cfd in design and development of heat ex changers

8/3/2019 CFD in Design and Development of Heat Ex Changers

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CFD in Design and Development of HeatExchangers

BENGT SUNDÉN

LUND INSTITUTE OF TECHNOLOGY

email: [email protected]



Flow and Heat Transfer in Heat Exchangers -governing equations

( ) 0= j

j

U x

ρ ∂

∂

( ) ( ) ji

ji

j

j

i

ji

ji

j

uu x x

U xU

x x pU U

x ρ

∂ ∂

∂ ∂

∂ ∂ µ

∂ ∂

∂ ∂ ρ

∂ ∂ −+

⎪⎭⎪⎬⎫

⎪⎩⎪⎨⎧ ⎟⎟

⎠ ⎞⎜⎜

⎝ ⎛ ++−=

( ) ( )⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −+= t u

x

T

xT U

xj

j j

j

j

ρ ∂

∂ µ

∂

∂ ρ

∂

∂

Pr



Turbulence Models

• Zero-equation models• One-equation models

• Two-equation models• Reynolds stress models

• Algebraic stress models

• Large Eddy Simulations (LES)

• Direct Numerical Simulations (DNS)



Turbulence Models -Wall Effects

• Wall Functions Approach

• Low Reynolds Number Modelling



ρε ∂

∂ ρ

∂

∂ µ µ

∂

∂ ρ

∂

∂ −−

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡+=

j

i

ji

jk

t

j

j

j x

U uu

x

k

xk U

x)

Pr()(

k f C

x

U uu

k

C

x x

U

x j

i

ji

j

t

j

j

j

2

2

1)

Pr

()(

ε ρ

∂

∂ ρ

ε

∂

∂ε µ µ

∂

∂ ε ρ

∂

∂

ε ε

ε

ε

−

−

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡+=

EXAMPLE OF A TWO-EQUATIONTURBULENCE MODEL

• Low-Re version k-ε model



• Abe et al. model

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎭⎬⎫

⎩⎨⎧

−+⎥⎦

⎤⎢⎣

⎡−−= 2

4 / 3

2*

)200

Re(exp

Re

51)

14exp(1 t

t

y f µ

µε

ρ 2

Rek

t = y

u n* =

ρ

µε

2*

2Re1 exp( ) 1 0.3exp ( )

3.1 6.5

t y f ε

⎡ ⎤ ⎡ ⎤⎧ ⎫= − − − −⎨ ⎬⎢ ⎥ ⎢ ⎥

⎩ ⎭⎣ ⎦⎣ ⎦



The general equation

• Arbitrary variable

S x x

u xt j j

j

j+⎟⎟

⎠

⎞

⎜⎜⎝

⎛ Γ=+ ∂

∂φ ∂ ∂ ρφ

∂ ∂

∂ ρφ ∂



NUMERICAL METHODS FOR PDEs -GeneralPurpose

• FDM - finite difference method

• FVM - finite volume method• FEM - finite element method

• CVFEM - control volume finite element method

• BEM -boundary element



Computational grid and a controlvolume

• Two-dimensional case

S

N

EW P

n

e

s

w



CONVECTION-DIFFUSION TERMS

• CDS -central difference scheme• UDS - upstream scheme

• HYBRID - hybrid scheme• Power law scheme

• QUICK

• Van Leer



PRESSURE - VELOCITY COUPLING

• SIMPLE (Semi-Implicit-Method-Pressure-Linked-Equations)

• SIMPLEC (SIMPLE-Consistent)

• SIMPLEX (SIMPLE-extended)

• PISO (Pressure-Implicit-Splitting-

Operators)



General algebraic equation

aPφ P= aEφ E+ aWφ W+ aNφ N+ aSφ S+ b



COMMERCIAL CFD COMPUTER CODES

• FLUENT• CFX

• STARCD

• PHOENICS• CFD2000

• FIDAP

• ADINA• etc.



Fig. 5 Gasketed plate-and-frame heat exchanger.



Surface Configurations of Plate Heat Exchangers -cross-corrugated surfaces PHE



Surface Configurations of Plate Heat Exchangers -cross-corrugated surfaces




p

b

t

2β

MFD

R




MFD

β

2 p

c o s



Surface Configurations of Plate Heat Exchangers - cross-

corrugated surfaces;

G1: β=45, Re=6042, Pr=12.8, b=3.6mm, R=1.2mm, p=10mm, (25x25x25) x 2 grid points



Surface Configurations of Plate Heat Exchangers -cross-corrugated surfaces; G1




Re

N u s s e l t n u m

b e r

100 1000 10000 1.E+51.0

10

100

1000

Modell 0-Laminar

Modell 0-Turbulent

Modell 45-LaminarModell 45-Turbulent

Modell 90-Laminar

Modell 90-Turbulent




Re

f r i c t i o n f a c

t o r

100 1000 10000 1.E+5.01

.05

0.1

0.5

1.0

Modell 0- Laminar

Modell 0-Turbulent

Modell 45-LaminarModell 45-Turbulent

Modell 90-Laminar

Modell 90-Turbulent



Surface Configurations of Plate HeatExchangers - cross-corrugated surfaces;

G2: b=3.05mm, p=10.7mm, R=2.3mm, Re =900-20000, Pr=4.33, (32x16x32) x 2 grid points



Surface Configurations of Plate Heat Exchangers -cross-corrugated surfaces: G2

Re

f r i c t i o n

f a c t o r

100 1000 10000 1.E+5 1.E+61.0

5.0

10

Numerical resultsExperimental correlationbest-fitting of numerical data




Re

N u / g ( P r )

100 1000 10000 1.E+510

50

100

500

1000

Numerical resultsExperimental correlationbest-fitting of numerical data



Plate Heat Exchangers - cross-corrugated surfaces;whole plate calculations



Plate Heat Exchangers - cross-corrugated surfaces; whole

plate calculations - flow field in neighborhood of contact

points



Surface Configurations of a Compact Heat Exchanger -triangular duct with bumps for regenerators



Secondary flow velocity vectors in a cross

sectional plane midway over a bump in a triangular duct



Surface Configurations of a Heat Exchangers withoffset strip fins



Surface Configurations of Compact Heat Exchangers- wavy ducts in recuperators



Surface Configurations of Compact Heat Exchangers - wavyducts in recuperators - grid cross-sectional plane



Surface Configurations of Compact Heat Exchangers- wavy ducts in recuperators

0.0

20.0

40.0

60.0

80.0

1 00.0

0.0 1.0 2.0 3.0 4.0 5.0

∆ p * V / Ah t

α

TCW 1

TCW 2

TCW 3

TCW 4

TCW 5

TCW 6

TCW 7

TCW 8

TCW 9

TC W 10

TC W 11

TC W 12

TC W 13

TC W 14

Po ly gonal

Squ are



Surface Configurations of Compact Heat Exchangers



Surface Configurations of Compact Heat Exchangers- wavy duct



Radiator - multilouvered Fin geometry

HP

Hw



Surface Configurations of Compact HeatExchangers -brazing joints in radiators



Surface Configurations of Compact HeatExchangers - brazing joints in radiators



Brazing joints in radiators - exampletemperature distribution



Multilouvered fin - sketch



Setup in Numerical Solution



Grid structure-Inlet section



Grid structure-louver section



Grid structure-Reverting section



Computed results

(a) Velocity at ReLp = 171 ( U = 2.5m/s )

(b) Temperature at ReLp = 171

(c) Velocity at ReLp = 513 ( U = 7.5 m/s )

(d) Temperature at ReLp = 513



Computed results

(a) Velocity at ReLp= 376 ( U=5.5 m/s )

(a) Temperature at ReLp= 376 ( U=5.5 m/s )

(c) Velocity vektors at ReLp=376



Computed results



TOPICS NOT TREATED

• Implementation of boundary conditions

• Complex geometries

• Adaptive grid methods

• Local grid refinements• Moving grids

• Solution of algebraic equations

• Convergence and accuracy

• Parallel computing



Summary

CFD might be a useful tool in engineering R & DArbirary geometries can be handled decently but

may require a huge amount of grid points

Computer demanding for complete real geometriesTurbulence modeling is critical or a weakness

cfd in design and development of heat ex changers

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