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 |
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 |
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 |
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) |
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 |
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 |
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 |
The function is used to limit the derivative of the following function at x=0:
y = if x ≥ 0 then xpow 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.
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 |
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 |
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:
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 |
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 |
Generated 2018-12-12 12:13:31 EST by MapleSim.