Pressure Reducing Valve (TL)

Pressure reducing valve in a thermal liquid network

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

Description

The Pressure Reducing Valve (TL) block represents a valve that reduces downstream pressure in a thermal liquid network. The valve remains open when the pressure at port B is less than a specified pressure. When the pressure at port B meets or surpasses this pressure, the valve closes. The block operates based on the differential between the set pressure and the pressure at port B.

Mass Balance

The mass conservation equation in the valve is

$${\dot{m}}_A+{\dot{m}}_B=0,$$

where:

• $${\dot{m}}_A$$ is the mass flow rate into the valve through port A.

• $${\dot{m}}_B$$ is the mass flow rate into the valve through port B.

Mass Flow Rate

The block calculates the mass flow rate as

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

where:

• C_d is the value of the Discharge coefficient parameter.

• A_valve is the instantaneous valve open area.

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

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

• Δp is the valve pressure difference p_A – p_B.

The critical pressure difference, Δp_crit, is the pressure differential associated with the Critical Reynolds number, Re_crit, the flow regime transition point between laminar and turbulent flow:

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

where μ is the dynamic viscosity of the thermal liquid.

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

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

The pressure recovery describes the positive pressure change in the valve due to an increase in area. When you clear the Pressure recovery check box, the block sets PR_loss to 1.

Opening Parameterization

When you set the Opening parameterization parameter to Linear - Area vs. pressure, the block calculates the opening area as

$$A_{valve}=\widehat{p}\left(A_{leak}-A_{max}\right)+A_{max},$$

where A_leak is the value of the Leakage Area parameter and A_max is the value of the Maximum opening area parameter. The normalized pressure, $$\widehat{p}$$, is

$$\widehat{p}=\frac{p_{control}-p_{set}}{p_{Max}-p_{set}},$$

where

• p_set is the valve set pressure:

  $$p_{set}=p_{set,gauge}+p_{Atm},$$

  where P_Atm is the atmospheric pressure.

• p_Max is the maximum pressure

  $$p_{Max}=p_{set,gauge}+p_{range}+p_{Atm}.$$

This figure shows how the block controls the opening area using the linear parameterization.

When the valve 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 control pressure between p_set and p_max. For more information, see Numerical Smoothing.

When you set Opening parameterization to Tabulated data - Area vs. pressure, the block calculates the opening area as

$$A_{valve}=tablelookup\left(p_{control,TLU,ref},A_{TLU},p_{control},interpolation=linear,extrapolation=nearest\right),$$

where:

• p_{control,TLU,ref} = p_TLU + p_offset.

• p_TLU is the Pressure differential vector parameter.

• p_offset is an internal pressure offset that causes the valve to start closing when p_{control,TLU,ref} = p_set.

• A_TLU is the Opening area vector parameter.

This figure shows how the block controls the opening area when Opening parameterization is Tabulated data - Area vs. pressure.

When you set Opening parameterization to Tabulated data - Volumetric flow rate vs. pressure, the valve opens according to the user-provided tabulated data of volumetric flow rate and pressure differential between ports A and B.

The block calculates the mass flow rate as

$$\dot{m}=\overline{\rho }\dot{V},$$

where:

• $$\dot{V}$$ is the volumetric flow rate.

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

The block calculates the relationship between the mass flow and pressure using

$$\dot{m}=K\overline{\rho }\sqrt{\Delta p},$$

where

$$\text{K=}\frac{\dot{V}}{\sqrt{\left|\Delta p\right|}}.$$

Opening Dynamics

When you select Opening dynamics, the block introduces a control pressure lag where p_control becomes the dynamic control pressure, p_dyn. The instantaneous change in dynamic opening area is calculated based on the Opening time constant parameter, τ:

$${\dot{p}}_{dyn}=\frac{p_{control}-p_{dyn}}{\tau }.$$

By default, the block clears the Opening dynamics check box.

Energy Balance

The energy conservation equation in the valve is

$${\varphi }_A+{\varphi }_B=0,$$

where:

• ϕ_A is the energy flow rate into the valve through port A.

• ϕ_B is the energy flow rate into the valve through port B.

Predefined Parameterization

You can populate the block with pre-parameterized manufacturing data, which allows you to model a specific supplier component.

To load a predefined parameterization:

1. In the block dialog box, next to Selected part, click the "<click to select>" hyperlink next to Selected part in the block dialogue box settings.

2. The Block Parameterization Manager window opens. Select a part from the menu and click Apply all. You can narrow the choices using the Manufacturer drop down menu.

3. You can close the Block Parameterization Manager menu. The block now has the parameterization that you specified.

4. You can compare current parameter settings with a specific supplier component in the Block Parameterization Manager window by selecting a part and viewing the data in the Compare selected part with block section.

Note

Predefined block parameterizations use available data sources to supply parameter values. The block substitutes engineering judgement and simplifying assumptions for missing data. As a result, expect some deviation between simulated and actual physical behavior. To ensure accuracy, validate the simulated behavior against experimental data and refine your component models as necessary.

To learn more, see List of Pre-Parameterized Components.

Ports

Conserving

A — Liquid port

thermal liquid

Thermal liquid conserving port associated with valve inlet A.

B — Liquid port

thermal liquid

Thermal liquid conserving port associated with valve inlet B.

Parameters

Opening parameterization — Opening parameterization

Linear - Area vs. pressure (default) | Tabulated data - Area vs. pressure | Tabulated data - Volumetric flow rate vs. pressure

Method of modeling the opening of the valve. When you set this parameter to Linear - Area vs. pressure or Tabulated data - Area vs. pressure, the block relates the opening area to the control pressure. When you set this parameter to Tabulated data - Volumetric flow rate vs. pressure, the block takes the reference flow rate and pressure differential curve of the reducing valve.

Set pressure (gauge) — Gauge pressure at which the valve begins to shut

0.1 MPa (default) | positive scalar

Pressure at which the valve begins to shut. The opening area remains variable throughout the pressure regulation range of the valve.

Pressure regulation range — Valve pressure range

0.01 MPa (default) | positive scalar

Pressure interval over which the valve opening area varies. The interval begins at the value of the Set pressure (gauge) parameter.

Dependencies

To enable this parameter, set Opening parameterization to Linear - Area vs. pressure.

Maximum opening area — Opening area in fully open position

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

Opening area of the valve in the fully open position due to sealing imperfections, when the valve is at the lower limit of the pressure regulation range. The block uses this parameter to scale the valve opening throughout the pressure regulation range.

Dependencies

To enable this parameter, set Opening parameterization to Linear - Area vs. pressure.

Leakage area — Gap area when in fully closed position

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

Sum of all gaps when the valve is in the fully shut position. The block saturates smaller numbers to this value. This parameter contributes to numerical stability by maintaining continuity in the flow.

Dependencies

To enable this parameter, set Opening parameterization to Linear - Area vs. pressure.

Pressure at port B (gauge) vector — Vector of gauge pressure values for tabulated area parameterization

[0.2 : 0.2 : 1.2] MPa (default) | 1-by-n vector

Vector of gauge pressure values for the tabulated area parameterization of the valve opening area. The vector elements must correspond one-to-one with the elements in the Opening area vector parameter. The elements must be positive and in ascending order. The block uses linear interpolation between the data points.

Dependencies

To enable this parameter, set Opening parameterization to Tabulated data - Area vs. pressure.

Opening area vector — Valve opening areas for tabulated area parameterization

[1e-05, 8e-06, 6e-06, 4e-06, 2e-06, 1e-10] m^2 (default) | 1-by-n vector

Vector of valve opening areas for the tabulated area parameterization of the valve opening area. The vector elements must correspond one-to-one with the elements in the Pressure at Port B (gauge) vector parameter. The elements must be positive and in ascending order. The block uses linear interpolation between the data points.

Dependencies

To enable this parameter, set Opening parameterization to Tabulated data - Area vs. pressure.

Reference pressure at port A (gauge) — Reference pressure at port A

1.5 MPa (default) | positive scalar

Constant pressure at port A that forms the basis of the reference curve. This value typically corresponds to the maximum operating pressure of the valve. The pressure at port A can be any value during simulation.

Dependencies

To enable this parameter, set Opening parameterization to Tabulated data - Volumetric flow rate vs. pressure.

Reference pressure at port B (gauge) vector — Reference pressure at port B

[1.2, 1, .8, .6, .4, .2] MPa (default) | 1-by-n vector

Vector of monotonically decreasing pressure values at port B in the reference curve as the valve opening area changes. The first element is the reference maximum pressure, which is the pressure where the valve fully shuts. The last element is the reference set pressure.

Dependencies

To enable this parameter, set Opening parameterization to Tabulated data - Volumetric flow rate vs. pressure.

Reference volumetric flow rate vector — Reference volumetric flow rate

[1e-09, 1.8e-05, 6.6e-05, .00013, .0002, .00028] m^3/s (default) | 1-by-n vector

Vector of monotonically increasing reference flow rates through the valve. The block uses this curve to generate a flow coefficient for the changing valve area.

Dependencies

To enable this parameter, set Opening parameterization to Tabulated data - Volumetric flow rate vs. pressure.

Cross-sectional area at ports A and B — Area at conserving ports

0.01 m^2 (default) | positive scalar

Area at ports A and B, which the block uses in the pressure-flow rate equation that determines the mass flow rate through the valve.

Discharge coefficient — Discharge coefficient

0.64 (default) | positive scalar

Correction factor that the block uses to account for discharge losses in theoretical flows.

Dependencies

To enable this parameter, set Opening parameterization to Linear - Area vs. pressure or Tabulated data - Area vs. pressure.

Critical Reynolds number — Upper Reynolds number limit for laminar flow

150 (default) | positive scalar

Upper Reynolds number limit for laminar flow through the valve.

Dependencies

To enable this parameter, set Opening parameterization to Linear - Area vs. pressure or Tabulated data - Area vs. pressure.

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 valve 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 Opening parameterization to Linear - Area vs. pressure.

Pressure recovery — Option to include pressure increase during area expansions

off (default) | on

Whether to capture the increase in pressure when fluid flows from a region of smaller cross-sectional area to a region of larger cross-sectional area.

Dependencies

To enable this parameter, set Opening parameterization to Linear - Area vs. pressure or Tabulated data - Area vs. pressure.

Opening dynamics — Option to include flow response to valve opening

off (default) | on

Whether to approximate the transient effects to the fluid system due to valve opening. Selecting Opening dynamics approximates opening conditions by introducing a first-order lag in the flow response.

Opening time constant — Valve opening time constant

0.1 s (default) | positive scalar

Time constant by which to compute the lag in the opening dynamics.

Dependencies

To enable this parameter, select Opening dynamics.

Extended Capabilities

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

Version History

Introduced in R2016a

R2023a: New Parameterization Options

Use the Opening parameterization parameter to choose the block parameterization Linear - Area vs. pressure, Tabulated data - Area vs. pressure, or Tabulated data - Volumetric flow rate vs. pressure.