Pressure Relief Valve (TL)

Pressure relief valve in a thermal liquid network

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

Description

The Pressure Relief Valve (TL) block represents a valve that relieves excess pressure in a thermal liquid network. The valve allows flow through the networks and opens to relieve excess flow when the control pressure reaches the value of the Valve set pressure (gauge) parameter. A control pressure above the set pressure causes the valve to gradually open, which allows 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 removes the abrupt opening area changes at the zero and maximum opening positions. The figure shows the effect of smoothing on the valve opening area curve.

Curve showing the smoothing regions and linear regions

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

$p_{A} - p_{B} = \frac{\dot{m} \sqrt{{\dot{m}}^{2} + {\dot{m}}_{c r}^{2}}}{2 ρ_{A v g} C_{d}^{2} S^{2}} [1 - {(\frac{S_{R}}{S})}^{2}] P R_{L o s s},$

where:

p_A and p_B are the pressures at port A and port B.
$\dot{m}$ is the mass flow rate.
${\dot{m}}_{c r}$ 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:

$P R_{L o s s} = \frac{\sqrt{1 - {(S_{R} / S)}^{2} (1 - C_{d}^{2})} - C_{d} (S_{R} / S)}{\sqrt{1 - {(S_{R} / S)}^{2} (1 - C_{d}^{2})} + C_{d} (S_{R} / S)} .$

The block computes the valve opening as

$S_{R} = {\hat{p}}_{s m o o t h e d} \cdot (S_{M a x} - S_{L e a k}) + S_{L e a k}$

$\hat{p} = \frac{p_{c o n t r o l} - p_{s e t}}{p_{M a x} - p_{s e t}}$

where:

S_Leak is the valve leakage area.
S_Max is the maximum valve opening area.
p_control is the valve control pressure:

$p_{c o n t r o l} = {\begin{array}{l} p_{A}, & Pressure at port A \\ p_{A} - p_{B}, & Pressure differential \end{array}$
p_set is the valve set pressure:

$p_{s e t} = {\begin{array}{l} p_{s e t, g a u g e} + p_{A t m}, & Pressure at port A \\ p_{s e t, d i f f}, & Pressure differential \end{array}$
p_Max is the maximum pressure:

$p_{m a x} = {\begin{array}{l} p_{s e t, g a u g e} + p_{r a n g e} + p_{A t m}, & Pressure at port A \\ p_{s e t, d i f f} + p_{r a n g e}, & Pressure differential \end{array}$
where the two equations refer to the settings of the Pressure control specification parameter.

The critical mass flow rate is

${\dot{m}}_{c r} = {Re}_{c r} μ_{A v g} \sqrt{\frac{π}{4} S_{R}} .$

Numerically-Smoothed Valve Area

When the valve is in a near-open or near-closed position, 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.

Energy Balance

The energy conservation equation in the valve is

$ϕ_{A} + ϕ_{B} = 0,$

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

Conserving

expand all

`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

expand all

`Pressure control specification` — Method to evaluate pressure
`Pressure at port A` (default) | `Pressure differential`

Specification method for the valve control pressure. When you select Pressure at port A, the block only uses the pressure at port A to determine when the flow exceeds the value of the Valve set pressure (gauge) parameter. When you select Pressure differential, the block uses the value of the Valve set pressure differential parameter to determine whether the pressure differential from port A to port B exceeds the range.

`Valve set pressure (gauge)` — Gauge pressure beyond which valve operation triggers
`0.1` `MPa` (default) | positive scalar

Pressure at which the opening mechanism triggers. The opening area remains variable throughout the pressure regulation range of the valve.

Dependencies

To enable this parameter, set Pressure control specification to Pressure pressure at port A.

`Valve set pressure differential` — Minimum opening pressure differential
`0` `MPa` (default) | nonnegative scalar

Minimum pressure differential between ports A and B required to open the valve. A pressure differential above this value causes the valve to gradually open until it reaches the fully open state.

Dependencies

To enable this parameter, set Pressure control specification to Pressure differential.

`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 Valve set pressure (gauge) or once the difference between ports A and B exceeds the value of the Valve set pressure differential parameter.

`Maximum opening area` — Opening area in the fully open position due to sealing imperfections
`1e-4` `m^2` (default) | positive scalar

Opening area of the valve in the fully open position, when the valve is at the upper limit of the pressure regulation range.

`Leakage area` — Gap area when in fully shut position
`1e-12` `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.

`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.

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 function with smooth nonlinear transitions at the set and maximum-area pressures. The figure shows the smoothing regions.

Curve showing the smoothing regions and linear regions

`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 are used in the pressure-flow rate equation that determines the mass flow rate through the valve.

`Discharge coefficient` — Discharge coefficient
`0.7` (default) | positive scalar

Correction factor that accounts for discharge losses in theoretical flows.

`Critical Reynolds number` — Upper Reynolds number limit for laminar flow
`12` (default) | positive scalar

Upper Reynolds number limit for laminar flow through the valve.

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.

Pressure Relief Valve (TL)

Description

Mass Balance

Momentum Balance

Energy Balance

Ports

Conserving

`A` — Liquid port
thermal liquid

`B` — Liquid port
thermal liquid

Parameters

`Pressure control specification` — Method to evaluate pressure
`Pressure at port A` (default) | `Pressure differential`

`Valve set pressure (gauge)` — Gauge pressure beyond which valve operation triggers
`0.1` `MPa` (default) | positive scalar

Dependencies

`Valve set pressure differential` — Minimum opening pressure differential
`0` `MPa` (default) | nonnegative scalar

Dependencies

`Pressure regulation range` — Valve pressure range
`0.01` `MPa` (default) | positive scalar

`Maximum opening area` — Opening area in the fully open position due to sealing imperfections
`1e-4` `m^2` (default) | positive scalar

`Leakage area` — Gap area when in fully shut position
`1e-12` `m^2` (default) | positive scalar

`Smoothing factor` — Numerical smoothing factor
`0.01` (default) | positive scalar in the range [0,1]

`Cross-sectional area at ports A and B` — Area at conserving ports
`0.01` `m^2` (default) | positive scalar

`Discharge coefficient` — Discharge coefficient
`0.7` (default) | positive scalar

`Critical Reynolds number` — Upper Reynolds number limit for laminar flow
`12` (default) | positive scalar

Model Examples

Reciprocal Actuator with Differential Cylinders

Extended Capabilities

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

Version History

See Also

Pressure Relief Valve (TL)

Description

Mass Balance

Momentum Balance

Energy Balance

Ports

Conserving

A — Liquid port thermal liquid

B — Liquid port thermal liquid

Parameters

Pressure control specification — Method to evaluate pressure Pressure at port A (default) | Pressure differential

Valve set pressure (gauge) — Gauge pressure beyond which valve operation triggers 0.1 MPa (default) | positive scalar

Dependencies

Valve set pressure differential — Minimum opening pressure differential 0 MPa (default) | nonnegative scalar

Dependencies

Pressure regulation range — Valve pressure range 0.01 MPa (default) | positive scalar

Maximum opening area — Opening area in the fully open position due to sealing imperfections 1e-4 m^2 (default) | positive scalar

Leakage area — Gap area when in fully shut position 1e-12 m^2 (default) | positive scalar

Smoothing factor — Numerical smoothing factor 0.01 (default) | positive scalar in the range [0,1]

Cross-sectional area at ports A and B — Area at conserving ports 0.01 m^2 (default) | positive scalar

Discharge coefficient — Discharge coefficient 0.7 (default) | positive scalar

Critical Reynolds number — Upper Reynolds number limit for laminar flow 12 (default) | positive scalar

Model Examples

Reciprocal Actuator with Differential Cylinders

Extended Capabilities

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

Version History

See Also

WeChat

`A` — Liquid port
thermal liquid

`B` — Liquid port
thermal liquid

`Pressure control specification` — Method to evaluate pressure
`Pressure at port A` (default) | `Pressure differential`

`Valve set pressure (gauge)` — Gauge pressure beyond which valve operation triggers
`0.1` `MPa` (default) | positive scalar

`Valve set pressure differential` — Minimum opening pressure differential
`0` `MPa` (default) | nonnegative scalar

`Pressure regulation range` — Valve pressure range
`0.01` `MPa` (default) | positive scalar

`Maximum opening area` — Opening area in the fully open position due to sealing imperfections
`1e-4` `m^2` (default) | positive scalar

`Leakage area` — Gap area when in fully shut position
`1e-12` `m^2` (default) | positive scalar

`Smoothing factor` — Numerical smoothing factor
`0.01` (default) | positive scalar in the range [0,1]

`Cross-sectional area at ports A and B` — Area at conserving ports
`0.01` `m^2` (default) | positive scalar

`Discharge coefficient` — Discharge coefficient
`0.7` (default) | positive scalar

`Critical Reynolds number` — Upper Reynolds number limit for laminar flow
`12` (default) | positive scalar

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