GaPFlow.models.sound

GaPFlow.models.sound#

Equation of state (sound speed).

Sound speed-density relations for the implemented models.

Functions

bayada_chupin(rho, rho_l, rho_v, c_l, c_v)

Computes the isothermal speed of sound using the Bayada-Chupin cavitation model.

bwr(rho, T[, gamma])

Computes the speed of sound using the Benedict–Webb–Rubin (BWR) equation of state.

cubic(dens[, a, b, c, d])

Computes the speed of sound from a cubic polynomial pressure law.

dowson_higginson(dens[, rho0, P0, C1, C2])

Computes the isothermal speed of sound using the Dowson-Higginson equation of state.

eos_sound_velocity(density, prop)

Wrapper around all implemented equation of state models.

murnaghan_tait(dens[, rho0, P0, K, n])

Computes the speed of sound from the Murnaghan-Tait equation of state.

power_law(dens[, rho0, P0, alpha])

Computes the isothermal speed of sound using a power-law equation of state.

van_der_waals(dens[, M, T, a, b])

Computes the speed of sound using the Van der Waals equation of state.
GaPFlow.models.sound.bayada_chupin(rho, rho_l, rho_v, c_l, c_v)#

Computes the isothermal speed of sound using the Bayada-Chupin cavitation model.

Parameters:

  • rho (float or np.ndarray) – Density.

  • rho_l (float) – Liquid density.

  • rho_v (float) – Vapor density.

  • c_l (float) – Speed of sound in liquid.

  • c_v (float) – Speed of sound in vapor.

Returns:

Speed of sound.

Return type:

float or np.ndarray

GaPFlow.models.sound.bwr(rho, T, gamma=3.0)#

Computes the speed of sound using the Benedict–Webb–Rubin (BWR) equation of state.

Parameters:

  • rho (float or np.ndarray) – Density.

  • T (float) – Temperature.

  • gamma (float, optional) – Exponential decay parameter (default is 3.0).

Returns:

Speed of sound.

Return type:

float or np.ndarray

GaPFlow.models.sound.cubic(dens, a=15.2, b=-9.6, c=3.35, d=-0.07)#

Computes the speed of sound from a cubic polynomial pressure law.

\[c = \sqrt{\frac{dp}{d\rho}} = \sqrt{3a \rho^2 + 2b \rho + c}\]
Parameters:

  • dens (float or np.ndarray) – Density.

  • a (float) – Polynomial coefficients.

  • b (float) – Polynomial coefficients.

  • c (float) – Polynomial coefficients.

  • d (float) – Polynomial coefficients.

Returns:

Speed of sound.

Return type:

float or np.ndarray

GaPFlow.models.sound.dowson_higginson(dens, rho0=877.7007, P0=101325.0, C1=350000000.0, C2=1.23)#

Computes the isothermal speed of sound using the Dowson-Higginson equation of state.

\[c = \sqrt{\frac{dp}{d\rho}} = \sqrt{\frac{C_1 \rho_0 (C_2 - 1)}{\rho^2 (C_2 \rho_0 / \rho - 1)^2}}\]
Parameters:

  • dens (float or np.ndarray) – Current density.

  • rho0 (float) – Reference density.

  • P0 (float) – Reference pressure.

  • C1 (float) – Empirical constant.

  • C2 (float) – Empirical constant.

Returns:

Speed of sound.

Return type:

float or np.ndarray

GaPFlow.models.sound.eos_sound_velocity(density, prop)#

Wrapper around all implemented equation of state models.

Computes the local speed of sound for a given density field.

\[c = \sqrt{\frac{dp}{d\rho}}\]
Parameters:

  • density (np.ndarray) – The mass density field

  • prop (dict) – Material properties

Returns:

Sound speed field for the corresponding density field

Return type:

np.ndarray

GaPFlow.models.sound.murnaghan_tait(dens, rho0=700, P0=101000.0, K=557000000.0, n=7.33)#

Computes the speed of sound from the Murnaghan-Tait equation of state.

\[c = \sqrt{\frac{dp}{d\rho}} = \sqrt{\frac{K}{\rho_0^n} \rho^{n - 1}}\]
Parameters:

  • dens (float or np.ndarray) – Current density.

  • rho0 (float) – Reference density.

  • P0 (float) – Reference pressure.

  • K (float) – Bulk modulus.

  • n (float) – Murnaghan exponent.

Returns:

Speed of sound.

Return type:

float or np.ndarray

GaPFlow.models.sound.power_law(dens, rho0=1.1853, P0=101325.0, alpha=0.0)#

Computes the isothermal speed of sound using a power-law equation of state.

\[c = \sqrt{\frac{dp}{d\rho}} = \sqrt{\frac{-2 P_0}{(\alpha - 2) \rho} \left(\frac{\rho}{\rho_0}\right)^{-2 / (\alpha - 2)}}\]
Parameters:

  • dens (float or np.ndarray) – Density.

  • rho0 (float) – Reference density.

  • P0 (float) – Reference pressure.

  • alpha (float) – Power-law exponent.

Returns:

Speed of sound.

Return type:

float or np.ndarray

GaPFlow.models.sound.van_der_waals(dens, M=39.948, T=100.0, a=1.355, b=0.03201)#

Computes the speed of sound using the Van der Waals equation of state.

\[c = \sqrt{\frac{dp}{d\rho}} = \sqrt{\frac{RTM}{(M - b\rho)^2} - \frac{2a\rho}{M^2}}\]
Parameters:

  • dens (float or np.ndarray) – Mass density (kg/m³).

  • M (float) – Molar mass (g/mol).

  • T (float) – Temperature (K).

  • a (float) – Attraction parameter (L^2 bar/mol^2).

  • b (float) – Repulsion parameter (L/mol).

Returns:

Speed of sound.

Return type:

float or np.ndarray