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**Consideration on heat and reaction in metal foam**

05/13/11 7th OpenFOAM workshop, Technische Universität Darmstadt, Germany 25-28 June, 2012 Consideration on heat and reaction in metal foam Mino Woo, Changhwan Kim and Gunhong Kim Kyungwon Engineering & communication Inc., S. Korea 1

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**Contents Motivation Porous model review Flow analysis Thermal analysis**

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

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Motivation Multi-scale consideration for analyzing phenomena within a porous media Research subject Reference : Micro-Scale CFD Modeling of Packed-Beds, Daniel P. Combest, 6th OpenFOAM Workshop Derive porous model parameters (Permeability, Quadratic drag factor) (a) Micro foam model (b) Porous model Validation and Reproduction

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Porous model review

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**05/13/11 porousSimpleFoam Governing equation where,**

Linear resistance of pressure due to the permeability Non-linear resistance due to the quadratic drag factor In case of homogeneous porous media(Isotropic), Porous media is modeled by attenuating the time derivative and by adding a sink term to the Navier-Stokes equations (1) The value of gamma should be between 0 and 1, where the latter is complete porosity. The source term S, is composed of two parts, a viscous loss term and an inertial loss term, creating a pressure drop that is proportional to the velocity and velocity squared, respectively. (2) This equation is known as the Darcy-Forchheimer equation. In the case of simple homogeneous porous media it becomes (3) Where tensor form of D and F are represented as the scalars D and F. Reference : Porous Media in OpenFOAM, Haukur Elvar Hafsteinsson, Chalmers spring 2009

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**porousSimpleFoam Setting porous model parameters constant/porousZones**

{ coordinateSystem e1 (1 0 0); e2 (0 1 0); } Darcy d d [ ] (2.5e10 2.5e10 0); f f [ ] ( ); Direction vector for defining local coordinate system Porous model parameters for each direction

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**porousSimpleFoam Validation Test case : channel flow Geometry Mesh**

Hexagonal type, 50X200 (#10000) Operating condition Reynolds number = 250 2 m 0.25 m 0.5 m Porous zone Inlet Outlet Symmetry Wall Reference : Flow Through Porous Media, Fluent Inc. [FlowLab 1.2], April 12, 2007

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**Pressure drop per unit length [Pa/m]**

porousSimpleFoam Test case and results Case # Viscous Resistance [1/m2] Inertial Resistance [1/m] Pressure drop per unit length [Pa/m] Theory OpenFOAM 1 2.50E+10 700 2.50E+04 2.48E+04 2 1.00E+10 100 1.00E+04 9.93E+03 3 1.34E+11 300 1.34E+05 1.33E+05 4 1.56E+12 500 1.56E+06 5 7.20E+08 1000 7.21E+02 7.15E+02 Reference : Flow Through Porous Media, Fluent Inc. [FlowLab 1.2], April 12, 2007

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**Porous model modification**

Physical velocity formulation Continuity Momentum equation 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 Superficial velocity (seepage velocity) 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 Modified model porousSimpleFoam porousSimpleFoam Modified model

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**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

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**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(CFD-ACE+, 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.

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**Porous model modification**

Fluid phase enthalpy equation hEqn.h fvScalarMatrix hEqn ( 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(); Interfacial heat and mass transfer

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**Porous model modification**

Solid phase enthalpy equation 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();}

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Flow analysis

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**Metal Foam Characteristics Application**

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.,) Foam manufacturer STL geometry from 3D scanning Pure Nickel foam before alloying and sintering process is used Isotropic structure(Not compressed) c bccb

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**Mesh generation Geometry cleaning**

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 Original STL geometry Internal shape Face shape

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**05/13/11 Mesh generation Surface extraction Fluid domain mesh**

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 Reference case (mesh# = 304,794) Meshes depend on the size of foam Meshed STL surface Fluid domain mesh of reference case

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**(a) Micro scale analysis**

Operating condition 05/13/11 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

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**05/13/11 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 Reference size Increase foam width Increase foam length 2x 4x 8x Width dependent cases Length dependent cases

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**05/13/11 Micro scale analysis Results (Repore ~ 20 )**

(a) velocity vector (b) pressure Velocity and pressure distribution within micro structure

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**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 their width Effect of width of porous media on the pressure distributions(1, 2, 4 and 8 times width), Repore ~20

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**Micro scale analysis Length dependency Darcy-Forchheimer equation**

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 Pressure drops gradually rise up with increasing length of porous media Darcy-Forchheimer equation Derive permeability and quadratic drag factor from above P-V plot

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**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

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**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

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**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 mm condition(10 times to the pore size)

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Thermal analysis

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**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

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**(a) Micro scale analysis**

Operating condition 05/13/11 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 : K Outlet (a) Micro scale analysis symmetry Inlet(air) 1~20m/s 293.15K Porous zone Wall : K Outlet (b) Porous model

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**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.

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**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

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**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

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Ongoing Topic

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**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) (b) CO2 (product) (c) temperature (d) Velocity magnitude

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**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

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**Thank you for your attention**

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