EEqn: Added rho*(U&g) source term

Generally this term has a VERY small effect on temperature, it is only
important for low-speed buoyancy-dominated flows.

Resolves bug-report http://www.openfoam.org/mantisbt/view.php?id=1755

See also http://cfd.direct/openfoam/energy-equation/

applications/solvers/combustion/reactingFoam/EEqn.H

@@ -17,7 +17,8 @@
         )
       - fvm::laplacian(turbulence->alphaEff(), he)
      ==
-        reaction->Sh()
+        rho*(U&g)
+      + reaction->Sh()
       + fvOptions(rho, he)
     );
 

applications/solvers/heatTransfer/buoyantPimpleFoam/EEqn.H

@@ -17,7 +17,8 @@
         )
       - fvm::laplacian(turbulence->alphaEff(), he)
      ==
-        radiation->Sh(thermo)
+        rho*(U&g)
+      + radiation->Sh(thermo)
       + fvOptions(rho, he)
     );
 

applications/solvers/heatTransfer/buoyantSimpleFoam/EEqn.H

@@ -11,7 +11,8 @@
         )
       - fvm::laplacian(turbulence->alphaEff(), he)
      ==
-        radiation->Sh(thermo)
+        rho*(U&g)
+      + radiation->Sh(thermo)
       + fvOptions(rho, he)
     );
 

applications/solvers/heatTransfer/chtMultiRegionFoam/chtMultiRegionSimpleFoam/fluid/EEqn.H

@@ -11,7 +11,8 @@
         )
       - fvm::laplacian(turb.alphaEff(), he)
      ==
-        rad.Sh(thermo)
+        rho*(U&g)
+      + rad.Sh(thermo)
       + fvOptions(rho, he)
     );
 

applications/solvers/heatTransfer/chtMultiRegionFoam/chtMultiRegionSimpleFoam/fluid/setRegionFluidFields.H

@@ -29,5 +29,7 @@
     const bool frozenFlow = frozenFlowFluid[i];
 
     volScalarField& p_rgh = p_rghFluid[i];
+
+    const dimensionedVector& g = gFluid[i];
     const volScalarField& gh = ghFluid[i];
     const surfaceScalarField& ghf = ghfFluid[i];

applications/solvers/heatTransfer/chtMultiRegionFoam/fluid/EEqn.H

@@ -17,7 +17,8 @@
         )
       - fvm::laplacian(turb.alphaEff(), he)
      ==
-        rad.Sh(thermo)
+        rho*(U&g)
+      + rad.Sh(thermo)
       + fvOptions(rho, he)
     );
 

applications/solvers/heatTransfer/chtMultiRegionFoam/fluid/setRegionFluidFields.H

@@ -15,6 +15,8 @@
     const volScalarField& psi = thermo.psi();
 
     volScalarField& p_rgh = p_rghFluid[i];
+
+    const dimensionedVector& g = gFluid[i];
     const volScalarField& gh = ghFluid[i];
     const surfaceScalarField& ghf = ghfFluid[i];
 

applications/solvers/lagrangian/coalChemistryFoam/EEqn.H

@@ -17,7 +17,8 @@
         )
       - fvm::laplacian(turbulence->alphaEff(), he)
      ==
-        combustion->Sh()
+        rho*(U&g)
+      + combustion->Sh()
       + coalParcels.Sh(he)
       + limestoneParcels.Sh(he)
       + radiation->Sh(thermo)

applications/solvers/lagrangian/reactingParcelFilmFoam/EEqn.H

@@ -17,7 +17,8 @@
         )
       - fvm::laplacian(turbulence->alphaEff(), he)
      ==
-        parcels.Sh(he)
+        rho*(U&g)
+      + parcels.Sh(he)
       + surfaceFilm.Sh()
       + radiation->Sh(thermo)
       + combustion->Sh()

applications/solvers/lagrangian/reactingParcelFoam/EEqn.H

@@ -17,7 +17,8 @@
         )
       - fvm::laplacian(turbulence->alphaEff(), he)
      ==
-        parcels.Sh(he)
+        rho*(U&g)
+      + parcels.Sh(he)
       + radiation->Sh(thermo)
       + combustion->Sh()
       + fvOptions(rho, he)

applications/solvers/lagrangian/reactingParcelFoam/simpleReactingParcelFoam/EEqn.H

@@ -11,7 +11,8 @@
         )
       - fvm::laplacian(turbulence->alphaEff(), he)
      ==
-        parcels.Sh(he)
+        rho*(U&g)
+      + parcels.Sh(he)
       + radiation->Sh(thermo)
       + combustion->Sh()
       + fvOptions(rho, he)

applications/solvers/multiphase/reactingTwoPhaseEulerFoam/EEqns.H

@@ -6,40 +6,42 @@
         heatTransfer = heatTransferPtr();
 
     {
-        tmp<fvScalarMatrix> he1Eqn(phase1.heEqn());
+        tmp<fvScalarMatrix> E1Eqn(phase1.heEqn());
 
-        if (he1Eqn.valid())
+        if (E1Eqn.valid())
         {
-            he1Eqn =
+            E1Eqn =
             (
-                he1Eqn
+                E1Eqn
              ==
                *heatTransfer[phase1.name()]
+              + alpha1*rho1*(U1&g)
               + fvOptions(alpha1, rho1, phase1.thermo().he())
             );
 
-            he1Eqn->relax();
-            fvOptions.constrain(he1Eqn());
-            he1Eqn->solve();
+            E1Eqn->relax();
+            fvOptions.constrain(E1Eqn());
+            E1Eqn->solve();
         }
     }
 
     {
-        tmp<fvScalarMatrix> he2Eqn(phase2.heEqn());
+        tmp<fvScalarMatrix> E2eqn(phase2.heEqn());
 
-        if (he2Eqn.valid())
+        if (E2eqn.valid())
         {
-            he2Eqn =
+            E2eqn =
             (
-                he2Eqn
+                E2eqn
              ==
                *heatTransfer[phase2.name()]
+              + alpha2*rho2*(U2&g)
               + fvOptions(alpha2, rho2, phase2.thermo().he())
             );
 
-            he2Eqn->relax();
-            fvOptions.constrain(he2Eqn());
-            he2Eqn->solve();
+            E2eqn->relax();
+            fvOptions.constrain(E2eqn());
+            E2eqn->solve();
         }
     }
 }

applications/solvers/multiphase/twoPhaseEulerFoam/EEqns.H

@@ -7,7 +7,7 @@
 
     volScalarField Kh(fluid.Kh());
 
-    fvScalarMatrix he1Eqn
+    fvScalarMatrix E1Eqn
     (
         fvm::ddt(alpha1, rho1, he1) + fvm::div(alphaRhoPhi1, he1)
       - fvm::Sp(contErr1, he1)
@@ -28,17 +28,18 @@
         )
     );
 
-    he1Eqn.relax();
+    E1Eqn.relax();
 
-    he1Eqn -=
+    E1Eqn -=
     (
         Kh*(thermo2.T() - thermo1.T())
       + Kh*he1/Cpv1
       - fvm::Sp(Kh/Cpv1, he1)
+      + alpha1*rho1*(U1&g)
       + fvOptions(alpha1, rho1, he1)
     );
 
-    fvScalarMatrix he2Eqn
+    fvScalarMatrix E2Eqn
     (
         fvm::ddt(alpha2, rho2, he2) + fvm::div(alphaRhoPhi2, he2)
       - fvm::Sp(contErr2, he2)
@@ -59,21 +60,22 @@
         )
     );
 
-    he2Eqn.relax();
+    E2Eqn.relax();
 
-    he2Eqn -=
+    E2Eqn -=
     (
         Kh*(thermo1.T() - thermo2.T())
       + Kh*he2/Cpv2
       - fvm::Sp(Kh/Cpv2, he2)
+      + alpha2*rho2*(U2&g)
       + fvOptions(alpha2, rho2, he2)
     );
 
-    fvOptions.constrain(he1Eqn);
-    he1Eqn.solve();
+    fvOptions.constrain(E1Eqn);
+    E1Eqn.solve();
 
-    fvOptions.constrain(he2Eqn);
-    he2Eqn.solve();
+    fvOptions.constrain(E2Eqn);
+    E2Eqn.solve();
 
     thermo1.correct();
     Info<< "min " << thermo1.T().name()