Local Resistance (IL)
Hydraulic resistance in a pipe in an isothermal liquid network.
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Description
Block Local Resistance (IL) simulates the pressure losses associated with the user-defined pipe resistance in an isothermal liquid network. In the block it is possible to set different values of loss coefficients for forward and reverse flows through the pipe section. For curved pipe sections, the isothermal liquid library blocks Pipe Bend (IL) and Sharp-Edged Elbow (IL) or, for sections with variable cross-sectional area, the block Gradual Area Change (IL) can be used. The loss coefficient can be set as a constant value determined by the pressure in the pipe, or it can be obtained from a custom table of loss coefficients and their corresponding Reynolds numbers.
Constant loss factor
The drag coefficient of the sections where it can be considered constant over a given velocity range are calculated as: ,
where
-
and are the values of the parameters Forward flow loss coefficient (from A to B) and Reverse flow loss coefficient (from B to A) respectively;
-
- pressure drop .
The critical pressure drop is the pressure difference determined by the critical Reynolds number Critical Reynolds number, , which is the transition point between laminar and turbulent flow regimes:
,
where
-
- loss coefficient determined by critical pressure and based on the average value of loss coefficients in forward and reverse directions;
-
- kinematic viscosity of the fluid;
-
- average density of the fluid;
-
- hydraulic diameter of the section, which is the equivalent diameter of a pipe with a non-circular cross-section: , where is the value of the Flow area parameters.
Tabular method of parameterization
The loss factor can be determined using the Reynolds number and loss factor data provided by the user. The Reynolds number vector can have both positive and negative values, indicating forward and reverse flow respectively:
Intermediate values between neighbouring points are determined by linear interpolation, and beyond the table boundaries the nearest neighbour method is used.
Law of conservation of mass
.
The mass flow rate through a port is calculated as:
,
where is the flow loss coefficient, which is selected between the values of the parameters Forward flow loss coefficient (from A to B) and Reverse flow loss coefficient (from B to A) depending on the direction of flow in the block.
Ports
Non-directional
A - isothermal liquid port
isothermal liquid
Isothermal liquid port, corresponds to the inlet or outlet of liquid from the pipe section. When the flow direction is positive, the liquid flows from port A to port B.
B is the isothermal liquid port.
isothermal liquid
Isothermal liquid port, corresponds to the entrance or exit of liquid from the pipe section. When the flow direction is positive, the liquid flows from port A to port B.
Parameters
Local loss parameterization - method of calculation of hydraulic losses
Constant (by default) | Tabulated data - loss coefficient vs. Reynolds number
Method of calculation of loss coefficient on the pipe section.
The loss coefficient can be set as a constant value determined by the pressure in the pipe, or it can be derived from a custom table of loss coefficients and their corresponding Reynolds numbers.
Forward flow loss coefficient (from A to B) - loss coefficient for flow from A to B
1 (by default)
Loss coefficient associated with pressure loss for flows from port A to port B.
Reverse flow loss coefficient (from B to A) - loss coefficient for flow from B to A
1 (by default).
Pressure loss coefficient for flows from port B to port A.
Reynolds number vector - vector of Reynolds number values in case of tabular parameterization method
[-500, -200, -100, -50, -40, -30, -20, -10, 10, 20, 30, 40, 40, 50, 100, 200, 500, 1000, 2000] (by default) | vector 1 to n
Vector of Reynolds number values for the tabular parameterization of the loss factor. The vector must correspond element by element to the Loss coefficient vector. The elements in the vector are given in ascending order.
Dependencies
To use this parameter, set the Local loss parameterization parameters to `Tabulated data - loss coefficient vs. Reynolds number'.
Loss coefficient vector - loss coefficient vector
[.65, .75, .9, 1.15, 1.35, 1.65, 2.3, 3.1, 4, 2.7, 1.8, 1.46, 1.3, .9, .65, .42, .3, .2] (by default) | vector 1 to n
A vector of loss coefficients for the tabular parameterization of the loss factor, where n is the length of the vector of Reynolds number values. The elements of the vector must be greater than 0.
Dependencies
To use this parameter, set the Local loss parameterization parameters to `Tabulated data - loss coefficient vs. Reynolds number'.
Flow area - cross-sectional area of the section
1e-3 m^2 (by default) | positive scalar.
Cross-sectional area of the pipe section.
Critical Reynolds number - upper limit of Reynolds number for laminar flow
150 (By default) | Positive scalar
Upper limit of Reynolds number for laminar flow regime.