Engee documentation

Variable Local Restriction (MA)

Localised flow constriction in a network of moist air.

blockType: AcausalFoundation.MoistAir.Elements.LocalRestriction

local restriction (ma)

Local Restriction (MA)

Path in the library:

/Physical Modeling/Fundamental/Moist Air/Elements/Local Restriction (MA)

variable local restriction (ma)

Variable Local Restriction (MA)

Path in the library:

/Physical Modeling/Fundamental/Moist Air/Elements/Variable Local Restriction (MA)

Description

The Variable Local Restriction (MA) unit simulates the pressure drop due to a local reduction in the flow cross-section, such as a valve or orifice, in a wet air network. The local flow narrowing becomes critical when the moist air reaches the speed of sound.

Ports A and B represent the input and output of the unit Local Restriction (MA). The input signal on the AR port determines the cross-sectional area.

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

The local flow constriction 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 passage 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.

local restriction (il) 1 s

Humid air flow through this unit can become critical if the unit Controlled Mass Flow Rate Source (MA), connected to the unit Pipe (MA), sets a higher mass flow rate than the possible mass flow rate of the unit Local Restriction (MA).

Mass conservation:

,

,

,

where

  • - mass flow rate;

  • Lower indices and are ports A and B respectively;

  • 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:

,

,

where

  • 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;

  • - the area of local flow constriction;

  • - density of the mixture;

  • - pressure;

  • - flow coefficient.

The equation for the mass flow rate of the mixture is obtained by combining Eqs:

  • Impulse balance for the contraction of flow area from the inlet port to the local flow constriction.

  • 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:

ρ ,

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:

γ ,

γ ,

where is 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.

ρρρ .

The local flow constriction is assumed to be an adiabatic system, so the total enthalpies of the mixture are equal. Consequently, the changes in the specific enthalpies of the mixture are equal:

ρρ ,

ρρ .

Assumptions and limitations

  • The local flow constriction is considered an adiabatic system, i.e., it does not exchange heat with the environment.

  • This block does not model supersonic flow.

Ports

Conserving

# A — humid air inlet or outlet
`humid air

Details

Humid air port, corresponds to the inlet or outlet of the local flow constriction. This unit has no internal directionality.

Program usage name

port_a

# B — humid air inlet or outlet
`humid air

Details

Humid air port, corresponds to the inlet or outlet of the local flow constriction. This unit has no internal directionality.

Program usage name

port_b

Input

# AR — control signal of the cross-sectional area, m²
scalar

Details

An input port that controls the area of the local flow constriction cross-section. If the value on the port is outside the minimum and maximum limits of the local flow constriction area set by the block parameters, it is equated to these values.

Dependencies

This port is only used if the parameters Restriction type are set to Variable.

Data types

Float64
Complex numbers support

No

Parameters

Parameters

# Restriction type — Variable cross-sectional area
Fixed | Variable

Details

Select whether the cross-section can be changed during the simulation:

  • Variable - The input signal on the AR port defines the cross-sectional area that can be changed during simulation. The parameters Minimum restriction area and Maximum restriction area set the lower and upper limits of the cross-sectional area.

  • Fixed - The cross-sectional area defined by the value of the parameter Restriction area remains constant during the simulation. The AR port is hidden.

Values

Fixed | Variable
Default value

—
Program usage name

type
Evaluatable

No

# Restriction area — area of the passage section along the normal to the path of local flow constriction
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

The area of the passage section normal to the path of the local flow constriction.

Dependencies

To use this parameter, set the parameter Restriction type to . Fixed.

Units

m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2
Default value

1.e-3 m^2
Program usage name

fixed_restriction_area
Evaluatable

Yes

# Minimum restriction area — lower boundary of the area of the passage section of the local flow constriction
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

The lower limit of the cross-sectional area of the local flow constriction. You can use this parameter to represent the leakage area. If the value on the AR port is less than Minimum restriction area, it is equated to this value to prevent further reduction of the through-flow cross-section.

Dependencies

To use this parameter, set the parameter Restriction type to Variable.

Units

m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2
Default value

1e-10 m^2
Program usage name

min_restriction_area
Evaluatable

Yes

# Maximum restriction area — upper limit of the cross-sectional area of the local flow constriction
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

Upper limit of the cross-sectional area of the local flow restriction. If the value at port AR is greater than Maximum restriction area, it is equalised to this value to prevent further increases in the cross-sectional area.

Dependencies

To use this parameter, set the parameter Restriction type to Variable.

Units

m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2
Default value

0.005 m^2
Program usage name

max_restriction_area
Evaluatable

Yes

# Cross-sectional area at ports A and B — cross-sectional area normal to the flow path at the ports
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

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.

Units

m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2
Default value

0.01 m^2
Program usage name

port_area
Evaluatable

Yes

# Discharge coefficient — ratio of the actual mass flow rate to the theoretical mass flow rate through the local flow constriction

Details

The ratio of the actual mass flow rate to the theoretical mass flow rate through the local flow constriction. Discharge coefficient is an empirical parameter to account for non-ideal flow.

Default value

0.64
Program usage name

C_d
Evaluatable

Yes

# Laminar flow pressure ratio — pressure coefficient at which the humid air flow transitions between laminar and turbulent regimes

Details

Pressure ratio at which the humid air flow transitions from laminar to turbulent flow regime. 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.

Default value

0.999
Program usage name

B_laminar
Evaluatable

Yes

Examples