関数IAPWS95_calculate_psi マニュアル

(The documentation of function IAPWS95_calculate_psi)

Last Update: 2023/9/20

◆機能・用途(Purpose)

残差項の計算式に登場する\(\psi\)とその導関数を計算する。関数IAPWS95_calculate_residual の内部で用いる補助関数である。
Compute \(\psi\) and its derivatives that appear in the equations of the residual part. This is a supplementary function used internally in function IAPWS95_calculate_residual.

◆形式(Format)

#include <IAPWS95/forward.h>
inline double IAPWS95_calculate_psi
(const double delta,const double tau,const int i,
const int Ndiff_delta,const int Ndiff_tau)

◆引数(Arguments)

delta	規格化した密度(\(\delta=\rho/\rho_c\))。 The normalized density (\(\delta=\rho/\rho_c\)).
tau	規格化した温度の逆数(\(\tau=T_c/T\))。 Inverse of the normalized temperature (\(\tau=T_c/T\)).
i	項の番号。残差項の計算式における\(i\)の値であり、55または56でなければならない。 The index of the term, i.e., the value of \(i\) in the equation of the residual term, which must be either 55 or 56.
Ndiff_delta	\(\delta\)での微分回数。「戻り値」の項目参照。 The number of differentiation by \(\delta\). See “Return value” section for more detail.
Ndiff_tau	\(\tau\)での微分回数。「戻り値」の項目参照。 The number of differentiation by \(\tau\). See “Return value” section for more detail.

◆戻り値(Return value)

指定した密度・温度および\(i\)の値に対応する \(\psi\)またはその導関数の値。引数Ndiff_delta, Ndiff_tauの値に応じて以下の量が計算される。
The value of \(\psi\) or its derivative for the given density, temperature, and the value of \(i\). The following quantities are computed depending on the values of arguments Ndiff_delta and Ndiff_tau.

Ndiff_delta	Ndiff_tau	計算する量 Quantity to compute	計算式(Wagner and Pruss (2002)の表6.5に基づく) The equation (based on Table 6.5 of Wagner and Pruss (2002))
0	0	\(\psi\)	\(\exp\left[-C_i(\delta-1)^2-D_i(\tau-1)^2\right]\)
1	0	\(\PartialDiff{\psi}{\delta}\)	\(-2C_i(\delta-1)\psi\)
2	0	\(\PartialDDiff{\psi}{\delta}\)	\([2C_i(\delta-1)^2-1]2C_i\psi\)
0	1	\(\PartialDiff{\psi}{\tau}\)	\(-2D_i(\tau-1)\psi\)
0	2	\(\PartialDDiff{\psi}{\tau}\)	\([2D_i(\tau-1)^2-1]2D_i\psi\)
1	1	\(\PartialCrossDiff{\psi}{\delta}{\tau}\)	\(4C_iD_i(\delta-1)(\tau-1)\psi\)

ここで\(C_i\), \(D_i\)は定数であり、 Wagner and Pruss (2002)の表6.2で以下のように与えられている。
Here, \(C_i\) and \(D_i\) are constants given as follows, based on Table 6.2 of Wagner and Pruss (2002).

\(i\)	\(C_i\)	\(D_i\)
55	28	700
56	32	800

◆使用例(Example)

const double rho=20.0;
const double T=600.0;
const int i=55;
double dpsi_ddelta=IAPWS95_calculate_psi (rho/IAPWS95_rhoc,IAPWS95_Tc/T,i,1,0);