Transcript 7th OpenFOAM workshop, Technische Universität Darmstadt, Germany 25-28 June, 2012 Consideration on heat and reaction in metal foam 2012.

7th OpenFOAM workshop, Technische Universität Darmstadt, Germany
25-28 June, 2012
Consideration on heat and reaction in metal foam
2012. 6. 26
Mino Woo, Changhwan Kim and Gunhong Kim
Kyungwon Engineering & communication Inc.,
S. Korea
KWEnC
CAE solutions provider
Contents
• Motivation
• Porous model review
 porousSimpleFoam
 Porous model modification
• Flow analysis
 Derivation of porous model parameter
• Thermal analysis
 Comparison micro scale analysis to porous model approach
• Ongoing topic
 Apply surface reaction on micro structure
KWEnC
CAE solutions provider
2/35
Motivation
•
Multi-scale consideration for analyzing phenomena within a porous media
Reference : Micro-Scale CFD Modeling of Packed-Beds, Daniel P. Combest, 6th OpenFOAM Workshop
•
Research subject
Derive porous model parameters
(Permeability, Quadratic drag factor)
(a) Micro foam model
(b) Porous model
Validation and Reproduction
KWEnC
CAE solutions provider
3/35
Porous model review
KWEnC
CAE solutions provider
porousSimpleFoam
• Governing equation
 ij

p
uj
 Si
  ui     
x j
xi
x j
where,
1


Si     Dij   | ukk | Fij  ui
2


Linear resistance of pressure due to
the permeability
Non-linear resistance due to the
quadratic drag factor
In case of homogeneous porous media(Isotropic),
1


Si     D   | u jj | F  ui
2


Reference : Porous Media in OpenFOAM, Haukur Elvar Hafsteinsson, Chalmers spring 2009
KWEnC
CAE solutions provider
5/35
porousSimpleFoam
• Setting porous model parameters
 constant/porousZones
porous
{
coordinateSystem
{
e1 (1 0 0);
e2 (0 1 0);
}
Darcy
{
d
f
}
Direction vector for defining
local coordinate system
d [0 -2 0 0 0 0 0] (2.5e10 2.5e10 0);
f [0 -1 0 0 0 0 0] (700 700 0);
}
Porous model parameters for each direction
D
KWEnC
CAE solutions provider
1
,
K
F 2
cF
K
6/35
porousSimpleFoam
• Validation
 Test case : channel flow
 Geometry
2m
Wall
Inlet
Porous zone
Outlet
0.25 m
Symmetry
0.5 m
 Mesh
• Hexagonal type, 50X200 (#10000)
 Operating condition
• Reynolds number = 250
Reference : Flow Through Porous Media, Fluent Inc. [FlowLab 1.2], April 12, 2007
KWEnC
CAE solutions provider
7/35
porousSimpleFoam
• Test case and results
Case #
1
2
3
4
5
Viscous Resistance
[1/m2]
2.50E+10
1.00E+10
1.34E+11
1.56E+12
7.20E+08
Inertial Resistance
[1/m]
700
100
300
500
1000
Pressure drop per unit length [Pa/m]
Theory
OpenFOAM
2.50E+04
2.48E+04
1.00E+04
9.93E+03
1.34E+05
1.33E+05
1.56E+06
1.56E+06
7.21E+02
7.15E+02
Reference : Flow Through Porous Media, Fluent Inc. [FlowLab 1.2], April 12, 2007
KWEnC
CAE solutions provider
8/35
Porous model modification
• Physical velocity formulation
Superficial velocity
(seepage velocity)
U u
Porosity(γ) : measure of the void spaces
in a material, and is a fraction of the
volume of voids over the total volume,
between 0–1
Physical velocity
(true velocity)
porosity
- Pressure drops are equally calculated from each model.
- Physical velocity formulation is more realistic to analyze heat and mass transfer
phenomena within porous media
• Continuity
  U i 
xi
0
porousSimpleFoam
• Momentum equation
 ij

p
uj
 U i       Si
x j
xi
x j
porousSimpleFoam
KWEnC
CAE solutions provider
   ui 
xi
0
Modified model
 ( ij )

p
uj
  Si
  ui     
x j
xi
x j
Modified model
9/35
Porous model modification
• Comparison
Porosity = 0.5
Original porousSimpleFoam
(Superficial velocity formulation)
Modified porousSimpleFoam
(Physical velocity formulation)
- Pressure drops are same, but inner velocities are different from each model
KWEnC
CAE solutions provider
10/35
Porous model modification
• Axial velocity distribution
Comparison the results of axial velocity distribution
between physical velocity formulation and
superficial velocity formulation
Comparison with commercial CFD software(CFDACE+, ESI)
 In the porous part, result of superficial velocity formulation differs from the result of physical velocity
formulation; the difference is 1/γ times
 The result from commercial software is almost same as OpenFOAM result.
KWEnC
CAE solutions provider
11/35
Porous model modification
• Fluid phase enthalpy equation
  U      eff h   ah Ts  T 
hEqn.h
fvScalarMatrix hEqn
(
Interfacial heat and mass transfer
fvm::div(phi, h)
- fvm::Sp(fvc::div(phi), h)
- fvm::laplacian(turbulence->alphaEff(), h)
==
- fvc::div(phi, 0.5*magSqr(U), "div(phi,K)")
);
pZones.addTwoEquationsEnthalpySource(thermo, gamma, ts, hEqn);
hEqn.relax();
hEqn.solve();
thermo.correct();
KWEnC
CAE solutions provider
12/35
Porous model modification
• Solid phase enthalpy equation
1      (k T )  ah T  T   0
s
s
s
where, a : specific surface area (1/m)
h : heat transport coefficient (W/m2-K)
Interfacial heat and mass transfer
tsEqn.h
fvScalarMatrix tsEqn
(
-fvm::laplacian(kappa,ts)
);
pZones.addTwoEquationsTsSource(thermo, gamma, ts, tsEqn);
tsEqn.relax();
tsEqn.solve();}
KWEnC
CAE solutions provider
13/35
Flow analysis
KWEnC
CAE solutions provider
Metal Foam
- Foam manufacturer
- STL geometry from 3D scanning
- Pure Nickel foam before alloying and
sintering process is used
- Isotropic structure(Not compressed)
• Characteristics
 High specific stiffness, surface area and low pressure drop
 Possibility to operate efficiently at higher space velocity compared to
traditional flow-through substrates
• Application
 After-treatment system(DPF, DOC etc.,)
 Heat exchanger
 Catalytic reactor(SMR, LNT etc.,)
KWEnC
CAE solutions provider
15/35
Mesh generation
• Geometry cleaning
Original STL geometry
Internal shape
Face shape
 High resolution 3D scanning provides the
basic STL geometry
 STL contains both box boundary and inner
foam structure
 All surfaces are merged, and boundaries
are unclearly
 Hard to define foam surface
KWEnC
CAE solutions provider
16/35
Mesh generation
• Surface extraction
 Pre-meshing to extract only foam structure
 Need to clean up for small volume or skew
cells
 Smeared by surface mesh size  easy to
mesh for fluid domain
• Fluid domain mesh
Meshed STL surface
 Reference case (mesh# = 304,794)
 Meshes depend on the size of foam
Fluid domain mesh of reference case
KWEnC
CAE solutions provider
17/35
Operating condition
• Computational domain(reference case)
 Extend fluid domain back and forth from micro structure
 Calculate the pressure drop with respect to inlet velocity
1.5L
L
1.5L
symmetry
Outlet
Inlet(air)
Rep=20~2000
(a) Micro scale analysis
symmetry
Porous zone
Outlet
Inlet(air)
Rep=20~2000
(b) Porous model
KWEnC
CAE solutions provider
18/35
Operating condition
• Test case
 Foam width dependency
• Effects on width normal to the flow direction
 Foam length dependency
• Effects on length along the flow direction
Increase foam width
Reference size
Increase foam length
2x
4x
8x
Width dependent cases
KWEnC
CAE solutions provider
Length dependent cases
19/35
Micro scale analysis
• Results (Repore ~ 20 )
(a) velocity vector
(b) pressure
Velocity and pressure distribution within micro structure
KWEnC
CAE solutions provider
20/35
Micro scale analysis
• Width dependency
Relationship between Reynolds number and pressure
drop by changing width of porous media
 Pressure resistance rising non-linearly upon the
increasing flow speed.
 Pressure drop though porous media is independent of
Effect of width of porous media on the pressure
distributions(1, 2, 4 and 8 times width), Repore
~20
KWEnC
CAE solutions provider
their width
21/35
Micro scale analysis
• Length dependency
Effect of length of porous media on the pressure
distributions(1, 2, 4 and 8 times width), Repore ~20
Relationship between Reynolds number and pressure
drop by changing length of porous media
 Non-linear pressure resistance of increasing velocity
 Darcy-Forchheimer equation
P  

K
u  cF K
1/ 2
f uu
 : viscosity , K : permeablil ity, cF : Forchheime r coefficien t
KWEnC
CAE solutions provider
 Pressure drops gradually rise up with increasing length of
porous media
 Derive permeability and quadratic drag factor from
above P-V plot
22/35
Porous model
• Reference case
(a) velocity vector
(b) pressure
Velocity and pressure distribution of porous model result for reference case
 Total pressure resistance is similar to micro scale analysis, but internal fields of velocity and pressure
are quite different.
 Pressure within porous part is gradually decreased along the length of porous media because
pressure drag term is uniformly applied to the porous part
KWEnC
CAE solutions provider
23/35
Porous model
• Comparison
Comparison between porous model results and micro scale results : Effect of pressure drop on
the length of porous media and Reynolds number
 Porous model can predict pressure drop which is almost same as results of micro scale because
porous model parameters are derived from micro scale results
 Although internal field cannot be predicted by porous model, it is useful to calculate pressure drop
between porous media
KWEnC
CAE solutions provider
24/35
Analysis of derived model parameters
• Derived K, CF in terms of length
 Derivation of model parameters is conducted in two different conditions
 The model parameters are conversed to certain value by increasing length
 In this case, change of model parameters is below 1% at 0.004 mm condition(10 times to the pore size)
KWEnC
CAE solutions provider
25/35
Thermal analysis
KWEnC
CAE solutions provider
Conjugate heat transfer
• combining mesh
mappedWall boundary
(chtMultiRegionSimpleFoam)
Fluid domain
solid domain

Interface meshes share the information
through mappedWall boundary condition.

Interface meshes need not completely equal
because the mappedWall calculates the
value using interpolation.

Mesh mismatches are found locally in final
mesh.
Local mesh mismatches
KWEnC
CAE solutions provider
27/35
Operating condition
• Conjugate heat transfer
 Analyze heat transfer characteristics in various velocity condition
1.5L
L
1.5L
symmetry
Inlet(air)
1~20m/s
293.15K
Wall : 323.15K
Outlet
Wall : 323.15K
Outlet
(a) Micro scale analysis
symmetry
Inlet(air)
1~20m/s
293.15K
Porous zone
(b) Porous model
KWEnC
CAE solutions provider
28/35
Micro scale analysis
• Temperature distributions
(a) Inlet velocity : 1m/s
(b) Inlet velocity : 5m/s
(c) Inlet velocity : 10m/s
(d) Inlet velocity : 20m/s
Fluid and solid temperature distributions with changing inlet velocity(1,5,10 and 20)
 Heat is transferred from each side of wall to the center through solid, and it is transferred to fluid
region.
 Heat transfer rate is changed by flow residence time.
KWEnC
CAE solutions provider
29/35
Porous model
• Fluid temperature
(a) Inlet velocity : 1m/s
(b) Inlet velocity : 5m/s
(c) Inlet velocity : 10m/s
(d) Inlet velocity : 20m/s
Fluid and solid temperature distributions with changing inlet velocity(1,5,10 and 20)
 Temperature fields are fairly similar to the results of micro scale analysis
 Porous model also shows the effect on residence time
KWEnC
CAE solutions provider
30/35
Comparison
• Outlet temperature
 In some condition, porous model predict micro scale results well, but it’s not all conditions.
 Additional study on interfacial heat transfer coefficient will be conducted to enhance heat transfer
performance of porous model
KWEnC
CAE solutions provider
31/35
Ongoing Topic
KWEnC
CAE solutions provider
Results
• CO-O2 binary reaction test
CO+0.5O2  CO2
A= 3.70e+21(cgs), Ea=105KJ/mol
 Reaction takes place in the near cell from the interface in fluid domain
 Based on chtMultiRegionSimpleFoam
(a) CO (reactant)
(c) temperature
KWEnC
CAE solutions provider
(b) CO2 (product)
(d) Velocity magnitude
33/35
Future work
• Light-off curve(conversion rate)
Validation case
Now researching
Conversion characteristics of ongoing reaction model
- Now we are studying reaction characteristics using micro structure analysis
- To develop surface reaction solver of metal foam using porous model concept.
Reference : From light-off curves to kinetic rate expressions for three-way catalyst M.Matthess et al., Topics in
Catalysis Vols. 16/17, Nov 1-4,2001
KWEnC
CAE solutions provider
34/35
Thank you for your attention
Email : [email protected]
KWEnC
CAE solutions provider