PengRobinsonEoS.h

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///////////////////////////////////////////////////////////////////////////////
//
// File: PengRobinsonEoS.h
//
// For more information, please see: http://www.nektar.info
//
// The MIT License
//
// Copyright (c) 2006 Division of Applied Mathematics, Brown University (USA),
// Department of Aeronautics, Imperial College London (UK), and Scientific
// Computing and Imaging Institute, University of Utah (USA).
//
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included
// in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
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//
// Description: Peng-Robinson equation of state
//
///////////////////////////////////////////////////////////////////////////////
 
#ifndef NEKTAR_SOLVERS_COMPRESSIBLEFLOWSOLVER_MISC_PENGROBINSONEOS
#define NEKTAR_SOLVERS_COMPRESSIBLEFLOWSOLVER_MISC_PENGROBINSONEOS
 
#include "EquationOfState.h"
 
namespace Nektar
{
 
/**
 * @brief Peng-Robinson equation of state:
 *       p = RT/(1/rho - b) - a*Alpha(T/Tc) / (1/rho^2 + 2*b/rho - b^2)
 *       with a = 0.45724 * (R*Tc)^2 / Pc
 *            b = 0.0778 * (R*Tc) / Pc
 *            Alpha(T/Tc) = [1 + fw * (1 - sqrt(T/ Tc))]^2
 *            fw = 0.37464 + 1.54226*omega - 0.2699*omega*omega
 */
class PengRobinsonEoS : public EquationOfState
{
public:
    friend class MemoryManager<PengRobinsonEoS>;
 
    /// Creates an instance of this class
    static EquationOfStateSharedPtr create(
        const LibUtilities::SessionReaderSharedPtr &pSession)
    {
        EquationOfStateSharedPtr p =
            MemoryManager<PengRobinsonEoS>::AllocateSharedPtr(pSession);
        return p;
    }
 
    /// Name of the class
    static std::string className;
 
protected:
    NekDouble m_a;
    NekDouble m_b;
    NekDouble m_Tc;
    NekDouble m_Pc;
    NekDouble m_omega;
    NekDouble m_fw;
 
    NekDouble GetTemperature(const NekDouble &rho, const NekDouble &e) final;
 
    vec_t GetTemperature(const vec_t &rho, const vec_t &e) final;
 
    NekDouble GetPressure(const NekDouble &rho, const NekDouble &e) final;
 
    vec_t GetPressure(const vec_t &rho, const vec_t &e) final;
 
    NekDouble v_GetEntropy(const NekDouble &rho, const NekDouble &e) final;
 
    NekDouble v_GetDPDrho_e(const NekDouble &rho, const NekDouble &e) final;
 
    NekDouble v_GetDPDe_rho(const NekDouble &rho, const NekDouble &e) final;
 
    NekDouble v_GetEFromRhoP(const NekDouble &rho, const NekDouble &p) final;
 
    NekDouble v_GetRhoFromPT(const NekDouble &rho, const NekDouble &p) final;
 
private:
    PengRobinsonEoS(const LibUtilities::SessionReaderSharedPtr &pSession);
 
    ~PengRobinsonEoS(void){};
 
    // Alpha term of Peng-Robinson EoS
    template <class T, typename = typename std::enable_if<
                           std::is_floating_point<T>::value ||
                           tinysimd::is_vector_floating_point<T>::value>::type>
    inline T Alpha(const T &temp)
    {
        T sqrtAlpha = 1.0 + m_fw * (1.0 - sqrt(temp / m_Tc));
        return sqrtAlpha * sqrtAlpha;
    }
 
    // Log term term of Peng-Robinson EoS
    template <class T, typename = typename std::enable_if<
                           std::is_floating_point<T>::value ||
                           tinysimd::is_vector_floating_point<T>::value>::type>
    inline T LogTerm(const T &rho)
    {
        return log((1.0 / rho + m_b - m_b * sqrt(2)) /
                   (1.0 / rho + m_b + m_b * sqrt(2)));
    }
 
    template <class T, typename = typename std::enable_if<
                           std::is_floating_point<T>::value ||
                           tinysimd::is_vector_floating_point<T>::value>::type>
    inline T GetTemperatureKernel(const T &rho, const T &e)
    {
        // First we need to evaluate the log term
        //    ln[(1/rho + b - b*sqrt(2)) / (1/rho + b + b*sqrt(2))]
        NekDouble sqrt2 = sqrt(2.0);
        T logTerm       = LogTerm(rho);
 
        // The temperature can be expressed as an equation in the form
        //      A * (T^1/2)^2 + B * T^1/2 + C = 0
 
        NekDouble A  = m_gasConstant / (m_gamma - 1.0);
        NekDouble f1 = m_a / (m_b * 2.0 * sqrt2);
        NekDouble f2 = (1.0 + m_fw);
        T B          = -f1 * logTerm / sqrt(m_Tc) * m_fw * f2;
        T C          = f1 * logTerm * f2 * f2 - e;
 
        // Solve for T^1/2 (positive root)
        T sqrtT = (sqrt(B * B - 4 * A * C) - B) / (2 * A);
        // Calculate the temperature
        return sqrtT * sqrtT;
    }
 
    template <class T, typename = typename std::enable_if<
                           std::is_floating_point<T>::value ||
                           tinysimd::is_vector_floating_point<T>::value>::type>
    inline T GetPressureKernel(const T &rho, const T &e)
    {
        T temp    = GetTemperatureKernel(rho, e);
        T oneOrho = 1.0 / rho;
        T p       = m_gasConstant * temp / (oneOrho - m_b) -
              m_a * Alpha(temp) /
                  (oneOrho * oneOrho + 2.0 * m_b * oneOrho - m_b * m_b);
 
        return p;
    }
};
} // namespace Nektar
 
#endif