BuildingSystems.Airflow.Multizone.BaseClasses.powerLaw

# .BuildingSystems.Airflow.Multizone.BaseClasses.powerLaw

Power law used in orifice equations

## 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| < 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 BuildingSystems.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 BuildingSystems.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.

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