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CFD in Design and Development of HeatExchangers
BENGT SUNDÉN
LUND INSTITUTE OF TECHNOLOGY
email: [email protected]
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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
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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)
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Turbulence Models -Wall Effects
• Wall Functions Approach
• Low Reynolds Number Modelling
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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
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• 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
⎡ ⎤ ⎡ ⎤⎧ ⎫= − − − −⎨ ⎬⎢ ⎥ ⎢ ⎥
⎩ ⎭⎣ ⎦⎣ ⎦
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The general equation
• Arbitrary variable
S x x
u xt j j
j
j+⎟⎟
⎠
⎞
⎜⎜⎝
⎛ Γ=+ ∂
∂φ ∂ ∂ ρφ
∂ ∂
∂ ρφ ∂
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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
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Computational grid and a controlvolume
• Two-dimensional case
S
N
EW P
n
e
s
w
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CONVECTION-DIFFUSION TERMS
• CDS -central difference scheme• UDS - upstream scheme
• HYBRID - hybrid scheme• Power law scheme
• QUICK
• Van Leer
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PRESSURE - VELOCITY COUPLING
• SIMPLE (Semi-Implicit-Method-Pressure-Linked-Equations)
• SIMPLEC (SIMPLE-Consistent)
• SIMPLEX (SIMPLE-extended)
• PISO (Pressure-Implicit-Splitting-
Operators)
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General algebraic equation
aPφ P= aEφ E+ aWφ W+ aNφ N+ aSφ S+ b
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COMMERCIAL CFD COMPUTER CODES
• FLUENT• CFX
• STARCD
• PHOENICS• CFD2000
• FIDAP
• ADINA• etc.
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Fig. 5 Gasketed plate-and-frame heat exchanger.
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Surface Configurations of Plate Heat Exchangers -cross-corrugated surfaces PHE
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Surface Configurations of Plate Heat Exchangers -cross-corrugated surfaces PHE
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Surface Configurations of Plate Heat Exchangers -cross-corrugated surfaces
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Surface Configurations of Plate Heat Exchangers -cross-corrugated surfaces
p
b
t
2β
MFD
R
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Surface Configurations of Plate Heat Exchangers -cross-corrugated surfaces
MFD
β
2 p
c o s
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Surface Configurations of Plate Heat Exchangers -cross-corrugated surfaces
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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
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Surface Configurations of Plate Heat Exchangers -cross-corrugated surfaces; G1
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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
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Surface Configurations of Plate Heat Exchangers -cross-corrugated surfaces; G1
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
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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
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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
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Surface Configurations of Plate Heat Exchangers -cross-corrugated surfaces; G2
Re
N u / g ( P r )
100 1000 10000 1.E+510
50
100
500
1000
Numerical resultsExperimental correlationbest-fitting of numerical data
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Plate Heat Exchangers - cross-corrugated surfaces;whole plate calculations
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Plate Heat Exchangers - cross-corrugated surfaces;whole plate calculations
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Plate Heat Exchangers - cross-corrugated surfaces; whole
plate calculations - flow field in neighborhood of contact
points
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Surface Configurations of a Compact Heat Exchanger -triangular duct with bumps for regenerators
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Secondary flow velocity vectors in a cross
sectional plane midway over a bump in a triangular duct
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Surface Configurations of a Heat Exchangers withoffset strip fins
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Surface Configurations of Compact Heat Exchangers- wavy ducts in recuperators
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Surface Configurations of Compact Heat Exchangers - wavyducts in recuperators - grid cross-sectional plane
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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
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Surface Configurations of Compact Heat Exchangers
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Surface Configurations of Compact Heat Exchangers- wavy duct
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Radiator - multilouvered Fin geometry
HP
Hw
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Surface Configurations of Compact HeatExchangers -brazing joints in radiators
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Surface Configurations of Compact HeatExchangers - brazing joints in radiators
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Brazing joints in radiators - exampletemperature distribution
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Multilouvered fin - sketch
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Setup in Numerical Solution
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Grid structure-Inlet section
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Grid structure-louver section
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8/3/2019 CFD in Design and Development of Heat Ex Changers
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Grid structure-Reverting section
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8/3/2019 CFD in Design and Development of Heat Ex Changers
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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
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8/3/2019 CFD in Design and Development of Heat Ex Changers
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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
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8/3/2019 CFD in Design and Development of Heat Ex Changers
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Computed results
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8/3/2019 CFD in Design and Development of Heat Ex Changers
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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
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8/3/2019 CFD in Design and Development of Heat Ex Changers
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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