Local Restriction (IL)

Restriction in flow area in isothermal liquid network

Since R2020a

Libraries:
Simscape / Foundation Library / Isothermal Liquid / Elements

Description

The Local Restriction (IL) block models the pressure drop due to a localized reduction in flow area, such as a valve or an orifice, in an isothermal liquid network.

Ports A and B represent the restriction inlet and outlet. The input physical signal at port AR specifies the restriction area. Alternatively, you can specify a fixed restriction area as a block parameter.

The block icon changes depending on the value of the Restriction type parameter.

Restriction Type Block Icon

Restriction Type	Block Icon
`Variable`
`Fixed`

Variable

Fixed

The restriction is adiabatic. It does not exchange heat with the environment.

The restriction consists of a contraction followed by a sudden expansion in flow area. The fluid accelerates during the contraction, causing the pressure to drop. In the expansion zone, if the Pressure recovery check box is cleared, the momentum of the accelerated fluid is lost. If the Pressure recovery check box is selected, the sudden expansion recovers some of the momentum and allows the pressure to rise slightly after the restriction.

Local Restriction Schematic

The block equations express the mass flow rate in terms of the pressure difference between ports A and B:

$\begin{array}{l} {\dot{m}}_{A} + {\dot{m}}_{B} = 0 \\ {\dot{m}}_{A} = C_{d} S_{R} \frac{Δ p}{{(Δ p^{2} + Δ p_{c r}^{2})}^{1 / 4}} \sqrt{\frac{2 \bar{ρ}}{P R_{l o s s} (1 - {(\frac{S_{R}}{S})}^{2})}} \\ Δ p = p_{A} - p_{B} \\ Δ p_{c r} = \frac{π}{4} \cdot \frac{\bar{ρ}}{2 S_{R}} {(\frac{{Re}_{c r} ν_{a t m}}{C_{d}})}^{2} \end{array}$

$\bar{ρ} = \frac{ρ_{A} + ρ_{B}}{2}$

where:

Δp is the pressure differential.
p_A and p_B are pressures at ports A and B, respectively.
S_R is the cross-sectional area at the restriction.
S is the cross-sectional area at ports A and B.
Δp_cr is the critical pressure differential for the transition between the laminar and turbulent flow regimes.
Re_cr is the critical Reynolds number.
ν_atm is the liquid kinematic viscosity at atmospheric pressure, which is a global parameter defined by the Isothermal Liquid Properties (IL) block connected to the circuit.
C_d is the discharge coefficient.
$\bar{ρ}$ is the average fluid mixture density.
ρ_A and ρ_B are fluid mixture density values at ports A and B, respectively. Equations used to compute the fluid mixture density depend on the selected isothermal liquid model. For detailed information, see Isothermal Liquid Modeling Options.
PR_loss is the pressure loss ratio.

The pressure loss ratio, PR_loss, depends on the Pressure recovery check box:

If pressure recovery is off, then
$P R_{loss} = 1.$
If pressure recovery is on, then
$P R_{loss} = \frac{\sqrt{1 - {(\frac{S_{R}}{S})}^{2} (1 - C_{d}^{2})} - C_{d} \frac{S_{R}}{S}}{\sqrt{1 - {(\frac{S_{R}}{S})}^{2} (1 - C_{d}^{2})} + C_{d} \frac{S_{R}}{S}} .$

The cross-sectional area at the restriction, S_R, depends on the Restriction type parameter value:

For variable restrictions,
$S_{R} = {\begin{array}{l} S_{\min}, & A R \leq S_{\min} \\ S_{\max}, & A R \geq S_{\max} \\ A R, & S_{\min} < A R < S_{\max} \end{array},$
where AR is the value of the input physical signal, and S_min and S_max are the values of the Minimum restriction area and Maximum restriction area block parameters, respectively.
For fixed restrictions, S_R is the value of the Restriction area parameter.

By default, the block assumes that the cross-sectional area at the restriction ports is much greater than the restriction area, setting the Cross-sectional area at ports A and B parameter value to inf and all the S_R/S terms in the equations to 0, to improve computation efficiency. Specify an actual value for the Cross-sectional area at ports A and B parameter if the two cross-sectional areas are comparable in size and their ratio has an impact on flow computations.

Examples

Hydraulic Actuator with Analog Position Controller

How the Foundation library can be used to model systems that span electrical, mechanical and isothermal liquid domains. In the model, a hydraulic system implemented in the isothermal liquid domain controls the mechanical load position in response to a voltage reference demand. If the reference demand is zero, then the hydraulic actuator (and load) displacement is zero, and if the reference is +5 volts, then the displacement is 100 mm.

Open Model

Entrained Air Effects

The effects of entrained air in a custom double acting cylinder. During the repeating cycle of oscillating pressure, the absolute pressure does not get below absolute zero as the bulk modulus of the homogeneous liquid-gas mixture decreases accordingly at low pressures.

Open Model

Ports

Input

expand all

AR — Restriction area control signal, m^2
physical signal

Input physical signal that controls the flow restriction area. The signal saturates when its value is outside the minimum and maximum restriction area limits, specified by the block parameters.

Dependencies

This port is visible only if you set the Restriction type parameter to Variable.

Conserving

expand all

A — Inlet or outlet
isothermal liquid

Isothermal liquid conserving port associated with the inlet or outlet of the local restriction. This block has no intrinsic directionality.

B — Inlet or outlet
isothermal liquid

Isothermal liquid conserving port associated with the inlet or outlet of the local restriction. This block has no intrinsic directionality.

Parameters

expand all

Restriction type — Specify whether restriction area can change during simulation
`Variable` (default) | `Fixed`

Select whether the restriction area can change during simulation:

Variable — The input physical signal at port AR specifies the restriction area, which can vary during simulation. The Minimum restriction area and Maximum restriction area parameters specify the lower and upper bounds for the restriction area.
Fixed — The restriction area, specified by the Restriction area block parameter value, remains constant during simulation. Port AR is hidden.

Minimum restriction area — Lower bound for the restriction cross-sectional area
`1e-10 m^2` (default) | positive scalar

The lower bound for the restriction cross-sectional area. You can use this parameter to represent the leakage area. The input signal AR saturates at this value to prevent the restriction area from decreasing any further.

Dependencies

Enabled when the Restriction type parameter is set to Variable.

Maximum restriction area — Upper bound for the restriction cross-sectional area
`0.005 m^2` (default) | positive scalar

The upper bound for the restriction cross-sectional area. The input signal AR saturates at this value to prevent the restriction area from increasing any further.

Dependencies

Enabled when the Restriction type parameter is set to Variable.

Restriction area — Area normal to flow path at the restriction
`1e-3 m^2` (default) | positive scalar

Area normal to flow path at the restriction.

Dependencies

Enabled when the Restriction type parameter is set to Fixed.

Cross-sectional area at ports A and B — Area normal to flow path at the ports
`inf m^2` (default) | positive scalar

Area normal to flow path at ports A and B. This area is assumed to be the same for the two ports. The inf value assumes that the cross-sectional area at the ports is much greater than the restriction area, and therefore all the S_R/S terms in the block equations are negligibly small.

Discharge coefficient — Ratio of actual mass flow rate to theoretical mass flow rate through restriction
`0.64` (default) | positive scalar

The discharge coefficient is a semi-empirical parameter commonly used to characterize the flow capacity of an orifice. This parameter is defined as the ratio of the actual mass flow rate through the orifice to the ideal mass flow rate.

Critical Reynolds number — Reynolds number for transition between laminar and turbulent regimes
`150` (default) | positive scalar

The Reynolds number for the transition between laminar and turbulent regimes.

Pressure recovery — Specify whether to account for pressure recovery
`Off` (default) | `On`

Select the check box to account for pressure recovery at the local restriction outlet.

Extended Capabilities

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

Version History

Introduced in R2020a

Local Restriction (IL)

Description

Examples

Hydraulic Actuator with Analog Position Controller

Entrained Air Effects

Ports

Input

AR — Restriction area control signal, m^2
physical signal

Dependencies

Conserving

A — Inlet or outlet
isothermal liquid

B — Inlet or outlet
isothermal liquid

Parameters

Restriction type — Specify whether restriction area can change during simulation
`Variable` (default) | `Fixed`

Minimum restriction area — Lower bound for the restriction cross-sectional area
`1e-10 m^2` (default) | positive scalar

Dependencies

Maximum restriction area — Upper bound for the restriction cross-sectional area
`0.005 m^2` (default) | positive scalar

Dependencies

Restriction area — Area normal to flow path at the restriction
`1e-3 m^2` (default) | positive scalar

Dependencies

Cross-sectional area at ports A and B — Area normal to flow path at the ports
`inf m^2` (default) | positive scalar

Discharge coefficient — Ratio of actual mass flow rate to theoretical mass flow rate through restriction
`0.64` (default) | positive scalar

Critical Reynolds number — Reynolds number for transition between laminar and turbulent regimes
`150` (default) | positive scalar

Pressure recovery — Specify whether to account for pressure recovery
`Off` (default) | `On`

Extended Capabilities

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

Version History

See Also

Topics

Local Restriction (IL)

Description

Examples

Hydraulic Actuator with Analog Position Controller

Entrained Air Effects

Ports

Input

AR — Restriction area control signal, m^2 physical signal

Dependencies

Conserving

A — Inlet or outlet isothermal liquid

B — Inlet or outlet isothermal liquid

Parameters

Restriction type — Specify whether restriction area can change during simulation Variable (default) | Fixed

Minimum restriction area — Lower bound for the restriction cross-sectional area 1e-10 m^2 (default) | positive scalar

Dependencies

Maximum restriction area — Upper bound for the restriction cross-sectional area 0.005 m^2 (default) | positive scalar

Dependencies

Restriction area — Area normal to flow path at the restriction 1e-3 m^2 (default) | positive scalar

Dependencies

Cross-sectional area at ports A and B — Area normal to flow path at the ports inf m^2 (default) | positive scalar

Discharge coefficient — Ratio of actual mass flow rate to theoretical mass flow rate through restriction 0.64 (default) | positive scalar

Critical Reynolds number — Reynolds number for transition between laminar and turbulent regimes 150 (default) | positive scalar

Pressure recovery — Specify whether to account for pressure recovery Off (default) | On

Extended Capabilities

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

Version History

See Also

Topics

AR — Restriction area control signal, m^2
physical signal

A — Inlet or outlet
isothermal liquid

B — Inlet or outlet
isothermal liquid

Restriction type — Specify whether restriction area can change during simulation
`Variable` (default) | `Fixed`

Minimum restriction area — Lower bound for the restriction cross-sectional area
`1e-10 m^2` (default) | positive scalar

Maximum restriction area — Upper bound for the restriction cross-sectional area
`0.005 m^2` (default) | positive scalar

Restriction area — Area normal to flow path at the restriction
`1e-3 m^2` (default) | positive scalar

Cross-sectional area at ports A and B — Area normal to flow path at the ports
`inf m^2` (default) | positive scalar

Discharge coefficient — Ratio of actual mass flow rate to theoretical mass flow rate through restriction
`0.64` (default) | positive scalar

Critical Reynolds number — Reynolds number for transition between laminar and turbulent regimes
`150` (default) | positive scalar

Pressure recovery — Specify whether to account for pressure recovery
`Off` (default) | `On`

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