Pressure Reducing Valve (TL)

Pressure reducing valve in a thermal liquid network

Library:
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 is fully open when the pressure at port B is lower than the value of the Valve set pressure (gauge) parameter. At the set pressure, the valve control member moves to reduce the flow rate through the valve. The valve opening area gets smaller as pressure rises until the flow only consists of leakage. The figure illustrates the valve operation and 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

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

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 area as

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

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

where:

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

$p_{c o n t r o l} = p_{B} .$
p_set is the valve set pressure:

$p_{s e t} = p_{s e t, g a u g e} + p_{A t m} .$
p_Min is the minimum pressure.
p_Max is the maximum pressure:

$p_{m a x} = p_{s e t, g a u g e} + p_{r a n g e} + p_{A t m} .$
Δp is the portion of the pressure range to smooth.

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

`Valve set pressure (gauge)` — Gauge pressure beyond which valve operation triggers
`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 Valve set pressure (gauge) 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 lower limit of the pressure regulation range. The block uses this parameter to scale the valve opening throughout the pressure regulation range.

`Leakage area` — Gap area when in fully closed 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.

`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.

Pressure Reducing Valve (TL)

Description

Mass Balance

Momentum Balance

Energy Balance

Ports

Conserving

`A` — Liquid port
thermal liquid

`B` — Liquid port
thermal liquid

Parameters

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

Extended Capabilities

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

Version History

See Also

Pressure Reducing Valve (TL)

Description

Mass Balance

Momentum Balance

Energy Balance

Ports

Conserving

A — Liquid port thermal liquid

B — Liquid port thermal liquid

Parameters

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

Extended Capabilities

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

Version History

See Also

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`A` — Liquid port
thermal liquid

`B` — Liquid port
thermal liquid

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