Engee documentation

Rotational Mechanical Converter (G)

Interface between gas and mechanical rotating networks.

rotation mechanical converter (g)

Description

The Rotational Mechanical Converter (G) unit represents the interface (converter) between gas and mechanical rotational networks. The unit converts gas pressure into mechanical torque and vice versa. It can be used as a basis for gas drives and compressors.

The converter contains a variable volume of gas. The pressure and temperature vary according to the compressibility and heat capacity of the gas. The Mechanical orientation parameter allows you to specify whether an increase in gas volume causes the R port to rotate positively or negatively with respect to the C port.

Port A - gas port, corresponds to the inlet of the converter. Port H is a thermal port, related to the gas temperature inside the transmitter. Ports R and C are rotary mechanical ports corresponding to the shaft and the inverter housing.

Mass conservation

The mass conservation equation is similar to the equation for the Constant Volume Chamber (G) unit with an additional term related to the change in gas volume:

ρ ,

where:

  • - is the partial derivative of the mass of gas in terms of pressure at constant temperature and volume.

  • - is the partial derivative of the gas mass by temperature at constant pressure and volume.

  • - gas pressure. The pressure at port A is assumed to be equal to this pressure, .

  • - gas temperature. The temperature at port H is assumed to be equal to this temperature, .

  • ρ - gas density.

  • - volume of the gas.

  • - time.

  • - mass flow rate at port A. The flow rate through the port is positive if the gas flows into the block.

Energy balance

The energy balance equation relates the energy and heat expenditure to the pressure and temperature dynamics of an internal unit representing a volume of gas:

ρ ,

where:

  • - is the partial derivative of the internal energy of the gas in terms of pressure at constant temperature and volume.

  • - is the partial derivative of the internal energy on temperature at constant pressure and volume.

  • - energy flow rate at port A.

  • - heat flow rate at port H.

  • - specific enthalpy of gas.

Partial derivatives for ideal and semi-ideal gas models

The partial derivatives of the mass M and internal energy U of a gas in terms of pressure and temperature at constant volume depend on the model properties of the gas. For the ideal and semi-ideal gas models, the equations are as follows:

ρ

ρ

ρ

Where:

  • ρ - is the density of the gas.

  • - is the volume of the gas.

  • - specific enthalpy of a gas.

  • - compressibility coefficient.

  • - universal gas constant.

  • - specific heat capacity at constant gas pressure.

Partial derivatives for the real gas model

For the real gas model, the partial derivatives of the mass M and internal energy U of the gas with respect to pressure and temperature at constant volume are equal:

ρβ

ρα

ρβα

ρα

Where:

  • β - isothermal volume modulus of gas compression.

  • α - isobaric coefficient of thermal expansion of gas.

Gas volume

The volume of gas depends on the rotation of the rotor:

θε

Where:

  • - dead volume.

  • - rotor displacement (gas part of the transducer).

  • θ - shaft rotation angle (mechanical part of the converter).

  • ε - Transducer orientation. If Mechanical orientation is set to Pressure at A causes positive rotation of R relative to C, then ε . If the Mechanical orientation parameter is set to Pressure at A causes negative rotation of R relative to C then ε .

  • If the Mechanical orientation parameter is set to Pressure at A causes positive rotation of R relative to C, the shaft rotation angle increases when the gas volume increases from dead volume.

  • If Mechanical orientation is set to Pressure at A causes negative rotation of R relative to C, the shaft angle decreases when the gas volume increases from dead volume.

Torque balance

Torque balance:

τε ,

where:

  • τ - torque from port R to port C.

  • - ambient pressure.

Assumptions and limitations

  • The transmitter housing is absolutely rigid.

  • There is no flow resistance between port A and the inside of the transmitter.

  • There is no thermal resistance between port H and the inside of the transmitter.

  • There are no gas leaks.

  • The unit does not simulate mechanical effects such as hard stopping, friction and inertia.

Ports

Input

A - gas inlet
gas

Gas port, corresponds to the inverter input.

H - temperature inside the transmitter
heat

Heat port, related to the gas temperature inside the converter.

R - stem
`rotational mechanics

Mechanical rotational port, corresponds to a shaft.

C - housing
`rotational mechanics

Mechanical rotational port, corresponds to the hull.

Parameters

Mechanical orientation - Transducer orientation
Pressure at A causes positive rotation of R relative to C (by default) | `Pressure at A causes negative rotation of R relative `

Sets the orientation of the mechanical part motion with respect to the gas volume change:

  • Pressure at A causes positive rotation of R relative to C - increase in gas volume causes positive rotation of port R relative to port C.

  • `Pressure at A causes negative rotation of R relative to C' - an increase in gas volume causes negative rotation of port R relative to port C.

Initial interface rotation, rad - initial angular position of port R relative to port C
0.0 (By default)

Initial angular position of port R relative to port C. The value 0 corresponds to the initial gas volume equal to Dead volume.

Dependencies

  • If Mechanical orientation has the value Pressure at A causes positive rotation of R relative to C, the parameter value must be greater than or equal to 0.

  • If Mechanical orientation has the value Pressure at A causes negative rotation of R relative to C, the parameter value must be less than or equal to 0.

Interface volume displacement, m³/rad - volume of displaced gas per unit revolution
0.01 m³/rad (by default).

Volume of displaced gas per unit revolution of the mechanical part of the transmitter.

Dead volume, m³ - volume of gas at zero angle of rotation of the mechanical part
1e-5 m³ (by default).

Gas volume in the converter at the mechanical part rotation angle equal to 0.

Cross-sectional area at port A, m² - area normal to the flow cross-section at the inlet to the converter
0.01 m² (by default).

The cross-sectional area of the transmitter inlet port in the direction normal to the gas flow path.

Environment pressure specification - method of setting the ambient pressure
Atmospheric pressure (by default) | Specified pressure.

Specifies the way of specifying the ambient pressure:

  • `Atmospheric pressure' is the atmospheric pressure set by the Gas Properties (G) block connected to the circuit.

  • Specified pressure - the exact value from the Environment pressure parameter.

Environment pressure, Pa - pressure outside the transmitter
0.101325 MPa (by default).

Pressure outside the converter, counteracting the pressure of the converter gas volume. The value 0 indicates that the converter is operating in vacuum.

Dependencies

Available when Environment pressure specification is set to Specified pressure.

Initial pressure of gas volume, Pa - initial value of gas pressure
0.101325 MPa (by default).

Initial value of gas pressure.

Initial temperature of gas volume, K - initial value of gas temperature
`293.15 K (by default).

Initial value of gas temperature.

Initial density of gas volume, kg/m³ - initial value of gas density
1.2 kg/m³ (by default).

Initial value of gas density.