Local Restriction (MA)
Localised flow constriction in a network of moist air.
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Description
The Local Restriction (MA) unit simulates the pressure drop due to a local reduction in cross-section, such as a valve or orifice, in a wet air network. Local flow restriction becomes critical when the moist air reaches the speed of sound.
Ports A and B represent the input and output of the Local Restriction (MA) unit. The input signal on the AR port determines the cross-sectional area.
The block icon changes depending on the value of the Restriction type parameter.
The local flow restriction is considered an adiabatic system, i.e. it does not exchange heat with the environment.
Local flow constriction consists of a contraction followed by a sudden expansion of the flow cross-section. The moist air is accelerated during contraction, causing a pressure drop. It then separates from the wall during the sudden expansion, causing the pressure to recover only partially due to loss of momentum.
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| Wet air flow through this unit can become critical if the Flow Rate Source (MA) unit connected to the Pipe (MA) unit sets a higher mass flow rate than the possible mass flow rate of the Local Restriction (MA) unit. |
Mass Conservation:
,
,
,
Where:
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- mass flow rate.
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Lower indices and are ports A and B respectively.
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Lower indices and indicate water vapour and gas impurity properties respectively.
Energy balance:
,
where and are the energy flow through ports A and B respectively.
The mass flow rate of the mixture (positive from port A to port B) in the turbulent flow regime is:
-
The subscripts and denote input and output, respectively. If , then the input is port A and the output is port B; otherwise they are interchanged. The cross-sectional area of at ports A and B is assumed to be the same.
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- the area of local flow constriction.
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- density of the mixture.
-
- pressure.
-
- flow coefficient.
The equation for the mass flow rate of the mixture is obtained by combining the equations:
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Impulse balance for the contraction of flow area from the inlet port to the local flow constriction.
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The momentum balance for the sudden expansion of the flow area from the local flow constriction to the outlet.
In the case of flow area contraction, the pressure acts on the area at the inlet, , and the pressure acts on the area of the local flow constriction, . It is assumed that the pressure acting on the area outside the local flow constriction, , is equal to .
In the case of an expanded flow area, the pressure acting on both the area of the local flow constriction, , and the area outside the local flow constriction, , is assumed to be equal to , due to the separation of the flow from the local flow constriction. The pressure acting on the area at the outlet, is equal to .
The mass flow rate of the mixture (positive from orifice A to orifice B) in the laminar regime is linearised with respect to the pressure difference:
,
where the transition threshold between laminar and turbulent regimes is determined based on the pressure ratio of the laminar flow, , as:
When , it is assumed that the flow is turbulent and hence .
When there is a smooth transition from to .
When the flow is shut off, the localised flow contraction velocity is equal to the speed of sound and cannot increase further. Assuming that the flow is shut off, the mass flow rate of the mixture is:
,
,
where
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- is the specific heat capacity at constant pressure.
Consequently, the actual mass flow rate of the mixture is , but is limited by the value :
The expression for the local flow constriction pressure is obtained by considering the momentum balance only for the reduction in flow area from the inlet of the local flow constriction.
The local flow constriction is considered an adiabatic system, so the total enthalpies of the mixture are equal. Consequently, the changes in the specific enthalpies of the mixture are equal:
Ports
Input
AR - control signal of the passage section, m²
scalar
Input port that controls the passage cross-section of the local flow constriction. The port is saturated when its value is outside the minimum and maximum limits of the local flow constriction area set by the block parameters.
Dependencies
This port is only used if the Restriction type parameter is set to Variable.
Non-directional
A - humid air inlet or outlet
Wet air port, corresponds to the inlet or outlet of the local flow constriction. This unit has no internal directionality.
B - humid air inlet or outlet
Wet air port, corresponds to the inlet or outlet of the local 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 cross-sectional area 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 passage section area of the local flow restriction
1e-10 m² (by default).
The lower limit of the through-flow area of the local flow restriction. You can use this parameter to represent the leakage area. The AR input signal is saturated at this value to prevent further reduction of the flow area.
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 - cross-sectional area normal to the flow path at the ports
0.01 m² (by default).
The cross-sectional area normal to the flow path at ports A and B. 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).
The ratio of actual mass flow rate to theoretical mass flow rate through localised flow constriction. The Discharge factor is an empirical parameter to account for non-ideal flow.
Laminar flow pressure ratio is the pressure coefficient at which the wet air flow transitions between laminar and turbulent regimes
`0.999 (by default).
The pressure ratio at which the humid air flow transitions from laminar to turbulent flow regime. The pressure loss is linear with respect to mass flow rate in laminar flow regime and quadratic with respect to mass flow rate in turbulent flow regime.