dimensionlessnumbers.hh

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#ifndef DIMENSIONLESS_NUMBERS_HH
#define DIMENSIONLESS_NUMBERS_HH
 
#include <cmath>
#include <iostream>
 
#include <dune/common/exceptions.hh>
#include <dune/common/math.hh>
 
namespace Dumux {
 
enum class NusseltFormulation
{
    dittusBoelter, WakaoKaguei, VDI
};
 
enum class SherwoodFormulation
{
    WakaoKaguei
};
 
template <class Scalar>
class DimensionlessNumbers
{
 
public:
static Scalar reynoldsNumber(const Scalar darcyMagVelocity,
                             const Scalar charcteristicLength,
                             const Scalar kinematicViscosity)
{
    return darcyMagVelocity * charcteristicLength / kinematicViscosity ;
}
 
static Scalar prandtlNumber(const Scalar dynamicViscosity,
                            const Scalar heatCapacity,
                            const Scalar thermalConductivity)
{
    return dynamicViscosity * heatCapacity / thermalConductivity;
}
 
static Scalar nusseltNumberForced(const Scalar reynoldsNumber,
                                  const Scalar prandtlNumber,
                                  const Scalar porosity,
                                  NusseltFormulation formulation)
{
    if (formulation == NusseltFormulation::dittusBoelter){
       /* example: very common and simple case: flow straight circular pipe, only convection (no boiling),
        * 10000<Re<120000, 0.7<Pr<120, far from pipe entrance, smooth surface of pipe ...
        * Dittus, F.W and Boelter, L.M.K, Heat Transfer in Automobile Radiators of the Tubular Type,
        * Publications in Engineering, Vol. 2, pages 443-461, 1930
        */
       using std::pow;
       return 0.023 * pow(reynoldsNumber, 0.8) * pow(prandtlNumber,0.33);
    }
 
    else if (formulation == NusseltFormulation::WakaoKaguei){
        /* example: flow through porous medium *single phase*, fit to many different data
         * Wakao and Kaguei, Heat and mass Transfer in Packed Beds, Gordon and Breach Science Publishers, page 293
         */
        using std::pow;
        return 2. + 1.1 * pow(prandtlNumber,(1./3.)) * pow(reynoldsNumber, 0.6);
    }
 
    else if (formulation == NusseltFormulation::VDI){
       /* example: VDI Waermeatlas 10. Auflage 2006, flow in packed beds, page Gj1, see also other sources and limitations therein.
        * valid for 0.1<Re<10000, 0.6<Pr/Sc<10000, packed beds of perfect spheres.
        *
        */
        using std::sqrt;
        using std::pow;
        using Dune::power;
        Scalar numerator    = 0.037 * pow(reynoldsNumber,0.8) * prandtlNumber ;
        Scalar reToMin01    = pow(reynoldsNumber,-0.1);
        Scalar prTo23       = pow(prandtlNumber, (2./3. ) ) ; // MIND THE pts! :-( otherwise the integer exponent version is chosen
        Scalar denominator  = 1+ 2.443 * reToMin01 * (prTo23 -1.) ;
 
        Scalar nusseltTurbular       = numerator / denominator;
        Scalar nusseltLaminar        = 0.664 * sqrt(reynoldsNumber) * pow(prandtlNumber, (1./3.) );
        Scalar nusseltSingleSphere   = 2 + sqrt( power(nusseltLaminar,2) + power(nusseltTurbular,2));
 
        Scalar funckyFactor           = 1 + 1.5 * (1.-porosity); // for spheres of same size
        Scalar nusseltNumber          = funckyFactor * nusseltSingleSphere  ;
 
        return nusseltNumber;
    }
 
    else {
        DUNE_THROW(Dune::NotImplemented, "wrong index");
    }
}
 
 
static Scalar schmidtNumber(const Scalar dynamicViscosity,
                            const Scalar massDensity,
                            const Scalar diffusionCoefficient)
{
    return dynamicViscosity  / (massDensity * diffusionCoefficient);
}
 
static Scalar sherwoodNumber(const Scalar reynoldsNumber,
                             const Scalar schmidtNumber,
                             SherwoodFormulation formulation)
{
    if (formulation == SherwoodFormulation::WakaoKaguei){
        /* example: flow through porous medium *single phase*
         * Wakao and Kaguei, Heat and mass Transfer in Packed Beds, Gordon and Breach Science Publishers, page 156
         */
        using std::cbrt;
        using std::pow;
        return 2. + 1.1 * cbrt(schmidtNumber) * pow(reynoldsNumber, 0.6);
    }
 
    else {
        DUNE_THROW(Dune::NotImplemented, "wrong index");
    }
}
 
 
static Scalar thermalDiffusivity(const Scalar & thermalConductivity ,
                                  const Scalar & phaseDensity ,
                                  const Scalar & heatCapacity)
{
    return thermalConductivity / (phaseDensity * heatCapacity);
}
 
}; // end class DimensionlessNumbers
 
} // end namespace Dumux
 
#endif