AO Spivdruzhnist - T NTU KhPI
Olga Arsenyeva, Svetlana Buhkalo, Gennadiy Khavin
The influence of plate The influence of plate corrugations geometry on Plate corrugations geometry on Plate Heat Exchanger performance in Heat Exchanger performance in specified process conditionsspecified process conditions
VESZPREM CAPE-Forum 2012
AO “SPIVDRUZHNIST – T” , Kharkiv, Ukraine
National Technical University “Kharkiv Polytechnic Institute”,
Kharkiv, Ukraine
1
Leonid Tovazhnyanskyy, Petro Kapustenko
AO Spivdruzhnist - T NTU KhPI
� When integrating renewables,
polygeneration and CHP units with
traditional energy sources in process
industries, more sophisticated challenges
arise.
VESZPREM CAPE-Forum 2012
� Plate Heat Exchanger (PHE) is one of
advanced modern types of heat
recuperation equipment. Its application as
an elements of a heat exchange networks
gives efficient solutions.
2
AO Spivdruzhnist - T NTU KhPI
The design and operation principles of PHEs
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1 – heating heat carrier (hot side); 2 – heated heat carrier (cold side)
AO Spivdruzhnist - T NTU KhPI
The PHE plate
1 – heat carrier inlet
and outlet;
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and outlet;
2, 5 – zones for flow
distribution;
3 – rubber gasket;
4 – main corrugated
field
AO Spivdruzhnist - T NTU KhPI
Geometries of plates with different corrugation types
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� 1, 2 – the intersection of the adjacent plates;
5
AO Spivdruzhnist - T NTU KhPI
Geometries of plates with different corrugation types
� 3 – channel cross
sections for the
sinusoidal form of
corrugations;
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corrugations;
� 4 – channel cross
sections for the
triangular form of
corrugations
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AO Spivdruzhnist - T NTU KhPI
The problem
� To find
◦ the maximum overall heat transfer coefficients and
◦minimal heat transfer area
for the fixed corrugations parameters of plate
at given conditions due to full utilization of
VESZPREM CAPE-Forum 2012
at given conditions due to full utilization of
pressure drop.
� To determine the influence of plate
corrugations geometrical parameters on ability
of PHE to satisfy specific process conditions
with minimal required heat transfer area.
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AO Spivdruzhnist - T NTU KhPI
Mathematical model for Mathematical model for
prediction prediction of heat transfer and of heat transfer and
pressure droppressure drop
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AO Spivdruzhnist - T NTU KhPI
AssumptionsAssumptions
� The plate’s surface of industrial plate-and-frame PHE is under consideration.
� The inter-plate channel consists of
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� The inter-plate channel consists of
◦ its main corrugated field and
◦ distribution zone
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AO Spivdruzhnist - T NTU KhPI
The empirical equation for calculation of The empirical equation for calculation of friction factor ζ in friction factor ζ in crisscriss--crosscross flow flow channelschannels
( )
1
1212
3
2
12 2 18
Re
p
A B
ζ
+ = ⋅ + +
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( )2Re
A B +
16
0.9
5
54 ln
7 30.27 10
Re
pA p
p −
= ⋅ ⋅
+ ⋅
1637530 1
Re
pB
⋅ =
AO Spivdruzhnist - T NTU KhPI
The mentioned parameters The mentioned parameters defined defined
by channel corrugation formby channel corrugation form
( )1 exp 0.15705p β= − ⋅
2
23
pπ β γ⋅ ⋅
=2
13 exp
180p
βπ
γ
= − ⋅ ⋅
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3 180 γ
( )( )2.63
0.014 0.061 0.69 1 1 0.9180
p tgπ
β γ β
− = + + ⋅ ⋅ + − ⋅ ⋅
5 110
pβ
= +
AO Spivdruzhnist - T NTU KhPI
Accounting Accounting for the pressure losses in for the pressure losses in distribution zonesdistribution zones
� ζDZ is the coefficient of local hydraulic
resistance in distribution zones, ζDZ =381
� The total pressure loss in a PHE channel:
22L wρ
ζ ζ ρ⋅
∆ = ⋅ ⋅ + ⋅ ⋅
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� ρ is the fluid density, kg/m3 ; LF is the length of corrugated field, m; dE = 2·b is the equivalent diameter of the channel, m; w is the average velocity of stream at the main corrugated field
12
22
2
FDZ
E
L wp w
d
ρζ ζ ρ
⋅∆ = ⋅ ⋅ + ⋅ ⋅
1 Tovazhnyansky L.L., Kapustenko P.A., Tsibulnic V,A., Heat transfer and hydraulic resistance in channels of plate
heat exchangers, Energetika, Vol. 9, pp 123-125, 1980.
AO Spivdruzhnist - T NTU KhPI
The comparison of calculated pressure The comparison of calculated pressure
losses with experimental data losses with experimental data of paperof paper11
65
65
(Re)38
(2700)DZ
ζζ
ζ= ⋅
β=30º
β=60ºβ=30º
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≤ ± 15%≤ ± 3%
1 Muley A., Manglik R.M., Experimental study of turbulent flow heat transfer and pressure drop in a plate heat exchanger with chevron plates, ASME Journal of Heat Transfer, Vol. 121, pp 110-117, 1999.
β=60º
AO Spivdruzhnist - T NTU KhPI
The equation for The equation for calculation of film calculation of film heat transfer coefficients in channels heat transfer coefficients in channels
of PHEs of PHEs
( )0.14
6 30.47 70.065 Re Pr
w
Nuµψ ζ µ = ⋅ ⋅ ⋅ ⋅ ⋅
µ
- Nusselt number
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� and are the dynamic viscosities at
stream and at wall temperatures;
� ζ – friction factor accounting for total
pressure losses in channel;
� ψ – the share of pressure loss due to
friction on the wall in total loss of pressure
14
µ wµ
AO Spivdruzhnist - T NTU KhPI
Equation’s parametersEquation’s parameters
� Pr - Prandtl number
� Nusselt number
� Reynolds number
� The value of ψ can be estimated by the
/e
Nu h d λ= ⋅
Re /ew d ρ µ= ⋅ ⋅
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following Equation:
15
( )0.15 sin( )
11
1
Re
1
at Re AA
at Re A
β
ψ
ψ
− ⋅= >
= ≤
[ ]1.75
1 380 / ( )A tg β=
AO Spivdruzhnist - T NTU KhPI
Limits Limits � The corrugations inclination angle β varies
from 14o to 72o.
� The corrugation double height to pitch ratio
is from 0.52 to 1.02. 2 /b Sγ = ⋅
VESZPREM CAPE-Forum 2012
is from 0.52 to 1.02.
� The range of Reynolds numbers is from 5 to
25,000.
� The range of Prandtl number is from 1 to 15.
16
2 /b Sγ = ⋅
AO Spivdruzhnist - T NTU KhPI
The presented mathematical The presented mathematical model enables model enables
�To predict the friction factor and film heat transfer coefficients in PHE channels on a data of their corrugations geometrical parameters, such as
◦ corrugation angle β,
◦ aspect ratio γ and
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◦ aspect ratio γ and
◦ coefficient of surface area enlargement Fx.
�To investigate the influence of these parameters, as well as corrugations height, equal to inter-plate spacing, and size of the plate on PHE performance in specific process conditions.
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AO Spivdruzhnist - T NTU KhPI
The best geometry of plate for The best geometry of plate for
specific processspecific process
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AO Spivdruzhnist - T NTU KhPI
The specified conditions of heat The specified conditions of heat transfer transfer process in PHEprocess in PHE
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AO Spivdruzhnist - T NTU KhPI
Varied parameters Varied parameters of PHE construction of PHE construction
� Only internal parameters of PHE
construction can be varied, like
◦ number
◦ size
◦ corrugation pattern
of plates
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◦ corrugation pattern
◦ streams passes numbers.
� It can lead to different
◦ channel geometries,
◦ flow velocities and
◦ wall temperatures inside the heat exchanger.
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AO Spivdruzhnist - T NTU KhPI
The basic relationsThe basic relations� When pressure drop condition for hot stream
exactly satisfied the plate length is:
� The number of heat transfer units for hot stream in heat exchanger must be not less than
1
2
1 1 1 1
4
( )
o
FDZ
L P
b w wζ
ζ ρ
∆= ⋅ −
⋅
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in heat exchanger must be not less than
� The number of heat transfer units, which can be obtained in one PHE channel:
21
0 11 12
ln
( )t tNTU
t
−=
∆
1 1 1
2 pl
p ch
U FNTU
c w fρ
⋅ ⋅=
⋅ ⋅ ⋅
AO Spivdruzhnist - T NTU KhPI
� The plate length that will fulfill the process
conditions for NTU:
� When satisfied both conditions, for heat
load and pressure drop of hot stream, we
0
1 1 10.85
2
pF
x
NTU c wL
b U F
ρ⋅ ⋅ ⋅ ⋅=
⋅ ⋅
VESZPREM CAPE-Forum 2012
load and pressure drop of hot stream, we
have a system of two algebraic Equations
with two unknown variables LF and w1.
22
0
1 1 10.85
2
pF
x
NTU c wL
b U F
ρ⋅ ⋅ ⋅ ⋅=
⋅ ⋅
1
2
1 1 1 1
4
( )
o
FDZ
L P
b w wζ
ζ ρ
∆= ⋅ −
⋅
AO Spivdruzhnist - T NTU KhPI
The basic relationsThe basic relations� flow velocity of hot stream in PHE channels, m/s
� the overall heat transfer coefficient
0
11 0
1 1 11
1 1 1
1
1
0.85( ) ( )
8 ( )
p
DZ
x
Pw
NTU c ww w
U w F
ρρζ ζ
∆= ⋅
⋅ ⋅ ⋅ ⋅+ ⋅
⋅ ⋅
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� the overall heat transfer coefficient
� heat transfer area of one plate, m2
� W is the width of the channel, m
23
1 2
1 1 1w
foul
w
RU h h
δ
λ= + + +
/ 0.85pl F xF L W F= ⋅ ⋅
AO Spivdruzhnist - T NTU KhPI
Case studyCase study
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AO Spivdruzhnist - T NTU KhPI
PHE application in District PHE application in District Heating (DH) system.Heating (DH) system.
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11 12 1 1 22 21 2 2( ) ( )p p
Q t t c G t t c G= − ⋅ ⋅ = − ⋅ ⋅
AO Spivdruzhnist - T NTU KhPI
Dependence of heat transfer Dependence of heat transfer area area FFaa from the corrugations geometry from the corrugations geometry
Q = 3000 kW
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AO Spivdruzhnist - T NTU KhPI
Dependence of Dependence of plate length plate length LLFF from from the corrugations the corrugations geometrygeometry
Q = 3000 kW
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AO Spivdruzhnist - T NTU KhPI
The dependence of required plate length The dependence of required plate length LLFF and PHE and PHE heat transfer area from corrugations angle heat transfer area from corrugations angle β at β at b b = 1.5 mm= 1.5 mm
Fa2 = 30.28 m2
min Fa
LF = 710 mm
Fa2 = 42.4 m2
115 plates
Fa2(β)
L(β)
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Fa1 = 6.06 m2
β = 65º β = 65º
LF = 300 mm
min LF
Fpl =LF2 · Fx / (2 · 0.85) Fpl1 = 0.066 m2 92 plates for 600 kW
460 plates for 3000 kW≤≤≤≤ 120Fpl1 = 0.37 m2
β = 37º
Fa1(β)
AO Spivdruzhnist - T NTU KhPI
The dependence of required plate length The dependence of required plate length LLFF and PHE and PHE heat transfer area from corrugations angle heat transfer area from corrugations angle β β at at b b = 2 mm= 2 mm
Fa2=32.15 m2
Fa2(β)
L(β)
LF=700 mmFa2=38 m2
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β = 65º
Fa1=6.43 m2
Fa1(β)
β = 50º
Fpl1 = 0.35 m2 109 plates
AO Spivdruzhnist - T NTU KhPI
The dependence of required plate length The dependence of required plate length LLFF and PHE and PHE heat transfer area from corrugations angle heat transfer area from corrugations angle β β at at b b = 2.5 mm= 2.5 mm
Fa2(β)L(β)
Fa2=33.72 m2 LF=910 mm
Fa2=39.6 m2
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Fa1(β)
Fa1=6.74 m2
β=65º
Fpl1 = 0.61 m2 65 plates
β=50º
AO Spivdruzhnist - T NTU KhPI
Obtained data for corrugations Obtained data for corrugations inclination inclination angle β and for angle β and for plate plate spacing bspacing b
b = 1.5 mm b = 2 mm b = 2.5 mm
β = 65ºFa1 = 6.06 m2
Fa2 = 30.28 m2
Fa1 = 6.43 m2
Fa2 = 32.15 m2
Fa1 = 6.74 m2
Fa2 = 33.72 m2
LF = 710 mm
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β = 37º
LF = 710 mm
Fpl1 = 0.37 m2
Fa2 = 42.4 m2
115 plates
β = 50º
LF = 700 mm
Fpl1 = 0.35 m2
Fa2 = 38 m2
109 plates
LF = 910 mm
Fpl1 = 0.61 m2
Fa2 = 39.6 m2
65 plates
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AO Spivdruzhnist - T NTU KhPI
Case study showsCase study shows
� To satisfy process conditions with minimal
heat transfer area there are required plates
of different size with different geometrical
parameters.
� To maintain full utilization of allowable
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� To maintain full utilization of allowable
pressure drop with exact satisfaction of heat
load, it is possible
1. by decreasing β or
2. by increasing plate spacing b.
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AO Spivdruzhnist - T NTU KhPI
ConclusionsConclusions� The presented mathematical model enables
to predict the influence of plate corrugation
parameters on PHE performance.
� For the specified process conditions
◦ pressure drop,
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◦ pressure drop,
◦ temperature program,
◦ heat load and
◦ streams physical properties
the geometrical parameters of plate and its
corrugations enabling to make PHE with
minimal heat transfer area can be found.
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AO Spivdruzhnist - T NTU KhPI
AcknowledgementsAcknowledgements
The financial support of EC Project INTHEAT
(FP7-SME-2010-1-262205-INTHEAT)
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(FP7-SME-2010-1-262205-INTHEAT)
is sincerely acknowledged.
AO Spivdruzhnist - T NTU KhPI
THANK YOUTHANK YOU
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