The Effect of a Number of Baffles on the Performance of Shell-and-Tube Heat Exchangers

ABSTRACT

The number of baffles has an impact on the thermal-hydraulic performance of a shell-and-tube heat exchanger (STHX), thus a model was developed using Engineering Equations Solver software to solve the governing equations. The program uses Kern, Bell-Delaware, and flow-stream analysis (Wills Johnston) methods to predict both the heat-transfer coefficient and pressure drop on the shell side of an STHX. It was found that Bell-Delaware method is the most accurate method when compared with the experimental results. The effect of a number of baffles, mass flow rate, tube layout, fluid properties and baffle cut were investigated. The analysis revealed that an increase in the number of baffles increases both the heat-transfer coefficient and pressure drop on the shell-side. Increasing the mass flow rate, the heat transfer coefficient increases; however, the pressure drop increases at a higher rate. For a large number of baffles, the pressure drop decreases with an increase in the baffle cut. It also shows that the heat transfer coefficient increases at a higher rate with the square tube layout, whereas the rotated square and triangular layouts have approximately the same behavior.

Nomenclature

A	=	tube hole leakage stream, refer to Figure 1
a	=	exponent in Eq. 23(23) $$j_i=a_1{\left(\frac{1.33}{L_{tp}/D_t}\right)}^a{\mathrm{Re}}^{a_2}\left[5pt\right]$$(23) , given by Eq. 24(24) $$a=\frac{a_3}{1+0.14{\mathrm{Re}}^{a_4}}$$(24)
B	=	crossflow stream, refer to Figure 1
BC	=	baffle cut
b	=	flow bypasses the tube bundle
C	=	bundle by pass stream, refer to Figure 1
Cbh	=	empirical factor in Eq. 13(13) $$J_B=exp\left[-C_{bh}{F}_{sbp}\left(1-\sqrt[3]{2r_{ss}}\right)\right]$$(13)
Cbp	=	empirical factor in Eq. 31(31) $$R_B=exp\left[-C_{bp}{F}_{sbp}\left(1-\sqrt[3]{2r_{ss}}\right)\right]$$(31)
c	=	flow passes over the tubes in a cross flow
co	=	constant in Eq. 60(60) $$n_b=\frac{co(D_s-2L_c)/P_{TP}+N_{ss}}{2\rho {S_b}^2}$$(60) , co = 0.266 for square tube layout and 0.133 for triangular, rotated triangular, and rotated square layouts
cp	=	specific heat capacity, J.kg−1.K−1
D	=	diameter, m
Dotl	=	outer tube limit diameter, m
Dt	=	tube diameter, m
Dw	=	hydraulic diameter of the baffle window, m
d	=	exponent in Eq. 28(28) $$f_i=d_1{\left(\frac{1.33}{L_{tp}/D_t}\right)}^d{\mathrm{Re}}^{d_2}$$(28) , given by Eq. 29(29) $$d=\frac{d_3}{1+0.14{\mathrm{Re}}^{d_4}}$$(29)
E	=	shell to baffle bypass stream, refer to Figure 1
F	=	pass partition bypass stream, refer to Figure 1
f	=	friction factor
fi	=	friction factor for ideal bundle pressure drop
Fc	=	fraction of total flow over the tube bundle in a cross flow
Fsbp	=	bypass to crossflow area ratio
Fw	=	fraction of the cross-sectional area occupied by the window
G	=	mass flux, kg.s−1.m−2
Gw	=	mass flux in the window area, kg.s−1.m−2
h	=	heat transfer coefficient, W.m−2.K−1
J	=	correction factor for heat transfer coefficient
ji	=	heat transfer factor in Eq. 22(22) $$h_c=j_i{c}_{p}G{Pr}^{-2/3}$$(22) , given by Eq. 23(23) $$j_i=a_1{\left(\frac{1.33}{L_{tp}/D_t}\right)}^a{\mathrm{Re}}^{a_2}\left[5pt\right]$$(23)
Kf	=	parameter in Eq. 62(62) $$n_c=\frac{N_c{K}_f}{2\rho {S_m}^2}$$(62)
Lbb	=	bypass channel diametric gap, m
Lbc	=	central baffle spacing, m
Lbi	=	inlet baffle spacing, m
Lbo	=	outlet baffle spacing, m
Lc	=	baffle cut distance, m
Lpl	=	width of the bypass lane between the tubes, m
Lpp	=	horizontal tube pitch, m
Lsb	=	shell-to-baffle clearance, m
Ltp	=	tube pitch, m
Ltp,eff	=	effective tube pitch, m
$\dot{m}$	=	flow rate, kg/s
m	=	exponent in Eqs. 21(21) $$J_{\mu }={\left(\frac{{\mu }_b}{{\mu }_w}\right)}^m$$(21) and 30(30) $$R_{\mu }={\left(\frac{{\mu }_b}{{\mu }_w}\right)}^m$$(30) , for heating and cooling of liquid, m = 0.14
Nb	=	number of baffles
Nc	=	total number of tube rows in cross flow
Nss	=	number of sealing strips
Nt	=	number of tubes
Ntcc	=	number of tube rows crossed between baffle tips in one baffle section
Ntcw	=	number of tube rows in the window
Ntt	=	total number of tubes
Ntw	=	number of tubes in the window
Nu	=	Nusselt number
n	=	exponent in Eq. 17(17) $$J_S=\frac{\left(N_b-1\right)+{\left(L_{bi}/L_{bc}\right)}^{1-n}+{\left(L_{bo}/L_{bc}\right)}^{1-n}}{\left(N_b-1\right)+\left(L_{bi}/L_{bc}\right)+\left(L_{bo}/L_{bc}\right)}$$(17) , for laminar flow n = 1/3 while for transition and turbulent flow n = 0.6.
nc	=	exponent in Eq. 41(41) $$R_S={\left(\frac{L_{bc}}{L_{bo}}\right)}^{2-nc}+{\left(\frac{L_{bc}}{L_{bi}}\right)}^{2-nc}$$(41) , for laminar flow n = 1 while for transition and turbulent flow n = 0.2.
na	=	combined flow coefficient in Eq. 43(43) $$\Delta P=n_a{\dot{m}}_w^2$$(43) , given by Eq. 52(52) $$n_a=n_w+n_{cb}$$(52) in kg−1.m−1
nb	=	bypass flow resistance coefficient, kg−1.m−1
nc	=	crossflow resistance coefficient, kg−1.m−1
ncb	=	combined flow coefficient in Eq. 45(45) $$\Delta P_c=\Delta P_b=n_{cb}{\dot{m}}_w^2$$(45) , given by Eq. (53(53) $$n_{cb}=1/{\left(n_c^{-0.5}+n_b^{-0.5}\right)}^2$$(53) ) in kg−1.m−1
ni	=	flow coefficient, kg−1.m−1
np	=	combined flow coefficient in Eq. 44(44) $$\Delta P=n_p{\dot{m}}_{tot}^2$$(44) , given by Eq. 54(54) $$n_p=1/{\left(n_a^{-0.5}+n_s^{-0.5}+n_t^{-0.5}\right)}^2$$(54) in kg−1.m−1
ns	=	shell-to-baffle leakage resistance coefficient, kg−1.m−1
nt	=	tube-to-baffle clearance resistance coefficient, kg−1.m−1
nw	=	window flow resistance coefficient, kg−1.m−1
Pr	=	Prandtl number
PTP	=	spacing between tube rows in the flow direction
ΔP	=	pressure drop, Pa
ΔPAB	=	pressure drop from point A to point B, Pa
ΔPcb	=	pressure drop in central baffle spaces, Pa
ΔPe	=	pressure drop in entrance and exit baffle spaces, Pa
ΔPw	=	pressure drop in baffle windows, Pa
p	=	parameter in Eq. 33(33) $$p=-0.15\left(1+r_s\right)+0.8$$(33)
R	=	correction factor for pressure drop
Re	=	Reynolds number
rlm	=	shell-and-tube to baffle leakage area to crossflow area at the bundle center line
rs	=	shell-to-baffle leakage area to shell-and-tube to baffle leakage area ratio
rss	=	number of sealing strips to a number of tube rows crossed between baffle tips
S	=	leakage area, m2
Sb	=	bypass area, m2
Sm	=	crossflow area at the center line, m2
Ss	=	shell-to-baffle leakage area, m2
St	=	tube-to-baffle leakage area, m2
Sw	=	window flow area, m2
STHX	=	shell-and-tube heat exchanger
s	=	leakage flow between baffle and shell
T	=	temperature, °C
t	=	leakage flow between tubes and baffle
tb	=	baffle thickness, m
U	=	overall heat transfer coefficient, W.m−2K−1
$\dot{V}$	=	volumetric flow rate, m3.h−1
w	=	crossflow and bypass streams combined

Greek symbols

θ	=	angle, in degrees
θds	=	baffle cut angle, in degrees
ρ	=	density, kg.m−3
μ	=	viscosity, N.s.m−2
δby	=	bundle-to-shell radial clearance, m
δpp	=	radial clearance associated with an in-line pass partition, m
δsb	=	shell-to-baffle radial clearance, m
δtb	=	tube-to-baffle radial clearance, m

Subscripts

b	=	bulk fluid or bypasses the tube bundle
bI	=	ideal tube bundle
B	=	bypass
C	=	baffle cut
c	=	cross flow
cb	=	central baffle spaces
ctl	=	centerline tube
e	=	equivalent
i	=	index in Eq. 42(42) $$\Delta P_i=n_i{\dot{m}}_i^2$$(42) , representing flow stream
L	=	leakage
μ	=	viscosity
R	=	laminar flow
S	=	unequal baffle spacing
s	=	shell or between the baffle and shell
sb	=	shell-to-baffle
tot	=	total
t	=	between the tube and baffle
tb	=	tube-to-baffle
w	=	wall or window

Acknowledgments

The authors acknowledge the support provided by King Fahd University of Petroleum & Minerals through the project IN151001. We also gratefully acknowledge the graphics work carried out by Mr. Muhammad A. Jamil, Graduate Student in ME Department at KFUPM, in preparing Figures 1 to 5.

Funding

King Fahd University of Petroleum & Minerals through the project # 151001.

Additional information

Notes on contributors

Bassel A. Abdelkader

Bassel A. Abdelkader is an M.Sc. student in Mechanical Engineering Department at King Fahd University of Petroleum & Minerals (KFUPM), Saudi Arabia. He earned his Bachelor degree from Institute of Aviation Engineering & Technology, Egypt in 2011.

Syed M. Zubair

Syed M. Zubair is a Distinguished Professor in Mechanical Engineering Department at King Fahd University of Petroleum & Minerals (KFUPM). He earned his Ph.D. degree from Georgia Institute of Technology, Atlanta, Georgia, USA, in 1985. He has participated in several externally and internally funded research projects at KFUPM and has published over 200 research papers in internationally refereed journals. Due to his various activities in teaching and research, he was awarded Distinguished Researcher award by the university in academic years 1993–1994, 1997–1998, and 2005–2006 as well as Distinguished Teacher award in academic years 1992–1993 and 2002–2003. In addition, he received best Applied Research award on Electrical and Physical Properties of Soils in Saudi Arabia from GCC-CIGRE group in 1993.