Variable displacement pump in isothermal liquid network.
Description
Block Variable-Displacement Pump (IL) simulates a pump with variable displacement. The fluid flow can be from port A to port B (forward mode) or from port B to port A (reverse mode). Operation in pump mode occurs when pressure increases in the direction of flow. The hydraulic motor mode is realised by decreasing pressure in the flow direction.
The shaft rotation corresponds to the sign of the working volume, which is received as a scalar signal at port D. A positive displacement at port D corresponds to positive shaft rotation in the forward mode. A negative displacement at port D corresponds to a negative forward angular velocity of the shaft.
The operating modes are shown in the diagram.
The unit has eight operating modes. The mode of operation depends on the pressure drop from port A to port B, the angular velocity and the working volume. In the diagram above, these modes are shown as octants of the diagram :
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.
Mode 5, reverse hydraulic motor mode: flow from port B to port A causes a decrease in pressure from port B to port A and a positive shaft angular velocity.
Mode 6, forward pump mode: negative shaft angular velocity causes an increase in pressure from port A to port B and flow from port A to port B.
Mode 7, hydraulic motor forward mode: flow from port A to port B causes a decrease in pressure from port A to port B and a negative shaft angular velocity.
Mode 8, reverse pump mode: positive shaft angular velocity causes an increase in pressure from port B to port A and flow from port B to port A.
The pump unit has analytical parameterization, tabular parameterization and parameterization via input signals. With usage of tabular data or input signal for parameterization, a pump performance characteristic based on efficiency or volumetric and mechanical losses can be selected.
In the variants of table data and input signal parameterization, the threshold parameters are as follows Pressure gain threshold for pump-motor transition, Angular velocity threshold for pump-motor transition и Displacement threshold for pump-motor transition define the regions 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. For the displacement threshold, select a threshold value that is smaller than the typical displacement during normal operation.
Analytical parameterization of leakage and friction torque
If the parameters Leakage and friction parameterization is set to Analytical, the unit calculates the leakage and friction torque based on the nominal values of shaft speed, pressure drop, mechanical efficiency 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
- parameter value Nominal displacement;
- parameter value Nominal shaft angular velocity;
- parameter value Volumetric efficiency at nominal conditions;
- parameter value Nominal pressure gain.
The friction torque, which depends on the pressure drop across the pump, is calculated as:
where
- parameter value No-load torque;
- coefficient of friction torque dependence on pressure at nominal working volume, which is determined on the basis of the parameters value Mechanical efficiency at nominal conditions, :
where is the friction torque under nominal conditions:
- shaft angular velocity, or .
Tabular parameterization
In usage of 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 eight modes of operation, the unit calculates additional data for the other mode(s), extending the given data into the remaining octants.
Table data - parameterization of volumetric and mechanical efficiencies
If the parameters Leakage and friction parameterization is set to Tabulated data - volumetric and mechanical efficiencies, the unit performs the parameterization using the tabular data for volumetric and mechanical efficiency.
The leakage flow rate is
where
;
;
- volumetric efficiency, which is interpolated from tabular data provided by the user;
- transition term, represents
where
;
- parameter value 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 the parameters Leakage and friction parameterization is set to Tabulated data - volumetric and mechanical losses, the block performs the parameterization using the tabular data for volume and mechanical losses.
The leakage flow rate is:
where is an interpolation based on the parameters *Volumetric loss table; q_loss(dp;w;D)*which is based on user-supplied data on pressure drop, shaft angular velocity, and fluid working volume.
The shaft friction torque is equal to:
where is an interpolation based on the parameters *Mechanical efficiency table; e_m(dp;w;D)*which is based on user-supplied data on pressure drop, shaft angular velocity, and fluid working volume.
Parametrization via input signal
If the parameters Leakage and friction parameterization is set to `Input signal - volumetric and mechanical efficiencies`the EV and EM ports are switched on. The internal leakage and shaft friction are calculated in the same way as for parameterization `Tabulated data - volumetric and mechanical efficiencies`except that the values and are fed directly to the EV and EM ports respectively.
If the parameters Leakage and friction parameterization is set to Input signal - volumetric and mechanical losses, the ports LV and LM are switched on. 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 port LV;
- parameter value Pressure gain threshold for pump-motor transition.
The friction torque is calculated as:
where
- is the friction torque obtained at port LM;
- parameter value Angular velocity threshold for pump-motor transition.
Volumetric and mechanical efficiencies vary between the user-defined minimum and maximum setpoints. 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 whether the block works beyond the provided tabular data, you can set the parameters to Check if operating beyond the range of supplied tabulated data value `Error`to stop the simulation in this case. When parameterising by input signal for volumetric or mechanical losses, you can be notified when the simulation goes beyond the motor operating limits using the parameters Check if operating beyond pump mode.
The functionality of the pump can also be monitored. Set parameters Check if pressures are less than pump minimum pressure value `Error`to stop the simulation when the outlet pressure is below the minimum setpoint.
The mechanical losses of the pump in N⋅m, given as a scalar.
Dependencies
To use this port, set the parameters to Leakage and friction parameterization value 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 pump leakage and friction characteristics.
Analytical - leakage flow rate and friction torque are calculated using analytical equations.
Tabulated data - volumetric and mechanical efficiencies - volumetric and mechanical efficiencies are calculated using user defined parameters Pressure gain vector; dp и Shaft angular velocity vector; w и Displacement vector; D and interpolated from the corresponding three-dimensional tables Volumetric efficiency table; e_v(dp;w;D) и Mechanical efficiency table; e_m(dp;w;D).
Tabulated data - volumetric and mechanical loss - leakage flow rate and friction torque are calculated from user defined parameters Pressure gain vector; dp и Shaft angular velocity vector; w и Displacement vector; D and are interpolated from the corresponding three-dimensional tables Volumetric loss table; q_loss(dp;w;D) и Mechanical loss table; torque_loss(dp;w;D).
Input signal - volumetric and mechanical efficiencies - volumetric and mechanical efficiencies are signalled to the EV and EM ports respectively.
Input signal - volumetric and mechanical losses - leakage flow rate and friction torque are signalled at 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
The minimum torque value to overcome seal friction.
Dependencies
To use this parameter, set parameter Leakage and friction parameterization value Analytical.
Values
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 parameter Leakage and friction parameterization value Tabulated data - volumetric and mechanical efficiencies.
Values
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 values 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 parameter Leakage and friction parameterization value Tabulated data - volumetric and mechanical efficiencies.
Vector of work volume values for the tabular parameterization of leakage and friction torque. The elements of the vector must be listed in ascending order.
Dependencies
To use this parameter, set parameter Leakage and friction parameterization value Tabulated data - volumetric and mechanical efficiencies.
Array to to of volumetric efficiencies at a given fluid pressure drop, shaft angular speed and working volume. The block uses linear interpolation between the elements of the table.
The values , and are the dimensions of the corresponding vectors:
- number of vector elements in parameters Pressure gain vector; dp.
- number of vector elements in the parameters Shaft angular velocity vector; w.
- number of vector elements in the parameters Displacement vector, D.
Dependencies
To use this parameter, set parameter Leakage and friction parameterization value Tabulated data - volumetric and mechanical efficiencies.
Array to to of mechanical efficiencies at a given fluid pressure drop, shaft angular speed and working volume. The block uses linear interpolation between the elements of the table.
The values , and are the dimensions of the corresponding vectors:
- number of vector elements in parameters Pressure gain vector; dp.
- number of vector elements in the parameters Shaft angular velocity vector; w.
- number of elements of the vector in the parameters Displacement vector; D.
Dependencies
To use this parameter, set parameter Leakage and friction parameterization value Tabulated data - volumetric and mechanical efficiencies.
#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 parameter Leakage and friction parameterization value Tabulated data - volumetric and mechanical losses.
Values
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 parameter Leakage and friction parameterization value Tabulated data - volumetric and mechanical losses.
Vector of work volume values for the tabular parameterization of leakage and friction torque. The elements of the vector must be listed in ascending order.
Dependencies
To use this parameter, set parameter Leakage and friction parameterization value Tabulated data - volumetric and mechanical losses.
Array to to of volume losses at a given fluid pressure drop, shaft angular speed and working volume. The block uses linear interpolation between the table elements.
The values , and are the dimensions of the corresponding vectors:
- number of vector elements in parameters Pressure gain vector; dp.
- number of vector elements in the parameters Shaft angular velocity vector; w.
- number of elements of the vector in the parameters Displacement vector; D.
Dependencies
To use this parameter, set parameter Leakage and friction parameterization value Tabulated data - volumetric and mechanical losses.
#Mechanical loss table; torque_loss(dp;w;D) —
mechanical loss table
N*m | mN*m | lbf*ft
Details
Array to to of mechanical losses at a given fluid pressure drop, shaft angular speed and working volume. The block uses linear interpolation between the table elements.
The values , and are the dimensions of the corresponding vectors:
- number of vector elements in parameters Pressure gain vector; dp.
- number of vector elements in the parameters Shaft angular velocity vector; w.
- number of elements of the vector in the parameters Displacement vector; D.
Dependencies
To use this parameter, set parameter Leakage and friction parameterization value Tabulated data - volumetric and mechanical losses.
The minimum value of the volumetric efficiency. If the input signal is below this value, the volumetric efficiency is set to the minimum volumetric efficiency value.
Dependencies
To use this parameter, set parameter Leakage and friction parameterization value 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 the parameters to Leakage and friction parameterization value Input signal - volumetric and mechanical efficiencies.
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 parameter Leakage and friction parameterization value 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 parameter Leakage and friction parameterization value 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
The threshold value of the pressure increase for the transition between pump and hydraulic motor operation. The transition region is defined around 0 MPa between the positive and negative values of the threshold differential pressure. Within this region, the calculated leakage flow 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 this parameter to Leakage and friction parameterization one of the values:
Tabulated data - volumetric and mechanical efficiencies;
Input signal - volumetric and mechanical efficiencies;
Input signal - volumetric and mechanical losses.
Values
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 the value for Leakage and friction parameterization one of the values:
Tabulated data - volumetric and mechanical efficiencies;
Input signal - volumetric and mechanical efficiencies;
The threshold displacement value for the transition between pump and hydraulic motor operation. The transition region is defined around 0 cm3/s between the positive and negative values of the displacement threshold. Within this region, the calculated leakage flow rate and friction torque are adjusted according to the transition term , to ensure a smooth transition from one mode to the other.