Orifice (TL)

Constant-area or variable-area orifice in a thermal liquid system

Since R2022a

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Libraries:
Simscape / Fluids / Thermal Liquid / Valves & Orifices

Description

The Orifice (TL) block models the flow through a local restriction with a constant or variable opening area. For variable orifices, a control member connected to port S sets the opening position. The opening area is parametrized either linearly or by lookup table.

The block conserves mass such that

$${\dot{m}}_A+{\dot{m}}_B=\rho v_A{A}_A+\rho v_B{A}_B=0.$$

This mass balance implies that there is an increase in velocity when there is a decrease in area, and there is a reduction in velocity when the flow discharges into a larger area. In accordance with the Bernoulli principle, this change in velocity results in a region of lower pressure in the orifice and a higher pressure in the expansion zone. The resulting increase in pressure, which is called pressure recovery, depends on the discharge coefficient of the orifice and the ratio of the orifice and port areas.

Constant Orifices

For constant orifices, the orifice area, A_orifice, does not change over the course of the simulation.

Using the Constant Area Parameterization

The block calculates the mass flow rate as

$$\dot{m}=\frac{C_d{A}_{orifice}\sqrt{2\overline{\rho }}}{\sqrt{P{R}_{loss}\left(1-{\left(\frac{A_{orifice}}{A_{port}}\right)}^2\right)}}\sqrt{p_A-p_B}\approx \frac{C_d{A}_{orifice}\sqrt{2\overline{\rho }}}{\sqrt{P{R}_{loss}\left(1-{\left(\frac{A_{orifice}}{A_{port}}\right)}^2\right)}}\frac{p_A-p_B}{{\left[{\left(p_A-p_B\right)}^2+\Delta p_{crit}\right]}^{1/4}},$$

where:

• C_d is the Discharge coefficient parameter.

• A_orifice is the instantaneous orifice open area.

• A_port is the Cross-sectional area at ports A and B parameter.

• $$\overline{\rho }$$ is the average fluid density.

PR_loss and Δp_crit are calculated in the same manner for constant and variable orifices.

This approximation for $$\dot{m}$$ and the Local Resistance (TL) block are the same.

Using the Tabulated data - Volumetric flow rate vs. pressure drop Parameterization

The volumetric flow rate is determined from the tabulated values of the pressure differential, Δp, which you can provide. If you provide only non-negative values for both the volumetric flow rate and pressure drop vectors, the block extrapolates the table to contain negative values. The volumetric flow rate is interpolated from this extended table.

If the Volumetric flow rate vector and Pressure drop vector parameters contain both negative and positive values but no 0, the block inserts an origin into the vectors to ensure the valve does not have nonzero flow rate when the pressure drop is 0, which is non-physical.

Variable Orifices

For variable orifices, when you set Opening orientation to Positive control member displacement opens orifice opens the orifice when the signal at S is positive, while a Negative control member displacement opens orifice orientation opens the orifice when the signal at S is negative. In both cases, the signal is positive and the orifice opening is set by the magnitude of the signal.

Using the Linear - Area vs. control member position Parameterization

The orifice area A_orifice is based on the control member position and the ratio of orifice area and maximum control member position:

$$A_{orifice}=\frac{\left(A_{\max }-A_{leak}\right)}{\Delta S}\left(S-S_{\min }\right)\epsilon +A_{leak},$$

where:

• S_min is the Control member position at closed orifice parameter.

• ΔS is the Control member travel between closed and open orifice parameter.

• A_max is the Maximum orifice area parameter.

• A_leak is the Leakage area parameter.

• ε is the Opening orientation parameter.

The volumetric flow rate is determined by the pressure-flow rate equation:

$$\dot{m}=\frac{C_d{A}_{orifice}\sqrt{2\overline{\rho }}}{\sqrt{P{R}_{loss}\left(1-{\left(\frac{A_{orifice}}{A}\right)}^2\right)}}\frac{\Delta p}{{\left[\Delta p^2+\Delta p_{crit}^2\right]}^{1/4}},$$

where A is the Cross-sectional area at ports A and B.

When the orifice is in a near-open or near-closed position in the linear parameterization, you can maintain numerical robustness in your simulation by adjusting the Smoothing factor parameter. If the Smoothing factor parameter is nonzero, the block smoothly saturates the opening area between A_leak and A_max. For more information, see Numerical Smoothing.

Using the Tabulated data - Area vs. control member position Parameterization

When you use the Tabulated data - Area vs. control member position parameterization, the orifice area A_orifice is interpolated from the tabulated values of opening area and the control member position, ΔS, which you can provide. As with the Linear - Area vs. control member position parameterization, the volumetric flow rate is determined by the pressure-flow rate equation:

$$\dot{m}=\frac{C_d{A}_{orifice}\sqrt{2\overline{\rho }}}{\sqrt{P{R}_{loss}\left(1-{\left(\frac{A_{orifice}}{A}\right)}^2\right)}}\frac{\Delta p}{{\left[\Delta p^2+\Delta p_{crit}^2\right]}^{1/4}},$$

where A_orifice is:

• A_max, the last element of the Orifice area vector parameter, if the physical signal at port S is larger than the last element of the Control member position vector parameter.

• A_leak, the first element of the Orifice area vector parameter, if the physical signal at port S is smaller than the first element of the Control member position vector parameter.

• The linearly interpolated value of the Orifice area vector parameter if the calculated area is between the limits of the first and last element of the Control member position vector parameter.

A_orifice is a function of the control member position received at port S. The block queries between data points with linear interpolation and uses nearest extrapolation for points beyond the table boundaries.

Using the Tabulated data - Volumetric flow rate vs. control member position and pressure drop Parameterization

The Tabulated data - Volumetric flow rate vs. control member position and pressure drop parameterization interpolates the volumetric flow rate directly from a user-provided volumetric flow rate table, which is based on the control member position and pressure drop over the orifice. The block queries between data points with linear interpolation and uses nearest extrapolation with respect to control member position and linear extrapolation with respect to pressure drop.

This data can include negative pressure drops and negative opening values. If a negative pressure drop is included in the dataset, the volumetric flow rate will change direction. However, the flow rate will remain unchanged for negative opening values.

If the Pressure drop vector, dp parameter does not contain a 0 and the Volumetric flow rate table, q(s,dp) parameter does not contain a corresponding column of 0's, the block inserts them to ensure the valve does not have nonzero flow rate when the pressure drop is 0, which is non-physical.

Using the Tabulated data - Mass flow rate vs. control member position and pressure drop Parameterization

Tabulated data - Mass flow rate vs. control member position and pressure drop — Calculate the mass flow rate directly from the control member position and the pressure drop across the valve. The relationship between the three variables can be nonlinear and it is given by the tabulated data in the Control member position vector, s, Pressure drop vector, dp, and Mass flow rate table, mdot(s,dp) block parameters:

$${\dot{m}}_{\text{Tab}}=\frac{{\rho }_{\text{Avg}}}{{\rho }_{\text{Ref}}}\dot{m}(\Delta S,\Delta p),$$

where $$\dot{m}$$ is the tabulated form of the mass flow rate, a function of the control member position, h, and of the pressure drop across the orifice, Δp. The mass flow rate is adjusted for temperature and pressure by the ratio ρ_Avg/ρ_Ref, where ρ_Avg is the average fluid density in the orifice and ρ_ref is the reference density for the values of the Reference inflow temperature and Reference inflow pressure parameters.

Pressure Loss

Pressure loss describes the reduction of pressure in the valve due to a decrease in area. The block calculates the pressure loss term, PR_loss as:

$$P{R}_{loss}=\frac{\sqrt{1-{\left(\frac{A_{orifice}}{A_{port}}\right)}^2\left(1-C_d^2\right)}-C_d\frac{A_{orifice}}{A_{port}}}{\sqrt{1-{\left(\frac{A_{orifice}}{A_{port}}\right)}^2\left(1-C_d^2\right)}+C_d\frac{A_{orifice}}{A_{port}}}.$$

Pressure recovery describes the positive pressure change in the valve due to an increase in area. If you do not wish to capture this increase in pressure, clear the Pressure recovery check box. In this case, PR_loss is 1.

Critical Pressure

The critical pressure difference, Δp_crit, is the pressure differential associated with the Critical Reynolds number parameter, Re_crit, which is the point of transition between laminar and turbulent flow in the fluid:

$$\Delta p_{crit}=\frac{\pi \overline{\rho }}{8A_{orifice}}{\left(\frac{\nu {\mathrm{Re}}_{crit}}{C_d}\right)}^2.$$

Energy Balance

The block treats the orifice as an adiabatic component. No heat exchange can occur between the fluid and the wall that surrounds it. No work is done on or by the fluid as it traverses from inlet to outlet. With these assumptions, energy can flow by advection only, through ports A and B. By the principle of conservation of energy, the sum of the port energy flows must always equal zero:

$${\varphi }_{\text{A}}+{\varphi }_{\text{B}}=0,$$

where ϕ is defined as the energy flow rate into the orifice through one of the ports (A or B).

Examples

Engine Cooling System

Model an engine cooling system with an oil cooling circuit.

Open Model

Ports

Input

S — Control member displacement, m

physical signal

Instantaneous displacement of the valve control member.

Conserving

A — Flow passage

thermal liquid

Thermal liquid conserving port associated with the opening through which the flow can enter or exit the valve.

B — Flow passage

thermal liquid

Thermal liquid conserving port associated with the opening through which the flow can enter or exit the valve.

Parameters

Orifice type — Type of orifice

Variable (default) | Constant

Type of orifice, defined by the orifice area. When set to Variable, the orifice area varies according to the input signal received at port S.

• Orifice area—The assigned area does not change over the simulation.

• Tabulated data - Volumetric flow rate vs. pressure drop—The area remains constant, but the volumetric flow rate through the orifice can vary. This value is interpolated directly from the Volumetric flow rate vector and the Pressure drop vector dataset.

• Tabulated data - Mass flow rate vs. pressure drop—The area remains constant, but the volumetric flow rate through the orifice can vary. This value is interpolated directly from the Mass flow rate vector and the Pressure drop vector dataset.

When you set Orifice type to Variable, there are four options.

• Linear - Area vs. control member position. Area is determined by a linear relationship to the control member position with respect to a fully open or fully closed orifice. The position is set by a varying physical signal at port S.

• Tabulated data - Area vs. control member position. The opening area is interpolated from the Control member position vector and the Orifice area vector based on the control member position received at port S.

• Tabulated data - Volumetric flow rate vs. control member position and pressure drop. The volumetric flow rate is directly interpolated from the user- provided Control member position vector, s, Pressure drop vector, dp, and Volumetric flow rate table, q(s,dp) parameters based on the control member position received at port S and the pressure drop across ports A and B.

• Tabulated data - Mass flow rate vs. control member position and pressure drop. The mass flow rate is directly interpolated from the user- provided Control member position vector, s, Pressure drop vector, dp, and Mass flow rate table, mdot(s,dp) parameters based on the control member position received at port S and the pressure drop across ports A and B.

Orifice parameterization — Constant orifice parameterization

Orifice area (default) | Tabulated data - Volumetric flow rate vs. pressure drop | Tabulated data - Mass flow rate vs. pressure drop

Method by which to model the opening characteristics of the orifice. The default setting prescribes a linear relationship between the orifice opening area and the orifice opening. The alternative settings allow for a general, nonlinear relationship to be specified in tabulated form, in one case between the opening area and the orifice opening, in the other case between the mass flow rate and both the orifice opening and the pressure drop between the ports.

Dependencies

To enable this parameter, set Orifice type to Constant.

Orifice parameterization — Variable orifice parameterization

Linear - Area vs. control member position (default) | 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

When you set Orifice type to Variable, there are four options.

• Linear - Area vs. control member position. Area is determined by a linear relationship to the control member position with respect to a fully open or fully closed orifice. The position is set by a varying physical signal at port S.

• Tabulated data - Area vs. control member position. The opening area is interpolated from the Control member position vector and the Orifice area vector based on the control member position received at port S.

• Tabulated data - Volumetric flow rate vs. control member position and pressure drop. The volumetric flow rate is directly interpolated from the user- provided Control member position vector, s, Pressure drop vector, dp, and Volumetric flow rate table, q(s,dp) parameters based on the control member position received at port S and the pressure drop across ports A and B.

• Tabulated data - Mass flow rate vs. control member position and pressure drop. The mass flow rate is directly interpolated from the user- provided Control member position vector, s, Pressure drop vector, dp, and Mass flow rate table, mdot(s,dp) parameters based on the control member position received at port S and the pressure drop across ports A and B.

Dependencies

To enable this parameter, set Orifice type to Variable.

Orifice area — Area of orifice opening

1e-3 m^2 (default) | positive scalar

Cross-sectional area of the orifice opening.

Dependencies

To enable this parameter, set Orifice type to Constant and Orifice parameterization to Orifice area.

Pressure drop vector — Vector of differential pressure values for tabulated parameterization

[-4, -3, -2, -1, -.5, 0, .5, 1, 2, 3, 4] MPa (default) | 1-by-n vector

Vector of pressure differential values for the tabulated parameterization of volumetric flow rate. The values in this vector correspond one-to-one to values in the Volumetric flow rate vector parameter. The pressure drop vector values are listed in ascending order. The volumetric flow rate is interpolated directly from the Volumetric flow rate vector parameter, which depends on the Pressure drop vector parameter.

Dependencies

To enable this parameter, set Orifice type to Constant and Orifice parameterization to Tabulated data - Volumetric flow rate vs. pressure drop.

Volumetric flow rate vector — Vector of volumetric flow rate values

[-2.44, -2.12, -1.68, -1.22, -.84, 0, .85, 1.21, 1.7, 2.09, 2.41] .* 1e-3 m^3/s (default) | 1-by-n vector

Vector of volumetric flow rate values for the tabulated parameterization of volumetric flow rate. The values in this vector correspond one-to-one to values in the Pressure drop vector parameter. The volumetric flow rate is interpolated directly from the provided Volumetric flow rate vector parameter, which depends on the Pressure drop vector parameter.

Dependencies

To enable this parameter, set Orifice type to Constant and Orifice parameterization to Tabulated data - Volumetric flow rate vs. pressure drop.

Mass flow rate vector — Vector of mass flow rate values

[-2.44, -2.12, -1.68, -1.22, -.84, 0, .85, 1.21, 1.7, 2.09, 2.41] kg/s (default) | vector | 1-by-n vector

Vector of mass flow rate values for the tabulated parameterization of volumetric flow rate. The values in this vector correspond one-to-one to values in the Pressure drop vector parameter. The mass flow rate is interpolated directly from the provided Mass flow rate vector parameter, which depends on the Pressure drop vector parameter.

Dependencies

To enable this parameter, set Orifice type to Constant and Orifice parameterization to Tabulated data - Mass flow rate vs. pressure drop.

Control member position at closed orifice — Control member offset

0 m (default) | scalar

Initial control member offset when the variable orifice is fully closed.

Dependencies

To enable this parameter, set Orifice type to Variable and set Orifice parameterization to Linear – Area vs. control member position.

Control member travel between closed and open orifice — Control member maximum stroke

5e-3 m (default) | positive scalar

Maximum distance the control member travels between closed and open orifice. The orifice is fully open at the sum of the Control member position at closed orifice and Control member travel between closed and open orifice parameters.

Dependencies

To enable this parameter, set Orifice type to Variable and Orifice parameterization to Linear - Area vs. control member position.

Opening orientation — Direction of member movement that opens the orifice

Positive control member displacement opens orifice (default) | Negative control member displacement opens orifice

Direction of member displacement that opens a variable orifice. A positive orientation means that a positive signal at S opens the orifice. A negative orientation means that a negative signal at S opens the orifice.

Dependencies

To enable this parameter, set Orifice type to Variable and Orifice parameterization to Linear - Area vs. control member position.

Maximum orifice area — Maximum orifice opening area

1e-4 m^2 (default) | positive scalar

Maximum orifice area experienced during simulation. When using Tabulated data - Area vs. control member position, the maximum orifice area is the last element of the Orifice area vector parameter.

Dependencies

To enable this parameter, set Orifice type to Variable and Orifice parameterization to Linear - Area vs. control member position.

Leakage area — Orifice gap area when in fully closed position

1e-10 m^2 (default) | positive scalar

Sum of all gaps when the valve is in fully closed position. Any area smaller than this value is maintained at the specified leakage area. This parameter contributes to numerical stability by maintaining continuity in the flow.

Dependencies

To enable this parameter, set Orifice type to Variable and Orifice parameterization to Linear - Area vs. control member position.

Control member position vector — Vector of control member positions

[0, .002, .004, .007, .017] m (default) | 1-by-n vector

Vector of control member positions for the tabulated parameterization of orifice area. The vector elements correspond one-to-one to the values in the Orifice area vector parameter. The vector elements must be either strictly monotonically increasing or decreasing. The orifice opening area is interpolated from the Orifice area vector, which depends on the Control member position vector parameter.

Dependencies

To enable this parameter, set Orifice type to Variable and Orifice parameterization to Tabulated data - Area vs. control member position.

Orifice area vector — Vector of orifice opening area values

[1e-09, 2.0352e-07, 4.0736e-05, .00011438, .00034356] m^2 (default) | 1-by-n vector

Vector of orifice area values for the tabulated parameterization of orifice area. The values in this vector correspond one-to-one with the elements in the Control member position vector parameter. If the vector is increasing, the first element of this vector is the orifice leakage area and the last element is the maximum orifice area. If the vector is decreasing, the first element of this vector is the orifice maximum orifice area and the last element is the leakage area. The orifice opening area is interpolated from the Orifice area vector parameter, which depends on the Control member position vector parameter.

Dependencies

To enable this parameter, set Orifice type to Variable and Orifice parameterization to Tabulated data - Area vs. control member position.

Discharge coefficient — Discharge coefficient

0.64 (default) | positive scalar

Correction factor that accounts for discharge losses in theoretical flows.

Dependencies

To enable this parameter, set either:

• Orifice type to Variable and Orifice parameterization to either Linear - Area vs. control member position or Tabulated data - Area vs. control member position.

• Orifice type to Constant and Orifice parameterization to Orifice area.

Critical Reynolds number — Upper Reynolds number limit for laminar flow

150 (default) | positive scalar

Upper Reynolds number limit for laminar flow through the orifice.

Dependencies

To enable this parameter, set either:

• Orifice type to Variable and Orifice parameterization to either Linear - Area vs. control member position or Tabulated data - Area vs. control member position.

• Orifice type to Constant and Orifice parameterization to Orifice area.

Smoothing factor — Numerical smoothing factor

0.01 (default) | positive scalar in the range [0,1]

Continuous smoothing factor that introduces a layer of gradual change to the flow response when the orifice is in near-open or near-closed positions. Set this value to a nonzero value less than one to increase the stability of your simulation in these regimes.

Dependencies

To enable this parameter, set Orifice type to Variable and Orifice parameterization to Linear - Area vs. control member position.

Pressure recovery — Whether to account for pressure increase in area expansions

on (default) | off

Whether to account for pressure increase when fluid flows from a region of smaller cross-sectional area to a region of larger cross-sectional area. This increase in pressure is not captured when you clear Pressure recovery check box.

Dependencies

To enable this parameter, set either:

• Orifice type to Variable and Orifice parameterization to either Linear - Area vs. control member position or Tabulated data - Area vs. control member position.

• Orifice type to Constant and Orifice parameterization to Orifice area.

Control member position vector, s — Vector of opening values

[0, .002, .004, .007, .017] m (default) | 1-by-n vector

Vector of control member positions for tabulated parametrization of volumetric flow rate. The control member position vector forms an independent axis with the Pressure drop vector, dp parameter for the 2-D dependent Volumetric flow rate table, q(s,dp) parameter. A positive displacement corresponds to valve opening. The values are listed in ascending order and the first element must be 0. Linear interpolation is employed between table data points.

Dependencies

To enable this parameter, set Orifice type to Variable and Orifice parameterization 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.

Pressure drop vector, dp — Vector of pressure drop values

[.3, .5, .7] MPa (default) | 1-by-n vector

Vector of pressure drop values for tabulated parametrization of volumetric flow rate. The pressure drop vector forms an independent axis with the Control member position vector, s parameter for the 2-D dependent Volumetric flow rate table, q(s,dp) parameter. The values are listed in ascending order and must be greater than 0. Linear interpolation is employed between table data points.

Dependencies

To enable this parameter, set Orifice type to Variable and Orifice parameterization to Tabulated data - Volumetric flow rate vs. control member position and pressure drop.

Dependencies

To enable this parameter, set Orifice type to Variable and Orifice parameterization 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.

Volumetric flow rate table, q(s,dp) — Array of volumetric flow rate values

[1.7e-05, 2e-05, 2.6e-05; .0035, .0045, .0053; .7, .9, 1.06; 1.96, 2.5, 3; 6, 7.7, 9.13] .* 1e-3 m^3/s (default) | M-by-N matrix

M-by-N matrix of volumetric flow rates based on independent values of pressure drop and control member position. M and N are the sizes of the corresponding vectors:

• M is the number of elements in the Pressure drop vector, dp parameter.

• N is the number of elements in the Control member position vector, s parameter.

Dependencies

To enable this parameter, set Orifice type to Variable and Orifice parameterization to Tabulated data - Volumetric flow rate vs. control member position and pressure drop.

Mass flow rate table, mdot(s,dp) — Array of mass flow rate values

[1.7e-05, 2e-05, 2.6e-05; .0035, .0045, .0053; .7, .9, 1.06; 1.96, 2.5, 3; 6, 7.7, 9.13] kg/s (default) | M-by-N matrix

Mass flow rates based on independent values of pressure drop and control member position. M and N are the sizes of the corresponding vectors:

• M is the number of elements in the Pressure drop vector, dp parameter.

• N is the number of elements in the Control member position vector, s parameter.

Dependencies

To enable this parameter, set Orifice type to Variable and Orifice parameterization to Tabulated data - Mass flow rate vs. control member position and pressure drop.

Reference inflow temperature — Inlet temperature at which to specify the tabulated data

293.15 K (default) | positive scalar in units of temperature

Nominal inlet temperature, with reference to absolute zero, at which to specify the tabulated data. This parameter is used to adjust the mass flow rate according to the temperature measured during simulation.

Dependencies

To enable this parameter, set Orifice parameterization to Tabulated data - Mass flow rate vs. opening and pressure drop.

Reference inflow pressure — Inlet pressure at which to specify the tabulated data

0.101325 MPa (default) | positive scalar in units of pressure

Nominal inlet pressure, with reference to absolute zero, at which to specify the tabulated data. This parameter is used to adjust the mass flow rate according to the pressure measured during simulation.

Dependencies

To enable this parameter, set Orifice parameterization to Tabulated data - Mass flow rate vs. opening and pressure drop.

Cross-sectional area at ports A and B — Area at orifice entry or exit

0.01 m^2 (default) | positive scalar

Cross-sectional area at the entry and exit ports A and B. This area is used in the pressure-flow rate equation that determines the mass flow rate through the orifice.

Dependencies

To enable this parameter, set either:

• Orifice type to Variable and Orifice parameterization to either Linear - Area vs. control member position or Tabulated data - Area vs. control member position.

• Orifice type to Constant and Orifice parameterization to Orifice area.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2022a

R2023b: Model non-monotonic area and volumetric flow rate parameters

The block no loner requires the Orifice area vector, Volumetric flow rate table, q(s,dp), or Mass flow rate table, mdot(s,dp) parameters to monotonically increase or decrease with respect to the Control member position vector, s parameter.