APQ = APQ,O~L~B. (4

The first term in Eq. (2) is the pressure drop in an ideal tube bank in the abscence of bypass and leakage streams. To account for the influence of leakage streams and bypass streams, the pressure drop AP~,~ in the ideal case of a tube bank is multiplied by the correction factors fL and fB, respectively.

The pressure drop for an ideal tube bank is calcu- lated as follows [7,8]:

2

Apa,o = hv 9,

where 5 is the pressure drop coefficient, nw is the number of major restrictions in the path of the main flow in a cross flow section, p is the fluid density and W, is the velocity defined by Eq. (4).

The number of major restrictions in the path of the main flow in a cross flow section is equal to the number of the shortest connection lengthes between the tubes, which has to be crossed by the main flow during its motion in a cross flow section from one edge of the segmental baffles to the other edge. For an in-line tube layout and for a staggered tube layout having the shortest distance between the tubes present between neighbouring tubes in the same row, the number of major restrictions nw is equal to the number of the tube rows nR in the cross flow section. For a staggered layout having the shortest distance between the tubes present between tubes in two neighbouring rows, the number of major restrictions is equal to (nR - 1). Fur- ther, a major restriction that lies on the baffle edge marking the boundary between a cross flow section and

a window section counts onIy as a half restriction. Fig. 3 illustrates the rules for evaluating n,.

The velocity is calculated from

F w, = -

A,

with

(4)

A, = SL,, (5)

where A, is the flow area defined by Eq. (5), k is the fluid volumetric flow rate in the heat exchanger shell, S is the baffle spacing and L, is the sum of the shortest distances connecting neighbouring tubes and the short- est distances between the outermost tubes and the shell measured in the tube row on or near to the shell diameter parallel to the edge of the baffle cuts.

Fig. 4 shows the lengthes LE, e and e,. Tie rods connecting the baffles together and furing the baffle spacing, which influence the length L,, should be con- sidered in evaluating LE.

The following equations correlate the pressure drop coefficient 5 to the Reynolds number and the geometry of the tube bank [7,8]:

For an in-line layout:

4 = U,l + t&t [ c

1 - exp - Re2;;;00 II 9 (6)

fa,l,f = 280z[(b0.* - 0.6)2 + 0.751

(4ab - z)a’,6 ’ (8)

+ [O.O3(a - l)(b - I)].

For a staggered layout:

(10)

al in-line layout bi staggered Layout cl staggered layout

with bbi)%?? with bd-?$-l,&?

n,= 5 nW = 1 n, = 10

Fig. 3. Determination of the number of the major restrictions.

152 ES. Gaddis, V. Gnielinski/ Chemical Engineering and Processing 36 (1997) 149-159

0~2; b=%; LE=2e,+Ee 0 do

a) in -tine Layout bl staggered layout c) staggered layout

with bz+-vm with bdi-vf?%

e=(a-lIda e = (a-l)d, e=(c-l)do

Fig. 4. Definition of L,, e and e,.

(11)

(12)

fa,l,v = 280~c[(b~.~ - 0.6)2 + 0.751

(4ab - 7c)al.h for b >iJm

(13)

and

fa,*,v = 280n[(b”,’ - 0.6)2 + 0.751 (4ab - z)c 1.6

for b<&dm,

(14)

:,=&& (15)

and

-kw = 2.5 + (a _ ()85)1.08 1.2 +0.4(;-1)9-0.01(;-1)’

(16)

The Reynolds number is defined for both tube layouts by

tr, t1 are pressure drop coefficients for laminar and turbulent flow respectively. fa is an arrangement factor, which takes in consideration the influence of the ge- ometry of the ideal tube bank on the pressure drop. The associated subscripts 1, t, f and v indicate laminar flow, turbulent flow, in-line tube layout and staggered tube layout respectively. The factors f& and f,,, in Eqs. (6) and (11) are viscosity correction factors, which take in consideration the change in the pressure drop due to change in the viscosity near the wall during heating and cooling for laminar flow and turbulent flow respectively as compared with the pressure drop in the isothermal case and are correlated as follows:

0.57/[((4ob/x) - 1)Re]“~2S

and

fi,, = y ( > 0.14. The other variables in the above equations are

a = sg/da (transverse pitch ratio),

b = q/d, (longitudinal pitch ratio),

c = dm (diagonal pitch ratio),

(18)

(19)

(20)

(21)

(22)

where TV is the dynamic viscosity and vw is the dynamic viscosity at wall temperature and where sq is the trans- verse pitch, S, is the longitudinal pitch and & is the outer tube diameter.

The physical properties p and q should be evaluated at the arithmetic mean of the inlet and outlet fluid bulk temperatures and the dynamic viscosity qvv at the mean wall temperature. Because the cross flow changes its direction in the shell a number of times, the corrections recommended in [7,8] to account for the number of rows in the ideal tube bank are ignored.

2.1.1. Baffle leakage factor According to [9], the baffle leakage factor fL may be

calculated from

fL = exp[ - 1.33(1 -I- R,)RL]

with

(23)

I’ = [ - 0.15(1 + RM) + 0.81, (24)

A RM==, A (25)

SG

R,=+ E

and

A,,= A SRU + &MU* (27)

ES. Gaddis, V. Gnielinski/ Chemical Engineering and Processing 36 (1997) 149-159 153

R, and RL are ratios of flow areas and A,, is the sum of the gap areas between the tubes and the holes in the baffles A,,, and the gap area between a baffie and the shell AsMU. The areas AsRU and AsMU may be calulated from the following equations:

A

and

(30)

where II is the number of tubes in a tube bank including blind tubes, nF is the total number of tubes in upper and lower window sections including blind tubes, dB is the diameter of tube hole in a baffle, Di is the shell inside diameter, D, is the baffle diameter, y is the angle corresponding to baffle edge in degrees and H is the baffle cut.

The correction factorf, given in [9] and expressed by Eq. (23) differs slightly from that factor recommended initially in the Delaware method [5]. Fig. 5 relates the baffle leakage factor fL to the ratios RM and R,.

Sedimentation and corrosion-if present during op- eration of the heat exchanger-might reduce the area of the aforementioned gaps and thus might lead to an increase in the shell pressure drop with elapse of time. Depending on the expected amount of deposits during operation, the baffle leakage factor fL, calculated from the Eq. (23) might be correspondingly modified.

2.1.2. Bundle bypass factor According to [5], the bundle bypass factorf, may be

calculated from

0.8

RL

Fig. 5. Baffle leakage factory, as a function of the ratios R, and R,.

sealing strips

Fig. 6. Arrangement of sealing strips (n, = 2 in the figure).

fB = exp[ - PR,(l - m)] for Rs < 4 (31)

and

fB = 1 for R, 2 $, (32)

where

R,+ (33) E

and

A, is the flow area that causes the bypass stream and ns is the number of pairs of sealing strips encountered by the bypass stream during flow across one crossflow section (Fig. 6). The flow area A, may be calculated from

A,=S(Di-D,-e) for e<(Di-DB)

and

(35)

A,=0 for e>(Di-DB). (36)

Di is the inside shell diameter and DB is the diameter of the circle that touches the outer surface of the outer- most tubes in that part of the bundle in a crossflow section. Depending on the tube layout, the shortest distance between two neighbouring tubes e can lie either between two tubes in the same row or between two tubes in two different but neighbouring rows (see Fig. 3).

For an in-line tube la out and for a staggered tube layout with b 2 0.5 /- 2a + 1

e=(a- l)d, (37)

and for a staggered tube layout with b < 0.5dm

e = (c - l)d,. . (38)

According to [5], the constant p in Eq. (31) has a value of 5.0 for laminar flow (Re < 100) and a value of 4.0 in the transition region (100 < Re < 4000) as well as for tubulent flow (Re > 4000). Taborek [9] recommends for p the following values, which are slightly different than those values mentioned in [5]:

,B = 4.5 for Re < 100 (39)

and

ES. Gaddis, V. Gnielinski / Chemical Engineering and Processing 36 (1997) 149-159

RB

Fig. 7. Bypass factor as a function of the ratios R, and R,.

/?=3.7 for Re2100. (40)

In this work, the values of p recommended by Taborek [9] were used in further calculations. The bundle bypass factorf, is shown in Fig. 7 as a function of the ratio R, with the ratio R, as a parameter.

2.2. Pressure drop in an end CYOSSJ¶OW section

An end cross flow section is that part of the heat exchanger shell, which lies between one of the tube plates and the adjacent baffle and is bounded at its outlet (for the inlet end cross flow section) or at its inlet (for the outlet end cross flow section) by the plane that touches the edges of the baffle cuts. An inlet end cross flow section does not have leakage streams that flow in that section from a previous cross flow section and an outlet end cross flow section does not have leakage streams that flow in a following cross flow section. The influence of leakage in both end cross flow sections is thus ignored. Fig. 8 shows the difference in the path of leakage streams between an end cross flow section and

inlet end cross outlet end cross flow section flow section cross flow section

main stream ----- leakage stream -‘-‘- tube axis

Fig. 8. Difference in the path of leakage streams between an end cross flow section and a cross flow section.

a cross flow section. The pressure drop Ap,, in an end cross flow section may be calculated from the following equation:

APQE = APQE,O~B. (41)

ApoE, is the pressure drop in an end cross flow section in the abscence of bypass streams. One has to distin- guish between two different cases. In the first case, the baffle spacing S, in an end cross flow section is equal to the baffle spacing S in a cross flow section. In that case, the pressure drop ApQE,O in an end cross flow section in the abscence of bypass streams can be calculated from

where EWE is the number of the major restrictions in the path of the main flow in an end cross flow section. The procedure for evaluating nWE is similar to that for evaluating n,. The other case is when S, # S. The pressure drop ApQE,O can be calculated in that case from

The velocity w,,n is based now on the flow area A,,, defined by

A,,, = sELE* (44)

Thus

(45)

Eqs. (6) and (11) can be used to calculate the pressure drop coefficient <. The Reynolds number Re in Eqs. (6), (7), (9), (ll), (12), (15) and (18) should be replaced by the Reynolds number Re, in an end cross flow section, which is defined by

Re, = Re g. (46) E

To evaluate the bundle bypass factory,, Eq. (31) or Eq. (32) (depending on the value of R,) may be used. The numerical value of the constant p in Eq. (31) depends on the numerical value of the Reynolds number Re, (p = 4.5 for Re, < 100 and p = 3.7 for Re, 2 100).

2.3. Pressure drop in a window section

According to [5], the pressure drop in a window section may be calculated from the following equations:

For Re I 100:

APF~1 =

56 52

(ew,p /q~) nWF + (d,wq/q) (47)

and for Re > 100:

ES. Gaddis, Y. Gnielinski / Chemical Engineering and Processing 36 (1997) 149- 159 155

where AP~,~ window pressure drop for laminar flow and AP~,~ window pressure drop at Re > 100.

nWF is the number of the major restrictions in a window section. Its numerical value shouldn’t be an integer and can be calculated from

0.8H nw=-,

Xl

Eq. (49) is valid when (~1~~ I 2n,,), otherwise (11~~ = 2n,,), where nZRF is the number of the tube rows in a window section. d, is the equivalent diameter of the flow area in a window section, which can be calculated from

where AF is the flow area and U, the wetted perimeter for a window section. AF and U, can be evaluated from

A, = A,, - A,,, (51)

AFG= sin(;)],

and

(52)

(53)

A ro is the cross-sectional area of a window section including the area of the window tubes and A,, is the cross-sectional area of the window tubes. In evaluating the equivalent diameter d,, the wetted area of the edge of the baffle has been ignored. The characteristic veloc- ity w, in Eq. (47) Eq. (48) is evaluated from

w, = (w,wp,

where

(55)

P wp = -.

AF (56)

Eqs. (47) and (48) give in most cases different values for the pressure drop in a window section at Re = 100. Therefore, Taborek [9] suggests to use intermediate values of those values given by Eqs. (47) and (48) in the range 50 I Re I 200 based on engineering judgment, or to use the higher value as a factor of safety. In the present work, superposition was used and the equation recommended in this work to calculate the pressure drop ApF in a window section is given by

where

(57)

f, =fi,, for Re < 100 (see Eq. (18)) (58)

and

f, =fi,t for Re 2 100 (see Eq. (19)). (59)

The influence of bypass streams on the pressure drop in a window section has been ignored.

2.4. Pressure drop in inlet and outlet nozzles

The pressure drop Ap, in both inlet and outlet heat exchanger nozzles, as a result of sudden expansion at the inlet nozzle and sudden contraction at the outlet nozzle, may be calculated from

where

(60)

i” \vs and d, are the nozzle pressure drop coefficient fti both nozzles, the nozzle velocity and the nozzle diameter respectively. The inlet and outlet nozzle di- ameters have been assumed to be equal.

The nozzle pressure drop coefficient 4s is the summa- tion of the nozzle pressure drop coefficient <s,rN for the inlet nozzle and the nozzle pressure drop coefficient 4 s,oN for the outlet nozzle. Since the flow area at the outlet of the inlet nozzle is usually much larger than the flow area based on the nozzle diameter, ts,TN M 1 (sud- den enlargement of flow area corresponding to the case of a tube connected to a large vessel). The nozzle pressure drop coefficient 5s,oN for the outlet nozzle depends on the Reynolds number Re, for the flow through the outlet nozzle (Res = wsdsp/v) and on the ratio of the flow areas before and after the sudden contraction. If the flow area before the sudden contrac- tion is much larger than the flow area after the contrac- tion (flow area of the nozzle) rS,oN M 1 for laminar flow and koN < 0.6 for turbulent flow [14]. Thus, assuming ls z 2 for both laminar and turbulent flow will be on the safe side.

3. Available experimental measurements

A number of investigators carried out experimental measurements on shell-and-tube heat exchangers with segmental baffles and variable geometries. Tinker [ll] examined 10 heat exchangers with different shell diame- ters varying from 90 to 260 mm using oil and water as shell-side fluid. Short [12] (B.E. Short, private commu- nication) examined a heat exchanger with a shell diame- ter of 154 mm. Water and three different grades of oil covering a wide range of viscosity were used as shell

156 ES. Gaddis, V. Gnielinski/ Chemical Engineering and Processing 36 (1997) 149-159

Table 1 Range of examined geometrical and operating parameters

Baffle spacing Inside shell diameter

Baffle cut Inside shell diameter

Pitch ratio

Reynolds number 0.5<Re<5x lo4 Prandtl number 31Pr16x 103

fluid. The geometry of the heat exchanger was varied by changing the tube diameter, tube pitch, baffle cut and baffle spacing. The extensive research work on shell- and-tube heat exchangers of the University of Delaware [5,10] was carried out on a small unit of 133 mm shell diameter and a larger unit of a shell diameter varying from 212 to 232 mm. All important geometrical parameters as well as the viscosity of the oil, which was used as the shell side fluid, were changed in a wide range in this investigation. The measurements in the above investigations [5, lo- 121 (B.E. Short, private communication) were made with equilateral triangulars and staggered squares as tube layouts. No experimental measurements are availabe for in-line square layouts. Gas was not used as shell side fluid. The total number of the experimental points was about 1450. The range, in which the different geometrical and operating parameters were varied, is shown in Table 1.

The tube pitch t is related to the transverse pitch sq and the longitudinal pitch si for the examined tube layouts by the following relationships:

For an equilateral triangle:

t = sq

and for a staggered square:

(62)

J( 1 2 t= 3 +s2

2 1. (63)

4. Comparison between experimental measurements and theoretical predictions

The measured shell side pressure drop Apm was com- pared with the shell side pressure drop Ap, calculated by the above procedure. The comparison as represented by the ratio (Ap,/ApJ is shown in Fig. 9 for all available experimental points as a function of the Reynolds number Re. Fig. 9 shows that for a large number of the experimental points the deviation be- tween measurements and theoretical predictions lies within f 35%. However, about one third of the experi- mental points has a deviation higher than 5 35%. In extreme cases, the measured pressure drop is as low as one fifth or as high as four times the calculated values.

This indicates that the above procedure cannot be applied safely in its present form for an unlimited range of the geometrical and operating parameters. As shown in Table 1, the ratio of the baffle spacing to the inside shell diameter (S/Oi) and the ratio of the baffle cut to the inside shell diameter (HIDi) have been varied within a wide range. A well designed shell-and-tube heat ex- changer has usually these ratios lying in a much nar- rower range. It is considered to be a good practice, when 0.2 I (S/Oi) I 1.0 and 0.15 5 (HIDi) I 0.4. For some of the examined geometries, the bundle bypass factor fB and the baffle leakage factor fL were as low as 0.11 and 0.19 respectively. A very low bundle bypass factor and a very low baffle leakage factor will lead to a reduced pressure drop but the shell side heat transfer coefficient will correspondingly decrease drastically. In Fig. 10, the experimental points with heat exchanger geometries having numerical values for the ratio (S/OJ that lie outside the range 0.2 I (S/OJ < 1.0 or numeri- cal values for the ratio (HIDi) that lie outside the range 0.15 I (HIDi) I 0.4 or having a bundle bypass factor fB < 0.4 or a baffle leakage factor fL < 0.4 have been eliminated from the figure. Fig. 10 shows then that the rest of the experimental points has a deviation not greater than about f 35%. The number of the experi- mental points in that figure with a deviation slightly higher than + 35% is very low.

5. Validity range of the equations s 1.0

The experimental points in Fig. 10 have geometrical and operating parameters, which lie within the ranges shown in Table 2. These ranges may thus be considered as the validity ranges of the computational procedure presented in this work. The expected deviations be- tween actual and calculated pressure drops will lie then most probably within + 35%. Since measurements with gases as shell side fluid are not available, this procedure should be applied only for liquids.

6. Nomenclature

L3 transverse pitch ratio flow area leading to bypass streams

AE flow area defined by Eq. (5) A J%E flow area defined by Eq. (44) AF flow area in a window section A FG cross-sectional area of a window section

including area of window tubes A FR cross-sectional area of window tubes A SG sum of all gap areas as defined by Eq.

(27) A SMU sum of the gap areas between the tubes

and the holes in the baffles A SRU gap area between a baffle and the shell

ES. Gaddis, V. Gnielimki / Chemical Engineering and Processing 36 (1997) 149-159 157

o Delaware (large unit) [5] q Delaware (small unit) [5,10] a Short[lZ] v Short[13] 0 Tinker [I 11

Fig. 9. Comparison between experimental measurements and theoretical predictions for all available experimental points.

longitudinal pitch ratio diagonal pitch ratio outer tube diameter diameter of tube hole in a baffle equivalent diameter of the flow area in a window section nozzle diameter diameter of the circle that touches the outer surface of the outermost tubes of a bundle in a cross-flow section inside shell diameter baffle diameter shortest distance connecting neighbour- ing tubes shortest distance between outermost tubes and shell arrangement factor bundle bypass factor baffle leakage factor viscosity factor baffle cut sum of the shortest connecting dis- tances e between neighbouring tubes and the distances e, between the outer- most tubes and the shell measured in the tube row on or near to the shell diameter parallel to the edge of the baffle cut number of tubes in a tube bank includ- ing blind tubes total number of tubes in upper and lower window sections including blind tubes number of tube rows in a cross flow section

nRF

%VE

%VF

AP APT APF APF,I APFJ A~rn 'PQ 'pQ,O APQE

APQE,O

APS

Pr r

RB

RL

&VI RS

number of tube rows in a window sec- tion number of pairs of sealing strips number of segmental baffles number of the major restrictions in the path of the main flow in a cross flow section number of the major restrictions in the path of the main flow in an end cross flow section number of major restrictions in a win- dow section shell side pressure drop calculated shell side pressure drop pressure drop in a window window pressure drop at Rel 100 window pressure drop at Re > 100 measured shell side pressure drop pressure drop in a cross flow section pressure drop in an ideal tube bank pressure drop in an end cross flow sec- tion pressure drop in an end cross flow sec- tion in the abscence of bypass streams pressure drop in both inlet and outlet heat exchanger nozzles Prandtl number dimensionless number defined by Eq. (24) bypass flow area ratio defined by Eq. (33) leakage flow area ratio defined by Eq. (26) flow area ratio defined by Eq. (25) Ratio defined by Eq. (34)

158 ES. Gaddis, V. Gnielinski/Chemieal Engineering and Processing 36 (1997) 149-1.59

c _ 0 Delaware (large unit) [5] - 0 Delaware (small unit) [5,10] - a Short[l2]

v Short[13] _ 0 Tinker[ll]

Fig. 10. Comparison between experimental measurements and theoretical predictions for experimental points having geometrical and operational parameters within the ranges given in Table 2.

Re ReE

Reynolds number in a cross flow section Reynolds number in an end cross flow section

Res Reynolds number for the flow through a P nozzle Y

%I sl. t u .F V

longitudinal pitch transverse pitch baffle spacing bypass stream baffle spacing in an end cross flow sec- tion main stream leakage stream tube pitch wetted perimeter for a window section fluid volumetric flow rate in the heat ex- changer shell

P Y VW

velocity defined by Eq. (4) velocity defined by Eq. (45) velocity defined by Eq. (56)

Validity range of the equations

Additional subscripts f for in-line tube layout IN for inlet nozzle 1 for laminar flow ON for 0utIet nozzle t for turbulent flow V for staggered tube layout

Baffle spacing Inside shell diameter

Baffle cut Inside shell diameter Bypass flow area ratio Pitch ratio

Inside shell diameter Outer tube diameter

Bundle bypass factor Baffle leakage factor Reynolds number Prandtl number

0.25 g $1.0 0

0.151 g 10.4 0

R,10.5

&0.4 f&O.4 1<Re<105 1 <Pr<103

nozzle velocity characteristic velocity in Eqs. (47) and (48) calculated from Eq. (55) constant in Eq. (31) angle corresponding to baffle edge in de- grees pressure drop coefficient pressure drop coefficient for laminar flow nozzle pressure drop coefficient pressure drop coefficient for turbulent flow fluid density dynamic viscosity dynamic viscosity at wall temperature

References

[l] D.A. Donohue, Heat transfer and pressure drop in heat ex- changers, Ind. Eng. Chem., 41 (1949) 2499-2511.

[2] D.Q. Kern, Process Heat Transfer, McGraw-Hill, New York, 1950.

[3] T. Tinker, Shell-side characteristics of shell and tube heat ex- changers, Parts I, II, III, General Discussion on Heat Transfer, Inst. Mech. Eng., London, 1951, pp. 97-116.

[4] T. Tinker, Shell-side characteristics of shell and tube heat ex- changers: a simplified rating system for commercial heat ex- changers, Trans. ASME, 80 (1958) 36-52.

ES. Gaddis, V. Gnielinski/ Chemical Engineering and Processing 36 (1997) 149-159 159

[5] K.J. Bell, Final Report of the Cooperative Research Program on Shell and Tube Heat Exchangers, University of Delaware, Engi- neering Experimental Station, Bulletin No. 5, 1963.

[6] J.W. Palen and J. Taborek, Solution of shell side flow pressure drop and heat transfer by stream analysis method, Chem. Eng. Progr. Symp. Series, 65 (1969) 53-63.

[7] ES. Gaddis and V. Gnielinski, Druckverlust in querdurch- striimten Rohrbiindeln, ut verfahrenstechnik, 17 (1983) 410-418.

[S] ES. Gaddis and V. Gnielinski, Pressure drop in cross flow across tube bundles, ht. Chem. Eng., 25 (1985) 1-15.

[9] J. Taborek, Shell-and-tube heat exchangers: single-phase-flow, Section 3.3, Heat Exchanger Design Handbook, Hemisphere, 1983.

[lo] O.P. Bergelin, M.D. Leighton, W.L. Lafferty Jr. and R.L. Pig- ford, Heat Transfer and Pressure Drop during Viscous and Turbu- lent Flow Across Baffled and Unbafjed Tube Banks, University of

Delaware, Engineering Experimental Station, Bulletin No. 4, 1958.

[Ill T. Tinker, Shell Side Heat Transfer Characteristics of Segmen- tally Baffled Shell and Tube Heat Exchangers, Preprint of paper presented at the Annual Meeting, American Society of Mechan- ical Engineers, 1947.

[12] B.E. Short, Heat Transfer and Pressure Drop in Heat Exchang- ers, The University of Texas, Publication No. 4324, 1943.

[14] W. Kast, VDI-Warmeatlas, Section Lc, 7th edn., VDI-Verlag, Frankfurt, 1994.

[15] E.S. Gaddis, VDI- Wtirmeatlas, Section Ll, 4th edn., VDI-Verlag, Frankfurt, 1984 and the corresponding section in the following editions.

1161 ES. Gaddis, VDZ Heat Atlas, Section Lm, 1st English edn., VDI-Verlag, Frankfurt, 1992 (translation of the 6th german edition (1991)) and the corresponding section in the following editions.