Engee documentation

Fixed-Displacement Pump (IL)

Constant displacement pump in an isothermal liquid network.

blockType: EngeeFluids.IsothermalLiquid.Turbomachinery.FixedDisplacementPump

fixed displacement pump il

Path in the library:

/Physical Modeling/Fluids/Isothermal Liquid/Pumps & Motors/Fixed-Displacement Pump (IL)

Description

The Fixed-Displacement Pump (IL) unit simulates a constant displacement pump. Fluid flow can be from port A to port B (forward mode) or from port B to port A (reverse mode). Pump mode operation occurs when pressure increases in the direction of flow. Hydraulic motor operation occurs when pressure drops in the direction of flow.

fixed displacement pump il 1

The unit has four modes of operation. The mode of operation depends on the pressure drop from port A to port B and the angular velocity :

  • Mode 1, forward pump mode: positive shaft angular velocity causes pressure rise from port A to port B and flow from port A to port B.

  • Mode 2, reverse hydraulic motor mode: flow from port B to port A causes pressure decrease from port B to port A and negative shaft angular velocity.

  • Mode 3, reverse pump mode: negative shaft angular velocity causes pressure increase from port B to port A and flow from port B to port A.

  • Mode 4, forward hydraulic motor mode: flow from port A to port B causes a decrease in pressure from port A to port B and a positive shaft angular velocity.

The pump unit has analytical parameterization, tabular parameterization and parameterization via input signals. When using tabular data or an input signal for parameterization, a pump performance characteristic based on efficiency or volumetric and mechanical losses can be selected.

The threshold parameters Pressure gain threshold for pump-motor transition and Angular velocity threshold for pump-motor transition define the areas in which a numerically smoothed flow transition between pump modes can occur. Select a transition region that provides some margin for the transition term, but which is small enough with respect to pressure and angular velocity not to affect the calculation results.

Analytical parameterization of leakage and friction torque

If Leakage and friction parameterization is set to `Analytical', the unit calculates leakage and friction torque based on nominal values of shaft speed, pressure gain and mechanical and volumetric efficiency. The leakage rate, which depends on the pressure drop across the pump, is calculated as:

where

  • ;

  • - is the average density of the liquid;

  • - Hagen-Poiseuille coefficient for calculation of analytical losses:

    where

    • - is the value of the Displacement parameter;

    • - is the value of parameter Nominal shaft angular velocity;

    • - parameter value Volumetric efficiency at nominal conditions;

    • - parameter value Nominal pressure gain.

The friction torque, which is related to the pressure drop of the pump, is calculated as follows:

where

  • - is the value of the No-load torque parameter;

  • - coefficient of dependence of friction torque on pressure at nominal working volume, which is determined by the value of parameter Mechanical efficiency at nominal conditions, :

    where is the friction torque at nominal conditions:

  • - shaft angular velocity, or .

Tabular data for parameterization

When using tabular data for pump efficiency or losses, data for one or more operating modes can be provided. The signs of the tabular data define the operating mode of the unit. If data is provided for less than four operating modes, the unit calculates additional data for the other mode(s) by extending the given data into the remaining quadrants.

*Table data - parameterization of volumetric and mechanical efficiencies.

If Leakage and friction parameterization is set to `Tabulated data - volumetric and mechanical efficiencies', the block performs parameterization using tabulated data for volumetric and mechanical efficiencies.

The leakage flow rate is

where

  • ;

  • ;

  • - volumetric efficiency, which is interpolated from tabular data provided by the user;

  • - transition term, represents

    where

    • ;

    • - is the value of the parameter Pressure gain threshold for pump-motor transition;

    • ;

    • - parameter value Angular velocity threshold for pump-motor transition.

The friction torque is equal to

where

  • ;

  • ;

  • - mechanical efficiency, which is interpolated from user-supplied tabular data.

*Table data - parameterization of volumetric and mechanical losses.

If Leakage and friction parameterization is set to Tabulated data - volumetric and mechanical loss, the unit performs parameterization using tabulated data for volumetric and mechanical loss.

The leakage flow rate is

where is an interpolation based on the Volumetric loss table parameter, q_loss(dp,w).

The shaft friction torque is equal to

where is an interpolation from the Mechanical loss table parameter, torque_loss(dp,w), which is based on user-supplied data for pressure drop and shaft angular velocity.

parameterization via input signal

When Leakage and friction parameterization is set to Input signal - volumetric and mechanical efficiencies', the EV and EM ports are enabled. The internal leakage and shaft friction are calculated in the same way as with the `Tabulated data - volumetric and mechanical efficiencies parameterization, except that the values and are fed directly to the EV and EM ports respectively.

If Leakage and friction parameterization is set to Input signal - volumetric and mechanical losses, then the LV and LM ports are enabled. These ports receive the leakage flow and friction torque values as positive scalars. The leakage flow rate is calculated as:

where

  • - is the leakage volume flow rate obtained at the LV port;

  • - is the value of Pressure gain threshold for pump-motor transition.

The friction torque is calculated as:

where

  • - is the friction torque obtained at the LM port;

  • - is the value of parameter Angular velocity threshold for pump-motor transition.

The volumetric and mechanical efficiencies vary between the user defined minimum and maximum values. Any values below or above this range will take the minimum and maximum setpoints respectively.

Pump operation

The pump flow rate is:

where .

The torque of the pump is:

where .

The mechanical power developed by the pump shaft is:

The hydraulic power of the pump is:

If you want to know if the unit is operating outside the range of supplied tabulated data, you can set Check if operating outside the range of supplied tabulated data to `Error' to stop the simulation in this case. When parameterising by input signal for volumetric or mechanical losses, you can be notified if the simulation goes beyond the range of motor operating modes by using the parameter Check if operating outside of motor mode.

Pump functionality can also be monitored. Set Check if pressures are less than pump minimum pressure to `Error' to stop the simulation when the output pressure is less than the minimum setpoint.

Ports

Conserving

# A — isothermal liquid port
isothermal liquid

Details

The fluid inlet or outlet port of a pump.

Program usage name

port_a

# B — isothermal liquid port
isothermal liquid

Details

The fluid inlet or outlet port of a pump.

Program usage name

port_b

# R — mechanical port
`rotational mechanics

Details

Angular velocity of rotation and torque of a shaft.

Program usage name

rod_flange

# C — mechanical port
`rotational mechanics

Details

Angular velocity and torque of the body.

Program usage name

case_flange

Input

# EV — volumetric efficiency
scalar

Details

Volumetric efficiency specified as a scalar. The value must be in the range from 0 to 1.

Dependencies

To use this port, set Leakage and friction parameterization to `Input signal - volumetric and mechanical efficiencies'.

Data types

Float64.
Complex numbers support

No

# EM — mechanical efficiency
scalar

Details

The mechanical efficiency of the pump, given as a scalar. The value must be in the range from 0 to 1.

Dependencies

To use this port, set Leakage and friction parameterization to `Input signal - volumetric and mechanical efficiencies'.

Data types

Float64.
Complex numbers support

No

# LV — leakage volume flow rate
scalar

Details

Pump volumetric losses in m3/s, given as a scalar.

Dependencies

To use this port, set Leakage and friction parameterization to `Input signal - volumetric and mechanical losses'.

Data types

Float64.
Complex numbers support

No

# LM — friction moment
scalar

Details

The mechanical losses of the pump in N⋅m, given as a scalar.

Dependencies

To use this port, set Leakage and friction parameterization to `Input signal - volumetric and mechanical losses'.

Data types

Float64.
Complex numbers support

No

Parameters

Parameters

# Leakage and friction parameterization — method for calculating leakage rate and friction moment
Analytical | Tabulated data - volumetric and mechanical efficiencies | Tabulated data - volumetric and mechanical losses | Input signal - volumetric and mechanical efficiencies | Input signal - volumetric and mechanical losses

Details

Parameterization of the characteristics of leakage and friction of the hydraulic motor.

  • Analytical — the leakage rate and the friction moment are calculated using analytical equations.

  • Tabulated data - volumetric and mechanical efficiencies — volumetric and mechanical efficiency are calculated using user-defined parameters Pressure gain vector, dp and Shaft angular velocity vector, w and interpolated based on the corresponding two-dimensional tables Volumetric efficiency table, e_v(dp,w) and Mechanical efficiency table, e_m(dp,w).

  • Tabulated data - volumetric and mechanical loss — leakage flow rate and friction moment are calculated using user-defined parameters Pressure gain vector, dp and Shaft angular velocity vector, w and interpolated based on the corresponding two-dimensional tables Volumetric loss table, q_loss(dp,w) and Mechanical loss table, torque_loss(dp,w).

  • Input signal - volumetric and mechanical efficiencies — Volumetric and mechanical efficiency are transmitted as signals to the EV and EM ports, respectively.

  • Input signal - volumetric and mechanical loss — the leakage flow rate and the friction moment are sent as signals to the ports LV and LM, respectively.

Values

Analytical | Tabulated data - volumetric and mechanical efficiencies | Tabulated data - volumetric and mechanical losses | Input signal - volumetric and mechanical efficiencies | Input signal - volumetric and mechanical losses
Default value

Analytical
Program usage name

leakage_and_friction_parameterization_pump
Evaluatable

No

# Displacement — working volume
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 amount of liquid displaced by the rotating shaft under nominal or typical operating conditions.

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

30.0 cm^3/rev
Program usage name

displacement
Evaluatable

Yes

# Nominal shaft angular velocity — nominal angular velocity of the shaft
rad/s | deg/s | rad/min | deg/min | rpm | rps

Details

Angular velocity of the shaft under nominal operating conditions.

Dependencies

To use this parameter, set the Leakage and friction parameterization parameter to Analytical.

Units

rad/s | deg/s | rad/min | deg/min | rpm | rps
Default value

1800.0 rpm
Program usage name

w_nominal
Evaluatable

Yes

# Nominal pressure gain — nominal pressure increase between liquid inlet and outlet
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

Details

Increasing the pressure between the pump inlet and outlet under nominal operating conditions.

Dependencies

To use this parameter, set the Leakage and friction parameterization parameter to Analytical.

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

10.0 MPa
Program usage name

p_nominal
Evaluatable

Yes

# Volumetric efficiency at nominal conditions — volumetric EFFICIENCY

Details

The ratio of the actual flow rate to the ideal flow rate under nominal conditions.

Dependencies

To use this parameter, set the Leakage and friction parameterization parameter to Analytical.

Default value

0.92
Program usage name

nominal_volumetric_efficiency
Evaluatable

Yes

# Mechanical efficiency at nominal conditions — mechanical efficiency under nominal conditions

Details

The ratio of the actual torque to the ideal torque generated under rated conditions.

Dependencies

To use this parameter, set the Leakage and friction parameterization parameter to Analytical.

Default value

0.88
Program usage name

nominal_mechanical_efficiency
Evaluatable

Yes

# No-load torque — moment of friction at rest
N*m | uN*m | mN*m | kN*m | MN*m | GN*m | kgf*m | lbf*in | lbf*ft

Details

The minimum torque value to overcome the seal friction.

Dependencies

To use this parameter, set the Leakage and friction parameterization parameter to Analytical.

Units

N*m | uN*m | mN*m | kN*m | MN*m | GN*m | kgf*m | lbf*in | lbf*ft
Default value

0.0 N*m
Program usage name

no_load_torque
Evaluatable

Yes

# Pressure gain vector; dp — vector of pressure increase values for tabular parameterization
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

Details

A vector of pressure increase values for tabular parameterization of leaks and torque friction. The elements of the vector should be listed in ascending order.

Dependencies

To use this parameter, set the Leakage and friction parameterization parameter to Tabulated data - volumetric and mechanical efficiencies or Tabulated data - volumetric and mechanical losses.

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

[0.1, 1.0, 2.0] MPa
Program usage names

delta_p_vector_efficiency, delta_p_vector_loss
Evaluatable

Yes

# Shaft angular velocity vector; w — vector of angular velocity values for tabular parameterization
rad/s | deg/s | rad/min | deg/min | rpm | rps

Details

An angular velocity data vector for tabular parameterization of leakage and friction moment. The elements of the vector should be listed in ascending order.

Dependencies

To use this parameter, set the Leakage and friction parameterization parameter to Tabulated data - volumetric and mechanical efficiencies or Tabulated data - volumetric and mechanical losses.

Units

rad/s | deg/s | rad/min | deg/min | rpm | rps
Default value

[250.0, 500.0, 1000.0, 2000.0, 3000.0, 4000.0] rpm
Program usage names

w_vector_efficiency, w_vector_loss
Evaluatable

Yes

# Volumetric efficiency table; e_v(dp;w) — volumetric efficiency table

Details

The matrix on volumetric efficiency with a given increase in fluid pressure and angular velocity of the shaft. The block uses linear interpolation between the table elements.

Values and — these are the sizes of the corresponding vectors:

  • — the number of elements in the pressure gain vector Pressure gain vector, dp.

  • — the number of elements in the angular velocity vector Shaft angular velocity vector, w.

Dependencies

To use this parameter, set the Leakage and friction parameterization parameter to Tabulated data - volumetric and mechanical efficiencies.

Default value

[0.816 0.908 0.954 0.977 0.981 0.984; 0.325 0.663 0.831 0.916 0.925 0.946; 0.137 0.568 0.78 0.892 0.893 0.910]
Program usage name

volumetric_efficiency_matrix
Evaluatable

Yes

# Mechanical efficiency table; e_m(dp;w) — mechanical efficiency table

Details

The matrix on mechanical efficiency at a given increase in fluid pressure and angular velocity of the shaft. The block uses linear interpolation between table elements. Values and — these are the sizes of the corresponding vectors:

  • — the number of elements in the pressure gain vector Pressure gain vector, dp.

  • — the number of elements in the angular velocity vector Shaft angular velocity vector, w.

Dependencies

To use this parameter, set the Leakage and friction parameterization parameter to Tabulated data - volumetric and mechanical efficiencies.

Default value

[0.996 0.996 0.996 0.996 0.996 0.996; 0.988 0.989 0.989 0.989 0.989 0.990; 0.981 0.981 0.982 0.982 0.983 0.984]
Program usage name

mechanical_efficiency_matrix
Evaluatable

Yes

# Volumetric loss table; q_loss(dp;w) — volume losses for tabular parameterization
m^3/s | mm^3/s | cm^3/s | m^3/hr | m^3/min | l/hr | l/min | l/s | gal/hr | gal/min | gal/s | ft^3/hr | ft^3/min | ft^3/s

Details

The matrix on volume losses at a given increase in fluid pressure and angular velocity of the shaft. The block uses linear interpolation between table elements.

Values and — these are the sizes of the corresponding vectors:

  • — the number of elements in the pressure gain vector Pressure gain vector, dp.

  • — the number of vector elements in the Shaft angular velocity vector parameter, w.

Dependencies

To use this parameter, set the Leakage and friction parameterization parameter to Tabulated data - volumetric and mechanical losses.

Units

m^3/s | mm^3/s | cm^3/s | m^3/hr | m^3/min | l/hr | l/min | l/s | gal/hr | gal/min | gal/s | ft^3/hr | ft^3/min | ft^3/s
Default value

1e-3*[0.0230 0.0230 0.0230 0.0230 0.0285 0.0320; 0.0844 0.0842 0.0845 0.0840 0.1125 0.1080; 0.1079 0.1080 0.1100 0.1080 0.1605 0.1800] m^3/s
Program usage name

volumetric_loss_matrix
Evaluatable

Yes

# Mechanical loss table; torque_loss(dp;w) — mechanical losses for tabular parameterization
N*m | uN*m | mN*m | kN*m | MN*m | GN*m | kgf*m | lbf*in | lbf*ft

Details

The matrix on mechanical losses at a given increase in fluid pressure and angular velocity of the shaft.

The block uses linear interpolation between the table elements. Values and — these are the sizes of the corresponding vectors:

  • — the number of elements in the pressure gain vector Pressure gain vector, dp.

  • — the number of elements in the angular velocity vector Shaft angular velocity vector, w.

Dependencies

To use this parameter, set the Leakage and friction parameterization parameter to Tabulated data - volumetric and mechanical losses.

Units

N*m | uN*m | mN*m | kN*m | MN*m | GN*m | kgf*m | lbf*in | lbf*ft
Default value

[0.0020 0.0020 0.0020 0.0020 0.0020 0.0020; 0.0607 0.0556 0.0556 0.0556 0.0556 0.0505; 0.1937 0.1937 0.1833 0.1833 0.1729 0.1626] N*m
Program usage name

mechanical_loss_matrix
Evaluatable

Yes

# Minimum volumetric efficiency — minimum value of volumetric efficiency

Details

The minimum value of volumetric efficiency. If the input scalar is below this value, then the volumetric efficiency is set to the minimum value of the volumetric efficiency.

Dependencies

To use this parameter, set the Leakage and friction parameterization parameter to Input signal - volumetric and mechanical efficiencies.

Default value

1e-3
Program usage name

min_volumetric_efficiency
Evaluatable

Yes

# Maximum volumetric efficiency — the maximum value of volumetric efficiency

Details

The maximum value of volumetric efficiency. If the input signal exceeds this value, the volumetric efficiency is set to the maximum value of the volumetric efficiency.

Dependencies

To use this parameter, set the Leakage and friction parameterization parameter to Input signal - volumetric and mechanical efficiencies.

Default value

1.0
Program usage name

max_volumetric_efficiency
Evaluatable

Yes

# Minimum mechanical efficiency — minimum value of mechanical efficiency

Details

The minimum value of mechanical efficiency. If the input signal is below this value, the mechanical efficiency is set to the minimum value of the mechanical efficiency.

Dependencies

To use this parameter, set the Leakage and friction parameterization parameter to Input signal - volumetric and mechanical efficiencies.

Default value

1e-3
Program usage name

min_mechanical_efficiency
Evaluatable

Yes

# Maximum mechanical efficiency — maximum value of mechanical efficiency

Details

The maximum value of mechanical efficiency. If the input signal is higher than this value, the mechanical efficiency is set to the maximum value of the mechanical efficiency.

Dependencies

To use this parameter, set the Leakage and friction parameterization parameter to Input signal - volumetric and mechanical efficiencies.

Default value

1.0
Program usage name

max_mechanical_efficiency
Evaluatable

Yes

# Pressure gain threshold for pump-motor transition — threshold pressure for the transition mode
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 threshold value of pressure increase for switching between pump and hydraulic motor operation modes. The transition area is defined in the region of 0 MPa between the positive and negative values of the threshold pressure increase. Within this area, the calculated leakage rate and friction moment are adjusted according to the transition term to ensure a smooth transition from one mode to another.

Dependencies

To use this parameter, set Leakage and friction parameterization to one of the following values:

  • Tabulated data - volumetric and mechanical efficiencies;

  • Input signal - volumetric and mechanical efficiencies;

  • Input signal - volumetric and mechanical losses.

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

1e-3 MPa
Program usage name

p_threshold
Evaluatable

Yes

# Angular velocity threshold for pump-motor transition — threshold angular velocity for the transition mode
rad/s | deg/s | rad/min | deg/min | rpm | rps

Details

The threshold value of the angular velocity for switching between the operating modes of the pump and the hydraulic motor. The transition area is defined around 0 rpm between the positive and negative values of the threshold angular velocity. Within this area, the calculated leakage rate and friction moment are adjusted according to the transition term to ensure a smooth transition from one mode to another.

Dependencies

To use this parameter, set Leakage and friction parameterization to one of the following values:

  • Tabulated data - volumetric and mechanical efficiencies;

  • Input signal - volumetric and mechanical efficiencies;

  • Input signal - volumetric and mechanical losses.

Units

rad/s | deg/s | rad/min | deg/min | rpm | rps
Default value

100.0 rpm
Program usage name

w_threshold
Evaluatable

Yes

# Check if operating beyond the range of supplied tabulated data — a message about going beyond the limits of the provided data
None | Error

Details

Select a value Error to stop the simulation when the block uses values outside the provided data range.

If the Leakage and friction parameterization parameter is set to Tabulated data - torque and speed, then this parameter also checks whether the block is working in the range of values . NaN.

Dependencies

To use this parameter, set the Leakage and friction parameterization parameter to one of the values:

  • Tabulated data - volumetric and mechanical efficiencies;

  • Tabulated data - volumetric and mechanical losses.

Values

None | Error
Default value

None
Program usage name

supplied_range_assert_action
Evaluatable

No

# Check if operating beyond pump mode — a message about the operation of the unit outside the pump mode
None | Error

Details

Choose Error to stop the simulation when the unit is operating in forward or reverse pump modes.

Dependencies

To use this parameter, set the Leakage and friction parameterization parameter to Input signal - volumetric and mechanical losses.

Values

None | Error
Default value

None
Program usage name

operating_mode_assert_action
Evaluatable

No

# Check if pressures are less than pump minimum pressure — a message about low liquid pressure at the pump outlet
None | Error

Details

Choose Error to stop the simulation when the outlet pressure drops below the minimum setpoint.

This parameter helps determine the potential conditions for cavitation when the liquid pressure drops below the vapor pressure of the liquid.

Values

None | Error
Default value

None
Program usage name

pressure_assert_action
Evaluatable

No

# Pump minimum pressure — lower threshold of permissible pressure at the pump outlet
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 lower threshold of the allowable pressure at the pump inlet or outlet.

Dependencies

To use this parameter, set Check if pressures are less than pump minimum pressure to Error.

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

p_valid_min
Evaluatable

Yes

Examples