functionpowerLaw

Power law used in orifice equations

Information

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

V = k sign(Δp) |Δp|m

where V is the volume flow rate, k > 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| < Δpt, where Δpt 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| < Δpt, 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 Buildings.Airflow.Multizone.BaseClasses.powerLawFixedM, which allows to compute these values outside of this function, for example as parameters of a model.

Inputs

TypeNameDefaultDescription
RealkFlow coefficient, k = V_flow/ dp^m
Modelica.SIunits.PressureDifferencedpPressure difference
RealmFlow exponent, m=0.5 for turbulent, m=1 for laminar
Modelica.SIunits.PressureDifferencedp_turbulent0.001Pressure difference where regularization starts

Outputs

TypeNameDefaultDescription
Modelica.SIunits.VolumeFlowRateV_flowVolume flow rate

Revisions

  • 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.