functionpowerLawFixedM

Power law used in orifice equations when m is constant

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| < 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. It is identical to Buildings.Airflow.Multizone.BaseClasses.powerLaw but it requires the polynomial coefficients as an input. This allows a more efficient simulation if m and therefore also a, b, c and d are constant.

The model is also identical to Buildings.Airflow.Multizone.BaseClasses.powerLaw05, except that it allows a flow coefficient m that is different from 0.5.

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, and therefore also a, b, c and d, change with time, then it is more convenient and efficient to use Buildings.Airflow.Multizone.BaseClasses.powerLaw.

If m = 0.5, use Buildings.Airflow.Multizone.BaseClasses.powerLaw05.

Inputs

TypeNameDefaultDescription
RealCFlow coefficient, C = V_flow/ dp^m
Modelica.Units.SI.PressureDifferencedpPressure difference
RealmFlow exponent, m=0.5 for turbulent, m=1 for laminar
RealaPolynomial coefficient
RealbPolynomial coefficient
RealcPolynomial coefficient
RealdPolynomial coefficient
Modelica.Units.SI.PressureDifferencedp_turbulent0.001Pressure difference where regularization starts

Outputs

TypeNameDefaultDescription
Modelica.Units.SI.VolumeFlowRateV_flowVolume flow rate

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 Buildings.Fluid.BaseClasses.FlowModels.
  • February 2, 2022, by Michael Wetter:
    Revised implementation.
    This is for IBPSA, #1436.
  • April 6, 2021, by Klaas De Jonge:
    Generalised the function by removing the units for flow. This is done because the function is used to compute both mass flow rates and volume flow rates.
  • January 22, 2016, by Michael Wetter:
    Corrected type declaration of pressure difference. This is for #404.
  • August 12, 2011 by Michael Wetter:
    First implementation.