multiphaseEulerFoam/.../BrownianCollisions: Added slip correction

Patch contributed by Institute of Fluid Dynamics,
Helmholtz-Zentrum Dresden - Rossendorf (HZDR)

applications/solvers/multiphase/multiphaseEulerFoam/phaseSystems/Make/files

@@ -42,7 +42,7 @@ populationBalanceModel/populationBalanceModel/populationBalanceModel.C
 coalescenceModels = populationBalanceModel/coalescenceModels
 $(coalescenceModels)/coalescenceModel/coalescenceModel.C
 $(coalescenceModels)/ballisticCollisions/ballisticCollisions.C
-$(coalescenceModels)/brownianCollisions/brownianCollisions.C
+$(coalescenceModels)/BrownianCollisions/BrownianCollisions.C
 $(coalescenceModels)/constantCoalescence/constantCoalescence.C
 $(coalescenceModels)/CoulaloglouTavlaridesCoalescence/CoulaloglouTavlaridesCoalescence.C
 $(coalescenceModels)/DahnekeInterpolation/DahnekeInterpolation.C

applications/solvers/multiphase/multiphaseEulerFoam/phaseSystems/diameterModels/velocityGroup/sizeGroup/shapeModels/fractal/fractal.H

@@ -33,7 +33,7 @@ Description
     area is taken into account by a separate source term.
 
     Kappa is transported between the size groups as a secondary property by
-    means of coalescence (coagulation/aggregation), breakup as well as drift.
+    means of coalescence (coagulation), breakup as well as drift.
 
     By assuming a monodisperse size distribution of the primary particles in the
     aggregate, the collisional diameter of a size group can then be computed by

applications/solvers/multiphase/multiphaseEulerFoam/phaseSystems/populationBalanceModel/coalescenceModels/BrownianCollisions/BrownianCollisions.C

@@ -23,9 +23,10 @@ License
 
 \*---------------------------------------------------------------------------*/
 
-#include "brownianCollisions.H"
+#include "BrownianCollisions.H"
 #include "addToRunTimeSelectionTable.H"
 #include "fundamentalConstants.H"
+#include "mathematicalConstants.H"
 
 // * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
 
@@ -35,11 +36,11 @@ namespace diameterModels
 {
 namespace coalescenceModels
 {
-    defineTypeNameAndDebug(brownianCollisions, 0);
+    defineTypeNameAndDebug(BrownianCollisions, 0);
     addToRunTimeSelectionTable
     (
         coalescenceModel,
-        brownianCollisions,
+        BrownianCollisions,
         dictionary
     );
 }
@@ -47,24 +48,55 @@ namespace coalescenceModels
 }
 
 using Foam::constant::physicoChemical::k;
+using Foam::constant::mathematical::pi;
+
 
 // * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
-Foam::diameterModels::coalescenceModels::brownianCollisions::
+Foam::diameterModels::coalescenceModels::BrownianCollisions::
-brownianCollisions
+BrownianCollisions
 (
     const populationBalanceModel& popBal,
     const dictionary& dict
 )
 :
-    coalescenceModel(popBal, dict)
+    coalescenceModel(popBal, dict),
+    A1_(dict.lookupOrDefault<scalar>("A1", 2.514)),
+    A2_(dict.lookupOrDefault<scalar>("A2", 0.8)),
+    A3_(dict.lookupOrDefault<scalar>("A3", 0.55)),
+    sigma_("sigma", dimLength, dict),
+    lambda_
+    (
+        IOobject
+        (
+            "lambda",
+            popBal_.time().timeName(),
+            popBal_.mesh()
+        ),
+        popBal_.mesh(),
+        dimensionedScalar
+        (
+            "lambda",
+            dimLength,
+            Zero
+        )
+    )
 {}
 
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
+void Foam::diameterModels::coalescenceModels::BrownianCollisions::correct()
+{
+    const volScalarField& T = popBal_.continuousPhase().thermo().T();
+    const volScalarField& p = popBal_.continuousPhase().thermo().p();
+
+    lambda_ = k*T/(sqrt(2.0)*pi*p*sqr(sigma_));
+}
+
+
 void
-Foam::diameterModels::coalescenceModels::brownianCollisions::
+Foam::diameterModels::coalescenceModels::BrownianCollisions::
 addToCoalescenceRate
 (
     volScalarField& coalescenceRate,
@@ -78,9 +110,17 @@ addToCoalescenceRate
     const volScalarField& T = popBal_.continuousPhase().thermo().T();
     const volScalarField& mu = popBal_.continuousPhase().thermo().mu();
 
-    coalescenceRate +=
+    const volScalarField Cci
-        8.0*k*T/(3*mu)*(fi.d() + fj.d())
+    (
-       *(1.0/fi.d() + 1.0/fj.d());
+        1 + lambda_/fi.d()*(A1_ + A2_*exp(-A3_*fi.d()/lambda_))
+    );
+
+    const volScalarField Ccj
+    (
+        1 + lambda_/fj.d()*(A1_ + A2_*exp(-A3_*fj.d()/lambda_))
+    );
+
+    coalescenceRate += 8*k*T/(3*mu)*(fi.d() + fj.d())*(Cci/fi.d() + Ccj/fj.d());
 }
 
 

applications/solvers/multiphase/multiphaseEulerFoam/phaseSystems/populationBalanceModel/coalescenceModels/BrownianCollisions/BrownianCollisions.H

@@ -22,19 +22,54 @@ License
     along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
 
 Class
-    Foam::diameterModels::coalescenceModels::brownianCollisions
+    Foam::diameterModels::coalescenceModels::BrownianCollisions
 
 Description
-    Model describing aggregation due to brownian motion. Utilizes physical, i.e.
+    Model describing coagulation due to Brownian motion. Utilizes collisional
-    collisional diameters.
+    diameters and the Cunningham slip correction. The slip correction
+    coefficient is implemented in the following form:
+
+    \f[
+        C_{c_i} = 1 + \lambda [A_1 + A_2 \exp(-A_3 d_i/\lambda)]/d_i\,.
+    \f]
+
+    The coefficients default to the values proposed by Davis (1945). The mean
+    free path is computed by
+
+    \f[
+        \lambda = \frac{kT}{\sqrt{2} \pi p \sigma^{2}}\,.
+    \f]
+
+    \vartable
+        A_1       | Coefficient [-]
+        A_2       | Coefficient [-]
+        A_3       | Coefficient [-]
+        \sigma    | Lennard-Jones parameter [m]
+    \endvartable
+
+    Reference:
+    \verbatim
+        Davies, C. N. (1945).
+        Definitive equations for the fluid resistance of spheres.
+        Proceedings of the Physical Society, 57(4), 259.
+    \endverbatim
+
+Usage
+    \table
+        Property    | Description                | Required    | Default value
+        A1          | Coefficient A1             | no          | 2.514
+        A2          | Coefficient A2             | no          | 0.8
+        A3          | Coefficient A2             | no          | 0.55
+        sigma       | Lennard-Jones parameter    | yes         | none
+    \endtable
 
 SourceFiles
-    brownianCollisions.C
+    BrownianCollisions.C
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef brownianCollisions_H
+#ifndef BrownianCollisions_H
-#define brownianCollisions_H
+#define BrownianCollisions_H
 
 #include "coalescenceModel.H"
 
@@ -48,21 +83,39 @@ namespace coalescenceModels
 {
 
 /*---------------------------------------------------------------------------*\
-                     Class brownianCollisions Declaration
+                     Class BrownianCollisions Declaration
 \*---------------------------------------------------------------------------*/
 
-class brownianCollisions
+class BrownianCollisions
 :
     public coalescenceModel
 {
+    // Private Data
+
+        //- Cunningham slip correction coefficient A1
+        const dimensionedScalar A1_;
+
+        //- Cunningham slip correction coefficient A2
+        const dimensionedScalar A2_;
+
+        //- Cunningham slip correction coefficient A3
+        const dimensionedScalar A3_;
+
+        //- Lennard-Jones sigma parameter
+        const dimensionedScalar sigma_;
+
+        //- Mean free path
+        volScalarField lambda_;
+
+
 public:
 
     //- Runtime type information
-    TypeName("brownianCollisions");
+    TypeName("BrownianCollisions");
 
     // Constructor
 
-        brownianCollisions
+        BrownianCollisions
         (
             const populationBalanceModel& popBal,
             const dictionary& dict
@@ -70,12 +123,15 @@ public:
 
 
     //- Destructor
-    virtual ~brownianCollisions()
+    virtual ~BrownianCollisions()
     {}
 
 
     // Member Functions
 
+        //- Correct diameter independent expressions
+        virtual void correct();
+
         //- Add to coalescenceRate
         virtual void addToCoalescenceRate
         (

applications/solvers/multiphase/multiphaseEulerFoam/phaseSystems/populationBalanceModel/coalescenceModels/DahnekeInterpolation/DahnekeInterpolation.C

@@ -25,7 +25,7 @@ License
 
 #include "DahnekeInterpolation.H"
 #include "addToRunTimeSelectionTable.H"
-#include "brownianCollisions.H"
+#include "BrownianCollisions.H"
 #include "ballisticCollisions.H"
 
 // * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
@@ -58,20 +58,20 @@ DahnekeInterpolation
 )
 :
     coalescenceModel(popBal, dict),
-    brownian_(new brownianCollisions(popBal, dict)),
+    Brownian_(new BrownianCollisions(popBal, dict)),
-    brownianCollisionRate_
+    BrownianRate_
     (
         IOobject
         (
-            "brownianCollisionRate",
+            "BrownianCollisionRate",
             popBal_.mesh().time().timeName(),
             popBal_.mesh()
         ),
         popBal_.mesh(),
-        dimensionedScalar("brownianCollisionRate", dimVolume/dimTime, 0.0)
+        dimensionedScalar("BrownianCollisionRate", dimVolume/dimTime, Zero)
     ),
     ballistic_(new ballisticCollisions(popBal, dict)),
-    ballisticCollisionRate_
+    ballisticRate_
     (
         IOobject
         (
@@ -80,13 +80,19 @@ DahnekeInterpolation
             popBal_.mesh()
         ),
         popBal_.mesh(),
-        dimensionedScalar("ballisticCollisionRate", dimVolume/dimTime, 0.0)
+        dimensionedScalar("ballisticCollisionRate", dimVolume/dimTime, Zero)
     )
 {}
 
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
+void Foam::diameterModels::coalescenceModels::DahnekeInterpolation::correct()
+{
+    Brownian_().correct();
+}
+
+
 void
 Foam::diameterModels::coalescenceModels::DahnekeInterpolation::
 addToCoalescenceRate
@@ -96,19 +102,15 @@ addToCoalescenceRate
     const label j
 )
 {
-    brownianCollisionRate_ = Zero;
+    BrownianRate_ = Zero;
-    ballisticCollisionRate_ = Zero;
+    ballisticRate_ = Zero;
 
-    brownian_().addToCoalescenceRate(brownianCollisionRate_, i, j);
+    Brownian_().addToCoalescenceRate(BrownianRate_, i, j);
-    ballistic_().addToCoalescenceRate(ballisticCollisionRate_, i, j);
+    ballistic_().addToCoalescenceRate(ballisticRate_, i, j);
 
-    const volScalarField KnD
+    const volScalarField KnD(BrownianRate_/(2*ballisticRate_));
-    (
-        brownianCollisionRate_/(2.0*ballisticCollisionRate_)
-    );
 
-    coalescenceRate +=
+    coalescenceRate += BrownianRate_*(1 + KnD)/(1 + 2*KnD + 2*sqr(KnD));
-        brownianCollisionRate_*(1.0 + KnD)/(1.0 + 2.0*KnD + 2.0*sqr(KnD));
 }
 
 

applications/solvers/multiphase/multiphaseEulerFoam/phaseSystems/populationBalanceModel/coalescenceModels/DahnekeInterpolation/DahnekeInterpolation.H

@@ -25,8 +25,8 @@ Class
     Foam::diameterModels::coalescenceModels::DahnekeInterpolation
 
 Description
-    Aggregation model of Dahneke (1983). Utilizes physical, i.e. collisional
+    Interpolation formula of Dahneke (1983) as presented by Otto et al. (1999).
-    diameters.
+    Utilizes collisional diameters.
 
     References:
     \verbatim
@@ -35,6 +35,14 @@ Description
         In Theory of dispersed multiphase flow (pp. 97-133). Academic Press.
     \endverbatim
 
+    \verbatim
+        Otto, E., Fissan, H., Park, S. H., & Lee, K. W. (1999).
+        The log-normal size distribution theory of Brownian aerosol coagulation
+        for the entire particle size range: part II—analytical solution using
+        Dahneke’s coagulation kernel.
+        Journal of aerosol science, 30(1), 17-34.
+    \endverbatim
+
 SourceFiles
     DahnekeInterpolation.C
 
@@ -54,7 +62,7 @@ namespace diameterModels
 namespace coalescenceModels
 {
 
-class brownianCollisions;
+class BrownianCollisions;
 class ballisticCollisions;
 
 /*---------------------------------------------------------------------------*\
@@ -67,17 +75,17 @@ class DahnekeInterpolation
 {
     // Private Data
 
-        //- Model for coagulation due to brownian collisions
+        //- Model for coagulation due to Brownian collisions
-        autoPtr<brownianCollisions> brownian_;
+        autoPtr<BrownianCollisions> Brownian_;
 
-        //- Rate for coagulation due to brownian collisions
+        //- Rate for coagulation due to Brownian collisions
-        volScalarField brownianCollisionRate_;
+        volScalarField BrownianRate_;
 
         //- Model for coagulation due to ballistic collisions
         autoPtr<ballisticCollisions> ballistic_;
 
         //- Rate for coagulation due to ballistic collisions
-        volScalarField ballisticCollisionRate_;
+        volScalarField ballisticRate_;
 
 
 public:
@@ -101,6 +109,9 @@ public:
 
     // Member Functions
 
+        //- Correct diameter independent expressions
+        virtual void correct();
+
         //- Add to coalescenceRate
         virtual void addToCoalescenceRate
         (

applications/solvers/multiphase/multiphaseEulerFoam/phaseSystems/populationBalanceModel/coalescenceModels/ballisticCollisions/ballisticCollisions.C

@@ -79,8 +79,8 @@ addToCoalescenceRate
     const volScalarField& rhoP = fi.phase().rho();
 
     coalescenceRate +=
-        sqrt(3*k*T/rhoP)*sqr((fi.d() + fj.d()))
+        sqrt(3*k*T/rhoP)*sqr(fi.d() + fj.d())
-       *sqrt(1.0/pow3(fi.d()) + 1.0/pow3(fj.d()));
+       *sqrt(1/pow3(fi.d()) + 1/pow3(fj.d()));
 }
 
 

applications/solvers/multiphase/multiphaseEulerFoam/phaseSystems/populationBalanceModel/coalescenceModels/ballisticCollisions/ballisticCollisions.H

@@ -25,8 +25,8 @@ Class
     Foam::diameterModels::coalescenceModels::ballisticCollisions
 
 Description
-    Model describing aggregation due to ballistic collisions. Utilizes physical,
+    Model describing coagulation due to ballistic collisions. Utilizes
-    i.e. collisional diameters.
+    collisional diameters.
 
 SourceFiles
     ballisticCollisions.C

applications/solvers/multiphase/multiphaseEulerFoam/phaseSystems/populationBalanceModel/coalescenceModels/turbulentShear/turbulentShear.H

@@ -25,7 +25,7 @@ Class
     Foam::diameterModels::coalescenceModels::turbulentShear
 
 Description
-    Model describing aggregation due to turbulent shear. Utilizes physical, i.e.
+    Model describing coagulation due to turbulent shear. Utilizes physical, i.e.
     collisional diameters.
 
 SourceFiles

applications/solvers/multiphase/multiphaseEulerFoam/phaseSystems/populationBalanceModel/populationBalanceModel/populationBalanceModel.H

@@ -31,7 +31,7 @@ Description
     a transport equation of the volume-based number density function. The
     discretization is done using the fixed pivot technique of Kumar and
     Ramkrishna (1996). The source terms are written in a way that particle
-    number and mass are preserved. Coalescence (aggregation), breakup, drift
+    number and mass are preserved. Coalescence (coagulation), breakup, drift
     (growth and surface loss) as well as nucleation are supported.
     For the discrete breakup term two recipes are available, depending on the
     model choice. For models which state a total breakup rate and a separate

tutorials/multiphase/multiphaseEulerFoam/laminar/titaniaSynthesis/constant/phaseProperties

@@ -104,7 +104,10 @@ populationBalanceCoeffs
 
         coalescenceModels
         (
-            DahnekeInterpolation{}
+            DahnekeInterpolation
+            {
+                sigma           340e-12;
+            }
         );
 
         binaryBreakupModels

tutorials/multiphase/multiphaseEulerFoam/laminar/titaniaSynthesisSurface/constant/phaseProperties

@@ -110,7 +110,10 @@ populationBalanceCoeffs
 
         coalescenceModels
         (
-            DahnekeInterpolation{}
+            DahnekeInterpolation
+            {
+                sigma           340e-12;
+            }
         );
 
         binaryBreakupModels