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Local Resistance - Simulate all kinds of hydraulic resistances specified by loss coefficient

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Local Hydraulic Resistances

Description

The Local Resistance block represents a generic local hydraulic resistance, such as a bend, elbow, fitting, filter, local change in the flow cross section, and so on. The pressure loss caused by resistance is computed based on the pressure loss coefficient, which is usually provided in catalogs, data sheets, or hydraulic textbooks. The pressure loss coefficient can be specified either as a constant, or by a table, in which it is tabulated versus Reynolds number.

The pressure loss is determined according to the following equations:

where

`q`	Flow rate
`p`	Pressure loss
`p_A,p_B`	Gauge pressures at the block terminals
`K`	Pressure loss coefficient, which can be specified either as a constant, or as a table-specified function of the Reynolds number
`Re`	Reynolds number
`Re_cr`	Reynolds number of the transition from laminar to turbulent flow
`D_H`	Orifice hydraulic diameter
`A`	Passage area
ρ	Fluid density
ν	Fluid kinematic viscosity

Two block parameterization options are available:

By semi-empirical formulas — The pressure loss coefficient is assumed to be constant for a specific flow direction. The flow regime can be either laminar or turbulent, depending on the Reynolds number.
By table-specified K=f(Re) relationship — The pressure loss coefficient is specified as function of the Reynolds number. The flow regime is assumed to be turbulent all the time. It is your responsibility to provide the appropriate values in the K=f(Re) table to ensure turbulent flow.

The resistance can be symmetrical or asymmetrical. In symmetrical resistances, the pressure loss practically does not depend on flow direction and one value of the coefficient is used for both the direct and reverse flow. For asymmetrical resistances, the separate coefficients are provided for each flow direction. If the loss coefficient is specified by a table, the table must cover both the positive and the negative flow regions.

Connections A and B are conserving hydraulic ports associated with the block inlet and outlet, respectively.

The block positive direction is from port A to port B. This means that the flow rate is positive if fluid flows from A to B, and the pressure loss is determined as .

Basic Assumptions and Limitations

The model is based on the following assumption:

Fluid inertia is not taken into account.
If you select parameterization by semi-empirical formulas, the transition between laminar and turbulent regimes is assumed to be sharp and taking place exactly at Re=Re_cr.
If you select parameterization by the table-specified relationship K=f(Re), the flow is assumed to be completely turbulent.

Dialog Box and Parameters

Resistance area

The smallest passage area. The default value is 1e-4 m^2.

Model parameterization

Select one of the following methods for specifying the pressure loss coefficient:

By semi-empirical formulas — Provide a scalar value for the pressure loss coefficient. For asymmetrical resistances, you have to provide separate coefficients for direct and reverse flow. This is the default method.
By loss coefficient vs. Re table — Provide tabulated data of loss coefficients and corresponding Reynolds numbers. The loss coefficient is determined by one-dimensional table lookup. You have a choice of three interpolation methods and two extrapolation methods. For asymmetrical resistances, the table must cover both the positive and the negative flow regions.

Pressure loss coefficient for direct flow

Loss coefficient for the direct flow (flowing from A to B). For simple ideal configurations, the value of the coefficient can be determined analytically, but in most cases its value is determined empirically and provided in textbooks and data sheets (for example, see [1]). The default value is 2. This parameter is used if Model parameterization is set to By semi-empirical formulas.

Pressure loss coefficient for reverse flow

Loss coefficient for the reverse flow (flowing from B to A). The parameter is similar to the loss coefficient for the direct flow and must be set to the same value if the resistance is symmetrical. The default value is 2. This parameter is used if Model parameterization is set to By semi-empirical formulas.

Critical Reynolds number

The maximum Reynolds number for laminar flow. The transition from laminar to turbulent regime is supposed to take place when the Reynolds number reaches this value. The value of the parameter depends on geometrical profile, and the recommendations on the parameter value can be found in hydraulic textbooks. The default value is 150. This parameter is used if Model parameterization is set to By semi-empirical formulas.

Reynolds number vector

Specify the vector of input values for Reynolds numbers as a tabulated 1-by-m array. The input values vector must be strictly monotonically increasing. The values can be nonuniformly spaced. You must provide at least three values. The default values are [-4000, -3000, -2000, -1000, -500, -200, -100, -50, -40, -30, -20, -15, -10, 10, 20, 30, 40, 50, 100, 200, 500, 1000, 2000, 4000, 5000, 10000]. This parameter is used if Model parameterization is set to By loss coefficient vs. Re table.

Loss coefficient vector

Specify the vector of output values for the loss coefficient as a tabulated 1-by-m array. The loss coefficient vector must be the same size as the Reynolds numbers vector. The default values are [0.25, 0.3, 0.65, 0.9, 0.65, 0.75, 0.90, 1.15, 1.35, 1.65, 2.3, 2.8, 3.10, 5, 2.7, 1.8, 1.46, 1.3, 0.9, 0.65, 0.42, 0.3, 0.20, 0.40, 0.42, 0.25]. This parameter is used if Model parameterization is set to By loss coefficient vs. Re table.

Interpolation method

Select one of the following interpolation methods for approximating the output value when the input value is between two consecutive grid points:

Linear — Uses a linear interpolation function.
Cubic — Uses the Piecewise Cubic Hermite Interpolation Polinomial (PCHIP).
Spline — Uses the cubic spline interpolation algorithm.

For more information on interpolation algorithms, see the PS Lookup Table (1D) block reference page. This parameter is used if Model parameterization is set to By loss coefficient vs. Re table.

Extrapolation method

Select one of the following extrapolation methods for determining the output value when the input value is outside the range specified in the argument list:

From last 2 points — Extrapolates using the linear method (regardless of the interpolation method specified), based on the last two output values at the appropriate end of the range. That is, the block uses the first and second specified output values if the input value is below the specified range, and the two last specified output values if the input value is above the specified range.
From last point — Uses the last specified output value at the appropriate end of the range. That is, the block uses the last specified output value for all input values greater than the last specified input argument, and the first specified output value for all input values less than the first specified input argument.

For more information on extrapolation algorithms, see the PS Lookup Table (1D) block reference page. This parameter is used if Model parameterization is set to By loss coefficient vs. Re table.

Global Parameters

Fluid density: The parameter is determined by the type of working fluid selected for the system under design. Use the Hydraulic Fluid block or the Custom Hydraulic Fluid block to specify the fluid properties.
Fluid kinematic viscosity: The parameter is determined by the type of working fluid selected for the system under design. Use the Hydraulic Fluid block or the Custom Hydraulic Fluid block to specify the fluid properties.

Ports

The block has the following ports:

A: Hydraulic conserving port associated with the resistance inlet.
B: Hydraulic conserving port associated with the resistance outlet.

References

[1] Idelchik, I.E., Handbook of Hydraulic Resistance, CRC Begell House, 1994