.Buildings.Utilities.Math.Functions.regNonZeroPower

Information

Function that approximates y=|x|ⁿ where 0 < n < 2 so that

• y(0) is not equal to zero.
• dy/dx is bounded and continuous everywhere.

This function replaces y=|x|ⁿ in the interval -δ...+δ by a 4-th order polynomial that has the same function value and the first and second derivative at x=± δ.

A typical use of this function is to replace the function for the convective heat transfer coefficient for forced or free convection that is of the form h=c |dT|ⁿ for some constant c and exponent 0 < n ≤ 1. By using this function, the original function that has an infinite derivative near zero and that takes on zero at the origin is replaced by a function with a bounded derivative and a non-zero value at the origin. Physically, the region -δ...+δ may be interpreted as the region where heat conduction dominates convection in the boundary layer.

See the package Examples for the graph.

Interface

function regNonZeroPower
  extends Modelica.Icons.Function;
  input Real x "Abscissa value";
  input Real n(min = 0.000001, max = 1.999999) "Exponent";
  input Real delta = 0.01 "Abscissa value where transition occurs";
  output Real y "Function value";
end regNonZeroPower;

Revisions

• November 2, 2022, by Michael Wetter:
  Set minimum and maximum attribute on n, improved assertion and documentation.
  This is for Buildings, #3135.
• March 30, 2011, by Michael Wetter:
  Added zeroDerivative keyword.
• April 14, 2008, by Michael Wetter:
  First implementation.