CFD in Heat Transfer Equipment Professor Bengt Sunden Division of Heat Transfer Department of Energy Sciences Lund University email: [email protected]
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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
Turbulence Models - Wall Effects
• Wall Functions Approach
• Low Reynolds Number Modelling
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
The general equation
• Arbitrary variable
Sxx
uxt jj
jj
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
Computational grid and a control volume
• Two-dimensional case
S
N
EW P
n
e
s
w
Terms to be determined
• Convection flux Cf
• Diffusion flux Df
• Scalar value at a face Φf
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)
General algebraic equation, 2D case
aP P = aE E + aW W + aN N + aS S + b
Discretization - grid
Cartesian grid Body-fitted grid Unstructured grid
A typical multi-block BFC grid
0 2 4 6 8 10x/e
0
1
2
3
y/e
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
Effect of multi-blocking
• On final results
• On convergence
• Execution speed
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
Gasketed plate-and-frame heat exchanger
Plate Heat Exchanger
Surface Configurations of Plate Heat Exchangers
cross-corrugated surfaces PHE
Surface Configurations of Plate Heat Exchangers -
cross-corrugated surfaces PHE
Surface Configurations of Plate Heat Exchangers -
cross-corrugated surfaces
Surface Configurations of Plate Heat Exchangers -
cross-corrugated surfaces – unit cell
Reynolds number
Definition:
w
m
2Re
w
m
2Re
w
m
2Re
w
m
2Re
w
m
2Re
Re = 2m/
Surface Configurations of Plate Heat Exchangers -
cross-corrugated surfaces
Plate Heat Exchangers : cross-corrugated surfaces,
hexahedron cells and boundary layer grid
Plate Heat Exchangers - cross-corrugated surfaces
• Re = 3000-5000
• Grid density ~ 89 500-985 000
computational cells
Plate Heat Exchangers - cross-corrugated surfaces;
Flow distribution
Plate Heat Exchangers - cross-corrugated surfaces; whole plate
calculations - flow field in neighborhood of contact points
Plate Heat Exchangers - cross-corrugated surfaces;
Fanning friction factor
Plate Heat Exchangers - cross-corrugated surfaces;
Heat transfer coefficient
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
Radiator in vehicles
Radiator – flat tubes and multilouvered fin geometry
HP
Hw
Radiator – porous media concept
Copper fin – brass tube in a radiator - brazing joint
Copper fin – brass tube in a radiator - brazing joint
Brazing joints in radiators - example temperature
distribution
Multilouvered fin - sketch
Setup in Numerical Solution
Grid structure - inlet section
Grid structure - louver section
Grid structure - flow reverting section
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
Computed results – louvered fins
Impinging jet
Re=20,000
D
4D
V2F CALC-MPV2F Fluent
Mean velocities – comparisons with ANSYS
FLUENT
U
V
CALC-MP Fluent
Turbulence properties - Comparison with Fluent
TKE
ED
CALC-MP Fluent
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.
Impinging jet in cross flow
Impingement cooling
Aircraft vertical take off and landing
Flow structure with cross flow
xX
Z
Y
Jet
Cro
ssFlo
w
Flow at the symmetry plane
M = 0.1 M = 0.2
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
Horse shoe vortices
RANS LES
Cross flow
Jet flow (Re = 20,000)
Y/D = 3.2
Y/D = 2.3
Reynolds stresses
RANS
LES
uu uv
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
Summary
CFD might be a useful tool in engineering R & D in
heat transfer
Arbitrary geometries can be handled decently but
may require a huge amount of grid points
Computer demanding for complete real
geometries
Turbulence modeling is critical or a weakness
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