Heat Transfer Modeling using ANSYS FLUENT

Transcription

1 Lecture 7 Heat raner in Porou Media 14.5 Releae Heat raner Modeling uing ANSYS FLUEN 2013 ANSYS, Inc. March 28, Releae 14.5

2 Agenda Introduction Porou Media Characterization he Rereentative Elementary Volume (REV) Concet heory he Standard Aroach Ued in FLUEN Non-Equilibrium Heat raner wo-equation Model Concluion 2013 ANSYS, Inc. March 28, Releae 14.5

3 Introduction Indutrial examle Fuel cell Catalytic converter Filter Food roduct Like in all multihae or heterogeneou ytem, tranort henomena are imortant. he ocu o thi reentation i mainly heat traner by convection Introduction to the elementary rereentative volume concet Governing equation Cloure model wo model or redicting orou media heat traner One-equation model (local thermal equilibrium model) wo-equation model (non-equilibrium model) 2013 ANSYS, Inc. March 28, Releae 14.5

4 Agenda Introduction Porou Media Characterization he Rereentative Elementary Volume (REV) Concet heory he Standard Aroach Ued in FLUEN Non-Equilibrium Heat raner wo-equation Model Concluion 2013 ANSYS, Inc. March 28, Releae 14.5

5 Porou Media Characterization Deinition Porou media i a olid with many comlex ore. Shae and connectivity o the ore are imortant. Porou media exhibit large diverity in Structure (hae) Nature Satial cale Steel Filter (Ordered Structure) Steel Fiber Porou Match (Random Structure) Sand Pack (Random Structure) 2013 ANSYS, Inc. March 28, Releae 14.5

6 Porou Media Characterization raner henomena in orou media trongly deend on olid matrix geometry. Characteritic variable or orou media Poroity (deined a the ratio o void volume to total volume) Global oroity ercentage o ore volume or void ace, or that volume within the orou region that can contain luid Global Volume 1 Solid Matrix Volume Eective oroity the interconnected ore volume or void ace in a rock that contribute to luid low. Eective oroity exclude iolated ore and i thereore tyically le than the global oroity. Volume o Active Pore Sace e Samle Volume Seciic urace area Ratio o interacial area to eciic volume A S Fluid -Solid Interacial Area Samle Volume 2013 ANSYS, Inc. March 28, Releae 14.5

7 Agenda Introduction Porou Media Characterization he Rereentative Elementary Volume (REV) Concet heory he Standard Aroach Ued in FLUEN Non-Equilibrium Heat raner wo-equation Model Concluion 2013 ANSYS, Inc. March 28, Releae 14.5

8 Rereentative Elementary Volume Geometric roblem wo largely dierent length cale Pore or grain cale, d Porou media length cale, L >> d In general, olving the low ield at the ore cale i imractical Can we decribe the low ield at a larger, more ractical cale? Concet o ucaling Method o volumetric averaging 2013 ANSYS, Inc. March 28, Releae 14.5

9 Rereentative Elementary Volume Rereentative elementary volume Large enough to characterize the material Small enough to maintain atial decrition d r Comutational Domain Pore cale Volumetric Averaging REV cale L Local Dicretization 2013 ANSYS, Inc. March 28, Releae 14.5

10 Agenda Introduction Porou Media Characterization he Rereentative Elementary Volume (REV) Concet heory he Standard Aroach Ued in FLUEN Non-Equilibrium Heat raner wo-equation Model Concluion 2013 ANSYS, Inc. March 28, Releae 14.5

11 Aumtion and Limitation he orou media model in FLUEN introduce low reitance arameter that can be obtained either analytically or emirically. Porou zone remain luid tye. Sink term are included in the momentum equation which account or the reitance orce o olid material onto the luid. he orou media treatment i ubject to the ollowing aumtion and limitation: he volume blockage that i hyically reent i not modeled. Intead, a uericial velocity i calculated which rereent the luid velocity through the orou zone. Interaction between orou media and turbulence i aroximated. Other limitation aly. Reer to Chater o the FLUEN 14.5 Uer Guide ANSYS, Inc. March 28, Releae 14.5

12 heory In orou zone, the continuity equation remain unchanged, excet that it i ormulated in term o uericial velocity. t U 0 Momentum equation contain an additional body orce term, F t U U U P τ g F For homogenou orou media: U F C 2 U 2 U F Vicou erm i j D ij U j j C ij U U 2 Inertial erm Permeability Inertial reitance actor 2013 ANSYS, Inc. March 28, Releae 14.5

13 Agenda Introduction Porou Media Characterization he Rereentative Elementary Volume (REV) Concet heory he Standard Aroach Ued in FLUEN Non-Equilibrium Heat raner wo-equation Model Concluion 2013 ANSYS, Inc. March 28, Releae 14.5

14 Standard Aroach Ued in FLUEN FLUEN ue the local equilibrium (one-equation) aroach. hi roughly mean that the local luid temerature i aroximately equal to the orou matrix temerature. Range o alication: Situation where there i local heat balance in orou media Limited to artial aniotroy Energy equation m U k C m t m e m C 1 C How do we determine the eective conductivity? 2013 ANSYS, Inc. March 28, Releae 14.5

15 Local Equilibrium (One Equation Model) Fluid art: Solid art: C U k t C k t Pore Scale, d d m C U k k m t C 1 C m m d Ucaling (Phae Averaging) m Cloure model Real conductivity matrice k m ( k, k,, tructure) k d (microcoic velocity ield heterogeneity) REV or Domain Scale 2013 ANSYS, Inc. March 28, Releae 14.5

16 Cloure Model Volumetric averaging introduce eective conductivity matrice. Matrice deend on hermal conductivity o each void, Material oroity, Solid matrix tructure, hermal dierion Conequence o microcoic velocity ield heterogeneity Several method exit to characterize thee matrice Exerimental Geometric Emirical Local numerical imulation Characterization i a comlex roblem and will not be dicued in thi reentation ANSYS, Inc. March 28, Releae 14.5

17 Eective hermal Conductivity Iotroic orou media For iotroic orou media, the eective conductivity can be etimated uing a oroity-weighted average o luid and olid art. UDF i needed in order to imulate atial deendence. Aniotroic orou media For aniotroic orou media, eective conductivity can be etimated uing oroity-weighted average o luid calar conductivity and olid conductivity matrix. Satial deendence i oible via UDF. k 0 k 0 e k k 1 k 0 k 0 e k k11 k 12 k 13 k21 k 22 k 23 k k k Fluid contribution Solid contribution 2013 ANSYS, Inc. March 28, Releae 14.5

18 Standard Aroach Ued in FLUEN Uer-deined eective conductivity Fluid Scalar value Solid Scalar or matrix value Cell Zone Condition Edit... Material Solid Create/Edit 2013 ANSYS, Inc. March 28, Releae 14.5

19 Agenda Introduction Porou Media Characterization he Rereentative Elementary Volume (REV) Concet heory he Standard Aroach Ued in FLUEN Non-Equilibrium Heat raner wo-equation Model Concluion 2013 ANSYS, Inc. March 28, Releae 14.5

20 Non-Equilibrium Heat raner Range o validity hermal equilibrium i not aumed Iotroic heat traner wo earate but couled energy equation are olved. Energy equation or the luid region Energy equation or the olid matrix region In the non-equilibrium cae, the ytem o governing equation require additional cloure relationhi. Fluid thermal dierion (iotroic) Solid thermal diuion (iotroic) Exchange coeicient at luid-olid interace 2013 ANSYS, Inc. March 28, Releae 14.5

21 Local Imbalance (wo-equation Model) Fluid art: Solid art: C U k t C k t Pore Scale, d d Ucaling (Phae Averaging) C U k h t Cloure model Eective conductivity matrice C 1 k h t Couling REV or Domain Scale 2013 ANSYS, Inc. March 28, Releae 14.5

22 Non-Equilibrium Heat raner C C U k h t Uer-deined 1 C (1 ) k h t hermal Conductivity Fluid Energy Source erm hermal Conductivity Solid Energy Source erm Unteady erm Fluid Energy Equation Solid Energy Equation 2013 ANSYS, Inc. March 28, Releae 14.5

23 2013 ANSYS, Inc. March 28, Releae 14.5 Non-Equilibrium Heat raner Calculation o ource term in the luid energy equation Energy equation olved by FLUEN (deault) Equation to olve : Deine new equation : he ource term i thereore S k C t C U h k C t C V U t C h S 1 V t C h k C t C 1 V U Unteady Convection Diuion Source erm

24 Agenda Introduction Porou Media Characterization he Rereentative Elementary Volume (REV) Concet heory he Standard Aroach Ued in FLUEN Non-Equilibrium Heat raner wo-equation Model Concluion 2013 ANSYS, Inc. March 28, Releae 14.5

25 Concluion Convective heat traner in orou media can be aroached in FLUEN uing two dierent method. One-Equation Model wo-equation Model Cloure model remain a comlex roblem. Eective conductivity characterization Seciic heat traner coeicient in orou media. It i oible to introduce a diuivity matrix in the energy equation olved or olid region. Preented aroach can be generalized either directly or via UDF. Aniotroic thermal conductivity in olid zone (matrix tructure eect). hermal dierion matrix in luid zone (velocity ield heterogeneity eect) 2013 ANSYS, Inc. March 28, Releae 14.5

26 Reerence Kaviany (1999), Princile o Heat raner in Porou Media, Sringer-Verlag. Quintard, Modéliation de ranert hermique dan un Milieu Poreux. FLUEN Inc. (2003), Uer-Grou Meeting, France. Quintard, ranert en Milieux Poreux, htt://mquintard.ree.r Borie and Prat, ranert de chaleur dan le milieux oreux. echnique de l Ingénieur, traité Génie Énergétique Borie, ranert en Milieux Poreux, DEA ENSEEIH 2013 ANSYS, Inc. March 28, Releae 14.5