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applications/utilities/preProcessing/wallFunctionTable/tabulatedWallFunction/SpaldingsLaw/SpaldingsLaw.C

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+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | Copyright (C) 2011 OpenFOAM Foundation
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+    for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
+
+\*---------------------------------------------------------------------------*/
+
+#include "SpaldingsLaw.H"
+#include "addToRunTimeSelectionTable.H"
+
+// * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
+
+namespace Foam
+{
+    namespace tabulatedWallFunctions
+    {
+        defineTypeNameAndDebug(SpaldingsLaw, 0);
+        addToRunTimeSelectionTable
+        (
+            tabulatedWallFunction,
+            SpaldingsLaw,
+            dictionary
+        );
+    }
+}
+
+const Foam::label Foam::tabulatedWallFunctions::SpaldingsLaw::maxIters_ = 1000;
+
+const Foam::scalar
+    Foam::tabulatedWallFunctions::SpaldingsLaw::tolerance_ = 1e-4;
+
+
+// * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * * //
+
+void Foam::tabulatedWallFunctions::SpaldingsLaw::invertFunction()
+{
+    // Initialise u+ and R
+    scalar Re = 0.0;
+    scalar uPlus = 1;
+
+    // Populate the table
+    forAll(invertedTable_, i)
+    {
+        if (invertedTable_.log10())
+        {
+            Re = pow(10, (i*invertedTable_.dx() + invertedTable_.x0()));
+        }
+        else
+        {
+            Re = i*invertedTable_.dx() + invertedTable_.x0();
+        }
+
+        // Use latest available u+ estimate
+        if (i > 0)
+        {
+            uPlus = invertedTable_[i-1];
+        }
+
+        // Newton iterations to determine u+
+        label iter = 0;
+        scalar error = GREAT;
+        do
+        {
+            scalar kUPlus = min(kappa_*uPlus, 50);
+            scalar A =
+                E_*sqr(uPlus)
+              + uPlus
+               *(exp(kUPlus) - pow3(kUPlus)/6 - 0.5*sqr(kUPlus) - kUPlus - 1);
+
+            scalar f = - Re + A/E_;
+
+            scalar df =
+                (
+                    2*E_*uPlus
+                  + exp(kUPlus)*(kUPlus + 1)
+                  - 2/3*pow3(kUPlus)
+                  - 1.5*sqr(kUPlus)
+                  - 2*kUPlus
+                  - 1
+                )/E_;
+
+            scalar uPlusNew = uPlus - f/(df + ROOTVSMALL);
+            error = mag((uPlus - uPlusNew)/uPlusNew);
+            uPlus = uPlusNew;
+        } while (error > tolerance_ && ++iter < maxIters_);
+
+        if (iter == maxIters_)
+        {
+            WarningIn("SpaldingsLaw::invertFunction()")
+                << "Newton iterations not converged:" << nl
+                << "    iters = " << iter << ", error = " << error << endl;
+        }
+
+        // Set new values - constrain u+ >= 0
+        invertedTable_[i] = max(0, uPlus);
+    }
+}
+
+
+// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
+
+Foam::tabulatedWallFunctions::SpaldingsLaw::SpaldingsLaw
+(
+    const dictionary& dict,
+    const polyMesh& mesh
+)
+:
+    tabulatedWallFunction(dict, mesh, typeName),
+    kappa_(readScalar(coeffDict_.lookup("kappa"))),
+    E_(readScalar(coeffDict_.lookup("E")))
+{
+    invertFunction();
+
+    if (debug)
+    {
+        writeData(Info);
+    }
+}
+
+
+// * * * * * * * * * * * * * * * * Destructor  * * * * * * * * * * * * * * * //
+
+Foam::tabulatedWallFunctions::SpaldingsLaw::~SpaldingsLaw()
+{}
+
+
+// * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * * //
+
+Foam::scalar Foam::tabulatedWallFunctions::SpaldingsLaw::yPlus
+(
+    const scalar uPlus
+) const
+{
+    scalar kUPlus = min(kappa_*uPlus, 50);
+
+    return
+        uPlus
+      + 1/E_*(exp(kUPlus) - pow3(kUPlus)/6 - 0.5*sqr(kUPlus) - kUPlus - 1);
+}
+
+
+Foam::scalar Foam::tabulatedWallFunctions::SpaldingsLaw::Re
+(
+    const scalar uPlus
+) const
+{
+    return uPlus*yPlus(uPlus);
+}
+
+
+void Foam::tabulatedWallFunctions::SpaldingsLaw::writeData(Ostream& os) const
+{
+    if (invertedTable_.log10())
+    {
+        os  << "log10(Re), y+, u+:" << endl;
+        forAll(invertedTable_, i)
+        {
+            scalar uPlus = invertedTable_[i];
+            scalar Re = ::log10(this->Re(uPlus));
+            scalar yPlus = this->yPlus(uPlus);
+            os  << Re << ", " << yPlus << ", " << uPlus << endl;
+        }
+    }
+    else
+    {
+        os  << "Re, y+, u+:" << endl;
+        forAll(invertedTable_, i)
+        {
+            scalar uPlus = invertedTable_[i];
+            scalar Re = this->Re(uPlus);
+            scalar yPlus = this->yPlus(uPlus);
+            os  << Re << ", " << yPlus << ", " << uPlus << endl;
+        }
+    }
+}
+
+
+// ************************************************************************* //

applications/utilities/preProcessing/wallFunctionTable/tabulatedWallFunction/SpaldingsLaw/SpaldingsLaw.H

@@ -0,0 +1,139 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | Copyright (C) 2011 OpenFOAM Foundation
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+    for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
+
+Class
+    Foam::tabulatedWallFunctions::SpaldingsLaw
+
+Description
+    Computes U+ as a function of Reynolds number by inverting Spaldings law.
+
+    Example dictionary specification:
+
+        tabulatedWallFunction SpaldingsLaw;
+
+        // Output table info
+        tableName       uPlusWallFunctionData; // Output table name
+        log10           yes;                // Rey interpreted as log10(Rey)
+        dx              0.2;                // Interval log10(Rey)
+        x0              -3;                 // Minimum log10(Rey)
+        xMax            7;                  // Maximum log10(Rey)
+
+        SpaldingsLawCoeffs
+        {
+            kappa           0.41;           // Von Karman constant
+            E               9.8;            // Law-of-the-wall E coefficient
+        }
+
+
+SourceFiles
+    SpaldingsLaw.C
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef SpaldingsLaw_H
+#define SpaldingsLaw_H
+
+#include "tabulatedWallFunction.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+namespace tabulatedWallFunctions
+{
+
+/*---------------------------------------------------------------------------*\
+                        Class SpaldingsLaw Declaration
+\*---------------------------------------------------------------------------*/
+
+class SpaldingsLaw
+:
+    public tabulatedWallFunction
+{
+protected:
+
+    // Protected data
+
+        //- Von Karman constant
+        scalar kappa_;
+
+        //- Law-of-the-wall E coefficient
+        scalar E_;
+
+
+        // Newton iteration solution properties
+
+            //- Maximum number of iterations
+            static const label maxIters_;
+
+            //- Tolerance
+            static const scalar tolerance_;
+
+
+    // Protected Member Functions
+
+        //- Invert the function
+        virtual void invertFunction();
+
+
+public:
+
+    //- Run-time type information
+    TypeName("SpaldingsLaw");
+
+
+    // Constructors
+    SpaldingsLaw(const dictionary& dict, const polyMesh& mesh);
+
+    //- Destructor
+    virtual ~SpaldingsLaw();
+
+
+    // Member Functions
+
+        // Access
+
+            //- Return y+ as a function of u+
+            virtual scalar yPlus(const scalar uPlus) const;
+
+            //- Return Reynolds number as a function of u+
+            virtual scalar Re(const scalar uPlus) const;
+
+
+        // I-O
+
+            //- Write to Ostream
+            virtual void writeData(Ostream& os) const;
+};
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace tabulatedWallFunctions
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //