Heat exchangers (continuation) L3

Heat exchangers (continuation) L3Martin Andersson

Agenda

• Design and analysis of heat exchangers• Shell and tube heat exchangers• Plate heat exchangers

Methods for design and analysis of heat exchangers

LMTD method

ε-NTU method

Arbitrary Hex

LMTDFUAQ ⋅⋅=!

F korrektionsfaktor som beror av två parametrar P och R;

F correction factor depending on two parameters P and R

inin

inout

ch

cc

tttt

P−

−=

hp

cp

)(

)(

cmcm

R!

!=

R kan också skrivas; R can also be written

inout

outin

cc

hh

tttt

R−

−=

LMTD – always as for counter-current flow

)()(

ln

)()(

outin

inout

outininout

ch

ch

chchm

tttt

ttttLMTDt

−

−

−−−==Δ

ε - NTU method

maxflow heat letransferab maximumflow heat real

QQ!!

==ε

minCUANTU =

ε - NTU method, continued

)()(

)()(

inin

inout

inin

outin

chmin

ccc

chmin

hhh

ttCttC

ttCttC

−

−=

−

−=ε

)(inin chminmax ttCQ −=!

)(inin chmin ttCQ −= ε!

ε - NTU method, continued

min

/CLMTDQNTU

!= (15-18)

The temperature difference in LMTD can be re-written as

⎟⎟⎠

⎞⎜⎜⎝

⎛−=+−=

=−−−=−−−

hcch

cchhchch

11

)()()()(outininoutoutininout

CCQ

CQ

CQ

tttttttt

!!!

)()(

/)/()/(/

)()()()(

)()(

minch

minhc

cmin

minh

ccch

chhh

ch

ch

outininin

ininoutin

outin

inout

CCCCCC

CQCQCQCQ

tttttttt

tttt

εε

εε

−

−=

−

+−=

=−+−

−+−−=

−

−

!!!!

(15-20)

With (15-9), (15-18), (15-19) and (15-20) one obtains

hc

minc

minh

h

c

min11

ln1

CC

CCCC

CC

CNTU

−

⎟⎟⎠

⎞⎜⎜⎝

⎛

ε−ε−

⋅

= (15-21)

ε - NTU method

cmin CC = which means that hmax CC = . After a few calculations one finds

[ ][ ]NTUCCCC

NTUCC)/1(exp/1

)/1(exp1maxminmaxmin

maxmin

−−−−−−

=ε (15-22)

ε - NTU for Shell-and-tube heat exchanger with one shell pass, two tube passes

0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

C = 0

0.25

0.50

0.75

1.0

ε

tc,in

tc,ut

th,ut

th,in

NTU = UA/Cmin NTU = UA/Cmin

Shell-and-tube heat exchangers


Advantages:Robust designFlexibility in operating conditionsBig operating pressure rangeThermal stresses can be handled by using different materialsFins or extended surfaces can be used and thus the heat transferring area can be increased

Disadvantages:Suspect to flow-induced vibrationsSome difficulties to achieve accurate design


Temperaturedifferences:

Ctt !20outin ch >−

Ctt !5inout ch >−

Temperature level: The fluid with the highest operating temperature has to be on the tube side.

Pressure drop: On both the shell and tube sides but usually smaller on the shell side.

Pressure level: fluid with the highest pressure should be placed on the tube side

Viscosity: The most viscous fluid should be on the shell side.

Mass flow rate: The fluid with the lowest mass flow rate should be placed on the shell side.

Corrosion: The most corrosive fluid should be placed on the tube side.

Fouling: The most dirty and fouling fluid should be on the tube side.

Explenations

Pressure level: fluid with the highest pressure should be placed on the tube side

Viscosity: The most viscous fluid should be on the shell side.

Mass flow rate: The fluid with the lowest mass flow rate should be placed on the shell side.

Corrosion: The most corrosive fluid should be placed on the tube side.

Fouling: The most dirty and fouling fluid should be on the tube side.


.

A: Leakage flow between baffle holes and tubes

B: Mainstream, ideally cross flow

C: Bypass flow between tube bundle and shell inner wall

E: Leakage flow between baffles and shell wall

F: Bypass flow in areas where tubes are missing


.


.

bundle tubes αα c=The correction factor c includes effects of leakage, bypass flow etc. The orderof magnitude is

6.0≈c

α = heat transfer coefficient (W/m2/K)

Tabell, Table 15-II. ε - NTU samband för några vanliga värmeväxlartyper (VVX). ε - NTU relations for some hexs

VVX-typ, HEX type Verkningsgrad , Effectiveness ε

Medström,

Parallel flow [ ]

CCNTU

+

+−−=ε

1)1(exp1

Fig. 15-20b

Motström

Counter current

[ ][ ])1(exp1

)1(exp1CNTUCCNTU−−−−−−

=ε 1<C

NTUNTU+

=ε1

1=C

Fig. 15-20a

Tubvärmeväxlare (”Shell and tube”)

1 shell pass 2,4,6,..tube passs [ ]

[ ]1

2/12

2/122/12

1 )1(exp1)1(exp1)1(12

−

⎭⎬⎫

⎩⎨⎧

+−−

+−+×+++=ε

CNTUCNTUCC

Fig. 15-21a

n Shell passes 2n, 4n, ..tube passes

1

1

1

1

1

111

11

−

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛

ε−ε−

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛

ε−ε−

=ε CCCnn

n

Fig. 15-21b

Korsström, Cross flow (single pass)

Båda fluiderna oblandade

Both fluids unmixed [ ]{ }[ ]1)(exp)(exp1 78.022.01 −−−≈ε − NTUCNTUC

Fig. 15-21c

Båda fluiderna blandade

Both fluids mixed [ ]

1

1)(exp1

)()exp(1

−

⎥⎦

⎤⎢⎣

⎡−

−−+

−−=ε

NTUCNTUC

NTUNTUNTU

Fig. 15-21d

minC oblandad, unmixed

maxC blandad, mixed { }[ ]( ))(exp1exp11 NTUCC −−−−=ε −

Fig. 15-21f

minC blandad, mixed

maxC oblandad, unmixed [ ]{ }( ))(exp1exp1 1 NTUCC −−−−=ε −

Fig. 15-21e

Alla växlare 0=C

All hex

)exp(1 NTU−−=ε

maxmin /CCC =


.

wectot pppp ΔΔΔΔ ++=

1bbundle tubec )1( RNpp −Δ=Δ

2c

cwcbundle tubee R

NNNpp +

Δ=Δ

3btkww RNpp Δ=Δ

Plate Heat Exchangers (plate-and-frame heat exchangers)

Plates PHE

Plate heat exchangers, PHE

Configurations

(a) Ett stråk (1x6/1x6)

(a) Två stråk (2x3/2x3)

One streak

Two streaks

PHE

Thermal length

if Δt equals the temperature difference for the fluid with the smallestheat capacity flow rate θ equals NTU.

High θ = efficient heat transfer (but high pressure drop)

LMTDtΔ

=θ

Documents

Heat exchangers (continuation) L3