Development in Double Pipe HEAT EXCHANGER for Concurrence & Better Economy! More New Geometric Ideas : Just for Economy !!! P M V Subbarao Professor Mechanical.
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Development in Double Pipe HEAT EXCHANGER for Concurrence & Better
Economy!
More New Geometric Ideas : Just for Economy !!!
P M V SubbaraoProfessor
Mechanical Engineering Department
I I T Delhi
Double Pipe Heat Exchanger
• A double pipe heat exchanger is one of the simplest form of Heat Exchangers.
• The wall of the inner pipe is the heat transfer surface.
• The major use of these HX is sensible cooling or heating applications.
• But Very long, even for moderate capacities.
• Unviable to accommodate in an industrial space.
• To make a Unit Isotropically Compact, the arrangement is made in Multiple Times and Continuous Serial and Parallel flow.
Hairpin Heat Exchanger
The inner tube is connected by U – shaped return bend enclosed in a return bend housing
Hairpin Heat Exchangers in series
Well preferred for heat transfer areas upto 50 m2
NTU Curves: Counter flow
NTU
Ideas for Thermodynamic Betterment
U-tube
Annular in series & tubular in parallel
Annular in parallel & tubular in series
More Innovative Configurations of DTHXs
Annular flow in series & Tubular Flow in Parallel
Tubular stream mass flow is equally split between the two units.
Counter Flow
HX-
HX-
cm
cm
2cm
2cm
1,incT
1,excT
2,excT
hm
hm
hm
2,inhT
1,exhT
2,1, exhinh TT
Annular flow in series & Tubular Flow in Parallel
1exp1
1exp1
RNTUR
RNTU
max
min
max
min
2 C
C
cm
cmR
p
p
Flow Parameters
Annular flow: Hot Fluid & Tubular flow : Cold Fluid.
Parameter HX 1 HX 2
Hot fluid inlet temperature Th,in1 Th,in2
Hot fluid outlet temperature Th,ex1 Th,ex2
Cold fluid inlet temperature Tc,in1 Tc,in2
Cold fluid outlet temperature Tc,ex1 Tc,ex2
Hot fluid flow rate
Cold fluid flow rate
Surface area A/2 A/2
hm hm
2cm
2cm
Analysis of HX1
Analysis of HX2
Analysis of Global ASTP HX
New Dimensionless Parameters
hph
cpc
cm
cm
RR
,
,22
For same value of U in both the HXs
2,2,
2,2,
1,1,
1,1,
incinh
incexc
incinh
incexc
TT
TT
TT
TTP
Cold (Tubular) stream in parallel: 2,1, incinc TT
Hot (annular) stream in series: 2,1, exhinh TT
2,2,
2,2,
1,1,
1,1,
,
,2
incexc
exhinh
incexc
exhinh
hph
cpc
TT
TT
TT
TT
cm
cm
R
1,2,
2,2,
1,1,
1,2,
,
,2
incexc
exhinh
incexc
exhexh
hph
cpc
TT
TT
TT
TT
cm
cm
R
1,1,
1,2,
1,2,
1,1,
incinh
incexc
incexh
incexc
TT
TT
TT
TTP
PRP
TTRT icoc
CFLM
11
ln
1 ,,,
For simple counter flow heat exchanger:
For HX1 of ASTP:
RPP
TTRT incexc
CFLM
11
ln
1 1,1,1,
For HX2 of ASTP:
RPP
TTRT incexc
CFLM
11
ln
1 1,2,2,
Mean Temperature of Global ASTP
RPP
TTR
RPP
TTRT incexcincexc
M
11
ln
1
11
ln
1
2
1 1,2,1,1,
RPP
TTTRT incexcexc
M
11
ln2
21 1,2,1,
RPP
n
nTTR
Tinc
n
iiexc
M
11
ln
1 1,1
,,
For two level ASTP
For n level ASTP
RRPR
RR
R
TTT
UA
Q
avg
exhinh
M
21
1
2
12
ln
12
21
1,2,
Two level Annular flow in series & Tubular Flow in Parallel
1,,
1,2,
incexmc
exhinh
TT
TTR
1,2,
1,,
incinh
incexmcavg TT
TTP
21,2,
,excexc
exmc
TTT
Rn
RPnR
nR
RnR
TTT
UA
Q
n
avg
exhinh
M
1
1,2,
11
1ln
1
n level Annular flow in series & Tubular Flow in Parallel
1,,
1,,
incexmc
exhinnh
TT
TTR
1,,
1,,
incinnh
incexmcavg TT
TTP
n
iexicexmc T
nT
1,,
1
RP
P
TTRT
avg
avg
incexmcCFLM
1
1ln
1 1,,,
Rn
RPnR
nR
nR
TTT
UA
Q
n
avg
incexmc
M
1
1,,
11
1ln
1
For simple counter flow heat exchanger:
For n level ASTP
RP
P
R
Rn
RPnR
nR
nR
T
TF
avg
avg
n
avg
CFLM
M
1
1ln
1
11
1ln
1
1
,
F
Pavg
n
Rn
RPnR
nR
RnR
TT
TTNTU
n
avg
incinnh
exhinnhn
11,,
1,,max
11
1ln
1
avgincinnh
incexmc
incexmc
exhinnh
incexmc
incexmc
incinnh
exhinnh RPTT
TT
TT
TT
TT
TT
TT
TT
1,,
1,,
1,,
1,,
1,,
1,,
1,,
1,,
Rn
RPnR
nR
RnR
RPNTU
n
avg
avgn
1
max
11
1ln
1
Rn
RPnR
nR
nR
PNTU
n
avg
avg
n
1
max
11
1ln
1
RP
P
TTRT
avg
avg
incexmcCFLM
1
1ln
1 1,,,
Rn
RPnR
nR
nR
TTT
UA
Q
n
avg
incexmc
M
1
1,,
11
1ln
1
Comparison
PRP
RPNTU
11
ln
1max
Rn
RPnR
nR
nR
PNTU
n
avg
avg
n
1
max
11
1ln
1
NTU Curves: Counter Vs parallel flow
Need for Compact HXs
• Double Pipe Hxs are long, even for moderate capacities.
• Unviable to accommodate in an industrial space.
• The size of heat exchanger is very large in those applications where gas is a medium of heat exchange.
• Continuous research is focused on development of Compact Heat Exchangers --- High rates of heat transfer per unit volume.
• The rate of heat exchange is proportional to
– The value of Overall heat transfer coefficient.
– The surface area of heat transfer available.
– The mean temperature difference.
Large surface area Heat Exchangers
• The use of extended surfaces will reduce the gas side thermal resistance.
• To reduce size and weight of heat exchangers, many compact heat exchangers with various fin patterns were developed to reduce the air side thermal resistance.
• Fins on the outside the tube may be categorized as
– 1) flat or continuous (plain, wavy or interrupted) external fins on arrays of tubes,
– 2) Normal fins on individual tubes,
– 3) Longitudinal fins on individual tubes.
Innovative Designs for Extended Surfaces
Geometrical Classification
Longitudinal or strip
Radial Pins
Anatomy of A STRIP FIN
thickness
x
x
Flow
Dire
ctio
n
profile
PROFILE AREA
cross-section
CROSS-SECTION AREA
Basic Geometric Features of Longitudinal Extended Surfaces
Complex Geometry in NatureAn optimum body size is essential for the ability to regulate body temperature by blood-borne heat exchange. For animals in air, this optimum size is a little over 5 kg. For animals living in water, the optimum size is much larger, on the order of 100 kg or so.
This may explain why large reptiles today are largely aquatic and terrestrial reptiles are smaller.
0)(
TThPdx
dxdT
kAd c
Straight fin of triangular profile rectangular C.S.
b
xLxA )(
Straight fin of parabolic profile rectangular C.S.
b
L
x=0b
x=b
bx
qb
L
b
qb
b
x=b x=0
xb
2
)(
b
xLxA
Longitudinal Extended Surfaces with Variable C.S.A
For a constant cross section area:
0)(2
2
TThPdx
TdkAc
0)(2
2
TTkA
hP
dx
Td
kA
hPm 2
Most Practicable Boundary Condition
Corrected adiabatic tip:
2
bb adicorr
thickness
x
x
bb
Rate of Heat Transfer through a constant Area Fin
bSk
hPTTAhPkQ
finfluidwfinf tanh
fluidwf TTpbhQ max,
Fin Efficiency:
fluidw
finfluidwfin
f
ffin TTPbh
bSk
hPTTAhPk
Q
Q
tanh
max,
How to decide the height of fin for a Double Pipe HX ?
LONGITUDINAL FIN OF CONCAVE PARABOLIC PROFILE
The differential equation for temperature excess is an Euler equation:
xd
dxx
d
dxm b
mh
k b
22
22 2
1 2
2 0
2
/
L
b
qb
b
x=b x=a=0
x
b
The particular solution for temperature excess is: 2/12241
2
1
2
1bmp
b
xp
b
And the heat dissipation (L=1) is:
qk
bm bb
b b 2
1 1 4 2 2 1 2/
Efficiency:
2
1 1 4 2 2 1 2m b
/
Gardner’s curves for the fin efficiency of several types of longitudinal fins.
mbkyhw b/
Longitudinal Fins
nth order Longitudinal Fins
2/1
212
2
2
0
b
nnn
k
hm
bmdx
dnx
dx
dx
Helical Double-tube HX
Secondary Flow in Helical Coils
• The form of the secondary flow would depend on the ratio of the tube diameters and other factors.
• A representative secondary flow pattern is shown below:
• Thirdly, this configuration should lead to a more standard approach for characterizing the heat transfer in the exchanger.
• The ratio of the two tube diameters may be one of the ways to characterize the heat transfer.
Heat Transfer in Helical Tubes
Acharya et al. (1992, 2001) developed the following two correlations of the Nusselt number, for Prandtl numbers less than and greater than one, respectively.
Heat Transfer in Helical Annulus
Nusselt numbers for the annulus have been calculated and correlated to a modified Dean number.
The modified dean number for the annulus is calculated as it would be for a normal Dean number, except that the curvature ratio used is based on the ratio of the radius of the outer tube to the radius of curvature of the outer tube, and the Reynolds number based on the hydraulic radius of the annulus.
Thus the modified Dean number is:
Helical Coils: Laminar flow
• De is Dean Number. De=Re (a/R)1/2.
• Srinivasan et al. (7 < R/a < 104):
• Manlapaz and Churchill:
• Correction for vp:
0.275
0.5
1 for 30
0.419 for 30 300
0.1125 for 300
c
s
Def
De Def
De De
0.5
2
0.52
0.18 /1.0 1.0
3 88.331 35 /
m
c
s
f a R De
f De
0.25
0.91c w
cp b
f
f
Helical coils: turbulent flow
0.250.5 2 2
0.00725 0.076 Re for 0.034 Re 300c
R R Rf
a a a
0.20.5 2 2
0.0084 Re for Re 700 and 7 10c
R R R Rf
a a a a
0.33Pr
Prc m
cp w
f
f
Expenditure in A Heat Exchanger
• The capital investment on Heat exchanger material is proportional to double the Heat transfer Area.
• Investment on both cold side and hot side of a heat exchanger for a given surface area of heat exchanger.
• Another expenditure is running cost or operational cost.• Main operation cost is pumping power cost.• This again increases the size of the pump and capital cost.• This arises a question of inner and outer flow pressure
drop calculations and a suitable innovation for the same.
Idea 1: Multi-tube Heat Exchanger
•An exclusive continuous multi tube exchanger is used in laundry, textile, or paper mill applications. •Using "stacked" design the unit can be expanded as required by the addition of more sections. •Design is based on pure counter flow of fluids for most efficient heat transfer. •Temperature approaches as close as 3°C can be economically achieved for certain applications.
Idea 2: Multi Pass Heat Exchanger
inhh Tm , & outhh Tm , &
incc Tm , &
outhc Tm , &
1cT
2cThT
Heat lost by hot fluid:
2121, chchhhphot TTTTUadzQQdTcm
21, 2 cchhhphot TTTUadzdTcm
21, 2 cch
hhphot TTTdz
dT
Ua
cm
11,
chccpcold TT
dz
dT
Ua
cm
22,
chccpcold TT
dz
dT
Ua
cm
2,,
2,,,,,,
2,,
2,,,,,,
2,,
2,,
lnoutcincouthinhoutcincouthinh
outcincouthinhoutcincouthinh
outcincouthinhM
TTTTTTTT
TTTTTTTT
TTTTT
outcinc
outhinh
outcincouthinhLM
TT
TT
TTTTT
,,
,,
,,,,
ln
LM
M
T
TF
outcincouthinh
outcincouthinhoutcincouthinh
outcincouthinhoutcincouthinh
outcinc
outhinhoutcincouthinh
TTTTTTTTTTTT
TTTTTTTT
TT
TTTTTT
F
,,,,2,,
2,,,,,,
2,,
2,,,,,,
,,
,,2,,
2,,
ln
ln
112
112ln1
11
ln1
2
2
2
RRP
RRPR
PRP
RF
,,
,,
incoutc
outhinh
TT
TTR
incinh
incoutc
TT
TTP
,,
,,
Temperature Variations in Multi Pass HX.
1-2 Shell with Better Flow COnfiguration
TEMA – E : One parallel & Two counter Tube Flows
incinh
incoutc
TT
TTP
,,
,,1
,,
,,1
incoutc
outhinh
TT
TTR
TEMA – E : Two parallel & Two counter Tube Flows
TEMA – E : One parallel & One counter Tube Flows: Devided Shell Flow
TEMA 1-2 G Shell & Tube
TEMA 1-2 H Shell & Tube
TEMA 1-2 J Shell & Tube
TEMA 1-4 J Shell & Tube
inhhot Tm , &
outhhot Tm , &
inccold Tm , &
outccold Tm , &
Multiple Shell-Side Passes
• In an attempt to offset the disadvantage of values of F less than 1.0 resulting from the multiple tube side passes, some manufacturers regularly design shell and tube exchangers with longitudinal shell-side baffles.
The two streams are always countercurrent to one another, therefore superficially giving F = 1.0.
Multiple Shells in Series
Double Pipe HEAT EXCHANGERS with Low Thermal Resistance
P M V SubbaraoProfessor
Mechanical Engineering Department
I I T Delhi
Ideas for Better Heat Transfer!!!
Enhanced Heat Transfer…..
Double Pipe HX with finned inner Tube
Equivalent diameter of annulus heat transfer, De:
perimeter ledheated/coo
area freenet 4eD
Helical Double-tube HX
Secondary Flow in Helical Coils
• The form of the secondary flow would depend on the ratio of the tube diameters and other factors.
• A representative secondary flow pattern is shown below:
• Thirdly, this configuration should lead to a more standard approach for characterizing the heat transfer in the exchanger.
• The ratio of the two tube diameters may be one of the ways to characterize the heat transfer.
Heat Transfer in Helical Tubes
Acharya et al. (1992, 2001) developed the following two correlations of the Nusselt number, for Prandtl numbers less than and greater than one, respectively.
Heat Transfer in Helical Annulus
Nusselt numbers for the annulus have been calculated and correlated to a modified Dean number.
The modified dean number for the annulus is calculated as it would be for a normal Dean number, except that the curvature ratio used is based on the ratio of the radius of the outer tube to the radius of curvature of the outer tube, and the Reynolds number based on the hydraulic radius of the annulus.
Thus the modified Dean number is:
Helical Coils: Laminar flow
• De is Dean Number. De=Re (a/R)1/2.
• Srinivasan et al. (7 < R/a < 104):
• Manlapaz and Churchill:
• Correction for vp:
0.275
0.5
1 for 30
0.419 for 30 300
0.1125 for 300
c
s
Def
De Def
De De
0.5
2
0.52
0.18 /1.0 1.0
3 88.331 35 /
m
c
s
f a R De
f De
0.25
0.91c w
cp b
f
f
Helical coils: turbulent flow
0.250.5 2 2
0.00725 0.076 Re for 0.034 Re 300c
R R Rf
a a a
0.20.5 2 2
0.0084 Re for Re 700 and 7 10c
R R R Rf
a a a a
0.33Pr
Prc m
cp w
f
f
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