Engee documentation

Fixed-Displacement Pump (IL)

Constant displacement pump in an isothermal liquid network.

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 flow rate and friction torque
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

Parametrization of leakage and friction characteristics of a hydraulic motor.

  • `Analytical' - leakage flow rate and friction torque are calculated using analytical equations.

  • Tabulated data - volumetric and mechanical efficiencies - volumetric and mechanical efficiencies are calculated from user defined parameters Pressure gain vector, dp and Shaft angular velocity vector, w and interpolated from 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 torque are calculated from the user defined parameters Pressure gain vector, dp and Shaft angular velocity vector, w and interpolated from 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 efficiencies are input as signals to the EV and EM ports respectively.

  • Input signal - volumetric and mechanical loss - leakage flow rate and friction torque are input as signals to 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
l/rad | l/rev | gal/rad | gal/rev | igal/rad | m^3/deg | m^3/rad | m^3/rev | cm^3/rad | cm^3/rev | mm^3/rad | km^3/rad | ft^3/rad | in^3/deg | in^3/rad | in^3/rev | N*m/Pa/rad | N*m/bar/rad | lbf*ft/psi/rad

Details

The amount of fluid displaced by the rotating shaft under rated or typical operating conditions.

Units

l/rad | l/rev | gal/rad | gal/rev | igal/rad | m^3/deg | m^3/rad | m^3/rev | cm^3/rad | cm^3/rev | mm^3/rad | km^3/rad | ft^3/rad | in^3/deg | in^3/rad | in^3/rev | N*m/Pa/rad | N*m/bar/rad | lbf*ft/psi/rad
Default value

30.0 cm^3/rev
Program usage name

displacement
Evaluatable

Yes

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

Details

The angular speed of the shaft at rated operating conditions.

Dependencies

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

Units

rpm | deg/s | rad/s
Default value

1800.0 rpm
Program usage name

w_nominal
Evaluatable

Yes

# Nominal pressure gain — nominal pressure increase between fluid inlet and outlet
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

Increase in pressure between pump inlet and outlet at rated operating conditions.

Dependencies

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

Units

Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
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 Leakage and friction parameterization to `Analytical'.

Default value

0.92
Program usage name

nominal_volumetric_efficiency
Evaluatable

Yes

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

Details

The ratio of the actual torque to the ideal torque produced under nominal conditions.

Dependencies

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

Default value

0.88
Program usage name

nominal_mechanical_efficiency
Evaluatable

Yes

# No-load torque — rest friction torque
N*m | mN*m | lbf*ft

Details

The minimum torque value to overcome seal friction.

Dependencies

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

Units

N*m | mN*m | 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 | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

Vector of pressure increase values for the tabular parameterization of leakage and torque friction. The elements of the vector must be listed in ascending order.

Dependencies

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

Units

Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Default value

[0.1, 1.0, 2.0] MPa
Program usage name

delta_p_vector_efficiency
Evaluatable

Yes

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

Details

Vector of angular velocity data for tabular parameterization of leakage and friction torque. The elements of the vector must be listed in ascending order.

Dependencies

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

Units

rpm | deg/s | rad/s
Default value

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

w_vector_efficiency
Evaluatable

Yes

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

Details

Matrix at of volumetric efficiencies for a given increase in fluid pressure and angular speed of shaft rotation. The block uses linear interpolation between the elements of the table.

The values and are the dimensions of the corresponding vectors:

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

  • - 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

Matrix at mechanical efficiencies for a given increase in fluid pressure and shaft angular velocity. The block uses linear interpolation between the elements of the table. The values and are the dimensions of the corresponding vectors:

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

  • - 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

# Pressure gain vector; dp — vector of pressure increase values for tabular parameterization
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

Vector of pressure increase values for the tabular parameterization of leakage and torque friction. The elements of the vector must be listed in ascending order.

Dependencies

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

Units

Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Default value

[0.1, 1.0, 2.0] MPa
Program usage name

delta_p_vector_loss
Evaluatable

Yes

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

Details

Vector of angular velocity data for tabular parameterization of leakage and friction torque. The elements of the vector must be listed in ascending order.

Dependencies

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

Units

rpm | deg/s | rad/s
Default value

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

w_vector_loss
Evaluatable

Yes

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

Details

Matrix for volume losses for a given increase in fluid pressure and angular speed of the shaft. The block uses linear interpolation between the table elements.

The values and are the dimensions of the corresponding vectors:

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

  • - number of elements in 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

m^3/s | m^3/h | cm^3/s | mm^3/s | ft^3/s | lpm | l/s | gpm | gal/s | gal/h
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 | mN*m | lbf*ft

Details

Matrix at mechanical losses for a given increase in fluid pressure and angular speed of the shaft.

The block uses linear interpolation between the elements of the table. The values and are the dimensions of the corresponding vectors:

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

  • - 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 | mN*m | 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 volumetric efficiency

Details

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

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 — maximum volumetric efficiency

Details

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

Dependencies

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

Default value

1.0
Program usage name

max_volumetric_efficiency
Evaluatable

Yes

# Minimum mechanical efficiency — minimum mechanical efficiency

Details

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

Dependencies

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

Default value

1e-3
Program usage name

min_mechanical_efficiency
Evaluatable

Yes

# Maximum mechanical efficiency — maximum mechanical efficiency

Details

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

Dependencies

To use this parameter, set Leakage and friction parameterization 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 transient operation
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

Threshold pressure increase for the transition between pump and motor operation. The transition region is defined in the region of 0 MPa between the positive and negative values of the threshold pressure increase. Within this region, the calculated leakage rate and friction torque are corrected according to the transition term , to ensure a smooth transition from one mode to the other.

Dependencies

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

  • `Tabulated data - volumetric and mechanical efficiencies';

  • `Input signal - volumetric and mechanical efficiencies';

  • Input signal - volumetric and mechanical losses.

Units

Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Default value

1e-3 MPa
Program usage name

p_threshold
Evaluatable

Yes

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

Details

The angular velocity threshold for the transition between pump and hydraulic motor operation. The transition region is defined around 0 rpm between the positive and negative values of the angular velocity threshold. Within this region, the calculated leakage rate and friction torque are corrected according to the transition term , to ensure a smooth transition from one mode to the other.

Dependencies

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

  • `Tabulated data - volumetric and mechanical efficiencies';

  • `Input signal - volumetric and mechanical efficiencies';

  • Input signal - volumetric and mechanical losses.

Units

rpm | deg/s | rad/s
Default value

100.0 rpm
Program usage name

w_threshold
Evaluatable

Yes

# Check if operating beyond the range of supplied tabulated data — reporting of data overruns
None | Error

Details

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

If Leakage and friction parameterization is set to Tabulated data - torque and speed, this parameter also checks if the block is running in the NaN value range.

Dependencies

To use this parameter, set Leakage and friction parameterization 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 — message about unit operation outside pump mode
None | Error

Details

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

Dependencies

To use this parameter, set Leakage and friction parameterization 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 — low fluid pressure message at pump outlet
None | Error

Details

Select `Error' to stop the simulation when the outlet pressure drops below the minimum setpoint.

This parameter helps identify potential conditions for cavitation when the fluid pressure drops below the fluid vapour pressure.

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 | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

The lower threshold of the permissible inlet or outlet pressure of the pump.

Dependencies

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

Units

Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Default value

0.101325 MPa
Program usage name

p_valid_min
Evaluatable

Yes