functionpowerLaw

Power law used in orifice equations

Extends from Modelica.Icons.Function (Icon for functions).

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 Buildings.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 Buildings.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 Buildings.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.