Engee documentation

Pressure Relief Valve (IL)

Safety valve in the isothermal liquid network.

pressure relief valve il

Description

The Pressure Relief Valve (IL) unit is a pressure relief valve for relieving pressure in an isothermal liquid network. The valve is closed when the pressure is less than the pressure set point. When the pressure reaches or exceeds the set pressure, the valve opens. The set pressure is either the threshold pressure drop across the valve between ports A and B, or between port A and atmospheric pressure. For pressure control based on another fluid system component, see the block Pressure Compensator Valve (IL).

Pressure Control

For linear parameterization, the normalised pressure , which determines the valve opening area, depends on the value of the parameter Controlled set pressure.

If the Controlled set pressure check box is not selected and the Opening parameterization is set to `Linear - Area vs. pressure', the normalised pressure is defined as

where

  • - is the control pressure. If the Opening pressure specification is set to Pressure differential, the control pressure is . If the Opening pressure specification is set to Pressure at port A, the control pressure is the difference between the pressure at port A and the atmospheric pressure;

  • - setting pressure. If Opening pressure specification is set to Pressure differential, then is the value of Set pressure differential. If the Opening pressure specification is set to `Pressure at port A', is the value of the Set pressure (gauge) parameter;

  • - maximum pressure regulation range, defined as , where is the value of the Pressure regulation range parameter.

If the Controlled set pressure check box is selected, the normalised pressure is defined as

where

  • - is the value of the signal in the Ps port;

  • where is the value of Pressure regulation range;

  • - pressure drop between ports A and B, .

Opening parameterization

The mass flow rate depends on the values of the Controlled set pressure and Opening parameterization parameters.

Opening parameterization: pressure dependent area

If Controlled set pressure is checked or unchecked and Opening parameterization is set to `Linear - Area vs. pressure' or `Tabulated data - Area vs. pressure', the mass flow rate is as follows

where

  • - flow coefficient, the value of the Discharge coefficient parameter;

  • - is the instantaneous opening area of the valve;

  • - Cross-sectional area at ports A and B;

  • - average liquid density;

  • - pressure drop.

The critical pressure drop is the pressure drop determined from the value of the critical Reynolds number , given by the Critical Reynolds number parameter, the transition point between laminar and turbulent flow:

Pressure loss describes the pressure drop across the valve due to the reduction in valve area and is calculated as:

Pressure recovery allows you to account for the positive change in valve pressure due to an increase in area. To disregard pressure recovery, uncheck the Pressure recovery box. In this case the pressure loss .

If the Controlled set pressure checkbox is checked, or not checked and the Opening parameterization is set to Linear - Area vs. pressure, the opening area is as follows

where

  • - value of the Leakage area parameter;

  • - is the value of parameter Maximum opening area.

When the valve is in the nearly open or nearly closed position in the linear parameterization, it is possible to maintain numerical stability in the simulation by adjusting the Smoothing factor parameter. If the Smoothing factor is not zero, a smooth variation of the control pressure between and is ensured.

If the Controlled set pressure checkbox is unchecked and the Opening parameterization parameter is set to Tabulated data - Area vs. pressure, then the value of is interpolated from the Opening area vector parameter relative to the Pressure differential vector or Opening pressure (gauge) vector parameter, depending on the value of the Pressure control specification parameter. The unit also uses a smoothed, normalised pressure if the smoothing factor is non-zero, with linear interpolation and extrapolation to the nearest point.

Parametrization: pressure dependent volume flow rate.

If the Controlled set pressure checkbox is not selected and the Opening parameterization is set to `Tabulated data - Volumetric flow rate vs. pressure', the valve opens according to the user provided tabulated volumetric flow rate and differential pressure between ports A and B.

The mass flow rate is defined as

where

  • - is the average density of the liquid;

  • - pressure drop across the valve;

  • where

    • - flow coefficient;

    • - critical Reynolds number;

    • - kinematic viscosity.

In this parameterization and have fixed values of 0.64 and 150 respectively.

With differential pressure values within the tabulated data:

where

  • - is the value of the parameter Pressure differential vector;

  • where is the value of the Volumetric flow rate vector parameter.

If during the simulation the value of the pressure drop becomes less than the first element of the Pressure differential vector parameter :

where is the first element of the Volumetric flow rate vector.

If during the simulation the differential pressure becomes greater than the last element of the Pressure differential vector :

where is the last element of the Volumetric flow rate vector parameter.

Mass conservation

Mass conservation equation:

where is the mass flow rate entering the valve through the port, denoted by the subscript A or B.

Opening dynamics

If the Opening dynamics checkbox is selected, a delay is introduced in the flow response to valve opening and the value becomes the dynamic opening area , otherwise, is the steady-state opening area. The derivative of the dynamic control pressure is calculated from the Opening time constant :

By default, the Opening dynamics checkbox is unchecked.

Ports

Non-directional

A - isothermal liquid port
isothermal liquid

Isothermal liquid port, corresponds to the valve inlet.

B - isothermal liquid port
isothermal liquid

Isothermal liquid port, corresponds to the valve outlet.

Inlet

Ps - set pressure signal
scalar

Set pressure port for controlled valve operation.

Dependencies

To use this port, select the Controlled set pressure checkbox.

Parameters

Controlled set pressure - enable the port for setting the set pressure
off (by default) | on

If the checkbox is unchecked, the valve opens linearly within a fixed pressure control range or according to the provided tabulated differential pressure and opening area.

If the box is checked, the valve opens according to the set pressure signal at the Ps port within the fixed pressure control range.

Opening parameterization - method of calculating valve opening
| `Linear - Area vs. pressure (by default) | `Tabulated data - Area vs. pressure | `Tabulated data - Volumetric flow rate vs. pressure

Valve opening modelling method. The valve opening is parameterised either linearly or using a table of values that relate area to pressure drop.

Dependencies

To use this parameter, uncheck the Controlled set pressure box.

Opening pressure specification - the differential pressure used to control the valve
Pressure differential (by default) | Pressure at port A.

Defines the control pressure. The `Pressure differential' value defines the control pressure as the pressure difference between ports A and B. The `Pressure at port A' value defines the control pressure as the difference between the pressure at port A and the atmospheric pressure.

Dependencies

To use this parameter, uncheck Controlled set pressure and set Opening parameterization to Linear - Area vs. pressure or Tabulated data - Area vs. pressure.

Set pressure (gauge) - set pressure
0.1 MPa (by default) | positive scalar

The overpressure above which the valve is actuated. This pressure is set when the control pressure is the differential pressure between the A ports and the atmospheric pressure.

Dependencies

To use this parameter, uncheck Controlled set pressure, set Opening parameterization to `Linear - Area vs. pressure' and Opening pressure specification to `Pressure at port A'.

Set pressure differential - set pressure
0.01 MPa (by default) | positive scalar.

The differential pressure above which the valve is actuated. This pressure is set when the control pressure is the differential pressure between ports A and B.

Dependencies

To use this parameter, uncheck Controlled set pressure, set Opening parameterization to `Linear - Area vs. pressure' and Opening pressure specification to `Pressure differential'.

Pressure regulation range - operating pressure range of the valve
0.1 MPa (by default) | positive scalar.

The operating pressure range of the valve. The valve starts opening at the set pressure value and opens fully at the maximum value of the operating range , where .

Dependencies

To use this parameter:

  • Select the Controlled set pressure checkbox.

  • Uncheck Controlled set pressure and set Opening parameterization to `Linear - Area vs. pressure'.

Maximum opening area - area of the valve fully open
1e-4 m² (by default) | positive scalar.

The area of the valve cross-section in the fully open position.

Dependencies

To use this parameter:

  • Select the Controlled set pressure checkbox.

  • Uncheck Controlled set pressure and set Opening parameterization to `Linear - Area vs. pressure'.

Leakage area - valve clearance area in fully closed position
1e-10 m² (by default) | `positive scalar'.

The sum of all clearances when the valve is in the fully closed position. 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:

  • Select the Controlled set pressure checkbox.

  • Uncheck Controlled set pressure and set Opening parameterization to `Linear - Area vs. pressure'.

Opening pressure (gauge) vector - overpressure values for tabular parameterization
[0.2:0.2:1.2…​] MPa (by default) | ` vector`

Vector of overpressure values for the tabular parameterization of the valve opening area. The elements of the vector correspond to the elements of the vector from parameter Opening area vector. The elements are listed in ascending order and must be greater than 0. Linear interpolation is used between the tabular data points.

The first element of this parameter is the pressure value at which the valve starts to open. The last element is the maximum pressure at which the valve is fully open. The difference between these two values is the pressure control range of the valve.

Dependencies

To use this parameter, uncheck Controlled set pressure, set Opening parameterization to `Tabulated data - Area vs. pressure' and Opening pressure specification to `Pressure at port A'.

Pressure differential vector - differential pressure values for tabulated parameterization
[0.2:0.2:1.2…​] MPa (by default) | `vector'.

Vector of differential pressure values for tabular parameterization of the valve opening area. The elements of the vector correspond to the elements of the vector from parameter Opening area vector or from parameter Volumetric flow rate vector, depending on the selected parameterization type. The elements are listed in ascending order and must be greater than 0. Linear interpolation is used between tabulated data points.

Dependencies

To use this parameter:

  • Uncheck Controlled set pressure, set Opening parameterization to Tabulated data - Area vs. pressure and Opening pressure specification to Pressure differential.

  • Uncheck Controlled set pressure, set Opening parameterization to Tabulated data - Volumetric flow rate vs. pressure and Opening pressure specification to Pressure differential.

Volumetric flow rate vector - vector of volumetric flow rate values for tabular parameterization
[1.0e-9, 3.6e-5, 8.9e-5, 1.5e-4, 2.3e-4, 3.1e-4] m3/s (By default) | `vector'.

Vector of volumetric flow rate values for tabular parameterization. The values in this vector correspond to the elements of the vector from the Pressure differential vector parameter. The elements are listed in ascending order.

Dependencies

To use this parameter, uncheck the Controlled set pressure checkbox and set the Opening parameterization parameter to `Tabulated data - Volumetric flow rate vs. pressure'.

Opening area vector - vector of valve opening area values for tabulated parameterization
[1.0e-10, 0.2e-5, 0.4e-5, 0.6e-5, 0.8e-5, 1.0e-5] m² (by default) | `vector'.

Vector of valve opening area values for tabular parameterization. The values in this vector correspond to the elements of the vector from the Pressure differential vector parameter. The elements are listed in ascending order and must be greater than 0. Linear interpolation is used between the tabular data points.

Dependencies

To use this parameter, uncheck Controlled set pressure and set the Opening parameterization parameter to Tabulated data - Area vs. pressure.

Cross-sectional area at ports A and B - area at inlet or outlet of the valve
Inf (By default) | positive scalar

The cross-sectional area at ports A and B inlet and outlet. This area is used when calculating the mass flow rate through the valve.

Dependencies

To use this parameter:

  • Select the Controlled set pressure check box.

  • Uncheck Controlled set pressure and set Opening parameterization to Linear - Area vs. pressure or Tabulated data - Area vs. pressure.

Discharge coefficient - flow coefficient
0.64 (By default) | Positive scalar

The correction factor is the ratio of the actual mass flow rate to the theoretical mass flow rate through the valve.

Dependencies

To use this parameter:

  • Select the Controlled set pressure check box.

  • Uncheck Controlled set pressure and set Opening parameterization to Linear - Area vs. pressure or Tabulated data - Area vs. pressure.

Critical Reynolds number - upper limit of Reynolds number for laminar flow
150 (By default) | positive scalar

Upper Reynolds number limit for laminar flow through the valve.

Dependencies

To use this parameter:

  • Select the Controlled set pressure check box.

  • Uncheck Controlled set pressure and set Opening parameterization to Linear - Area vs. pressure or Tabulated data - Area vs. pressure.

Smoothing factor - numerical smoothing factor
0.01 (by default) | positive scalar

The continuous smoothing factor provides smooth opening by correcting the valve characteristic in the nearly open and nearly closed positions. Set a non-zero value less than one to increase the stability of the simulation in these modes.

Dependencies

To use this parameter, uncheck Controlled set pressure and set Opening parameterization to `Linear - Area vs. pressure' or `Tabulated data - Area vs. pressure'.

Pressure recovery - accounting for pressure rise during area expansion
Off (By default) | `On

Determines whether pressure rise is taken into account when fluid flows from a smaller cross-sectional area to a larger cross-sectional area.

Dependencies

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

Opening dynamics - take into account the valve opening dynamics
Opening parameterization* set to `Linear - Area vs. pressure or Tabulated data - Area vs. pressure.

Determines whether the transient effects in the fluid system caused by valve opening should be taken into account. Checking Opening dynamics introduces a first order lag to the valve signal pressure. The Opening time constant parameter determines the opening dynamics.

Dependencies

To use this parameter:

  • Select the Controlled set pressure check box.

  • Uncheck Controlled set pressure and set Opening parameterization to Linear - Area vs. pressure or Tabulated data - Area vs. pressure.

Opening time constant - valve opening time constant
0.1 s (By default) | on.

A constant that defines the time required for the fluid to reach a steady state when the valve is opened or closed. This parameter defines the opening dynamics.

Dependencies

To use this parameter, set the Opening parameterization parameter to `Linear - Area vs. pressure' or `Tabulated data - Area vs. pressure' and check the Opening dynamics box.