Development in Double Pipe HEAT EXCHANGER for Concurrence & Better Economy! More New Geometric Ideas : Just for Economy !!! P M V Subbarao Professor Mechanical.

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