.AixLib.Airflow.Multizone.BaseClasses.powerLaw

Information

This model describes the mass flow rate and pressure difference relation of an orifice in the form

V̇ = C sign(Δp) |Δp|^m

where V̇ is the volume flow rate, C > 0 is a flow coefficient Δ p is the pressure drop and m ∈ [0.5, 1] is a flow coefficient. The equation is regularized for |Δp| < Δp_t, where Δp_t is a parameter. For turbulent flow, set m=1 ⁄ 2 and for laminar flow, set m=1.

The model is used for the interzonal air flow models.

Implementation

For |Δp| < Δp_t, the equation is regularized so that it is twice continuously differentiable in Δp, and that it has an infinite number of continuous derivatives in m and in k.

If m is not a function of time, then a, b, c and d can be pre-computed. In this situation, use AixLib.Airflow.Multizone.BaseClasses.powerLawFixedM, which allows to compute these values outside of this function, for example as parameters of a model.

Interface

function powerLaw
  extends Modelica.Icons.Function;
  input Real C "Flow coefficient, C = V_flow/ dp^m";
  input Modelica.Units.SI.PressureDifference dp(displayUnit = "Pa") "Pressure difference";
  input Real m(min = 0.5, max = 1) "Flow exponent, m=0.5 for turbulent, m=1 for laminar";
  input Modelica.Units.SI.PressureDifference dp_turbulent(min = 0, displayUnit = "Pa") = 0.001 "Pressure difference where regularization starts";
  output Modelica.Units.SI.VolumeFlowRate V_flow "Volume flow rate";
end powerLaw;

Revisions

• February 8, 2022, by Michael Wetter:
  Changed to use C for volume flow coefficient (C = V_flow/dp^m), and k for mass flow coefficient (k = m_flow/dp^m). This is for consistency with AixLib.Fluid.BaseClasses.FlowModels.
• January 22, 2016, by Michael Wetter:
  Corrected type declaration of pressure difference. This is for #404.
• August 12, 2011 by Michael Wetter:
  Reimplemented model so that it is continuously differentiable.
• July 20, 2010 by Michael Wetter:
  Migrated model to Modelica 3.1 and integrated it into the Buildings library.
• February 4, 2005 by Michael Wetter:
  Released first version.