Local Restriction (IL)
Local flow constriction in an isothermal liquid network.
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Description
The Local Restriction (IL) block simulates the pressure drop due to a localised reduction in flow area, such as a valve or orifice, in an isothermal liquid network.
Ports A and B represent the input and output of the Local Restriction (IL) block. The input signal on the AR port defines the flow cross-section. Alternatively, you can specify a fixed cross-section as a block parameter.
The block icon changes depending on the value of the Restriction type parameter.
The block is adiabatic and does not exchange heat with the environment.
Local Restriction (IL) consists of a contraction followed by a sudden expansion. At the point of contraction, the fluid accelerates, causing a drop in pressure. In the expansion zone, if Pressure recovery is off, the momentum of the accelerated fluid is lost. If Pressure recovery is enabled, the sudden expansion recovers some of the momentum and allows the pressure to rise slightly after the local constriction.
Schematic representation of localised constriction
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The block equations define the mass flow rate through the pressure difference between ports A and B:
Where:
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- is the pressure difference.
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and are pressures at ports A and B respectively.
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- is the area of the passage section.
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- cross-sectional area at ports A and B.
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- critical pressure drop for transition between laminar and turbulent flow regimes.
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- critical Reynolds number.
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- kinematic viscosity of liquid at atmospheric pressure.
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- flow coefficient.
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- average density of the liquid mixture.
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and - values of liquid mixture density at ports A and B respectively. The equations used to calculate the density of the liquid mixture depend on the chosen isothermal liquid model.
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- pressure loss coefficient.
The pressure loss coefficient, , depends on the value of the Pressure recovery parameter:
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If Pressure recovery is switched off, then
.
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If Pressure recovery is on, then
The cross-sectional area, , depends on the value of the restriction type parameter:
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For variable constraint:
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where is the value of the input signal, and and are the values of the Minimum restriction area and Maximum restriction area block parameters, respectively.
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For fixed restriction is the value of the Restriction area parameter.
By default, it is assumed that the cross-sectional area at ports A and B, m²* is much larger than the through-sectional area, allowing the value of the parameter Cross-sectional area at ports A and B, m² to be inf and all terms of in the equations to be 0 to improve the efficiency of the calculations. Set the actual value for Cross-sectional area at ports A and B, m² if the two cross-sectional areas are comparable in size and their ratio affects the flow calculations.
Ports
Inlet
AR - signal specifying the value of the cross-sectional area, m²
scalar
Input signal specifying the value of the cross-sectional area. The value is limited by the minimum and maximum limits set by the block parameters.
Dependencies
This port is only used if the Restriction type parameter is set to Variable.
Non-directional
A - inlet or outlet port
isothermal liquid
isothermal liquid port, corresponds to the inlet or outlet of a localised flow constriction. This unit has no internal directionality.
B - inlet or outlet port
isothermal liquid
isothermal liquid port, corresponds to the inlet or outlet of a localised flow constriction. This unit has no internal directionality.
Parameters
Restriction type - possibility to change passage section
Variable (by default) | Fixed
Select whether the passage section can be changed during modelling:
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Variable- the input signal on the AR port defines the area of the through section that can be varied during the simulation. The Minimum restriction area and Maximum restriction area parameters set the lower and upper limits of the cross-sectional area. -
Fixed- the area of the through section specified by the Restriction area parameter value remains constant during the simulation. In this case the AR port is hidden.
Minimum restriction area - the lower limit of the restriction section area
1e-10 m² (by default).
The lower limit of the cross-sectional area. You can use this parameter to represent the leakage area. The AR input signal is limited to this value to prevent further cross-sectional reduction.
Dependencies
To use this parameter, set the Restriction type parameter to `Variable'.
Maximum restriction area - the upper limit of the passage cross-sectional area of the local flow restriction
5e-3 m² (by default).
Upper limit of the cross-sectional area of the local flow restriction. The AR input signal is saturated at this value to prevent further increase of the cross-sectional area.
Dependencies
To use this parameter, set the Restriction type parameter to `Variable'.
Restriction area is the area of the passage section normal to the path of localised flow restriction
1e-3 m² (by default).
The area of the passage section normal to the local flow restriction path.
Dependencies
To use this parameter, set the Restriction type parameter to Fixed.
Cross-sectional area at ports A and B - flow cross-sectional area at ports
Inf (By default).
Cross-sectional area of flow at ports A and B, m². This area is assumed to be the same for the two ports.
Discharge coefficient - ratio of actual mass flow rate to theoretical mass flow rate through the local flow constriction
0.64 (by default).
Ratio of actual mass flow rate to theoretical mass flow rate through localised flow constriction. An empirical parameter that takes into account the effects of non-ideality.
Critical Reynolds number - Reynolds number for transition between laminar and turbulent regimes
`150 (By default).
Reynolds number for transition between laminar and turbulent regimes.
Pressure recovery - pressure recovery accounting
off (by default) | on
Determines whether pressure recovery at the outlet of a localised flow restriction is taken into account.