AO Spivdruzhnist - T NTU KhPI The influence of plate ...intheat.dcs.uni-pannon.hu/wp-content/...INTHEAT-D6.pdf · AO Spivdruzhnist - T NTU KhPI The problem To find the maximum overall

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


� When integrating renewables,

polygeneration and CHP units with

traditional energy sources in process

industries, more sophisticated challenges

arise.


� 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


The design and operation principles of PHEs

VESZPREM CAPE-Forum 2012 3

1 – heating heat carrier (hot side); 2 – heated heat carrier (cold side)


The PHE plate

1 – heat carrier inlet

and outlet;


and outlet;

2, 5 – zones for flow

distribution;

3 – rubber gasket;

4 – main corrugated

field


Geometries of plates with different corrugation types


� 1, 2 – the intersection of the adjacent plates;

5


Geometries of plates with different corrugation types

� 3 – channel cross

sections for the

sinusoidal form of

corrugations;


corrugations;

� 4 – channel cross

sections for the

triangular form of

corrugations

6


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


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.

7


Mathematical model for Mathematical model for

prediction prediction of heat transfer and of heat transfer and

pressure droppressure drop



AssumptionsAssumptions

� The plate’s surface of industrial plate-and-frame PHE is under consideration.

� The inter-plate channel consists of


� The inter-plate channel consists of

◦ its main corrugated field and

◦ distribution zone

9


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

+ = ⋅ + +


( )2Re

A B +

16

0.9

5

54 ln

7 30.27 10

Re

pA p

p −

= ⋅ ⋅

+ ⋅

1637530 1

Re

pB

⋅ =


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

= − ⋅ ⋅


3 180 γ

( )( )2.63

0.014 0.061 0.69 1 1 0.9180

p tgπ

β γ β

− = + + ⋅ ⋅ + − ⋅ ⋅

5 110

pβ

= +


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⋅

∆ = ⋅ ⋅ + ⋅ ⋅


� 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.


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


≤ ± 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


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


� 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


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= ⋅ ⋅


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=


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 = ⋅


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 = ⋅


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


◦ 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.

17


The best geometry of plate for The best geometry of plate for

specific processspecific process



The specified conditions of heat The specified conditions of heat transfer transfer process in PHEprocess in PHE



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


◦ corrugation pattern

◦ streams passes numbers.

� It can lead to different

◦ channel geometries,

◦ flow velocities and

◦ wall temperatures inside the heat exchanger.

20


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

∆= ⋅ −

⋅


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

⋅ ⋅=

⋅ ⋅ ⋅


� 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⋅ ⋅ ⋅ ⋅=

⋅ ⋅


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

∆= ⋅ −

⋅


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

∆= ⋅

⋅ ⋅ ⋅ ⋅+ ⋅

⋅ ⋅


� 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= ⋅ ⋅


Case studyCase study



PHE application in District PHE application in District Heating (DH) system.Heating (DH) system.


11 12 1 1 22 21 2 2( ) ( )p p

Q t t c G t t c G= − ⋅ ⋅ = − ⋅ ⋅


Dependence of heat transfer Dependence of heat transfer area area FFaa from the corrugations geometry from the corrugations geometry

Q = 3000 kW



Dependence of Dependence of plate length plate length LLFF from from the corrugations the corrugations geometrygeometry

Q = 3000 kW



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)


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)


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


β = 65º

Fa1=6.43 m2

Fa1(β)

β = 50º

Fpl1 = 0.35 m2 109 plates


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


Fa1(β)

Fa1=6.74 m2

β=65º

Fpl1 = 0.61 m2 65 plates

β=50º


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


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

31


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


� 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.

32


ConclusionsConclusions� The presented mathematical model enables

to predict the influence of plate corrugation

parameters on PHE performance.

� For the specified process conditions

◦ pressure drop,


◦ 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.

33


AcknowledgementsAcknowledgements

The financial support of EC Project INTHEAT

(FP7-SME-2010-1-262205-INTHEAT)


(FP7-SME-2010-1-262205-INTHEAT)

is sincerely acknowledged.


THANK YOUTHANK YOU


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AO Spivdruzhnist - T NTU KhPI The influence of plate ...intheat.dcs.uni-pannon.hu/wp-content/...INTHEAT-D6.pdf · AO Spivdruzhnist - T NTU KhPI The problem To find the maximum overall