functionpowerLaw

Power law used in orifice equations

Extends from Modelica.Icons.Function.

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 IDEAS.Airflow.Multizone.BaseClasses.powerLawFixedM, which allows to compute these values outside of this function, for example as parameters of a model.

Inputs

Type	Name	Default	Description
Real	C		Flow coefficient, C = V_flow/ dp^m
Modelica.Units.SI.PressureDifference	dp		Pressure difference
Real	m		Flow exponent, m=0.5 for turbulent, m=1 for laminar
Modelica.Units.SI.PressureDifference	dp_turbulent	0.001	Pressure difference where regularization starts

Outputs

Type	Name	Default	Description
Modelica.Units.SI.VolumeFlowRate	V_flow		Volume flow rate

Revisions

September 19, 2025, by Michael Wetter:
Refactored implementation to allow function to be inlined. This leads to a 20% faster simulation of IDEAS.Airflow.Multizone.Examples.OneOpenDoor compared to the previous implementation.
This is for IBPSA, #2043.
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 IDEAS.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.