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KWEnC CAE solutions provider Consideration on heat and reaction in metal foam Kyungwon Engineering & communication Inc., S. Korea Mino Woo, Changhwan Kim and Gunhong Kim 7 th OpenFOAM workshop, Technische Universität Darmstadt, Germany June, 2012

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KWEnC CAE solutions provider 2/35 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

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KWEnC CAE solutions provider 3/35 Motivation Multi-scale consideration for analyzing phenomena within a porous media Research subject (a) Micro foam model(b) Porous model Reference : Micro-Scale CFD Modeling of Packed-Beds, Daniel P. Combest, 6 th OpenFOAM Workshop Derive porous model parameters (Permeability, Quadratic drag factor) Validation and Reproduction

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KWEnC CAE solutions provider Porous model review

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KWEnC CAE solutions provider 5/35 porousSimpleFoam Governing equation where, Reference : Porous Media in OpenFOAM, Haukur Elvar Hafsteinsson, Chalmers spring 2009 Linear resistance of pressure due to the permeability Non-linear resistance due to the quadratic drag factor In case of homogeneous porous media(Isotropic),

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KWEnC CAE solutions provider 6/35 porousSimpleFoam Setting porous model parameters constant/porousZones porous { 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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KWEnC CAE solutions provider 7/35 Validation Test case : channel flow Geometry Mesh Hexagonal type, 50X200 (#10000) Operating condition Reynolds number = 250 porousSimpleFoam 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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KWEnC CAE solutions provider 8/35 porousSimpleFoam Test case and results Case # Viscous Resistance [1/m2] Inertial Resistance [1/m] Pressure drop per unit length [Pa/m] TheoryOpenFOAM 12.50E E E E E E E E E E E E E E+02 Reference : Flow Through Porous Media, Fluent Inc. [FlowLab 1.2], April 12, 2007

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KWEnC CAE solutions provider 9/35 Porous model modification Physical velocity formulation Continuity Momentum equation porousSimpleFoam Modified model porousSimpleFoamModified model Superficial velocity (seepage velocity) porosity Physical velocity (true velocity) -Pressure drops are equally calculated from each model. -Physical velocity formulation is more realistic to analyze heat and mass transfer phenomena within porous media 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

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KWEnC CAE solutions provider 10/35 Porous model modification Comparison Porosity = 0.5 -Pressure drops are same, but inner velocities are different from each model Original porousSimpleFoam (Superficial velocity formulation) Modified porousSimpleFoam (Physical velocity formulation)

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KWEnC CAE solutions provider 11/35 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(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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KWEnC CAE solutions provider 12/35 Porous model modification Fluid phase enthalpy equation 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 hEqn.h

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KWEnC CAE solutions provider 13/35 Porous model modification Solid phase enthalpy equation where, a : specific surface area (1/m) h : heat transport coefficient (W/m 2 -K) fvScalarMatrix tsEqn ( -fvm::laplacian(kappa,ts) ); pZones.addTwoEquationsTsSource(thermo, gamma, ts, tsEqn); tsEqn.relax(); tsEqn.solve();} tsEqn.h Interfacial heat and mass transfer

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KWEnC CAE solutions provider Flow analysis

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KWEnC CAE solutions provider 15/35 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.,) -Foam manufacturer -STL geometry from 3D scanning -Pure Nickel foam before alloying and sintering process is used -Isotropic structure(Not compressed) Metal Foam

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KWEnC CAE solutions provider 16/35 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 shapeFace shape

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KWEnC CAE solutions provider 17/35 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 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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KWEnC CAE solutions provider 18/35 Computational domain(reference case) Extend fluid domain back and forth from micro structure Calculate the pressure drop with respect to inlet velocity Operating condition (a) Micro scale analysis (b) Porous model Porous zone Inlet(air) Re p =20~2000 Outlet Inlet(air) Re p =20~2000 Outlet L1.5L symmetry

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KWEnC CAE solutions provider 19/35 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 Reference size Increase foam width Increase foam length Width dependent casesLength dependent cases 2x 4x 8x

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KWEnC CAE solutions provider 20/35 Micro scale analysis Results (Re pore ~ 20 ) (a) velocity vector (b) pressure Velocity and pressure distribution within micro structure

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KWEnC CAE solutions provider 21/35 Micro scale analysis Width dependency Effect of width of porous media on the pressure distributions(1, 2, 4 and 8 times width), Re pore ~20 Pressure resistance rising non-linearly upon the increasing flow speed. Pressure drop though porous media is independent of their width Relationship between Reynolds number and pressure drop by changing width of porous media

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KWEnC CAE solutions provider 22/35 Micro scale analysis Length dependency 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 Effect of length of porous media on the pressure distributions(1, 2, 4 and 8 times width), Re pore ~20 Relationship between Reynolds number and pressure drop by changing length of porous media

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KWEnC CAE solutions provider 23/35 Reference case Porous model (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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KWEnC CAE solutions provider 24/35 Comparison Porous model 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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KWEnC CAE solutions provider 25/35 Analysis of derived model parameters Derived K, C F 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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KWEnC CAE solutions provider Thermal analysis

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KWEnC CAE solutions provider 27/35 Conjugate heat transfer combining mesh Fluid domainsolid domain mappedWall boundary (chtMultiRegionSimpleFoam) 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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KWEnC CAE solutions provider 28/35 Conjugate heat transfer Analyze heat transfer characteristics in various velocity condition Operating condition (a) Micro scale analysis (b) Porous model Porous zone Inlet(air) 1~20m/s K Outlet L1.5L symmetry Wall : K Inlet(air) 1~20m/s K

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KWEnC CAE solutions provider 29/35 Micro scale analysis 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. 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)

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KWEnC CAE solutions provider 30/35 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

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KWEnC CAE solutions provider 31/35 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

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KWEnC CAE solutions provider Ongoing Topic

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KWEnC CAE solutions provider 33/35 Results CO-O2 binary reaction test CO+0.5O2 CO2 A= 3.70e+21(cgs), Ea=105KJ/mol (a) CO (reactant)(b) CO2 (product) (c) temperature(d) Velocity magnitude Reaction takes place in the near cell from the interface in fluid domain Based on chtMultiRegionSimpleFoam

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KWEnC CAE solutions provider 34/35 Future work Light-off curve(conversion rate) 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 -Now we are studying reaction characteristics using micro structure analysis -To develop surface reaction solver of metal foam using porous model concept. Conversion characteristics of ongoing reaction model Validation case Now researching

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KWEnC CAE solutions provider Thank you for your attention

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