Background and Motivation multistepSoot model Case tutorial Implementation of a two-transport equation for the sprayFoam Min Zhang Department of mechanical engineering, Technical University of Denmark, Copenhagen, Denmark 2019-11-27 Min Zhang Implementation of a two-transport equation soot model for sparyFoam 2019-11-27 1 / 30
Background and Motivation multistepSoot model Case tutorial Table of Contents 1 Background and Motivation Background Motivation 2 multistepSoot model Theory Implementation 3 Case tutorial Case modification Results Min Zhang Implementation of a two-transport equation soot model for sparyFoam 2019-11-27 2 / 30
Background and Motivation multistepSoot model Case tutorial Background Background spray combustion event is recognized as one of the most complex in-cylinder phenomena this event refers to fuel droplet atomisation, mixture preparation, ignition, combustion and soot production soot particle is an imoportant source of PM2.5, which causes severely healthy problem Min Zhang Implementation of a two-transport equation soot model for sparyFoam 2019-11-27 3 / 30
Background and Motivation multistepSoot model Case tutorial Motivation Motivation only one soot model called mixtureFractionSoot has been implemented in openFoam this soot model is a simple state model which can not predict soot accurately. soot production is a physical and chemical process which refers to soot inception, coagulation, surface growth, oxidation by OH and O 2 . implementing a multistep soot model and transport equations to OpenFOAM is necessary. Min Zhang Implementation of a two-transport equation soot model for sparyFoam 2019-11-27 4 / 30
Background and Motivation multistepSoot model Case tutorial Theory Soot formation and oxidation A successful modelling of soot requires accurate accounting for both formation and oxidation of soot. Basically, we can classify the soot model to the following 4 kinds, empirical model semi-empirical model detailed model phenomenological multistep soot model Min Zhang Implementation of a two-transport equation soot model for sparyFoam 2019-11-27 5 / 30
Background and Motivation multistepSoot model Case tutorial Theory Multistep soot model phenomenological multistep models process Min Zhang Implementation of a two-transport equation soot model for sparyFoam 2019-11-27 6 / 30
Background and Motivation multistepSoot model Case tutorial Theory Reaction rate for submodels i Description C b n T a inc Inception 10000 0 21000 0 ( p / p ref ) 1 . 4 sg Surface growth 0 12100 0.5 Oxidation due to OH 0.36 0.5 0 1 OH O 2 Oxidation due to O 2 10000 0.5 19778 1 Table: The multistep soot model constant values � − T a,i � k i = C i T b,i · exp ( S soot ) n,i (1) T Min Zhang Implementation of a two-transport equation soot model for sparyFoam 2019-11-27 7 / 30
Background and Motivation multistepSoot model Case tutorial Theory Soot mass and density production rate Net soot production rate: dM soot = k inc [ X prec ] + k sgs [ C 2 H 2 ] − k OH [ OH ] − k O 2 [ O 2 ] (2) dt Particle number density production rate: dN soot = N a k inc − k coag (3) dt Note that the coagulation rate is given as: k cog = k cog ( 24 RT ) 1 / 2 (6 M soot ρ soot π ) 1 / 6 ( N soot ) 11 / 6 (4) ρ soot N A Min Zhang Implementation of a two-transport equation soot model for sparyFoam 2019-11-27 8 / 30
Background and Motivation multistepSoot model Case tutorial Theory Two-tansport equation The well-know transport equations are Moss-Brookes (MB) two transport equations which are able to account for the individual processes and turbulence effect. ∂ µ t ∇ Y soot ] + dM soot ∂t ( ρY soot ) + ∇ · ( ρ U Y soot ) = ∇ · [ (5) Pr soot dt 1 ∂ µ t dN soot ∂t ( ρb ∗ nuc ) + ∇ · ( ρ U b ∗ nuc ) = ∇ · [ ∇ b ∗ nuc ] + (6) Pr nuc N normal dt Min Zhang Implementation of a two-transport equation soot model for sparyFoam 2019-11-27 9 / 30
Background and Motivation multistepSoot model Case tutorial Implementation The structure of sprayFoam The momentum, energy and mass equation are solved by including the codes: #include "UEqn".C #include "YEqn".C #include "EEqn".C The spray is solved by including the codes calling the function: #include "basicSprayCloud.H" parcels.evolve Min Zhang Implementation of a two-transport equation soot model for sparyFoam 2019-11-27 10 / 30
Background and Motivation multistepSoot model Case tutorial Implementation The creation of myRadiation library copy the radiation library into the user project folder $WM_PROJECT_USER_DIR without any changes foam cp -r --parents src/thermophysicalModels/radiation $WM_PROJECT_USER_DIR cd $WM_PROJECT_USER_DIR/src/thermophysicalModels/ Rename the library mv radition myRadiation Min Zhang Implementation of a two-transport equation soot model for sparyFoam 2019-11-27 11 / 30
Background and Motivation multistepSoot model Case tutorial Implementation The creation of myRadiation library Modify the excutable name to libmyradiationModels.so cd myRadiation sed -i s/libradiationModels/libmyradiationModels/g Make/files make the excutable file ”libmyradiationModels.so” locate at the $FOAM_USER_LIBBIN instead of $FOAM_LIBBIN sed -i s/FOAM_LIBBIN/FOAM_USER_LIBBIN/g Make/files Compile it after changing, wmake Min Zhang Implementation of a two-transport equation soot model for sparyFoam 2019-11-27 12 / 30
Background and Motivation multistepSoot model Case tutorial Implementation The understanding of mixtureFractionSoot model Let’s go into mixtureFractionSoot model cd submodels/sootModel/mixtureFractionSoot The mixtureFractionSoot consists of three files: mixtureFractionSoots.C : making a new type for mixtureFractionSoot mixtureFractionSoot.H : declaring the member data and fuctions mixtureFractionSoot.C : initializing the data member and define the member function Min Zhang Implementation of a two-transport equation soot model for sparyFoam 2019-11-27 13 / 30
Background and Motivation multistepSoot model Case tutorial Implementation The understanding of mixtureFractionSoot model The soot mass fraction is calculated by the member function correct() , const volScalarField& mapField = mesh_.lookupObject<volScalarField>(mappingFieldName_); soot_ = sootMax_*(mapField/mapFieldMax_); Hence, the modified calculation process should be added into this member function. Min Zhang Implementation of a two-transport equation soot model for sparyFoam 2019-11-27 14 / 30
Background and Motivation multistepSoot model Case tutorial Implementation The creation of multistep soot model Based on mixtureFractionSoot model existed in OpenFOAM, copy the folder and rename it, cd .. cp -r mixtureFractionSoot multistepSoot Meanwhile, rename the files name inside the folder, mv mixtureFractionSoot.C multistepSoot.C mv mixtureFractionSoot.H multistepSoot.H mv mixtureFractionSoots.C multistepSoots.C Min Zhang Implementation of a two-transport equation soot model for sparyFoam 2019-11-27 15 / 30
Background and Motivation multistepSoot model Case tutorial Implementation The creation of multistep soot model Change the soot type from mixtureFractionSoot to multistepSoot in the multistepSoots.C, sed -i s/mixtureFractionSoot/multistepSoot/g multistepSoots.C For the multistepSoot.H, we also need to change the mixtureFractionSoot to multistepSoot , sed -i s/mixtureFractionSoot/multistepSoot/g multistepSoot.H In order to solve a couple of chemistry reactions, we have to change the singleStepReactingMixture.H to reactingMixture.H , sed -i s/singleStepReactingMixture/reactingMixture.H/g multistepSoot.H Min Zhang Implementation of a two-transport equation soot model for sparyFoam 2019-11-27 16 / 30
Background and Motivation multistepSoot model Case tutorial Implementation The declaration of member in .H header file considering to add the multistep soot model and two transport equations into the multistepSoot model, the following declarations should be added under the //Private data, volScalarField PDSoot_; scalar wPrec_; volScalarField dNSootdt_; scalar rhoS_; volScalarField SootVF_; scalar Ca_; volScalarField SSoot_; scalar Ta_; volScalarField dMSootdt_; scalar Cb_; volScalarField r1_; scalar Cg_; volScalarField r2_; scalar Tg_; volScalarField r3_; scalar m_; volScalarField r4_; scalar q_; volScalarField r5_; scalar Cw1_; volScalarField MSoot_; scalar CollEff_; volScalarField NSoot_; scalar Cw2_; scalar Sct_; scalar Tw2_; scalar MWc_; scalar NA_; Min Zhang Implementation of a two-transport equation soot model for sparyFoam 2019-11-27 17 / 30
Background and Motivation multistepSoot model Case tutorial Implementation Including the relevant header files for multistep model in .C source file The final file we need to modify is multistepSoot.C . Firstly, change the mixtureFractionSoot to the multistepSoot , sed -i s/mixtureFractionSoot/multistepSoot/g multistepSoot.C Change the singleStepReactingMixture.H to reactingMixture.H , sed -i s/singleStepReactingMixture/reactingMixture/g multistepSoot.C We need to add two transport equations to this model, following header file should be included, #include "fvmDdt.H" #include "fvmDiv.H" #include "fvcDiv.H" #include "fvmLaplacian.H" Min Zhang Implementation of a two-transport equation soot model for sparyFoam 2019-11-27 18 / 30
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