Pressure Relief Valve (TL)

Pressure control valve for maintaining preset pressure in fluid network

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Description

The Pressure Relief Valve (TL) block represents a valve for maintaining a preset pressure in a fluid network. The valve remains closed until the pressure at port A reaches the valve set pressure. A pressure rise above the set pressure causes the valve to gradually open, allowing the fluid network to relieve excess pressure.

A smoothing function allows the valve opening area to change smoothly between the fully closed and fully open positions. The smoothing function does this by removing the abrupt opening area changes at the zero and maximum ball positions. The figure shows the effect of smoothing on the valve opening area curve.

Opening-Area Curve Smoothing

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.

Momentum Balance

The momentum conservation equation in the valve is

$$p_A-p_B=\frac{\dot{m}\sqrt{{\dot{m}}^2+{\dot{m}}_{cr}^2}}{2{\rho }_{Avg}{C}_d^2{S}^2}\left[1-{\left(\frac{S_R}{S}\right)}^2\right]P{R}_{Loss},$$

where:

• p_A and p_B are the pressures at port A and port B.

• $$\dot{m}$$ is the mass flow rate.

• $${\dot{m}}_{cr}$$ is the critical mass flow rate.

• ρ_Avg is the average liquid density.

• C_d is the discharge coefficient.

• S_R is the valve opening area.

• S is the valve inlet area.

• PR_Loss is the pressure ratio:

  $$P{R}_{Loss}=\frac{\sqrt{1-{\left(S_R/S\right)}^2\left(1-C_d^2\right)}-C_d\left(S_R/S\right)}{\sqrt{1-{\left(S_R/S\right)}^2\left(1-C_d^2\right)}+C_d\left(S_R/S\right)}.$$

The valve opening area is computed as

$$S_R=\{\begin{array}{ll}{S}_{Leak},\hfill & p_{control}\le p_{set}\hfill \\ S_{Leak}\left(1-{\lambda }_L\right)+S_{Linear}{\lambda }_L,\hfill & p_{control}<p_{Min}+\Delta p_{smooth}\hfill \\ S_{Linear},\hfill & p_{control}\le p_{Max}-\Delta p_{smooth}\hfill \\ S_{Linear}\left(1-{\lambda }_R\right)+S_{Max}{\lambda }_R,\hfill & p_{control}<p_{Max}\hfill \\ S_{Max},\hfill & p_{control}\ge p_{Max}\hfill \end{array},$$

where:

• S_Leak is the valve leakage area.

• S_Linear is the linear valve opening area:

  $$S_{Linear}=\left(\frac{S_{Max}-S_{Leak}}{p_{Max}-p_{set}}\right)\left(p_{control}-p_{set}\right)+S_{Leak}$$

• S_Max is the maximum valve opening area.

• p_control is the valve control pressure:

  $$p_{control}=\{\begin{array}{ll}{p}_A,\hfill & \text{Pressure at port A}\hfill \\ p_A-p_B,\hfill & \text{Pressure differential}\hfill \end{array}$$

• p_set is the valve set pressure:

  $$p_{set}=\{\begin{array}{ll}{p}_{set,gauge}+p_{Atm},\hfill & \text{Pressure at port}\text{A}\hfill \\ p_{set,diff},\hfill & \text{Pressure differential}\hfill \end{array}$$

• p_Min is the minimum pressure.

• p_Max is the maximum pressure:

  $$p_{max}=\{\begin{array}{ll}{p}_{set,gauge}+p_{range}+p_{Atm},\hfill & \text{Pressure at port A}\hfill \\ p_{set,diff}+p_{range},\hfill & \text{Pressure differential}\hfill \end{array}$$

• Δp is the portion of the pressure range to smooth.

• λ_L and λ_R are the cubic polynomial smoothing functions

  $${\lambda }_L=3{\overline{p}}_L^2-2{\overline{p}}_L^3$$

  and

  $${\lambda }_R=3{\overline{p}}_R^2-2{\overline{p}}_R^3$$

  where:

  $${\overline{p}}_L=\frac{p_{control}-p_{set}}{\left(p_{set}+\Delta p_{smooth}\right)-p_{set}}$$

  and

  $${\overline{p}}_R=\frac{p_{control}-\left(p_{max}-\Delta p_{smooth}\right)}{p_{max}-\left(p_{max}-\Delta p_{smooth}\right)}$$

The critical mass flow rate is

$${\dot{m}}_{cr}={\mathrm{Re}}_{cr}{\mu }_{Avg}\sqrt{\frac{\pi }{4}{S}_R}.$$

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.

Ports

• A — Thermal liquid conserving port representing valve inlet A

• B — Thermal liquid conserving port representing valve inlet B

Parameters

Parameters Tab

Pressure control specification

Specification method for the valve set pressure parameter. Options include Pressure at port A and Pressure differential.

Valve set pressure (gauge)

Minimum gauge pressure at port A required to open the valve. A pressure rise above the set pressure causes the valve to gradually open until it reaches the fully open state. This parameter is active only when the Pressure control specification parameter is set to Pressure at port A. The default value is 0.1 MPa.

Valve set pressure differential

Minimum pressure differential between ports A and B required to open the valve. A pressure differential rise above this value causes the valve to gradually open until it reaches the fully open state. This parameter is active only when the Pressure control specification parameter is set to Pressure differential. The default value is 0 MPa.

Pressure regulation range

Difference between the maximum and set pressures at port A. The valve begins to open at the set pressure. It is fully open at the maximum pressure. The default value is 0.01 MPa.

Maximum opening area

Area normal to the direction of flow at the point of narrowest aperture when the valve is fully open—that is, when the pressure drop from port A to port B reaches or exceeds the upper limit of the pressure regulation range.

This upper limit is calculated from other block parameters and these depend on the Pressure control specification setting:

• If Pressure at port A is chosen, the upper limit is the sum of the Pressure regulation range parameter, the Valve set pressure (gauge) parameter, and the atmospheric pressure specified for the Thermal Liquid network of which this block is a part.

• If Pressure differential is used instead, the upper limit is the sum of the Pressure regulation range and Valve set pressure differential parameters.

The default value is 1e-4 MPa.

Leakage area

Aggregate area of all fluid leaks in the valve. The leakage area helps to prevent numerical issues due to isolated fluid network sections. For numerical robustness, set this parameter to a nonzero value. The default value is 1e-12.

Smoothing factor

Fraction of the opening-area curve, expressed as a fraction from 0 to 1, to smooth. The block replaces the discontinuities in the opening area curve with smooth transitions that span the specified fraction of the curve. The default value is 0.01.

A smoothing factor of 0 corresponds to a linear function that is discontinuous at the set and maximum-area pressures. A smoothing factor of 1 corresponds to a nonlinear function that changes continuously throughout the entire function domain.

A smoothing factor between 0 and 1 corresponds to a continuous piece-wise function with smooth nonlinear transitions at the set and maximum-area pressures and linear segments elsewhere.

Opening-Area Curve Smoothing

Cross-sectional area at ports A and B

Flow area at the valve inlets. The inlets are assumed equal in size. The default value is 0.01 m^2.

Discharge coefficient

Semi-empirical parameter commonly used as a measure of valve performance. The discharge coefficient is defined as the ratio of the actual mass flow rate through the valve to its theoretical value.

The block uses this parameter to account for the effects of valve geometry on mass flow rates. Textbooks and valve data sheets are common sources of discharge coefficient values. By definition, all values must be greater than 0 and smaller than 1. The default value is 0.7.

Critical Reynolds number

Reynolds number corresponding to the transition between laminar and turbulent flow regimes. The flow through the valve is assumed laminar below this value and turbulent above it. The appropriate values to use depend on the specific valve geometry. The default value is 12.

Variables Tab

Mass flow rate into port A

Mass flow rate into the component through port A at the start of simulation. The default value is 1 kg/s.

Model Examples

Reciprocal Actuator with Differential Cylinders

A double-acting actuator with differential cylinders. The pump output is connected to cylinder B of the actuator while cylinder A of the actuator can be connected to either the pump or the reservoir through the 3-way directional valve. When cylinder A is connected to the pump, pressures at both cylinders become equal. Because of the larger effective piston area in cylinder A, the interface force in cylinder A is larger than that of in cylinder B which causes the piston to extend. When cylinder A is connected to the reservoir, the piston starts to retract. The 3-way directional valve is controlled by a sinusoidal signal to achieve repeating reciprocal motion in the actuator.

Open Model

Extended Capabilities

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

Version History

Introduced in R2016a