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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:

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

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

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

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

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

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 |

D_{H} | Orifice hydraulic diameter |

A | Passage area |

ρ | Fluid density |

ν | Fluid kinematic viscosity |

p_{cr} | Minimum pressure for turbulent flow, for constant K |

For a constant pressure loss coefficient, the minimum pressure
for turbulent flow, *p*_{cr},
is calculated according to the laminar transition specification method:

By pressure ratio — The transition from laminar to turbulent regime is defined by the following equations:

*p*_{cr}= (*p*_{avg}+*p*_{atm})(1 –*B*_{lam})*p*_{avg}= (*p*_{A}+*p*_{B})/2where

*p*_{avg}Average pressure between the block terminals *p*_{atm}Atmospheric pressure, 101325 Pa *B*_{lam}Pressure ratio at the transition between laminar and turbulent regimes ( **Laminar flow pressure ratio**parameter value)By Reynolds number — The transition from laminar to turbulent regime is defined by the following equations:

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

where

*Re*_{cr}Critical Reynolds number ( **Critical Reynolds number**parameter value)

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 two 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`

.**Laminar transition specification**If

**Model parameterization**is set to`By semi-empirical formulas`

, select how the block transitions between the laminar and turbulent regimes:`Pressure ratio`

— The transition from laminar to turbulent regime is smooth and depends on the value of the**Laminar flow pressure ratio**parameter. This method provides better simulation robustness.`Reynolds number`

— The transition from laminar to turbulent regime is assumed to take place when the Reynolds number reaches the value specified by the**Critical Reynolds number**parameter.

**Laminar flow pressure ratio**Pressure ratio at which the flow transitions between laminar and turbulent regimes. The default value is

`0.999`

. This parameter is visible only if the**Laminar transition specification**parameter is set to`Pressure ratio`

.**Critical Reynolds number**The maximum Reynolds number for laminar flow. 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 visible only if the**Laminar transition specification**parameter is set to`Reynolds number`

.**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 smooth 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`

— Select this option to get the best performance.`Smooth`

— Select this option to produce a continuous curve with continuous first-order derivatives.

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:

`Linear`

— Select this option to produce a curve with continuous first-order derivatives in the extrapolation region and at the boundary with the interpolation region.`Nearest`

— Select this option to produce an extrapolation that does not go above the highest point in the data or below the lowest point in the data.

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`

.

**Flow rate**Volumetric flow rate through the local resistance at time zero. Simscape™ software uses this parameter to guide the initial configuration of the component and model. Initial variables that conflict with each other or are incompatible with the model may be ignored. Set the

**Priority**column to`High`

to prioritize this variable over other, low-priority, variables.**Pressure differential**Pressure differential between the local resistance ports at time zero. Simscape software uses this parameter to guide the initial configuration of the component and model. Initial variables that conflict with each other or are incompatible with the model may be ignored. Set the

**Priority**column to`High`

to prioritize this variable over other, low-priority, variables.

When your model is in Restricted editing mode, you cannot modify the following parameters:

**Model parameterization****Interpolation method****Extrapolation method****Laminar transition specification**

All other block parameters are available for modification. The
actual set of modifiable block parameters depends on the value of
the **Model parameterization** parameter at the time
the model entered Restricted mode.

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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