Ideal Gas Material - Revision history

Nairnj: /* Material Properties */

2025-11-07T17:27:40Z

Material Properties

← Older revision		Revision as of 17:27, 7 November 2025
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	\| mu0 \|\| Enter reference gas viscosity <math>\mu_0</math> (only used when <math>\mu_0\gt0</math>) \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|(length units)]] \|\| 0		\| mu0 \|\| Enter reference gas viscosity <math>\mu_0</math> (only used when <math>\mu_0\gt0</math>) \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|(length units)]] \|\| 0
	\|-		\|-
	\| Smu \|\| Enter Sutherland's temperature (only used when <math>\mu_0\gt0</math>) \|\| ~~(see description)~~ \|\| 111		\| Smu \|\| Enter Sutherland's temperature (only used when <math>\mu_0\gt0</math>) \|\| Degrees C \|\| 111
	\|-		\|-
	\| Cv \|\| Instead of heat capacity, this parameter determines if the gas is monatomic or diatomic. Enter 1 (or any number smaller than 1) for monatomic or 2 (or any number larger than 2) for diatomic. The resulting heat capacity is described [[#Heat Capacity and Thermal Expansion Coefficient\|below]] \|\| none \|\| 1		\| Cv \|\| Instead of heat capacity, this parameter determines if the gas is monatomic or diatomic. Enter 1 (or any number smaller than 1) for monatomic or 2 (or any number larger than 2) for diatomic. The resulting heat capacity is described [[#Heat Capacity and Thermal Expansion Coefficient\|below]] \|\| none \|\| 1

Nairnj: /* Material Properties */

2025-11-07T17:26:35Z

Material Properties

← Older revision		Revision as of 17:26, 7 November 2025
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	\| vdwb \|\| Enter the van der Waals ''b'' property (setting this property sets code to use van der Waals gas law). The units are [[ConsistentUnits Command#Legacy and Consistent Units\|(length units)]]<sup>3</sup>/mole \|\| (see description) \|\| none		\| vdwb \|\| Enter the van der Waals ''b'' property (setting this property sets code to use van der Waals gas law). The units are [[ConsistentUnits Command#Legacy and Consistent Units\|(length units)]]<sup>3</sup>/mole \|\| (see description) \|\| none
	\|-		\|-
	\| mu0 \|\| Enter reference gas viscosity <math>\mu_0</math> ~~The units are~~ [[ConsistentUnits Command#Legacy and Consistent Units\|(length units)]]~~<sup>3</sup>/mole \|\| (see description)~~ \|\| ~~none~~		\| mu0 \|\| Enter reference gas viscosity <math>\mu_0</math> (only used when <math>\mu_0\gt0</math>) \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|(length units)]] \|\| 0
	\|-		\|-
	\| Smu \|\| Enter Sutherland's temperature ~~in degrees C~~ (only used when <math>\mu_0\gt0</math> \|\| (see description) \|\| ~~none~~		\| Smu \|\| Enter Sutherland's temperature (only used when <math>\mu_0\gt0</math>) \|\| (see description) \|\| 111
	\|-		\|-
	\| Cv \|\| Instead of heat capacity, this parameter determines if the gas is monatomic or diatomic. Enter 1 (or any number smaller than 1) for monatomic or 2 (or any number larger than 2) for diatomic. The resulting heat capacity is described [[#Heat Capacity and Thermal Expansion Coefficient\|below]] \|\| none \|\| 1		\| Cv \|\| Instead of heat capacity, this parameter determines if the gas is monatomic or diatomic. Enter 1 (or any number smaller than 1) for monatomic or 2 (or any number larger than 2) for diatomic. The resulting heat capacity is described [[#Heat Capacity and Thermal Expansion Coefficient\|below]] \|\| none \|\| 1

Nairnj: /* Material Properties */

2025-11-07T17:23:04Z

Material Properties

← Older revision		Revision as of 17:23, 7 November 2025
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	\|-		\|-
	\| vdwb \|\| Enter the van der Waals ''b'' property (setting this property sets code to use van der Waals gas law). The units are [[ConsistentUnits Command#Legacy and Consistent Units\|(length units)]]<sup>3</sup>/mole \|\| (see description) \|\| none		\| vdwb \|\| Enter the van der Waals ''b'' property (setting this property sets code to use van der Waals gas law). The units are [[ConsistentUnits Command#Legacy and Consistent Units\|(length units)]]<sup>3</sup>/mole \|\| (see description) \|\| none
			\|-
			\| mu0 \|\| Enter reference gas viscosity <math>\mu_0</math> The units are [[ConsistentUnits Command#Legacy and Consistent Units\|(length units)]]<sup>3</sup>/mole \|\| (see description) \|\| none
			\|-
			\| Smu \|\| Enter Sutherland's temperature in degrees C (only used when <math>\mu_0\gt0</math> \|\| (see description) \|\| none
	\|-		\|-
	\| Cv \|\| Instead of heat capacity, this parameter determines if the gas is monatomic or diatomic. Enter 1 (or any number smaller than 1) for monatomic or 2 (or any number larger than 2) for diatomic. The resulting heat capacity is described [[#Heat Capacity and Thermal Expansion Coefficient\|below]] \|\| none \|\| 1		\| Cv \|\| Instead of heat capacity, this parameter determines if the gas is monatomic or diatomic. Enter 1 (or any number smaller than 1) for monatomic or 2 (or any number larger than 2) for diatomic. The resulting heat capacity is described [[#Heat Capacity and Thermal Expansion Coefficient\|below]] \|\| none \|\| 1

Nairnj: /* Gas Viscosity */

2025-11-07T17:19:49Z

Gas Viscosity

← Older revision		Revision as of 17:19, 7 November 2025
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	<math> \vec \tau = 2\~~eta~~(T) {\rm dev}({\bf D})		<math> \vec \tau = 2\mu(T) {\rm dev}({\bf D})
	\qquad{\rm where} \qquad		\qquad{\rm where} \qquad
	\~~eta~~(T) = \~~eta_0~~ \left(\frac{T}{T_0}\right)^{3/2} \frac{T_0+S}{T+S}		\mu(T) = \mu_0 \left(\frac{T}{T_0}\right)^{3/2} \frac{T_0+S_\mu}{T+S_\mu}
	</math>		</math>

	where '''D''' is rate of deformation tensor, 2 converts to engineering shear strain rate, <math>\~~eta_0~~</math> is a reference viscosity, and <math>S</math> is Sutherland's temperature. For example, air has <math>\eta_0=1.76\times10^{-5}</math> Pa sec and ~~''S''~~ = 111 for reference temperature ''T''<sub>0</sub>=273K.		where '''D''' is rate of deformation tensor, 2 converts to engineering shear strain rate, <math>\mu_0</math> is a reference viscosity, and <math>S_\mu</math> is Sutherland's temperature. For example, air has <math>\eta_0=1.76\times10^{-5}</math> Pa sec and <math>S_\mu=111</math> for reference temperature ''T''<sub>0</sub>=273K.

	== Isothermal and Adiabatic Modes ==		== Isothermal and Adiabatic Modes ==

Nairnj: /* Gas Viscosity */

2025-11-07T17:17:24Z

Gas Viscosity

← Older revision		Revision as of 17:17, 7 November 2025
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	</math>		</math>

	where '''D''' is rate of deformation tensor, 2 converts to engineering shear strain rate, <math>\eta_0</math> is a reference viscosity, and <math>S</math> is Sutherland's temperature. For example, air has <math>\eta_0=1.76\times10^{-5}</math> Pa sec and ''S''=111 for reference temperature ''T''<sub>0</sub>=273K.		where '''D''' is rate of deformation tensor, 2 converts to engineering shear strain rate, <math>\eta_0</math> is a reference viscosity, and <math>S</math> is Sutherland's temperature. For example, air has <math>\eta_0=1.76\times10^{-5}</math> Pa sec and ''S'' = 111 for reference temperature ''T''<sub>0</sub>=273K.

	== Isothermal and Adiabatic Modes ==		== Isothermal and Adiabatic Modes ==

Nairnj: /* Gas Viscosity */

2025-11-07T17:16:46Z

Gas Viscosity

← Older revision		Revision as of 17:16, 7 November 2025
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	<math> \vec \tau = 2\eta(T) {\rm dev}(\~~tens~~ D)		<math> \vec \tau = 2\eta(T) {\rm dev}({\bf D})
	\qquad{\rm where} \qquad		\qquad{\rm where} \qquad
	\eta(T) = \eta_0 \left(\frac{T}{T_0}\right)^{3/2} \frac{T_0+S}{T+S}		\eta(T) = \eta_0 \left(\frac{T}{T_0}\right)^{3/2} \frac{T_0+S}{T+S}
	</math>		</math>

	where <math>\eta_0</math> is a reference viscosity and <math>S</math> is Sutherland's temperature. For example, air has <math>\eta_0=1.76\times10^{-5}</math> Pa sec and ''S''=111 for reference temperature ''T''<sub>0</sub>=273K.		where '''D''' is rate of deformation tensor, 2 converts to engineering shear strain rate, <math>\eta_0</math> is a reference viscosity, and <math>S</math> is Sutherland's temperature. For example, air has <math>\eta_0=1.76\times10^{-5}</math> Pa sec and ''S''=111 for reference temperature ''T''<sub>0</sub>=273K.

	== Isothermal and Adiabatic Modes ==		== Isothermal and Adiabatic Modes ==

Nairnj: /* Reference State */

2025-11-07T17:15:15Z

Reference State

← Older revision		Revision as of 17:15, 7 November 2025
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	For example, air might have reference pressure of 1 atm = 0.101325 MPa, <math>M_g=28.97</math> g/mol at room temperature ''T''<sub>0</sub>=300K with ''R'' = 8.3144621 J/k/mol leading to <math>\rho_0=0.001176</math> g/cm<sup>3</sup>. This calculation assumed an ideal gas (where <math>P_0'=P_0</math>). Calculations for density of a van der Waals gas differ only slightly from density found by ideal gas law calculations.		For example, air might have reference pressure of 1 atm = 0.101325 MPa, <math>M_g=28.97</math> g/mol at room temperature ''T''<sub>0</sub>=300K with ''R'' = 8.3144621 J/k/mol leading to <math>\rho_0=0.001176</math> g/cm<sup>3</sup>. This calculation assumed an ideal gas (where <math>P_0'=P_0</math>). Calculations for density of a van der Waals gas differ only slightly from density found by ideal gas law calculations.

			== Gas Viscosity ==

			For dynamic simulations, this material implement gas velocity where deviatoric stress, which adds to pressure stress, is given by


			<math> \vec \tau = 2\eta(T) {\rm dev}(\tens D)
			\qquad{\rm where} \qquad
			\eta(T) = \eta_0 \left(\frac{T}{T_0}\right)^{3/2} \frac{T_0+S}{T+S}
			</math>

			where <math>\eta_0</math> is a reference viscosity and <math>S</math> is Sutherland's temperature. For example, air has <math>\eta_0=1.76\times10^{-5}</math> Pa sec and ''S''=111 for reference temperature ''T''<sub>0</sub>=273K.

	== Isothermal and Adiabatic Modes ==		== Isothermal and Adiabatic Modes ==

Nairnj: /* Reference State */

2025-11-07T00:40:23Z

Reference State

← Older revision		Revision as of 00:40, 7 November 2025
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	<math>\rho_0 = {P_0' M_g\over R T_0}</math>		<math>\rho_0 = {P_0' M_g\over R T_0} \qquad{\rm where}\qquad
			P_0' = \left(P_0+a'\right)\left(1-b'\right)</math>

	For example, air might have reference pressure of 1 atm = 0.101325 MPa, <math>M_g=28.97</math> g/mol at room temperature ''T''<sub>0</sub>=300K with ''R'' = 8.3144621 J/k/mol leading to <math>\rho_0=0.001176</math> g/cm<sup>3</sup>. This calculation assumed an ideal gas (where <math>P_0'=P_0</math>). Calculations for density of a van der Waals gas differ only slightly from density found by ideal gas law calculations.		For example, air might have reference pressure of 1 atm = 0.101325 MPa, <math>M_g=28.97</math> g/mol at room temperature ''T''<sub>0</sub>=300K with ''R'' = 8.3144621 J/k/mol leading to <math>\rho_0=0.001176</math> g/cm<sup>3</sup>. This calculation assumed an ideal gas (where <math>P_0'=P_0</math>). Calculations for density of a van der Waals gas differ only slightly from density found by ideal gas law calculations.

Nairnj: /* Reference State */

2025-11-06T01:43:24Z

Reference State

← Older revision		Revision as of 01:43, 6 November 2025
Line 72:		Line 72:
	<math>\rho_0 = {P_0' M_g\over R T_0}</math>		<math>\rho_0 = {P_0' M_g\over R T_0}</math>

	For example, air might have reference pressure of 1 atm = 0.101325 MPa, <math>M_g=28.97</math> g/mol at room temperature ''T''<sub>0</sub>=300K with ''R'' = 8.3144621 J/k/mol leading to <math>\rho_0=0.001176</math> g/cm<sup>3</sup>. This calculation assumed an ideal gas (where <math>P_0'=P_0</math>). Calculations for density of a van der Waals gas differ only ~~slight~~ from density found by ideal gas law calculations.		For example, air might have reference pressure of 1 atm = 0.101325 MPa, <math>M_g=28.97</math> g/mol at room temperature ''T''<sub>0</sub>=300K with ''R'' = 8.3144621 J/k/mol leading to <math>\rho_0=0.001176</math> g/cm<sup>3</sup>. This calculation assumed an ideal gas (where <math>P_0'=P_0</math>). Calculations for density of a van der Waals gas differ only slightly from density found by ideal gas law calculations.

	== Isothermal and Adiabatic Modes ==		== Isothermal and Adiabatic Modes ==

Nairnj: /* Reference State */

2025-11-06T01:42:47Z

Reference State

← Older revision		Revision as of 01:42, 6 November 2025
Line 72:		Line 72:
	<math>\rho_0 = {P_0' M_g\over R T_0}</math>		<math>\rho_0 = {P_0' M_g\over R T_0}</math>

	For example, air might have reference pressure of 1 atm = 0.101325 MPa, <math>M_g=28.97</math> g/mol at room temperature ''T''<sub>0</sub>=300K with ''R'' = 8.3144621 J/k/mol leading to <math>\rho_0=0.001176</math> g/cm<sup>2</sup>. This calculation assumed an ideal gas (where <math>P_0'=P_0</math>). Calculations for density of a van der Waals gas differ only slight from density found by ideal gas law calculations.		For example, air might have reference pressure of 1 atm = 0.101325 MPa, <math>M_g=28.97</math> g/mol at room temperature ''T''<sub>0</sub>=300K with ''R'' = 8.3144621 J/k/mol leading to <math>\rho_0=0.001176</math> g/cm<sup>3</sup>. This calculation assumed an ideal gas (where <math>P_0'=P_0</math>). Calculations for density of a van der Waals gas differ only slight from density found by ideal gas law calculations.

	== Isothermal and Adiabatic Modes ==		== Isothermal and Adiabatic Modes ==