Variable Local Restriction (MA)
Local narrowing of the humid air flow in the network.
blockType: AcausalFoundation.MoistAir.Elements.LocalRestriction
|
Local Restriction (MA) Path in the library: |
|
Variable Local Restriction (MA) Path in the library: |
.svg)
.svg)
Description
Block Variable Local Restriction (MA) simulates a pressure drop due to a local reduction in the flow section, such as a valve or an opening, in the humid air network. Local narrowing of the flow becomes critical when 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 parameter value. Restriction type.
The local narrowing of the flow is considered an adiabatic system, that is, it does not exchange heat with the environment.
A local narrowing of the flow consists of a narrowing followed by a sudden expansion of the flow section. Moist air accelerates during compression, causing a pressure drop. It then separates from the wall during a sudden expansion, as a result of which the pressure is only partially restored due to loss of momentum.
| The flow of humid air through this unit can become critical if the unit Controlled Mass Flow Rate Source (MA) connected to the block Pipe (MA), sets a higher mass flow rate than the possible mass flow rate of the block Local Restriction (MA). |
Conservation of mass:
,
,
,
where
-
— mass consumption;
-
Lower indexes and — ports A and B respectively;
-
Lower indexes and they indicate the properties of water vapor and gas impurities, respectively.
Energy balance:
,
where and — 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
-
Subscript indexes and indicate the entrance and exit, respectively. If , then the input is port A and the output is port B; otherwise, they swap places. The cross-sectional area is assumed to be It is the same on ports A and B.;
-
— the area of local narrowing of the flow;
-
— the density of the mixture;
-
— pressure;
-
— expense ratio.
The equation of the mass flow rate of the mixture is obtained by combining the equations:
-
Pulse balance to reduce the flow area from the inlet to the local narrowing of the flow.
-
Pulse balance for sudden expansion of the flow area from a local narrowing of the flow to the outlet.
In case of reduction of the flow area, the pressure affects the area at the entrance, , and the pressure it affects the area of local narrowing of the flow, . It is assumed that the pressure acting on the area beyond the local narrowing of the flow, , equal to .
In the case of expansion of the flow area, the pressure acting as on the area of local narrowing of the flow, , as well as to the area beyond the local narrowing of the flow, , is assumed to be equal due to the separation of the flow from the local narrowing of the flow. Pressure acting on the outlet area, equally .
The mass flow rate of the mixture (positive from hole A to hole B) in the laminar mode is linearized with respect to the pressure difference:
,
where the threshold of transition between laminar and turbulent modes is determined based on the pressure ratio of the laminar flow, Like:
.
When , it is assumed that the flow is turbulent and, therefore,, .
When there is a smooth transition from to .
When the flow is blocked, the rate of local narrowing of the flow is equal to the speed of sound and cannot increase further. Assuming that the flow is blocked, the mass flow rate of the mixture is:
,
,
where — specific heat capacity at constant pressure.
Therefore, the actual mass consumption of the mixture is , but at the same time is limited by the value :
The expression for the pressure of the local narrowing of the flow is obtained by taking into account the balance of pulses only to reduce the area of the flow from the inlet of the local narrowing of the flow.
.
The local narrowing of the flow is considered an adiabatic system, so the total enthalpies of the mixture are equal. Therefore, the changes in the specific enthalpies of the mixture are equal to:
,
.
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 |
|
#
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 |
|
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 |
|
| Complex numbers support |
No |
Parameters
Parameters
#
Restriction type —
the possibility of changing the passage section
Fixed | Variable
Details
Select whether the flow section can change during the simulation.:
-
Variable— the input signal on the AR port determines the cross-sectional area, which may change during the simulation. Parameters Minimum restriction area and Maximum restriction area set the lower and upper boundaries of the cross-sectional area. -
Fixed— the cross-sectional area specified by the parameter value Restriction area, remains constant during simulation. At the same time, the AR port is hidden.
| Values |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
No |
#
Restriction area —
the area of the passage section is normal to the path of local narrowing of the flow
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac
Details
The area of the passage section is normal to the path of local narrowing of the flow.
Dependencies
To use this parameter, set for the parameter Restriction type meaning Fixed.
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Minimum restriction area —
the lower boundary of the area of the passage section of the local narrowing of the flow
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac
Details
The lower boundary of the area of the passage section of the local narrowing of the flow. You can use this parameter to represent the leakage area. If the value on the AR port is less than Minimum restriction area, then it is equated to this value in order to prevent further reduction of the passage section.
Dependencies
To use this parameter, set for the parameter Restriction type meaning Variable.
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Maximum restriction area —
the upper boundary of the area of the passage section of the local narrowing of the flow
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac
Details
The upper boundary of the area of the passage section of the local narrowing of the flow. If the value on the AR port is greater Maximum restriction area, then it is equated to this value in order to prevent a further increase in the cross-sectional area.
Dependencies
To use this parameter, set for the parameter Restriction type meaning Variable.
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Cross-sectional area at ports A and B —
the cross-sectional area is normal to the flow path at the ports
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac
Details
The cross-sectional area is normal to the flow path at ports A and B. It is assumed that this area is the same for the two ports.
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
# Discharge coefficient — the ratio of the actual mass flow to the theoretical mass flow due to local flow narrowing
Details
The ratio of the actual mass flow to the theoretical mass flow through the local narrowing of the flow. Discharge coefficient It is an empirical parameter that takes into account the imperfection of the flow.
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
# Laminar flow pressure ratio — the pressure coefficient at which the humid air flow transitions between laminar and turbulent modes
Details
The pressure ratio at which the flow of moist air passes from a laminar flow mode to a turbulent one. The pressure loss is linear with respect to the mass flow rate in the laminar flow regime and quadratic with respect to the mass flow rate in the turbulent flow regime.
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |