Package with utility functions

Standard package icon.

Extends from `Modelica.Icons.FunctionsPackage`

(Icon for packages containing functions).

Name | Description |
---|---|

`CubicInterpolation_DP` | |

`CubicInterpolation_MFLOW` | |

`LambertW` | Closed approximation of Lambert's w function for solving f(x) = x exp(x) for x |

`LambertWIter` | Iterative form of Lambert's w function for solving f(x) = x exp(x) for x |

`PrandtlNumber` | calculation of Prandtl number |

`ReynoldsNumber` | calculation of Reynolds number |

`SmoothPower` | Limiting the derivative of function y = if x>=0 then x^pow else -(-x)^pow |

`SmoothPower_der` | The derivative of function SmoothPower |

`Stepsmoother` | Continuous interpolation for x |

`Stepsmoother_der` | Derivative of function Stepsmoother |

Icon for functions

This icon indicates Modelica functions.

Extends from `Modelica.Icons.Function`

(Icon for functions).

Type | Name | Description |
---|---|---|

`Real` | `Re_turbulent` | |

`ReynoldsNumber` | `Re1` | |

`ReynoldsNumber` | `Re2` | |

`Real` | `Delta` | |

`Real` | `lambda2` |

Type | Name | Description |
---|---|---|

`ReynoldsNumber` | `Re` |

Icon for functions

This icon indicates Modelica functions.

Extends from `Modelica.Icons.Function`

(Icon for functions).

Type | Name | Description |
---|---|---|

`ReynoldsNumber` | `Re` | |

`ReynoldsNumber` | `Re1` | |

`ReynoldsNumber` | `Re2` | |

`Real` | `Delta` |

Type | Name | Description |
---|---|---|

`Real` | `lambda2` |

Closed approximation of Lambert's w function for solving f(x) = x exp(x) for x

This function calculates an approximation of the ** inverse ** for

f(x) = y = x * exp( x )

within ∞ > y > -1/e. The relative deviation of this approximation for Lambert's w function **x = W(y)** is displayed in the following graph.

For y > 10 and higher values the relative deviation is smaller 2%.

Extends from `Modelica.Icons.Function`

(Icon for functions).

Type | Name | Description |
---|---|---|

`Real` | `y` | f(x) |

Type | Name | Description |
---|---|---|

`Real` | `x` | W(y) |

Iterative form of Lambert's w function for solving f(x) = x exp(x) for x

This function calculates an approximation of the ** inverse ** for

f(x) = y = x * exp( x )

within ∞ > y > -1/e. Please note, that for negative inputs **two** solutions exists. The function currently delivers the result x = -1 ... 0 for that particular range.

Extends from `Modelica.Icons.Function`

(Icon for functions).

Type | Name | Description |
---|---|---|

`Real` | `y` | f(x) |

Type | Name | Description |
---|---|---|

`Real` | `x` | W(y) |

`Integer` | `iter` |

calculation of Prandtl number

This icon indicates Modelica functions.

Extends from `Modelica.Icons.Function`

(Icon for functions).

Type | Name | Description |
---|---|---|

`SpecificHeatCapacityAtConstantPressure` | `cp` | specific heat capacity of fluid at constant pressure |

`DynamicViscosity` | `eta` | dynamic viscosity of fluid |

`ThermalConductivity` | `lambda` | thermal conductivity of fluid |

Type | Name | Description |
---|---|---|

`PrandtlNumber` | `Pr` | Prandtl number |

calculation of Reynolds number

This icon indicates Modelica functions.

Extends from `Modelica.Icons.Function`

(Icon for functions).

Type | Name | Description |
---|---|---|

`Area` | `A_cross` | Cross sectional area |

`Length` | `perimeter` | Wetted perimeter |

`Density` | `rho` | Density of fluid |

`DynamicViscosity` | `eta` | Dynamic viscosity of fluid |

`MassFlowRate` | `m_flow` | Mass flow rate |

Type | Name | Description |
---|---|---|

`ReynoldsNumber` | `Re` | Reynolds number |

`Velocity` | `velocity` | Mean velocity |

Limiting the derivative of function y = if x>=0 then x^pow else -(-x)^pow

The function is used to limit the derivative of the following function at x=0:

y =ifx ≥ 0thenx^{pow}else-(-x)^{pow}; // pow > 0

by approximating the function in the range -**deltax**< x < **deltax**
with a third order polynomial that has the same derivative at **abs**(x)=deltax, as the
function above.

In the picture below the input x is increased from -1 to 1. The range of interpolation is defined by the same range. Displayed is the output of the function SmoothPower compared to

y=x*|x|

For |x| > 1 both functions return identical results.

- ThermoFluid Library
**http://sourceforge.net/projects/thermofluid/**

Extends from `Modelica.Icons.Function`

(Icon for functions).

Type | Name | Description |
---|---|---|

`Real` | `x` | input variable |

`Real` | `deltax` | range for interpolation |

`Real` | `pow` | exponent for x |

Type | Name | Description |
---|---|---|

`Real` | `y` | output variable |

The derivative of function SmoothPower

This icon indicates Modelica functions.

Extends from `Modelica.Icons.Function`

(Icon for functions).

Type | Name | Description |
---|---|---|

`Real` | `x` | input variable |

`Real` | `deltax` | range of interpolation |

`Real` | `pow` | exponent for x |

`Real` | `dx` | derivative of x |

Type | Name | Description |
---|---|---|

`Real` | `dy` | derivative of SmoothPower |

Continuous interpolation for x

The function is used for continuous fading of variable inputs within a defined range. It allows a differentiable and smooth transition between function outputs, e.g., laminar and turbulent pressure drop or correlations for certain ranges.

The tanh-function is used, since it provides an existing derivative and the derivative is zero at the borders [**nofunc**, **func**] of the interpolation domain (smooth derivative for transitions).

In order to work correctly, the internal interpolation range in terms of the external arbitrary input ** x ** needs to be scaled such that:

f(func) = 0.5 π f(nofunc) = -0.5 π

In the picture below the input x is increased from 0 to 1. The range of interpolation is defined by:

- func = 0.75
- nofunc = 0.25

- Wischhusen, St.
**Simulation von Kältemaschinen-Prozessen mit MODELICA / DYMOLA**. Diploma thesis, Hamburg University of Technology, Institute of Thermofluiddynamics, 2000.

Extends from `Modelica.Icons.Function`

(Icon for functions).

Type | Name | Description |
---|---|---|

`Real` | `func` | input value for that result = 100% |

`Real` | `nofunc` | input value for that result = 0% |

`Real` | `x` | input variable for continuous interpolation |

Type | Name | Description |
---|---|---|

`Real` | `result` | output value |

Derivative of function Stepsmoother

This icon indicates Modelica functions.

Extends from `Modelica.Icons.Function`

(Icon for functions).

Type | Name | Description |
---|---|---|

`Real` | `func` | input for that result = 100% |

`Real` | `nofunc` | input for that result = 0% |

`Real` | `x` | input for interpolation |

`Real` | `dfunc` | derivative of func |

`Real` | `dnofunc` | derivative of nofunc |

`Real` | `dx` | derivative of x |

Type | Name | Description |
---|---|---|

`Real` | `dresult` |