functionpowerLaw_m_flow_inv_der2
Extends from Modelica.Icons.Function (Icon for functions).
Information
Function that implements the second order derivative of Buildings.Fluid.BaseClasses.FlowModels.powerLaw_m_flow_inv, assuming constant flow coefficients.
When called with dp_der=der(dp) and dp_der2=der(dp_der),
this function returns the second order derivative of m_flow
with respect to time.
When called with dp_der=1 and dp_der2=0,
this function returns the second order derivative of m_flow
with respect to dp.
Implementation
Let f denote
Buildings.Fluid.BaseClasses.FlowModels.powerLaw_m_flow.
Differentiating dp = f(m_flow) twice gives
dp_der2 = f'(m_flow) m_flow_der2 + f''(m_flow) m_flow_der^2,
which this function solves for m_flow_der2.
The term f'(m_flow) is computed by
Buildings.Fluid.BaseClasses.FlowModels.powerLaw_m_flow_der
with m_flow_der=1, and the term f''(m_flow) m_flow_der^2 by
Buildings.Fluid.BaseClasses.FlowModels.powerLaw_m_flow_der2
with m_flow_der2=0.
Inputs
| Type | Name | Default | Description |
|---|---|---|---|
| Modelica.Units.SI.PressureDifference | dp | Pressure difference | |
| Real | k | Flow coefficient, k = m_flow/ dp^(1/n) | |
| Real | n | Flow exponent, n=1 for laminar, n=2 for turbulent | |
| Modelica.Units.SI.MassFlowRate | m_flow_turbulent | Mass flow rate where transition to turbulent flow occurs | |
| Modelica.Units.SI.PressureDifference | dp_turbulent | Pressure difference where turbulent flow occurs | |
| Real | m | Flow exponent for the pressure drop | |
| Real | a1 | Polynomial coefficient for regularized implementation of flow resistance | |
| Real | a3 | Polynomial coefficient for regularized implementation of flow resistance | |
| Real | a5 | Polynomial coefficient for regularized implementation of flow resistance | |
| Real | C | Coefficient 1/k^n, based on the definition k = m_flow / dp^(1/n) | |
| Real | b1 | Polynomial coefficient for regularized implementation of flow resistance | |
| Real | b3 | Polynomial coefficient for regularized implementation of flow resistance | |
| Real | b5 | Polynomial coefficient for regularized implementation of flow resistance | |
| Real | dp_der | 1st derivative of pressure difference | |
| Real | dp_der2 | 2nd derivative of pressure difference |
Outputs
| Type | Name | Default | Description |
|---|---|---|---|
| Real | m_flow_der2 | 2nd derivative of mass flow rate |
Revisions
-
October 22, 2026, by Martin Sjölund:
First implementation.
This is for Buildings, #4798.