An opening of constant or variable area in a thermal liquid network.
Variable Orifice (TL)
Orifice (TL)
Description
Block Orifice (TL) simulates the flow through a local restriction with a constant or variable opening area. For variable area openings, a control element connected to the S port sets the opening position. The opening area is varied linearly or using an interpolation table.
The mass conservation equation in the block is realised as follows:
This mass conservation equation implies an increase in velocity when the area decreases and a decrease in velocity when the area of the bore increases. According to Bernoulli’s principle, this change in velocity results in a region of reduced pressure in the orifice and increased pressure in the expansion zone. The resulting increase in pressure, called pressure recovery, depends on the discharge coefficient of the orifice and the ratio of orifice to port area.
Holes with constant cross-sectional area
If `Constant' is selected for the Orifice type parameters, the block simulates flow through an orifice with a constant opening area , it is assumed that its value does not change during the simulation.
Parameterization of flow through orifice area value
If Orifice area is selected for the Orifice parameterization parameter, the block calculates the mass flow rate as:
,
where
- is the discharge coefficient Discharge coefficient;
- instantaneous open orifice area;
- cross-sectional area at ports A and B, Cross-sectional area at ports A and B;
- average density of the liquid.
Pressure drop and critical pressure drop are calculated in the same way for constant and variable area ports.
Table parameterization by flow rate
If Tabulated data - Volumetric flow rate vs. pressure drop or Tabulated data - Mass flow rate vs. pressure drop is selected for the Orifice parameterization, the flow rate is determined based on the tabulated pressure drop values , which are specified in the Pressure drop vector parameter. If you specify only non-negative values for the flow rate and pressure drop vectors, the block extrapolates the table to negative values. The flow value is interpolated from this extended table.
If the flow and differential pressure vectors contain both negative and positive values but do not contain 0, the block will set the origin to the vectors to ensure that there is no non-zero flow when the differential pressure is 0, which is unphysical.
Openings with variable cross-sectional area
If Variable is selected for the Orifice type parameters, the block will simulate flow through an orifice with a variable opening area.
If the Opening orientation parameters are set to Positive control member displacement opens orifice', the orifice opens when the signal at port S is positive. If the Opening orientation parameters are set to `Negative control member displacement opens orifice, the orifice opens when the signal at port S is negative. If the signal is positive in both cases, the opening of the orifice is determined by the magnitude of the signal.
Linear parameterization of the hole area value depending on the position of the control member
If `Linear - Area vs. control member position' is selected for the Orifice parameterization, the orifice area depends on the position of the control member and the ratio of the orifice area to the maximum position of the control member:
,
where
- is the position of the control member when the orifice is fully closed;
- value of the Control member travel between closed and open orifice parameters;
- value of parameter Maximum orifice area;
- value of parameter Leakage area;
- value of the Opening orientation parameters.
The volumetric flow rate can be determined from the pressure/flow ratio:
ρ,
where is the value of the parameter Cross-sectional area at ports A and B.
For linear parameterization, when the orifice is in the nearly open or nearly closed position, numerical stability can be maintained in the simulation by adjusting the Smoothing factor parameter. If the Smoothing factor parameters are not zero, a smooth change in the orifice area between and is achieved.
Table parameterization of the hole area value as a function of the position of the control element
If Tabulated data - Area vs. control member position is selected for the Orifice parameterization, the bore area of is interpolated from the tabulated values for bore area and control member position that you can provide.
As with the Linear data - Area vs. control member position parameterization, the volume flow rate can be determined from the pressure-flow ratio:
ρ,
where is:
- the last element of the Orifice area vector if the orifice is larger than the maximum specified orifice;
- the first element of the Orifice area vector if the hole is smaller than the minimum specified hole;
if the calculated area is between the limits of the Orifice area vector.
The value of depends on the position of the control element arriving at the S port. The block queries between data points using linear interpolation and uses nearest extrapolation for points outside the table boundaries.
Table parameterization by volumetric flow rate as a function of the position of the control element and pressure drop
If The Tabulated data - Volumetric flow rate vs. control member position and pressure drop is selected for the Orifice parameterization parameter, the volumetric flow rate values are interpolated directly from a user-supplied volumetric flow rate table based on the control member position and pressure drop across the orifice. The block queries between data points using linear interpolation and uses nearest extrapolation with respect to control member position and linear extrapolation with respect to pressure drop.
This data may include negative pressure drop and negative opening values. If a negative pressure drop is included in the data set, the volumetric flow rate will change direction. However, the flow rate will remain unchanged for negative opening values.
If the Pressure drop vector parameter, dp does not contain 0 and the Volumetric flow rate table parameter, q(s,dp) does not contain the corresponding 0 column, the block adds them to ensure that there is no non-zero flow rate at a pressure drop equal to 0, which is unphysical.
Table parameterization by mass flow rate as a function of control element position and pressure drop
If Tabulated data - Mass flow rate vs. control member position and pressure drop is selected for the Orifice parameterization parameter, the mass flow rate values are calculated directly from the control member position and pressure drop. The relationship between these three variables can be non-linear and is tabulated in the parameters Control member position vector, s, Pressure drop vector, dp and Mass flow rate table, mdot(s,dp):
where - tabular values of mass flow rate depending on the control member position and pressure drop .
The mass flow rate is corrected for temperature and pressure by the relationship , where is the average density of the liquid in the orifice and is the initial density for the parameters Reference inflow temperature and Reference inflow pressure.
Pressure losses
Pressure loss describes the reduction in pressure in a valve due to a reduction in area. The pressure loss term, , is calculated as:
Pressure loss, , accounts for the reduction in pressure in the orifice due to a reduction in area and is calculated as:
Pressure recovery describes the positive change in orifice pressure due to an increase in area. To disregard pressure recovery, uncheck the Pressure recovery box. In this case, will be set to 1.
Critical pressure drop
The critical pressure drop is the pressure drop determined from the value of the critical Reynolds number , which is the transition point between laminar and turbulent fluid flow:
Conservation of Energy
The unit treats the orifice as an adiabatic component. There is no heat exchange between the fluid and the wall that surrounds it. The fluid does not do any work as it moves from the inlet to the outlet. Under these assumptions, energy can only flow by convection through ports A and B. According to the principle of conservation of energy, the sum of energy flows in the ports must always be zero:
where is defined as the energy flux into the hole through one of the ports (A or B).
A hole type that determines whether the area of the hole can be varied:
Constant - the hole area is constant during the simulation.
Variable - the hole area varies depending on the input signal to port S.
Values
Constant | Variable
Default value
—
Program usage name
orifice_type
Evaluatable
No
#Orifice parameterization —
parameterization of a constant area hole
Orifice area | Tabulated data - Volumetric flow rate vs. pressure drop | Tabulated data - Mass flow rate vs. pressure drop
Details
The method by which the parameterization is performed. By default Orifice area defines the flow rate through the orifice area value. The values Tabulated data - Volumetric flow rate vs. pressure drop and Tabulated data - Mass flow rate vs. pressure drop allow the overall non-linear flow rate vs. pressure drop to be tabulated.
Dependencies
To use this parameter, set the Orifice type parameter to `Constant'.
Values
Orifice area | Tabulated data - Volumetric flow rate vs. pressure drop | Tabulated data - Mass flow rate vs. pressure drop
Default value
Orifice area
Program usage name
fixed_restriction_parameterization
Evaluatable
No
#Orifice parameterization —
Variable area hole parameterization
Linear - Area vs. control member position | Tabulated data - Area vs. control member position | Tabulated data - Volumetric flow rate vs. control member position and pressure drop | Tabulated data - Mass flow rate vs. control member position and pressure drop
Details
There are four parameterization options for variable area holes:
`Linear - Area vs. control member position' - the opening area depends linearly on the position of the control member in relation to the fully open or fully closed orifice. The position is set by the value at port S.
Tabulated data - Area vs. control member position - the opening area is interpolated from Control member position vector and Orifice area vector based on the position of the control element obtained at port S.
Tabulated data - Volumetric flow rate vs. control member position and pressure drop - volumetric flow rate is interpolated from user supplied parameters Control member position vector, s, Pressure drop vector, dp and Volumetric flow rate table, q(s,dp) based on control member position obtained at port S and pressure drop across ports A and B.
`Tabulated data - Mass flow rate vs. control member position and pressure drop' - mass flow rate is interpolated from user-supplied parameters Control member position vector, s, Pressure drop vector, dp, and Mass flow rate table, mdot(s,dp) based on control member position obtained at port S and pressure drop across ports A and B.
Dependencies
To use this parameter, set the Orifice type parameters to `Variable'.
Values
Linear - Area vs. control member position | Tabulated data - Area vs. control member position | Tabulated data - Volumetric flow rate vs. control member position and pressure drop | Tabulated data - Mass flow rate vs. control member position and pressure drop
#Pressure drop vector —
vector of differential pressure values
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Details
Vector of differential pressure values for tabular parameterization by flow rate. The differential pressure vector values correspond to the Volumetric flow rate vector or Mass flow rate vector. The differential pressure vector values are listed in ascending order. The flow rate value is interpolated from the Volumetric flow rate vector or Mass flow rate vector parameters, which depend on the Pressure drop vector parameter.
Dependencies
To use this parameter, set the Orifice type parameter to `Constant' and the Orifice parameterization parameter to `Tabulated data - Volumetric flow rate vs. pressure drop' or `Tabulated data - Mass flow rate vs. pressure drop'.
Values
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Vector of volume flow values for tabular parameterization by volume flow. The volume flow values correspond to the pressure drop values in the Pressure drop vector parameters. The flow rate value is interpolated from the Volumetric flow rate vector, which depends on the Pressure drop vector parameters.
Dependencies
To use this parameter, set the Orifice type parameter to `Constant' and the Orifice parameterization parameter to `Tabulated data - Volumetric flow rate vs. pressure drop'.
#Mass flow rate vector —
vector of mass flow rate values
kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)
Details
Vector of mass flow values for tabular mass flow parameterization. The mass flow rate values correspond to the pressure drop values in the Pressure drop vector parameters. The flow rate value is interpolated from the Mass flow rate vector, which depends on the Pressure drop vector parameters.
Dependencies
To use this parameter, set the Orifice type parameter to `Constant' and the Orifice parameterization parameter to `Tabulated data - Mass flow rate vs. pressure drop'.
#Control member position at closed orifice —
control element offset
m | cm | ft | in | km | mi | mm | um | yd
Details
Initial offset of the regulating element when the orifice is fully closed.
Dependencies
To use this parameter, set the Orifice type parameter to `Variable' and the Orifice parameterization parameter to `Linear - Area vs. control member position'.
Values
m | cm | ft | in | km | mi | mm | um | yd
Default value
0.0 m
Program usage name
min_control_displacement
Evaluatable
Yes
#Control member travel between closed and open orifice —
maximum stroke of the regulating element
m | cm | ft | in | km | mi | mm | um | yd
Details
The maximum distance that the control element travels between the closed and open orifices.
The orifice is fully open when the parameters Control member position at closed orifice and Control member travel between closed and open orifice are summed.
Dependencies
To use this parameter, set the Orifice type parameter to `Variable' and the Orifice parameterization parameter to `Linear - Area vs. control member position'.
Values
m | cm | ft | in | km | mi | mm | um | yd
Default value
5e-3 m
Program usage name
delta_control_displacement
Evaluatable
Yes
#Opening orientation —
direction of movement of the opening element
Positive control member displacement opens orifice | Negative control member displacement opens orifice
Details
The direction of movement of the element opening the variable orifice. Positive orientation means that a positive signal on the S port opens the hole. Negative orientation means that a negative signal on S opens the port.
Dependencies
To use this parameter, set the Orifice type parameter to `Variable' and the Orifice parameterization parameter to `Linear - Area vs. control member position'.
Values
Positive control member displacement opens orifice | Negative control member displacement opens orifice
Default value
Positive control member displacement opens orifice
Program usage name
opening_orientation
Evaluatable
No
#Maximum orifice area —
maximum opening area
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2
Details
Maximum opening area of the hole during simulation.
With usage of Tabulated data - Area vs. control member position, the maximum hole area is the last element of the Orifice area vector.
Dependencies
To use this parameter, set the Orifice type parameter to Variable and the Orifice parameterization parameter to Linear - Area vs. control member position.
#Leakage area —
leakage area through the opening in the fully closed position
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2
Details
The sum of all clearances when the orifice is fully closed. Any area less than this value equates to the specified leakage area. This parameter contributes to the stability of the numerical solution by maintaining flow continuity.
Dependencies
To use this parameter, set the Orifice type parameter to `Variable' and the Orifice parameterization parameter to `Linear - Area vs. control member position'.
#Control member position vector —
position vector of control elements
m | cm | ft | in | km | mi | mm | um | yd
Details
Control element position vector for the tabular parameterization of the hole area. The position values of the controls correspond to the values of the Orifice area vector. The elements of the vector must be strictly monotonically increasing or decreasing. The hole area is interpolated from the Orifice area vector, which depends on the Control member position vector parameters.
Dependencies
To use this parameter, set the Orifice type parameter to `Variable' and the Orifice parameterization parameter to `Tabulated data - Area vs. control member position'.
Values
m | cm | ft | in | km | mi | mm | um | yd
Default value
[0.0, 2.0e-3, 4.0e-3, 7.0e-3, 1.7e-2] m
Program usage name
control_displacement_vector_1D
Evaluatable
Yes
#Orifice area vector —
vector of hole opening area values
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2
Details
Value vector for the tabular parameterization of the opening area. The values in this vector correspond to the elements in the Control member position vector parameters. If the vector values are increasing, the first element of this vector is the leakage area of the hole and the last element is the maximum hole area. If the vector values are decreasing, the first element of this vector is the maximum hole area and the last element is the leakage area. The hole area is interpolated from the Orifice area vector parameter, which depends on the Control member position vector parameter.
Dependencies
To use this parameter, set the Orifice type parameter to `Variable' and the Orifice parameterization parameter to `Tabulated data - Area vs. control member position'.
Correction factor that takes into account the discharge losses.
Dependencies
To use this parameters, set:
Variable for the Orifice type parameter and Linear - Area vs. control member position or Tabulated data - Area vs. control member position for the Orifice parameterization parameter.
for the Orifice type parameter the value Constant, and for the Orifice parameterization the value Orifice area.
Default value
0.64
Program usage name
C_d
Evaluatable
Yes
#Critical Reynolds number —
upper limit of Reynolds number for laminar flow
Details
Upper limit of Reynolds number for laminar flow through an orifice.
Dependencies
To use this parameter, set:
Variable for the Orifice type parameter and Linear - Area vs. control member position or Tabulated data - Area vs. control member position for the Orifice parameterization parameter.
for the Orifice type parameter the value Constant, and for the Orifice parameterization the value Orifice area.
Numerical smoothing factor that ensures smooth opening by correcting the orifice characteristic in the nearly open and nearly closed positions.
The value must lie in the range [0, 1].
Dependencies
To use this parameter, set the Orifice type parameter to Variable and the Orifice parameterization parameter to Linear - Area vs. control member position.
Default value
0.01
Program usage name
smoothing_factor
Evaluatable
Yes
#Pressure recovery —
whether to take into account the increase in pressure when expanding the area
Details
Whether to take into account the pressure increase when the fluid flows from a region with a smaller cross-sectional area to a region with a larger cross-sectional area.
Dependencies
To use this parameter, set:
Variable for the Orifice type parameter and Linear - Area vs. control member position or Tabulated data - Area vs. control member position for the Orifice parameterization parameter.
for the Orifice type parameter the value Constant, and for the Orifice parameterization the value Orifice area.
Default value
false (switched off)
Program usage name
pressure_recovery
Evaluatable
No
#Control member position vector, s —
position vector of the control element
m | cm | ft | in | km | mi | mm | um | yd
Details
Control element position vector for flow rate table parameterization. The position values of the controls correspond to the differential pressure values Pressure drop vector, dp and the flow values Volumetric flow rate table, q(s,dp) or Mass flow rate table, mdot(s,dp). A positive offset corresponds to an opening of the orifice. Values are listed in ascending order, the first element must be equal to 0. Linear interpolation is used between data points.
Dependencies
To use this parameter, set the Orifice type parameter to Variable and the Orifice parameterization parameter to Tabulated data - Volumetric flow rate vs. control member position and pressure drop or Tabulated data - Mass flow rate vs. control member position and pressure drop.
Values
m | cm | ft | in | km | mi | mm | um | yd
Default value
[0.0, 2.0e-3, 4.0e-3, 7.0e-3, 1.7e-2] m
Program usage name
control_displacement_vector_2D
Evaluatable
Yes
#Pressure drop vector, dp —
vector of differential pressure values
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Details
Vector of differential pressure values for flow rate table parameterization. The differential pressure values correspond to the positions of the Control member position vector, s and the flow rates of the Volumetric flow rate table, q(s,dp) or Mass flow rate table, mdot(s,dp). Values are listed in ascending order and must be greater than 0. Linear interpolation is used between data points.
Dependencies
To use this parameter, set the Orifice type parameter to Variable and the Orifice parameterization parameter to Tabulated data - Volumetric flow rate vs. control member position and pressure drop or Tabulated data - Mass flow rate vs. control member position and pressure drop.
Values
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Matrix at of volume flow rates corresponding to differential pressure values and positions of the control element.
The values and are the dimensions of the corresponding vectors:
- number of elements in the pressure drop vector Pressure drop vector, dp.
- number of elements in the control member position vector Control member position vector, s.
Dependencies
To use this parameter, set the Orifice type parameter to `Variable' and the Orifice parameterization parameter to `Tabulated data - Volumetric flow rate vs. control member position and pressure drop'.
Matrix at of mass flow rates corresponding to differential pressure values and positions of the control element.
The values and are the dimensions of the corresponding vectors:
- number of elements in the pressure drop vector Pressure drop vector, dp.
- number of elements in the control member position vector Control member position vector, s.
Dependencies
To use this parameter, set the Orifice type parameter to `Variable' and the Orifice parameterization parameter to `Tabulated data - Mass flow rate vs. control member position and pressure drop'.
#Reference inflow temperature —
inlet temperature at which tabular data is to be specified
K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR
Details
Nominal inlet temperature including absolute zero at which to specify tabular data. This parameters is used to adjust the mass flow rate according to the temperature measured during the simulation.
Dependencies
To use this parameters, set:
Variable for the Orifice type parameter and Tabulated data - Mass flow rate vs. control member position and pressure drop for the Orifice parameterization parameter.
for Orifice type the value Constant and for Orifice parameterization the value Tabulated data - Mass flow rate vs. pressure drop.
#Reference inflow pressure —
inlet pressure at which tabulated data should be specified
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Details
Nominal inlet pressure including absolute zero at which to specify tabular data. This parameters is used to adjust the mass flow rate according to the pressure measured during the simulation.
Dependencies
To use this parameters, set:
Variable for the Orifice type parameter and Tabulated data - Mass flow rate vs. control member position and pressure drop for the Orifice parameterization parameter.
for Orifice type the value Constant and for Orifice parameterization the value Tabulated data - Mass flow rate vs. pressure drop.
Values
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Default value
0.101325 MPa
Program usage name
p_inflow_ref
Evaluatable
Yes
#Cross-sectional area at ports A and B —
area at the inlet or outlet of the hole
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2
Details
The cross-sectional area of the orifices at the inlet and outlet A and B. This area is used in calculating the mass flow rate through the orifice.