Engee documentation

Rotational Mechanical Converter (G)

The interface between the gas and mechanical rotary networks.

blockType: AcausalFoundation.Gas.Elements.RotationalMechanicalConverter

rotation mechanical converter (g)

Path in the library:

/Physical Modeling/Fundamental/Gas/Elements/Rotational Mechanical Converter (G)

Description

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

The converter contains a variable volume of gas. Pressure and temperature vary depending on the compressibility and heat capacity of the gas. Parameter Mechanical orientation allows you to specify whether an increase in gas volume leads to a positive or negative rotation of port R relative to port C.

Port A is the gas port corresponding to the input of the converter. Port H is a thermal port connected to the temperature of the gas inside the converter. Ports R and C are rotary mechanical ports corresponding to the shaft and housing of the converter.

Conservation of mass

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

where

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

  • is the partial derivative of the mass of a gas with respect to temperature at constant pressure and volume;

  • — gas pressure. The pressure at port A is considered to be equal to this pressure, ;

  • — gas temperature. It is assumed that the temperature at port H is equal to this temperature, ;

  • — gas density;

  • — gas volume;

  • — time;

  • — mass consumption at the port A. The flow rate through the port is positive if gas flows into the unit.

Energy conservation

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

where

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

  • is the partial derivative of internal energy about temperature at constant pressure and volume;

  • — power consumption on port A;

  • — the rate of heat flow at the port H;

  • — specific enthalpy of the gas.

Partial derivatives for models of ideal and semi-ideal gases

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

,

,

,

,

where

  • — gas density;

  • — gas volume;

  • — specific enthalpy of the gas;

  • — the coefficient of compressibility;

  • — universal gas constant;

  • — specific heat capacity at constant gas pressure.

Partial derivatives for the real gas model

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

,

,

,

,

where

  • — isothermal volumetric gas compression module;

  • — isobaric coefficient of thermal expansion of the gas.

Gas volume

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

where

  • — dead volume;

  • — change in the volume of the transducer per unit angle of rotation of the rotor relative to the housing;

  • — the angle of rotation of the rotor;

  • — orientation of the converter. If the parameter Mechanical orientation set to the value Pressure at A causes positive rotation of R relative to C Then . If the parameter Mechanical orientation set to the value Pressure at A causes negative rotation of R relative to C that .

    The angle of rotation of the rotor varies depending on the value of the parameter *{blockLibraryPP_blockTypesPP_AcausalFoundationBB_PP_GasBB_PP_ElementsBB_PP_RotationalMechanicalConverterPP_BasePP_paramsPP_PP_ParametersPP_orientationPP_label}*:

  • If the parameter Mechanical orientation set to the value Pressure at A causes positive rotation of R relative to C The angle of rotation of the rotor increases as the volume of gas increases from the dead volume.

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

Torque balance

The torque balance between the movable rotor and the gas volume is as follows:

where

  • — torque from port R to port C;

  • — ambient pressure.

Assumptions and limitations

  • The converter housing is absolutely rigid.

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

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

  • There are no gas leaks.

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

Ports

Conserving

# A — gas inlet
gas

Details

The gas port corresponds to the input of the converter.

Program usage name

port

# R — the rotor
rotational mechanics

Details

Mechanical rotary port, corresponds to the rotor.

Program usage name

rod_flange

# H — temperature inside the converter
warm

Details

The thermal port is connected to the temperature of the gas inside the converter.

Program usage name

thermal_port

# C — body
rotational mechanics

Details

Mechanical rotary port, corresponds to the body.

Program usage name

case_flange

Parameters

Parameters

# Mechanical orientation — orientation of the converter
Pressure at A causes positive rotation of R relative to C | Pressure at A causes negative rotation of R relative to C

Details

Sets the orientation of the movement of the mechanical part in relation to the change in gas volume:

  • Pressure at A causes positive rotation of R relative to C — an increase in the volume of gas leads to the rotation of port R relative to port C in a positive direction.

  • Pressure at A causes negative rotation of R relative to C — an increase in the volume of gas leads to the rotation of port R relative to port C in a negative direction.

Values

Pressure at A causes positive rotation of R relative to C | Pressure at A causes negative rotation of R relative to C
Default value

Pressure at A causes positive rotation of R relative to C
Program usage name

orientation
Evaluatable

No

# Initial interface rotation — initial angular position of port R relative to port C
rad | deg | rev | mrad | arcsec | arcmin | gon

Details

The initial angular position of port R relative to port C. Meaning 0 corresponds to an initial volume of gas equal to Dead volume.

Dependencies

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

Units

rad | deg | rev | mrad | arcsec | arcmin | gon
Default value

0.0 rad
Program usage name

delta_phi_start
Evaluatable

Yes

# Interface volume displacement — volume of displaced gas per unit rotation angle
m^3/rad | mm^3/rad | cm^3/rad | km^3/rad | m^3/deg | cm^3/rev | m^3/rev | l/rad | l/rev | in^3/rad | ft^3/rad | gal/rad | igal/rad | in^3/deg | in^3/rev | gal/rev

Details

The volume of displaced gas per unit angle of rotation of the mechanical part of the converter.

Units

m^3/rad | mm^3/rad | cm^3/rad | km^3/rad | m^3/deg | cm^3/rev | m^3/rev | l/rad | l/rev | in^3/rad | ft^3/rad | gal/rad | igal/rad | in^3/deg | in^3/rev | gal/rev
Default value

0.01 m^3/rad
Program usage name

volume_displacement
Evaluatable

Yes

# Dead volume — the volume of gas at zero angle of rotation of the mechanical part
m^3 | um^3 | mm^3 | cm^3 | km^3 | ml | l | gal | igal | in^3 | ft^3 | yd^3 | mi^3

Details

The volume of gas in the converter at an angle of rotation of the mechanical part equal to 0.

Units

m^3 | um^3 | mm^3 | cm^3 | km^3 | ml | l | gal | igal | in^3 | ft^3 | yd^3 | mi^3
Default value

1e-5 m^3
Program usage name

dead_volume
Evaluatable

Yes

# Cross-sectional area at port A — the area normal to the flow section at the inlet to the converter
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

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

Units

m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac
Default value

0.01 m^2
Program usage name

port_area
Evaluatable

Yes

# Environment pressure specification — the method of setting the ambient pressure
Atmospheric pressure | Specified pressure

Details

Sets the method for setting the ambient pressure:

  • Atmospheric pressure — atmospheric pressure set by the unit Gas Properties (G), connected to the network.

  • Specified pressure — the value set by the parameter Environment pressure.

Values

Atmospheric pressure | Specified pressure
Default value

Atmospheric pressure
Program usage name

environment_spec
Evaluatable

No

# Environment pressure — pressure outside the transducer
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

Details

The pressure outside the transducer that counteracts the pressure of the transducer’s gas volume. Meaning 0 This means that the converter operates in a vacuum.

Dependencies

To use this parameter, set for the parameter Environment pressure specification meaning Specified pressure.

Units

Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg
Default value

0.101325 MPa
Program usage name

environment_pressure
Evaluatable

Yes