Fixed-Displacement Pump (TL)
Constant displacement pump in a thermal liquid network.
Description
The Fixed-Displacement Pump (TL) unit is a pump that receives energy from a mechanical rotary system and transfers it to a thermal liquid network. The working volume of the pump is fixed at a constant value, which is set with the Displacement parameters.
Ports A and B represent the inlet ports of the pump. Ports R and C represent the drive shaft and pump casing. 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.
Operation Modes
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 time constant is negligible compared to the system time constant. The pump reaches steady state almost instantaneously and is considered as a quasi-stationary component.
Conservation of energy
The mechanical work done by the pump involves the exchange of energy. The energy conservation equation is of the form:
where
-
and are energy flows in ports A and B respectively;
-
- is the hydraulic power of the pump. It is a function of the pressure difference between the pump ports: .
The mechanical power of the pump is derived from the torque and angular velocity :
Flow rate and torque
The mass flow rate of the pump is:
where
-
- is the actual mass flow rate;
-
- ideal mass flow rate;
-
- mass flow rate of internal leakage.
The torque required to drive the pump is:
where
-
- is the actual torque;
-
- ideal torque;
-
- friction torque.
The ideal flow rate and ideal torque are calculated as
Where:
-
- average value of liquid density in thermal liquid ports A and B;
-
- value of the Displacement parameters;
-
- angular speed of shaft rotation;
-
- pressure increase from inlet to outlet.
Analytical parameterization of leakage and friction torque
If the Leakage and friction parameterization is set to `Analytical', the unit calculates the leakage and friction torque based on nominal values of shaft speed, mechanical pressure drop and volumetric efficiency. The leakage rate, which depends on the pressure drop across the hydraulic motor, is calculated as:
and the friction torque is calculated as:
where
-
- is the Hagen-Poiseuille coefficient for laminar flows. The unit calculates this coefficient from the specified nominal parameters;
-
- average dynamic viscosity of the liquid in the ports;
-
- average density of the liquid in the ports;
-
- coefficient of friction torque dependence on pressure at nominal working volume, which is determined from the value of the parameter Mechanical efficiency at nominal conditions, :
where is the friction torque under nominal conditions:
-
- pressure gain for a given volumetric efficiency, the value of the parameter Nominal pressure gain. This value is the pressure gain at which the nominal volumetric efficiency is specified;
-
- the value of the No-load torque parameters;
-
- angular velocity for a given volumetric efficiency, the value of the Nominal shaft angular velocity parameter. This value represents the angular velocity at which the unit specifies the nominal volumetric efficiency.
The unit determines the Hagen-Poiseuille coefficient based on the nominal fluid and component parameters
where:
-
- Dynamic viscosity for a given volumetric efficiency, the value of the parameter Nominal Dynamic viscosity. This value represents the dynamic viscosity at which the unit determines the nominal volumetric efficiency;
-
- Volumetric efficiency at nominal conditions, the value of parameter Volumetric efficiency at nominal conditions, This is the volumetric efficiency corresponding to the specified nominal conditions.
Tabular data for parameterization
In usage of tabular data for efficiency or losses of the hydraulic motor, 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 efficiency.
If the Leakage and friction parameterization parameter 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:
and the friction torque is:
where
-
- is the numerical smoothing parameter for the transient process from the hydraulic motor to the pump;
-
- leakage flow rate in pump mode;
-
- leakage flow rate in the hydraulic motor mode;
-
- friction moment in the pump mode;
-
- friction torque in the hydraulic motor mode.
Smoothing parameters is given by hyperbolic function
where
-
- is the value of the parameter Pressure gain threshold for motor-pump transition;
-
- value of the parameter Angular velocity threshold for motor-pump transition.
The volumetric flow rate is calculated based on the volumetric efficiency, which is set in tabular form in the area using the Volumetric efficiency table block parameters.
When operating in pump mode, the leakage flow rate is:
where is the volumetric efficiency obtained by interpolation or extrapolation of tabular data.
Similarly, when operating in the hydraulic motor mode, the leakage flow rate is:
The friction torque is similarly calculated from the mechanical efficiency, a value that is set in tabular form in the area using the Mechanical efficiency table block parameters.
When operating in pump mode, the friction torque is:
where is the mechanical efficiency obtained either by interpolation or extrapolation of tabular data.
Similarly, when operating in the hydraulic motor mode, the friction torque is:
Table data - parameterization of volumetric and mechanical losses
If the parameter Leakage and friction parameterization is set to Tabulated data - volumetric and mechanical loss
, the leakage volume flow rate is specified directly in tabular form in the area :
The leakage mass flow rate is calculated from the volumetric flow rate:
The friction torque is equal to:
where and are volumetric and mechanical losses obtained by interpolation or extrapolation of tabulated data given in the parameters Volumetric loss table and Mechanical loss table.
Parametrization via input signal
When the 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 efficiency values and are fed directly to the EV and EM ports respectively.
The efficiencies are positive values with a value between 0
and 1
. The values of input signals outside these limits are set equal to the nearest limit (0
for inputs less than 0
and 1
for inputs greater than 1
). Volumetric and mechanical efficiencies vary between a user-defined minimum and maximum value. Any values below or above this range will take the minimum and maximum setpoints respectively.
When the Leakage and friction parameterization parameter is set to `Input signal - volumetric and mechanical losses', the LV and LM ports are enabled. These ports receive the leakage flux and friction torque values as positive scalars.
Ports
Conserving
#
R
—
mechanical port
`rotational mechanics
Details
Angular velocity of rotation and torque of a shaft.
Program usage name |
|
#
C
—
mechanical port
`rotational mechanics
Details
Angular velocity of rotation and torque of the body.
Program usage name |
|
#
A
—
thermal liquid port
thermal liquid
Details
The fluid inlet or outlet port of a pump.
Program usage name |
|
#
B
—
thermal liquid port
thermal liquid
Details
The fluid inlet or outlet port of a pump.
Program usage name |
|
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 the Leakage and friction parameterization parameters to `Input signal - volumetric and mechanical efficiencies'.
Data types |
|
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 the Leakage and friction parameterization parameters to `Input signal - volumetric and mechanical efficiencies'.
Data types |
|
Complex numbers support |
No |
#
LV
—
leakage volume flow rate
scalar
Details
Pump losses, in m3/s, given as a scalar.
Dependencies
To use this port, set the Leakage and friction parameterization parameters to `Input signal - volumetric and mechanical losses'.
Data types |
|
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 the Leakage and friction parameterization parameters to `Input signal - volumetric and mechanical losses'.
Data types |
|
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 and friction torque are calculated using analytical equations.
-
Tabulated data - volumetric and mechanical efficiencies
- volumetric and mechanical efficiencies 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 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 |
|
Default value |
|
Program usage name |
|
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 volume of fluid displaced when the shaft is rotated by a certain angle. The unit stores this value throughout the simulation.
Values |
|
Default value |
|
Program usage name |
|
Evaluatable |
Yes |
#
Nominal shaft angular velocity —
nominal angular speed of the shaft
rpm
| deg/s
| rad/s
Details
The angular speed of the rotating shaft corresponding to a given volumetric efficiency. This value under standard operating conditions is usually given in the manufacturer’s specification. The unit uses this parameters to calculate leakage flow and friction torque.
Dependencies
To use this parameter, set the Leakage and friction parameterization parameter to `Analytical'.
Values |
|
Default value |
|
Program usage name |
|
Evaluatable |
Yes |
#
Nominal pressure gain —
nominal pressure increase between inlet and outlet
Pa
| GPa
| MPa
| atm
| bar
| kPa
| ksi
| psi
| uPa
| kbar
Details
The pressure increase corresponding to the specified volumetric efficiency. This value under standard operating conditions can usually be found in the manufacturer’s specification. The unit uses this parameters to calculate the internal leakage flow rate.
Dependencies
To use this parameter, set the Leakage and friction parameterization parameter to `Analytical'.
Values |
|
Default value |
|
Program usage name |
|
Evaluatable |
Yes |
#
Nominal dynamic viscosity —
nominal dynamic viscosity for a given volumetric efficiency
P
| cP
| reyn
| s*uPa
Details
The nominal dynamic viscosity of the fluid corresponding to a given volumetric efficiency. This value under standard operating conditions can usually be found in the manufacturer’s specification. The unit uses this parameters to calculate the internal leakage flow rate.
Dependencies
To use this parameter, set the Leakage and friction parameterization parameter to `Analytical'.
Values |
|
Default value |
|
Program usage name |
|
Evaluatable |
Yes |
# Volumetric efficiency at nominal conditions — volumetric efficiency at nominal conditions
Details
The ratio of the actual flow rate to the ideal flow rate under nominal conditions. This value under standard operating conditions can usually be found in the manufacturer’s specification. The unit uses this parameters to calculate the internal leakage flow rate.
Dependencies
To use this parameter, set the Leakage and friction parameterization parameter to `Analytical'.
Default value |
|
Program usage name |
|
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 the Leakage and friction parameterization parameters to `Analytical'.
Default value |
|
Program usage name |
|
Evaluatable |
Yes |
#
No-load torque —
rest friction torque
N*m
| mN*m
| lbf*ft
Details
The minimum torque value to overcome seal friction. This torque is the load-independent component of the total friction torque.
Dependencies
To use this parameter, set the Leakage and friction parameterization parameter to `Analytical'.
Values |
|
Default value |
|
Program usage name |
|
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 differential pressure 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 the Leakage and friction parameterization parameters to `Tabulated data - volumetric and mechanical efficiencies'.
Values |
|
Default value |
|
Program usage name |
|
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 the Leakage and friction parameterization parameters to `Tabulated data - volumetric and mechanical efficiencies'.
Values |
|
Default value |
|
Program usage name |
|
Evaluatable |
Yes |
# Volumetric efficiency table, e_v(dp,w) — table of volumetric efficiency values
Details
Matrix at of volumetric efficiencies at a given fluid pressure drop 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 vector elements in the Pressure gain vector parameters, dp.
-
- number of vector elements in the Shaft angular velocity vector parameters, w.
Dependencies
To use this parameter, set the Leakage and friction parameterization parameters to `Tabulated data - volumetric and mechanical efficiencies'.
Default value |
|
Program usage name |
|
Evaluatable |
Yes |
# Mechanical efficiency table, e_m(dp,w) — table of mechanical efficiency values
Details
Matrix at mechanical efficiencies at a given fluid pressure drop 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 drop vector 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 parameters to `Tabulated data - volumetric and mechanical efficiencies'.
Default value |
|
Program usage name |
|
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 the Leakage and friction parameterization parameters to `Tabulated data - volumetric and mechanical losses'.
Values |
|
Default value |
|
Program usage name |
|
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 the Leakage and friction parameterization parameters to `Tabulated data - volumetric and mechanical losses'.
Values |
|
Default value |
|
Program usage name |
|
Evaluatable |
Yes |
#
Volumetric loss table, q_loss(dp,w) —
table of volume loss values
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 at volume losses at a given fluid pressure drop 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 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 parameters to `Tabulated data - volumetric and mechanical losses'.
Values |
|
Default value |
|
Program usage name |
|
Evaluatable |
Yes |
#
Mechanical loss table, torque_loss(dp,w) —
table of mechanical loss values
N*m
| mN*m
| lbf*ft
Details
Matrix at of mechanical losses at a given fluid pressure drop 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 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 parameters to `Tabulated data - volumetric and mechanical losses'.
Values |
|
Default value |
|
Program usage name |
|
Evaluatable |
Yes |
# Minimum volumetric efficiency — minimum volumetric efficiency
Details
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 the Leakage and friction parameterization parameters to `Input signal - volumetric and mechanical efficiencies'.
Default value |
|
Program usage name |
|
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 Leakage and friction parameterization parameters to `Input signal - volumetric and mechanical efficiencies'.
Default value |
|
Program usage name |
|
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 the Leakage and friction parameterization parameters to `Input signal - volumetric and mechanical efficiencies'.
Default value |
|
Program usage name |
|
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 the Leakage and friction parameterization parameters to `Input signal - volumetric and mechanical efficiencies'.
Default value |
|
Program usage name |
|
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 differential pressure threshold 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 differential pressure. 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
.
Values |
|
Default value |
|
Program usage name |
|
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
.
Values |
|
Default value |
|
Program usage name |
|
Evaluatable |
Yes |
#
Cross-sectional area at ports A and B —
cross-sectional area of ports A and B
m^2
| cm^2
| ft^2
| in^2
| km^2
| mi^2
| mm^2
| um^2
| yd^2
Details
Cross-sectional area of ports A and B. It is assumed that the areas are equal.
Values |
|
Default value |
|
Program usage name |
|
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 the Leakage and friction parameterization parameter 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 the Leakage and friction parameterization to one of the values:
-
Tabulated data - volumetric and mechanical efficiencies
; -
`Tabulated data - volumetric and mechanical losses'.
Values |
|
Default value |
|
Program usage name |
|
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 hydraulic motor modes.
Dependencies
To use this parameter, set the Leakage and friction parameterization parameters to `Input signal - volumetric and mechanical losses'.
Values |
|
Default value |
|
Program usage name |
|
Evaluatable |
No |