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CFD in Heat Transfer Equipment
Professor Bengt Sunden
Division of Heat Transfer
Department of Energy Sciences
Lund University
email: [email protected]
CFD ?
• CFD = Computational Fluid Dynamics;
Numerical solution methodology of
governing equations for mass
conservation, momentum and heat
transfer
• Focus on thermal issues; Computational
Heat Transfer or Numerical Heat
Transfer more appropriate names
Flow and Heat Transfer in Heat Transfer Equipment -
Governing Equations, steady state, Reynolds averaging
0jj
Ux
ji
ji
j
j
i
ji
ji
j
uuxx
U
x
U
xx
pUU
x
tu
x
T
xTU
xj
jjj
j
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, RANS based
• Standard k-ε model
• RNG k-ε model
• Realizable k-ε model
• Standard k-ω model
• SST k-ω model
• Reynolds Stress Model
• v2f
j
i
ji
jk
t
j
j
j x
Uuu
x
k
xkU
x)
Pr()(
kfC
x
Uuu
kC
xxU
x j
iji
j
t
j
j
j
2
2
1)Pr
()(
EXAMPLE OF A TWO-EQUATION
TURBULENCE MODEL
• Low-Re version k- model
EXAMPLE OF A TWO-EQUATION
TURBULENCE MODEL
• Low-Re version k- model, turbulent kinematic viscosity
/2kCft
μt= ρνt
• Abe et al. model
2
4/3
2*
)200
Re(exp
Re
51)
14exp(1 t
t
yf
2
Rek
t yu n
*
2*
2Re1 exp( ) 1 0.3exp ( )
3.1 6.5
tyf
Damping functions
NUMERICAL METHODS FOR PDEs -General
Purpose
• FDM - finite difference method
• FVM - finite volume method
• FEM - finite element method
• CVFEM - control volume finite element method
• BEM -boundary element
Control volume method-FVM
dS
B
n
Vthj
j j jV V V
UdV dV S dV
x x x
S S V
U dS dS S dV
Divergence theorem
Discretization - Sum over all the CV faces
IO
Ae
1 1
nf nf
f f ff f
C D S V
Sum up
S S V
U dS dS S dV
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)
• SIMPLER (SIMPLE-revised)
Why multi-block?
• To ease the grid-generation of complex
geometries
• Natural way for domain decomposition
used by parallel computation
• Better cache usage: smaller blocks are
easier to fit in the cache
Strategy for multi-blocking
• Keep most of the single-block code unchanged
• Same way of thinking as a single-block code
• Hide the multi-blocking from the end-user to ease the implementation of physical models
• Introduce no difference in the results
Grids - examples
-4 -3 -2 -1 0 1 2 3 4 5 6x/e0
1
2
3
y/e
0 2 4 6 8 10x/e
0
1
2
3
y/e
0 2 4 6 8 10x/e
0
1
2
3
y/e
Orthogonal-mb
Non-Orthogonal-mb
Non-Orthogonal-sb
COMMERCIAL CFD COMPUTER CODES
• ANSYS FLUENT
• ANSYS CFX
• STAR CCM+
• COMSOL
• PHOENICS
• NUMECA
• CONVERGENT
• OPEN FOAM
• In-house codes
Examples of CFD in Heat Transfer
• Plate heat exchangers
• Radiators
• Impinging jet
• Impinging jet in cross flow
Ways to adopt CFD in heat exchanger analysis
and design
• 1) entire heat exchanger. a) detailed
simulations with large scales meshes,
b) local volume averaging or porous
media approach including distribution
of resistances
• 2) Modules or group of modules are
identified and streamwise periodic or
cyclic boundary conditions are
imposed
Plate Heat Exchangers - cross-corrugated surfaces
• Re = 3000-5000
• Grid density ~ 89 500-985 000
computational cells
Plate Heat Exchangers - cross-corrugated surfaces; whole plate
calculations - flow field in neighborhood of contact points
Computed results - louvered fins
(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 – louvered fins
(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
Nusselt number on the impingement wall
0 1 2 3 4 50
50
100
150
200 Exp. Lee et al.
V2F Fluent
V2F CALC-MP
Nu
r/D
Jet Impinging on a Flat Surface
Re = 11000,
H/B = 4.0
0 2 4 6 8 10 12 14 16 18
0
10
20
30
40
50
60
70
80
90
100
Present simulation (EASM)
Present simulation (V2F Durbin 1995)
Exp. Gau & Lee (1992)
Exp. Schlunder (1977)
Exp. Gardon (1966)
Nu
x/B
The secondary peak of the Nusselt number is
predicted faithfully, using V2F.
Flow at two cross sections
-4 -2 0 2 4z/D
0
1
2
3
4
y/D
X = 1.5D
-4 -2 0 2 4z/D
0
1
2
3
4
y/D
Cross flow
Jet flow (Re = 20,000)
X = 20D
Nusselt number at symmetry line
5 6 7 8 9 10 11 12 13 14 150
50
100
150
200
250M = 0.1
LES
V2F
Nu
x/D
TOPICS NOT TREATED
• Implementation of boundary conditions
• Complex geometries
• Adaptive grid methods
• Local grid refinements
• Solution of algebraic equations
• Convergence and accuracy
• Parallel computing