POLITECNICO DI MILANO Characterization of flow regimes and heat/mass transfer inside Kelvin cell type foams by means of OpenFOAM Augusto Della Torre, Gianluca Montenegro Department of Energy, Politecnico di Milano, Italy Federico Brusiani, Gian Marco Bianchi ALMA MATER STUDIORUM - Università di Bologna, Italy WCCM XI – ECCM V - ECFD VI Barcelona 2014 Introduction POLITECNICO DI MILANO ! Open cell foams are interesting supports for catalysts in various application fields (reforming, after-treatment, etc.) ! Flow resistance, heat and mass transfer properties must be determined in detail to assess ad-hoc optimization for best performance (pressure drop, chemical conversion) ! Micro-structure behaviour can be investigated to extract information which can be up-scaled for full scale simulations ! Real foam geometries needs to be reconstructed with sophisticated technology. Artificial and repeatable structures may be used as templates. WCCM XI – ECCM V - ECFD VI Barcelona 2014 POLITECNICO DI MILANO Main concept: applied to ICE Engine scale Component scale Quasi-3D Micro-structure scale CFD F. Lucci et al. / Chemical Engineering Science 112 (2014) 143–151 Fig. 3. Sample of the fina 1000 ∆xP [Pa/mm] 100 10 1 0.1 0.01 Fig. 2. Sample view of randomized Kelvin cell structure. Grid resolution is plotted on the foam surface. WCCM XI – ECCM V - ECFD VI Barcelona 2014 We simulate the transport of methane CH4 in air. A Sutherland model is applied for the transport air properties and the thermal properties are extracted from Janaf tables. The methane inflow mass concentration is X CH4 ¼ 0:001 and is assumed to have Smidth number equal to 1. The catalyst operates in a transport limited regime so the temperature at the inflow is kept constant at 700 K. No conjugate heat transfer between the solid and the fluid is solved but a constant temperature of 750 K is imposed at the solid–fluid Richa Richa Dimopoulos Eggensch Dimopoulos Eggensch 0 2 4 6 Fig. 4. Pressure drop per unit length in Pa/ cases. Lines: literature correlations; Symbol that are most used in the literature different characteristic length scale the definition of pore diameter. E present work is computed using th respective author. Then it is resca characteristic length of the externa In Fig. 4 the pressure drop is p Outline ! Choice of the best idealized representative for open cell foams ! Impact of geometrical parameters of flow ! Detailed modeling (DNS and RANS) ! Up scaling for full scale simulations ! Adding the chemistry ! Examples and conclusions WCCM XI – ECCM V - ECFD VI Barcelona 2014 POLITECNICO DI MILANO POLITECNICO DI MILANO Geometry reconstruction Foam samples Geometry idealization: Cubic cell model Kelvin cell model Geometry reconstruction: Micro-CT scanner WCCM XI – ECCM V - ECFD VI Barcelona 2014 X-ray image Image segmentation Analysis of the flow field Cubic cell Kelvin cell Micro-CT WCCM XI – ECCM V - ECFD VI Barcelona 2014 POLITECNICO DI MILANO Analysis of the temperature field Cubic cell Kelvin cell WCCM XI – ECCM V - ECFD VI Barcelona 2014 POLITECNICO DI MILANO Comparison of the pressure drop ! Same porosity and cell size measured real foam Kelvin cell cubic cell WCCM XI – ECCM V - ECFD VI Barcelona 2014 POLITECNICO DI MILANO POLITECNICO DIPOLITECNICO MILANO POLITECNICO DI DI MILANO MILANO Correction of the KC model Correction of the KC model Correction of the KC model X-ray images X-ray X-rayimages images 𝑆 , 𝑆𝑆 , , 𝑆 , Porosity, Porosity, Cell size Porosity, Cell Cellsize size A = const ≈ 1.37 ≈ 1.37 Si-C Si-C Si-CAl AlAl Test on 3 samples: Test Testonon3 3samples: samples: Sample A A A Correction procedure: Correction Correction procedure: procedure: 𝜑, 𝑑 𝜑, 𝑑 𝐾𝐶 𝐾𝐶 WCCM XI – ECCM V - ECFD VI Barcelona 2014 WCCM XI – ECCM V - ECFD VI Barcelona 2014 WCCM XI – ECCM V - ECFD VI Barcelona 2014 𝑆 , 𝑆 , 𝜑, 𝑑 ∗ 𝜑, 𝑑 ∗ Cu Cu Cu 𝐾𝐶 𝐾𝐶 Correction of the KC model: pressure drop Correction of the KC model: pressure drop 𝜑 𝑆 , =𝜑 =𝑆 , measure d real foam KC corr KC CUB corr CUB WCCM XI – ECCM V - ECFD VI Barcelona 2014 WCCM XI – ECCM V - ECFD VI Barcelona 2014 real foam KC corr KC CUB corr CUB POLITECNICO POLITECNICO DI MILANO DI MILANO POLITECNICO DI MILANO Comparison of pressure drop on different foams ! Reconstruction of real sample by Kelvin cell type idealized foam B Measured sample B Measured sample C Measured sample D Calculated sample B Calculated sample C C D WCCM XI – ECCM V - ECFD VI Barcelona 2014 Calculated sample D POLITECNICO DI MILANO Further enhancement ! A. Della Torre et al. / Introduction of an additional degree of freedom Material clustering at cell vertexes (a) (b) F. Lucci et al. / Chemical Engineering Science Fig. 1. Approaches adopted for the foam micro-structure modeli idealization and (b) micro-CT geometry reconstruction. Randomization (edge length) WCCM XI – ECCM V - ECFD VI Barcelona 2014 pore density, has been considered in this work. Mi Tomography has been applied for the reconstruction geometry of the sample. In a micro-CT scanner a X-r passes through the sample and is collected by a sample is rotated providing a series of 2D projection ferent angles. A 3D voxel dataset is then reconstru stack of 2D images using inverse methods. In the c Nikon Metrology Benchtop 160 micro-CT system w is equipped with an electron gun operating at up to with a metal target to generate a cone of X-rays th strahlung; both the electron gun voltage and target altered to provide a range of spectra and penetratio POLITECNICO DI MILANO Detailed simulation: cold flow Numerical schemes accuracy: • Time: second order • Space: third order Pressure WCCM XI – ECCM V - ECFD VI Barcelona 2014 TKE spectrum UDeNS: heat Analysis of transfer the temperature field Velocity Temperature mesh: 16 mln cells – runtime: 30 days on 16 processors WCCM XI – ECCM V - ECFD VI Barcelona 2014 POLITECNICO DI MILANO POLITECNICO DI MILANO Cold flow RANS simulations ! Similar results obtained with: • Laminar simulation • RANS simulation • DNS simulation DNS ! Investigation of the velocity field at different Reynolds Re = 5 Re = 50 WCCM XI – ECCM V - ECFD VI Barcelona 2014 Re = 700 toReturbulence nFOAMOpenFOAM vsSensitivity Fluent: UvsmagFluent: = 1000 Umag Re =models 1000 Laminare POLITECNICO POLITECNICO DI MILANO DI MILANO k-epsilon OF - k-Epsilon Lien-Leschziner OFLaminar - Laminare OF - k-Epsilon Lien-Leschziner Lien Leschziner OpenFOAM vs Fluent: caduta di pressione con modello di turbolenza Le simulazioni OF forniscono Le simulazioni OF forniscono campi di velocità simili neldi velocità simili nel campi caso senza e con modello di e con modello di caso senza turbolenza. turbolenza. nFOAM: kOmegaSST, Re = OpenFOAM 1000 essione POLITECNICO DI MILANO k-omega Velocità SST Fluent POLITECNICO DI MILANO vs Fluent: Umag Re = 1000 k-epsilon OF - Laminare Fluent OF - k-Epsilon Lien-Leschziner Residui Setup POLITE Mode DI MILA • • • • OF kE kO Lie Le simulazioni Fluent Le simulazioni FluentLe simulazioni OF forniscon Condi campi di velocità simili evidenziano gli effetti di una gli effetti di una evidenziano • nelNo caso senza e con modello d elevata viscosità turbolenta elevata viscosità turbolenta nel caso si applichi ilnel modello caso si applichi ilturbolenza. modello k-Epsilon k-Epsilon • Le simulazioni OpenFOAM forniscono gli stessi valori della caduta di pres laminare sia nel caso venga adottato un modello di turbolenza. FluentOF ottenuti con modello kEpsilon differiscono sensibilmente da I risultati WCCM XI – ECCM V - ECFD VI Barcelona• 2014 w.engines.polimi.it http://www.engines.polimi.it simulato con Fluent, mentre sono in accordo con altri modelli di turbole POLITECNICO DI MILANO Geometry tranformations Mathematical transformations of the geometry of the real foam: dilation • Dilation: pore density modification • Opening: porosity modification Pore density WCCM XI – ECCM V - ECFD VI Barcelona 2014 Porosity di ‟slip” a paretevalida può essere considerata valida a per valori di Kn superiori a 1e-3. L’ipotesi di ‟slip” a pareteL’ipotesi può essere considerata per valori di Kn superiori 1e-3. Verifica dei La schiuma considerata, quindi, ricadente nel regime del continuo. La schiuma considerata, quindi, ricadente nel regime del continuo. Ciò nonostante, in previsione di un possibile utilizzo futuro, si è provveduto ad implementare Ciò nonostante, in di un utilizzo si è provveduto ad implementare inPOLITECNICO Fluent 14 il F attore scala Lcprevisione [m] modello ddis possibile [m] Kn[futuro, ] il quale Maxwell attraverso è possibile gestire condizioni di slip a parete. M esh di Maxwell attraversoin il quale è possibile gestirethe condizioni di slipsize? a parete. Ismodello there a limit reducing cell 1 4.3 ⇥ 10 0.66 ⇥ 10 7.52 ⇥ 10 3 Base 0.1 0.01 0.005 𝐾𝑛 = 0.001 Ridotta 1 Ridotta 2 Ridotta 3 3 DI MILANO 5 4 4.3 ⇥ 10 4 0.66 ⇥ 10 4 7.52 ⇥ 10 No-Slip No-Slip Slip 4.3 ⇥ 10 5 0.66 ⇥ 10 5 7.52 ⇥ 10 3 𝜋 ∙ 𝛾 𝑀𝑎 5 0.33 ⇥ 10 2 𝜋 ∙ 2.15 𝛾 𝑀𝑎⇥ 10 𝐾𝑛 = ⇥ 10 5 1.50 essere 6 210 6𝑅𝑒 7.52 ⇥ 10 2 analizzato 4.3 ⇥ 10 0.66 ⇥ 2 𝑅𝑒 Slip con le classiche equazioni di Na soluzioni speciali delle equazioni di Boltzmann, Tabella 5.2: Parametri geometrici e valutazione Kn per le mesh utilizzate layer le equazioni di Navier-Stokes rimangono an Per Kn < Equazione 0.1 per`odiilMaxwell Knudsen layer copre me 4000 Equazione di Maxwell DP no-slip BC canale, perci`o 2questo substrato pu` o𝜇essere trascu − 𝜎 𝜕𝑢 𝜕𝑢 3 𝜕𝑇 3500 DP Maxwell BC − = 3 𝜇 fuori λ + Knudsen + 2 −𝑢soluzione 𝜎 𝜕𝑢𝑢 𝜕𝑢 𝜕𝑇 calcolata dal layer fino a 𝜎 𝜕𝑦 𝜕𝑥 4 𝜌𝑇 𝜕𝑥 Ridotta 4 3000 DP [Pa] 2500 2000 𝑢 Limit for cordierite pore structure −𝑢 = 𝜎 λ 𝜕𝑦 + 𝜕𝑥 + 4 𝜌𝑇 𝜕𝑥 𝜎 = tangential momentum accomodation coefficient 𝜎 = tangential momentum accomodation coefficient http://www.engines.polimi.it http://www.engines.polimi.it 1500 1000 500 0 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Kn [] Figura 5.2: Schematizzazione di un metodo WCCM XIE↵etto – ECCM - ECFD VI Barcelona 2014 Figura 5.4: dellaVcondizione al bordo di Maxwell Ci`o da luogo ad una velocit`a di slittamento From Micro-scale to Macro-scale WCCM XI – ECCM V - ECFD VI Barcelona 2014 POLITECNICO DI MILANO POLITECNICO DI MILANO Double-average of continuity and momentum • Continuity equation: No source terms • Momentum equation: Form drag Viscous drag WCCM XI – ECCM V - ECFD VI Barcelona 2014 Resistance source term in macro-scale equation Turbulent Reynolds stress, dispersion, turbulent dispersion Modelling the resistance source term Extracting information for upscaling POLITECNICO POLITECNICO MILANO DIDI MILANO Resistance source term in macro-scale equation Non-dimensional Non-dimensional relationshipsevaluated evaluated relationships onthe thebasis basisofofmicromicroon scalesimulations simulations scale Variable Variablepore poredensity density Π 𝑅𝑒 Π 𝑅𝑒 http://www.engines.polimi.it WCCM XI – ECCM V - ECFD VI Barcelona 2014 Variable Variableporosity porosity POLITECNICO DI MILANO Double-average of energy equations • Energy equation – fluid phase: Inter-phase heat transfer Effects of time fluctuations, spatial deviation and combined time-space dev. • Energy equation – solid phase: WCCM XI – ECCM V - ECFD VI Barcelona 2014 Extra-terms related to viscosity Inter-phase heat transfer Modelling the heat transfer source term Non-dimensional relationship evaluated on the basis of microscale simulations Al foam 𝑁𝑢(𝑅𝑒) WCCM XI – ECCM V - ECFD VI Barcelona 2014 POLITECNICO DI MILANO Inter-phase heat transfer source term in macroscale energy equation SiC foam Micro-scale: conjugate heat-transfer Al foam 10x10x10 mm 6.0 mln cells SiC foam 3x3x3 mm 2.1 mln cells WCCM XI – ECCM V - ECFD VI Barcelona 2014 POLITECNICO DI MILANO Cordierite 0.35x0.35x0.35 mm 3.2 mln cells POLITECNICO POLITECNICO DI MILANO DI MILANO Mass and heat transfer Modelling catalytic reactions ! ! A library modelling of surface has been implemented on Heat for andthe mass transfer analogyreactions makes validation easier the basis of the OpenFOAM code. Surface reaction chemistry has been implemented in OpenFOAM Mass transfer between gas phase and washcoat catalytic surface gas near wall gas washcoat solid wall Reaction heat is released and transferred to fluid and solid phase WCCM XI – ECCM V - ECFD VI Barcelona 2014 http://www.engines.polimi.it 773 K 473 K Diffusion limit Figure 11: Foam-type reactor, sample E: CO field inside the channel for an inlet CO mass fraction YCO = 3000Ncc/min. 100 100 80 80 60 40 CO conversion [%] km [m/s] CO conversion [%] 773 K 573 K 6. Conclusio 100 573 K 473 K POLITECNICO DI MILANO 4.6% and a feed flow rate Q = 60 40 Figure 11: Foam-type reactor, sample E: CO field inside the channel for an inlet CO mass fraction YCO = 4.6% and a feed flow rate Q = CFD (YCO 3 %) 20 3000Ncc/min. CFD (Y 3 %) foam A (Y 3 %) - CFD foam D - CFD 20 measured (YCO 3 %) CO CO foam A (YCO 3 %) - measured 473 K foam A (YCO 1 %) - CFD foam A (YCO 1 %) - measured 10−1 foam D - measured foam E - CFD foam E - measured B N u= A ( R e ) P r 0 1 10! 0 "YCO = 4.6% and a feed flow rate100 Figure 11: Foam-type reactor, E: CO field inside the channel for an inlet CO mass Q = 10sample 5fraction 3 Q 10 · m /s 3000Ncc/min. 400 CFD (YCOCFD 5 %) (YCO 5 %) measuredmeasured (YCO 5(Y%) CO 5 %) 0 400 500 B S h= A ( R e ) S c (1/3) 500 600700 700 800 800 600 T [K] T [K] CO conversion [%] ( Rflow N u= A e ) rate P rQ = 6000Ncc/min. feed 60 foam-type one does not allow an efficient surface, which are responsible for its mass transfer to- B figuration, S h= A ( R e ) Sremoval c (1/3) ofthe 60 the heat from the catalytic surface. Therewards the reaction region. It can be seen in Figures 12 fore, the temperature of the catalyst is expected to be and 13 that CFD simulations give a reasonable predic40 higher than the temperature measured in the front of tion of the light-off curve,40describing the transition from the foam, where the thermocouple is located. For this a kinetic-controlled to a diffusion-controlled process. CFD (Y 3 %) foam D - CFD 20 CFDis (YCO 3 %) towards a foam A (YCO 3 %) - CFD foam D CFD reason, the computed light-off curve shift 20 measured (Y 3 %) foam D - measured The CO conversionfoam atDhigh temperature is correctly foam - CFD foam AE(Y measured (YCO 3 %) CFD (Y 5 %) - measured CO 3 %) - measured higher temperature, if compared to CFD the(Ymeasured one. foam E - measured 5 %) (Y predicted while an overestimation of the light-offmeasured temfoam E - CFD foam A (Y 1 %) - CFD 5 %) CO conversion [%] km [m/s] 80 km [m/s] (1/3) Figure 10: Foam-type reactor: mass-transfer coefficients for different Figure 12: Foam-type reactor, sample E: CO conversion for an inlet 80 100 Figure 13:B Foam-type reactor, sample E: CO conversion for an inlet (1/3) foam samples. feed flow rate Q = 3000Ncc/min. 100 foam A (YCO 3 %) - CFD foam A (YCO 3 %) - measured foam A (YCO 1 %) - CFD foam A (YCO 1 %) - measured 10−1 measured (YCO 3 %) 101 CO CO CO CO CO 0 CO 1 %) - measured "foam A (Y perature with 500 600 700 measurements T [K]can be CO measured CO 5 %) respect to the ob-800 Moreover, it can be seen that, at the (Ylight-off temQ 105 · m3/s −1 0 10 served, for the lower CO concentration. perature, the conversion is700 reaching 400 when500 600 800its maxi10!1in particular " 3 T [K] This Q can10 be5 explained considering the assumption, made mum value, the curve exhibits a smooth transition from Figure 10: Foam-type reactor: mass-transfer coefficients for different · m /s Figure 12: Foam-type reactor, sample E: CO conversion for an inlet in the simulations, temperature distribution kinetic- to reactor, diffusion-controlled conversion. Figure 14: Foam-type sample E: COCO iso-surfaces for As an a foam samples. feedof flowuniform rate Q = 3000Ncc/min. on the foam catalyst surface. Actually, this assumption matter of fact, model does include inlet CO mass fraction YCO the = present 4.6% and a feed flownotrate Q = a 3000Ncc/min. WCCM – ECCM V mass-transfer - ECFD VI Barcelona 2014condition Figure 10:XI Foam-type reactor: coefficients different Figure 12: Foam-type reactor, sample E: CO conversion an inlet does not describe accurately theforexperimental pore-diffusion sub-model, therefore a sharp for transition figuration, thewere foam-type one doesAs notaallow an efficient surface, which aresamples. responsible for its mass transfer to- measurements foam feed rate Q = be 3000Ncc/min. under which performed. mat-flow should expected in this region. However, in this case of of thethe heatplate-type from the catalytic wards the reaction region. It can be seen ter in Figures of fact,12on theremoval contrary reactor surface. con- Therethe explanation for the smoothness of the curve can be ! 400 foam E - measured In this wor alytic surface sis of the ope solver was co in order to de account the d the washcoat surface. Stead sumption of the surface. T Langmuir-Hi priori on the b ture for simila validated for plate-type rea ing a satisfac experiments. a foam subst curve was co tal data is reg the simplifica lar, the slight curve is consi perature of th istic for this sumption, a m model is nee mal balance o actual temper Examples of application POLITECNICO DI MILANO ! Macro-scale approach is based on a multi-regions framework, in which fluid and solid phases are simulated on different (partially or totally) overlapping mesh. ! Models are introduced for the coupling between the solid and fluid phases. Micro-scale approach Macro-scale approach Check on consistency between macro- and microscale approaches WCCM XI – ECCM V - ECFD VI Barcelona 2014 POLITECNICO DI MILANO Examples of application Heating runs WCCM XI – ECCM V - ECFD VI Barcelona 2014 Cooling runs POLITECNICO DI MILANO Examples of application Simulation of flow trhrough a couple of DPF channels EX80-100/17 WCCM XI – ECCM V - ECFD VI Barcelona 2014 EX80-200/14 Examples of application DPF thermal transient Multi-layer foam catalyst thermal transient WCCM XI – ECCM V - ECFD VI Barcelona 2014 POLITECNICO DI MILANO Conclusions ! ! ! ! ! POLITECNICO DI MILANO Full set of libraries for volume averaging and surface chemistry has been implemented in OpenFOAM. Real open cell foams can be approximated by Kelvin cell type structures having similar properties and similar behaviour (pressure drop and heat/mass transfer). Flow resistance is mainly dependent on inertial effect of the fluid dodging the foam struts. Properties can be summarized in look up tables and used for full scale simulations with coupled multi regions. Applications have shown that the approach can be used to perform full scale simulation exploiting the information extracted with detailed simulation of the micro scale. WCCM XI – ECCM V - ECFD VI Barcelona 2014
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