heat exchanger design
DESCRIPTION
BELL'S METHOD KERN'S METHODTRANSCRIPT
![Page 1: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/1.jpg)
Heat Exchanger Design
Anand V P GurumoorthyAssociate Professor
Chemical Engineering DivisionSchool of Mechanical & Building Sciences
VIT University[EDITED BY AFRAZ ]
ICET PU[UNIVERSITY OF THE PUNJAB LAHORE]
![Page 2: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/2.jpg)
Heat Exchanger Classification
• Recuperative:–Cold and hot fluid flow through the unit without mixing
with each other. The transfer of heat occurs through the metal wall.
• Regenerative:–Same heating surface is alternately exposed to hot and
cold fluid. Heat from hot fluid is stored by packings or solids; this heat is passed over to the cold fluid.
• Direct contact:–Hot and cold fluids are in direct contact and mixing occurs
among them; mass transfer and heat transfer occur simultaneously.
![Page 3: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/3.jpg)
Heat Exchanger Standards and Codes• British Standard BS-3274• TEMA standards are universally used.• TEMA standards cover following classes of
exchangers:–Class R – designates severe requirements of petroleum
and other related processing applications–Class C – moderate requirements of commercial and
general process applications–Class B – specifies design and fabrication for chemical
process service.
![Page 4: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/4.jpg)
Shell and Tube Heat Exchanger
• Most commonly used type of heat transfer equipment in the chemical and allied industries.
• Advantages:–The configuration gives a large surface area in a small
volume.–Good mechanical layout: a good shape for pressure
operation.–Uses well-established fabrication techniques.–Can be constructed from a wide range of materials.–Easily cleaned.–Well established design procedures.
![Page 5: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/5.jpg)
![Page 6: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/6.jpg)
Types of Shell and Tube Heat Exchangers• Fixed tube design
–Simplest and cheapest type.–Tube bundle cannot be removed for cleaning.–No provision for differential expansion of shell and tubes.–Use of this type limited to temperature difference upto
800C.• Floating head design
–More versatile than fixed head exchangers.–Suitable for higher temperature differentials.–Bundles can be removed and cleaned (fouling liquids)
![Page 7: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/7.jpg)
Design of Shell and Tube Heat Exchangers• Kern method:
– Does not take into account bypass and leakage streams.– Simple to apply and accurate enough for preliminary design
calculations.– Restricted to a fixed baffle cut (25%).
• Bell-Delaware method– Most widely used.– Takes into account:
• Leakage through the gaps between tubes and baffles and the baffles and shell.
• Bypassing of flow around the gap between tube bundle and shell.• Stream Analysis method (by Tinker)
– More rigorous and generic.– Best suited for computer calculations; basis for most commercial
computer codes.
![Page 8: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/8.jpg)
Construction Details – Tube Dimensions• Tube diameters in the range 5/8 inch (16 mm) to 2
inch (50 mm).• Smaller diameters (5/8 to 1 inch) preferred since
this gives compact and cheap heat exchangers.• Larger tubes for heavily fouling fluids.• Steel tubes – BS 3606; Other tubes – BS 3274.• Preferred tube lengths are 6 ft, 8 ft, 12 ft, 16 ft, 20 ft
and 24 ft; optimum tube length to shell diameter ratio ~ 5 – 10.
• ¾ in (19 mm) is a good starting trial tube diameter.
![Page 9: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/9.jpg)
Construction Details – Tube Arrangements • Tubes usually arranged in equilateral triangular, square or rotated
square patterns.
• Tube pitch, Pt, is 1.25 times OD.
![Page 10: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/10.jpg)
Construction Details - Shells
• Shell should be a close fit to the tube bundle to reduce bypassing.• Shell-bundle clearance will depend on type of heat exchanger.
![Page 11: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/11.jpg)
Construction Details - Shell-Bundle Clearance
![Page 12: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/12.jpg)
Construction Details – Tube Count• Bundle diameter depends not only on number of tubes but also number of tube
passes.
• Nt is the number of tubes• Db is the bundle diameter (mm)• D0 is tube outside diameter (mm)
• n1 and K1 are constants
1/1
10
n
tb K
NdD
![Page 13: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/13.jpg)
Construction Details - Baffles• Baffles are used:
– To direct the fluid stream across the tubes– To increase the fluid velocity– To improve the rate of transfer
• Most commonly used baffle is the single segmental baffle.
• Optimal baffle cut ~ 20-25%
![Page 14: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/14.jpg)
Basic Design Procedure
• General equation for heat transfer is:
where Q is the rate of heat transfer (duty),U is the overall heat transfer coefficient,A is the area for heat transferΔTm is the mean temperature difference
• We are not doing a mechanical design, only a thermal design.
mTUAQ
![Page 15: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/15.jpg)
Overall Heat Transfer Coefficient• Overall coefficient given by:
h0 (hi) is outside (inside) film coefficient
hod (hid) is outside (inside) dirt coefficient
kw is the tube wall conductivity
do (di) is outside (inside) tube diameters
iiidiw
i
od hd
d
hd
d
k
d
dd
hhU
11
2
ln111 00
00
00
![Page 16: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/16.jpg)
Individual Film Coefficients
• Magnitude of individual coefficients will depend on:–Nature of transfer processes (conduction, convection,
radiation, etc.)–Physical properties of fluids–Fluid flow rates–Physical layout of heat transfer surface
• Physical layout cannot be determined until area is known; hence design is a trial-and-error procedure.
![Page 17: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/17.jpg)
Typical Overall Coefficients
![Page 18: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/18.jpg)
Typical Overall Coefficients
![Page 19: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/19.jpg)
Fouling Factors (Dirt Coeffs)
• Difficult to predict and usually based on past experience
![Page 20: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/20.jpg)
Mean Temperature Difference (Temperature Driving Force)
• To determine A, ΔTm must be estimated• True counter-current flow – “logarithmic temperature difference”
(LMTD)
mTUAQ
![Page 21: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/21.jpg)
LMTD• LMTD is given by:
where T1 is the hot fluid temperature, inlet
T2 is the hot fluid temperature, outlet
t1 is the cold fluid temperature, inlet
t2 is the cold fluid temperature, outlet
12
21
1221
ln
)()(
tT
tT
tTtTTlm
![Page 22: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/22.jpg)
Counter-current Flow – Temperature Proflies
![Page 23: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/23.jpg)
1:2 Heat Exchanger – Temperature Profiles
![Page 24: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/24.jpg)
True Temperature Difference
• Obtained from LMTD using a correction factor:
ΔTm is the true temperature difference
Ft is the correction factor• Ft is related to two dimensionless ratios:
lmtm TFT
)(
)(
12
21
tt
TTR
)(
)(
11
12
tT
ttS
![Page 25: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/25.jpg)
Temp Correction Factor Ft
Temperature correction factor, one shell pass, two or more even tube passes
![Page 26: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/26.jpg)
Fluid Allocation: Shell or Tubes?
• Corrosion• Fouling• Fluid temperatures• Operating pressures• Pressure drop• Viscosity• Stream flow rates
![Page 27: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/27.jpg)
Shell and Tube Fluid Velocities
• High velocities give high heat-transfer coefficients but also high pressure drop.
• Velocity must be high enough to prevent settling of solids, but not so high as to cause erosion.
• High velocities will reduce fouling• For liquids, the velocities should be as follows:
–Tube side: Process liquid 1-2m/sMaximum 4m/s if required to reduce fouling
Water 1.5 – 2.5 m/s–Shell side: 0.3 – 1 m/s
![Page 28: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/28.jpg)
Pressure Drop
• As the process fluids move through the heat exchanger there is associated pressure drop.
• For liquids: viscosity < 1mNs/m2 35kN/m2
Viscosity 1 – 10 mNs/m2 50-70kN/m2
![Page 29: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/29.jpg)
Tube-side Heat Transfer Coefficient• For turbulent flow inside conduits of uniform cross-section, Sieder-Tate
equation is applicable:
C=0.021 for gases =0.023 for low viscosity liquids =0.027 for viscous liquidsμ= fluid viscosity at bulk fluid temperatureμw=fluid viscosity at the wall
14.0
33.08.0 PrRe
w
CNu
f
eik
dhNu etduRe
f
p
kC
Pr
![Page 30: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/30.jpg)
Tube-side Heat Transfer Coefficient
• Butterworth equation:
• For laminar flow (Re<2000):
• If Nu given by above equation is less than 3.5, it should be taken as 3.5
505.0205.0 PrRe ESt
pt
iCu
hNuSt PrRe
2Pr)(ln0225.0exp0225.0 E
14.033.033.0Pr)(Re86.1
w
e
L
dNu
![Page 31: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/31.jpg)
Heat Transfer Factor, jh
• “j” factor similar to friction factor used for pressure drop:
• This equation is valid for both laminar and turbulent flows.
14.0
33.0PrRe
wh
f
ii jk
dh
![Page 32: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/32.jpg)
Tube Side Heat Transfer Factor
![Page 33: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/33.jpg)
Heat Transfer Coefficients for Water• Many equations for hi have developed specifically
for water. One such equation is:
where hi is the inside coefficient (W/m2 0C) t is the water temperature (0C) ut is water velocity (m/s) dt is tube inside diameter (mm)
2.0
8.0)02.035.1(4200
i
ti d
uth
![Page 34: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/34.jpg)
Tube-side Pressure Drop
where ΔP is tube-side pressure drop (N/m2) Np is number of tube-side passes ut is tube-side velocity (m/s) L is the length of one tube m is 0.25 for laminar and 0.14 for turbulent jf is dimensionless friction factor for heat
exchanger tubes
25.28
2t
m
wifpt
u
d
LjNP
![Page 35: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/35.jpg)
Tube Side Friction Factor
![Page 36: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/36.jpg)
Shell-side Heat Transfer and Pressure Drop
•Kern’s method•Bell’s method
![Page 37: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/37.jpg)
![Page 38: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/38.jpg)
Procedure for Kern’s Method
• Calculate area for cross-flow As for the hypothetical row of tubes in the shell equator.
pt is the tube pitchd0 is the tube outside diameterDs is the shell inside diameterlB is the baffle spacing, m.
• Calculate shell-side mass velocity Gs and linear velocity, us.
where Ws is the fluid mass flow rate in the shell in kg/s
t
bsts p
DdpA
)( 0
s
ss A
WG
s
s
Gu
![Page 39: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/39.jpg)
Procedure for Kern’s Method
• Calculate the shell side equivalent diameter (hydraulic diameter).– For a square pitch arrangement:
– For a triangular pitch arrangement
0
20
2
44
d
dp
d
t
e
2
42
187.0
24
0
20
d
dp
p
dt
t
e
![Page 40: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/40.jpg)
Shell-side Reynolds Number
• The shell-side Reynolds number is given by:
• The coefficient hs is given by:
where jh is given by the following chart
eses dudG
Re
14.0
3/1PrRe
wh
f
es jk
dhNu
![Page 41: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/41.jpg)
Shell Side Heat Transfer Factor
![Page 42: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/42.jpg)
Shell-side Pressure Drop
• The shell-side pressure drop is given by:
where jf is the friction factor given by following chart.
14.02
28
w
s
Be
sfs
uL
d
DjP
![Page 43: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/43.jpg)
Shell Side Friction Factor
![Page 44: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/44.jpg)
)(
)(
12
21
tt
TTR
)(
)(
11
12
tT
ttS
(Figure 8 in notes)
![Page 45: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/45.jpg)
mTUAQ
1/1
10
n
tb K
NdD
(Figure 4 in notes)
(Figure 2)
![Page 46: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/46.jpg)
2.0
8.0)02.035.1(4200
i
ti d
uth
![Page 47: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/47.jpg)
(Figure 9 in notes)
![Page 48: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/48.jpg)
t
bsts p
DdpA
)( 0
2
42
187.0
24
0
20
d
dp
p
dt
t
e
![Page 49: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/49.jpg)
![Page 50: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/50.jpg)
iiidiw
i
od hd
d
hd
d
k
d
dd
hhU
11
2
ln111 00
00
00
(Figure 10 in notes)
(Table 3 in notes)
![Page 51: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/51.jpg)
25.28
2t
m
wifpt
u
d
LjNP
14.02
28
w
s
Be
sfs
uL
d
DjP
(Figure 12 in notes)
![Page 52: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/52.jpg)
![Page 53: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/53.jpg)
Bell’s Method
• In Bell’s method, the heat transfer coefficient and pressure drop are estimated from correlations for flow over ideal tube banks.
• The effects of leakage, by-passing, and flow in the window zone are allowed for by applying correction factors.
![Page 54: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/54.jpg)
Bell’s Method – Shell-side Heat Transfer Coefficient
where hoc is heat transfer coeff for cross flow over ideal tube banksFn is correction factor to allow for no.
of vertical tube rowsFw is window effect correction factorFb is bypass stream correction factorFL is leakage correction factor
Lbwnocs FFFFhh
![Page 55: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/55.jpg)
![Page 56: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/56.jpg)
![Page 57: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/57.jpg)
Bell’s Method – Ideal Cross Flow Coefficient• The Re for cross-flow through the tube bank is given by:
Gs is the mass flow rate per unit area
d0 is tube OD• Heat transfer coefficient is given by:
00RedudG ss
14.0
3/10 PrRe
wh
f
oc jk
dh
![Page 58: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/58.jpg)
Bell’s Method – Tube Row Correction Factor• For Re>2100, Fn is obtained as a function of Ncv (no. of tubes between
baffle tips) from the chart below:
• For Re 100<Re<2100, Fn=1.0• For Re<100,
18.0' )( cn NF
![Page 59: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/59.jpg)
Bell’s Method – Window Correction Factor• Fw, the window correction factor is obtained from the
following chart:
where Rw is the ratio of bundle cross-sectional area in the window zone to the tube bundle cross-sectional area (obtained from simple formulae).
![Page 60: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/60.jpg)
Bell’s Method – Bypass Correction Factor• Clearance area[Ab] between the bundle and the shell
• For the case of no sealing strips, Fb as a function of Ab/As can be obtained from the following chart
)( bsBb DDA
![Page 61: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/61.jpg)
![Page 62: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/62.jpg)
Bell’s Method – Bypass Correction Factor• For sealing strips, for Ns<Ncv/2 (Ns is the number of
baffle strips)
where α=1.5 for Re<100 and α=1.35 for Re>100.
3/12
1expcv
s
s
bb N
N
A
AF
![Page 63: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/63.jpg)
Bell’s Method – Leakage Correction Factor• Tube-baffle clearance area Atb is given by:
• Shell-baffle clearance area Asb is given by:
where Cs is baffle to shell clearance and θb is the angle subtended by baffle chord• AL=Atb+Asb
where βL is a factor obtained from following chart
)(2
8.0 0wttb NN
dA
)2(2 bss
sb
DCA
L
sbtbLL A
AAF
)2(1
![Page 64: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/64.jpg)
Coefficient for FL, Heat Transfer
![Page 65: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/65.jpg)
Shell-side Pressure Drop
• Involves three components:– Pressure drop in cross-flow zone– Pressure drop in window zone– Pressure drop in end zone
![Page 66: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/66.jpg)
Pressure Drop in Cross Flow Zone
where ΔPi pressure drop calculated for an equivalent ideal tube bank
Fb’ is bypass correction factorFL’ is leakage correction factor
where jf is given by the following chart Ncv is number of tube rows crossed us is shell-side velocity
''Lbic FFPP
14.02
28
w
scvfi
uNjP
![Page 67: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/67.jpg)
Friction Factor for Cross Flow Banks
![Page 68: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/68.jpg)
Bell’s Method – Bypass Correction Factor for Pressure Drop
α is 5.0 for laminar flow, Re<1004.0 for transitional and turbulent flow, Re>100
Ab is the clearance area between the bundle and shell
Ns is the number of sealing strips encountered by bypass stream
Ncv is the number of tube rows encountered in the cross-flow section
3/1
' 21exp
cv
s
s
bb N
N
A
AF
![Page 69: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/69.jpg)
Bell’s Method – Leakage Factor for Pressure Drop
where Atb is the tube to baffle clearance area Asb is the shell to baffle clearance area AL is total leakage area = Atb+Asb
βL’ is factor obtained from following chart
L
sbtbLL A
AAF
)2(1 ''
![Page 70: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/70.jpg)
Coefficient for FL’
![Page 71: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/71.jpg)
Pressure Drop in Window Zones
where us is the geometric mean velocity
uw is the velocity in the window zone
Ws is the shell-side fluid mass flowNwv is number of restrictions for cross-flow in window
zone, approximately equal to the number of tube rows.
2)6.00.2(
2' z
wvLw
uNFP
swz uuu
ws
w A
Wu
![Page 72: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/72.jpg)
Pressure Drop in End Zones
• Ncv is the number of tube rows encountered in the cross-flow section• Nwv is number of restrictions for cross-flow in window zone,
approximately equal to the number of tube rows.
')(b
cv
cvwvie F
N
NNPP
![Page 73: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/73.jpg)
Bell’s Method – Total Shell-side Pressure Drop
zoneswindowN
zonescrossflowNzonesendP
b
bs
)1(2
wbcbes PNPNPP )1(2
![Page 74: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/74.jpg)
Effect of Fouling
• Above calculation assumes clean tubes
• Effect of fouling on pressure drop is given by table above
![Page 75: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/75.jpg)
Condensers
• Construction of a condenser is similar to other shell and tube heat exchangers, but with a wider baffle spacing
• Four condenser configurations:– Horizontal, with condensation in the shell– Horizontal, with condensation in the tubes– Vertical, with condensation in the shell– Vertical, with condensation in the tubes
• Horizontal shell-side and vertical tube-side are the most commonly used types of condenser.
sB Dl
![Page 76: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/76.jpg)
Heat Transfer Mechanisms
• Filmwise condensation– Normal mechanism for heat transfer in commercial condensers
• Dropwise condensation– Will give higher heat transfer coefficients but is unpredictable– Not yet considered a practical proposition for the design of
condensers• In the Nusselt model of condensation laminar flow is
assumed in the film, and heat transfer is assumed to take place entirely by conduction through the film.
• Nusselt model strictly applied only at low liquid and vapor rates when the film is undisturbed.
• At higher rates, turbulence is induced in the liquid film increasing the rate of heat transfer over that predicted by Nusselt model.
![Page 77: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/77.jpg)
Condensation Outside Horizontal Tubes
where (hc)1 is the mean condensation film coefficient, for a single tubekL is the condensate thermal conductivityρL is the condensate densityρv is the vapour densityμL is the condensate viscosityg is the gravitational accelerationΓ is the tube loading, the condensate flow per unit length of tube.
• If there are Nr tubes in a vertical row and the condensate is assumed to flow smoothly from row to row, and if the flow is laminar, the top tube film coefficient is given by:
3/1
1
)(95.0)(
L
vLLLc
gkh
4/11)()( rcNc Nhh
r
![Page 78: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/78.jpg)
•
![Page 79: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/79.jpg)
Condensation Outside Horizontal Tubes• In practice, condensate will not flow smoothly from tube to
tube.• Kern’s estimate of mean coefficient for a tube bundle is
given by:
L is the tube lengthWc is the total condensate flowNt is the total number of tubes in the bundleNr is the average number of tubes in a vertical tube row
• For low-viscosity condensates the correction for the number of tube rows is generally ignored.
6/1
3/1)(
95.0)(
rhL
vLLLbc N
gkh
t
ch LN
W
![Page 80: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/80.jpg)
Condensation Inside and Outside Vertical Tubes• For condensation inside and outside vertical tubes the Nusselt
model gives:
where (hc)v is the mean condensation coefficientΓv is the vertical tube loading, condensate per unit tube perimeter
• Above equation applicable for Re<30• For higher Re the above equation gives a conservative (safe)
estimate.• For Re>2000, turbulent flow; situation analyzed by Colburn and
results in following chart.
3/1)(
926.0)(
vL
vLLLvc
gkh
![Page 81: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/81.jpg)
Colburn’s Results
![Page 82: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/82.jpg)
Boyko-Kruzhilin Correlation• A correlation for shear-controlled condensation in tubes; simple to use.• The correlation gives mean coefficient between two points at which vapor quality, x, (mass fraction
of vapour) is known.
1,2 refer to inlet and outlet conditions respectively
• In a condenser, the inlet stream will normally be saturated vapour and vapour will be totally condensed. For these conditions:
• For design of condensers with condensation inside the tubes and downward vapor flow, coefficient should be evaluated using Colburn’s method and Boyko-Kruzhilin correlation and the higher value selected.
xJwhereJJ
hhv
vLiBKc
12
)(2/1
22/1
1
43.08.0 PrRe021.0
i
Li d
kh
2
1)( v
L
iBKc hh
![Page 83: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/83.jpg)
Flooding in Vertical Tubes
• When the vapor flows up the tube, tubes should not flood.
• Flooding should not occur if the following condition is satisfied:
where uv and uL are velocities of vapor and liquid and di is in metres.
• The critical condition will occur at the bottom of the tube, so vapor and liquid velocities should be evaluated at this point.
4/14/12/14/12/1 )(6.0 vLiLLvv gduu
![Page 84: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/84.jpg)
Condensation Inside Horizontal Tubes• When condensation occurs, the heat transfer coefficient at any point along the
tube will depend on the flow pattern at that point.
• No general satisfactory method exists that will give accurate predictions over a wide flow range.
![Page 85: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/85.jpg)
Two Flow Models• Two flow models:
– Stratified flow• Limiting condition at low condensate and vapor rates
– Annular flow• Limiting condition at high vapor and low condensate rates
– For stratified flow, the condensate film coefficient can be estimated as:
– For annular flow, the Boyko-Kruzhilin equation can be used– For condenser design, both annular and stratified flow should be considered and the
higher value of mean coefficient should be selected.
3/1)(
76.0)(
hL
vLLLsc
gkh
![Page 86: HEAT EXCHANGER DESIGN](https://reader036.vdocuments.site/reader036/viewer/2022062312/554a1f14b4c90507558b59aa/html5/thumbnails/86.jpg)
• Condensation of steam– For air-free steam a coefficient of 8000 W/m2-0C should be used.
• Mean Temperature Difference– A pure, saturated, vapor will condense at a constant temperature, at
constant pressure.– For an isothermal process such as this, the LMTD is given by:
where Tsat is saturation temperature of vapor t1 (t2) is the inlet (outlet) coolant temperature
– No correction factor for multiple passes is needed.
2
1
12
ln
)(
tT
tT
ttlm
sat
satT