Hydraulic resistance specified by loss coefficient

Local Hydraulic Resistances

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:

$$q=A\sqrt{\frac{2}{K\cdot \rho}}\cdot \frac{p}{{\left({p}^{2}+{p}_{cr}^{2}\right)}^{1/4}}$$

$$p={p}_{A}-{p}_{B}$$

$${p}_{cr}=K\frac{\rho}{2}{\left(\frac{{\mathrm{Re}}_{cr}\cdot \nu}{{D}_{H}}\right)}^{2}$$

$$K=\{\begin{array}{l}\text{const}\hfill \\ K(\mathrm{Re})\text{}\hfill \end{array}$$

$$\mathrm{Re}=\frac{q\cdot {D}_{H}}{A\cdot \nu}$$

$${D}_{H}=\sqrt{\frac{4A}{\pi}}$$

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 |

p_{cr} | Minimum pressure for 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

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.`K=f(Re)`

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 $$p={p}_{A}-{p}_{B}$$.

Fluid inertia is not taken into account.

If you select parameterization by the table-specified relationship

, the flow is assumed to be completely turbulent.`K=f(Re)`

**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 assumed to take place when the Reynolds number reaches this value. The value of the parameter depends on the orifice geometrical profile. You can find recommendations on the parameter value in hydraulics 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 one-dimensional array. The input values vector must be strictly increasing. The values can be nonuniformly spaced. The minimum number of values depends on the interpolation method: you must provide at least two values for linear interpolation, at least three values for cubic or spline interpolation. 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 the loss coefficient values as a one-dimensional array. The loss coefficient vector must be of 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 Polynomial (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`

.

Parameters determined by the type of working fluid:

**Fluid density****Fluid kinematic viscosity**

Use the Hydraulic Fluid block or the Custom Hydraulic Fluid block to specify the fluid properties.

The block has the following ports:

`A`

Hydraulic conserving port associated with the resistance inlet.

`B`

Hydraulic conserving port associated with the resistance outlet.

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

Elbow | Gradual Area Change | Pipe Bend | Sudden Area Change | T-junction

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