Flow Resistance (TL)
Hydraulic resistance in a thermal liquid network.
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Description
The Flow Resistance (TL) block models the total pressure drop in a thermal liquid network. The pressure drop is proportional to the square of the mass flow rate. The proportional coefficient is determined based on the nominal characteristics specified in the parameters of the unit.
This block is used when only the pressure drop at the corresponding mass flow rate is known for a component, or when detailed information on the geometry of the component is not available, or when it is not possible to theoretically determine the pressure drop of a component based on its duct geometry.
Mass conservation
It is assumed that the volume of fluid within the hydraulic resistance is negligibly small. Then the mass flow rate at the inlet through one port is equal to the mass flow rate at the outlet through the other port:
,
where:
-
- mass flow rate.
-
Lower indices and are ports A and B respectively.
Energy conservation
There is no energy exchange in the block, energy can only be transferred through the ports of the thermal liquid. There is no heat exchange between the walls and the environment, the fluid does not do any work. The amount of energy entering per unit of time through one port is equal to the amount of energy leaving through the other port per unit of time:
,
where
-
and are the energy flow through ports A and B respectively.
Conservation of momentum
An approximation is used when the pressure drop is proportional to the square of the mass flow rate. At small values of the mass flow rate in a small region of laminar flow, the dependence of the pressure drop on the square of the mass flow rate is linear, resulting in the following
,
where:
-
and are pressures at ports A and B respectively.
-
- is the crisis value of mass flow rate for the laminar-turbulent transition.
-
- proportionality coefficient:
,
where
-
- is the value of the Nominal pressure drop parameter.
-
- value of the Nominal mass flow rate parameter.
-
Ports
Non-directional
A - input or output
thermal liquid
Thermal liquid port, corresponds to the input or output of the hydraulic resistance. This block has no specific directionality.
B - input or output
thermal liquid.
Thermal liquid port, corresponds to the input or output of the hydraulic resistance. This block has no specific directionality.
Parameters
Nominal pressure drop - pressure drop at known operating mode
`0.001 MPa (by default)
Pressure drop from inlet to outlet at known operating mode. The block uses nominal parameters to calculate the coefficient of proportionality between pressure drop and mass flow rate.
Nominal mass flow rate - mass flow rate at known operating mode
`0.1 kg/s (By default)
Mass flow rate from inlet to outlet at known operating mode. The block uses nominal parameters to calculate the coefficient of proportionality between pressure drop and mass flow rate.
Cross-sectional area at ports A and B - cross-sectional area of the hydraulic resistance ports
0.01 m² (by default)
Cross-sectional area of the hydraulic resistance ports. It is assumed that the dimensions of the ports are the same.
Fraction of nominal mass flow rate for laminar flow - ratio of mass flow rate threshold to nominal mass flow rate
1e-3 (by default).
Ratio of crisis mass flow rate to nominal mass flow rate. In the block, this parameter is used to calculate the mass flow crisis value, and ultimately to set the linear approximation limits for the differential pressure calculation.