functionpowerLaw_dp_inv_der2
Extends from Modelica.Icons.Function (Icon for functions).
Information
Function that implements the second order derivative of Buildings.Fluid.BaseClasses.FlowModels.powerLaw_dp_inv, assuming constant flow coefficients.
When called with m_flow_der=der(m_flow) and m_flow_der2=der(m_flow_der),
this function returns the second order derivative of dp
with respect to time.
When called with m_flow_der=1 and m_flow_der2=0,
this function returns the second order derivative of dp
with respect to m_flow.
Implementation
Let f denote
Buildings.Fluid.BaseClasses.FlowModels.powerLaw_dp.
Differentiating m_flow = f(dp) twice gives
m_flow_der2 = f'(dp) dp_der2 + f''(dp) dp_der^2,
which this function solves for dp_der2.
The term f'(dp) is computed by
Buildings.Fluid.BaseClasses.FlowModels.powerLaw_dp_der
with dp_der=1, and the term f''(dp) dp_der^2 by
Buildings.Fluid.BaseClasses.FlowModels.powerLaw_dp_der2
with dp_der2=0.
Inputs
| Type | Name | Default | Description |
|---|---|---|---|
| Modelica.Units.SI.MassFlowRate | m_flow | Mass flow rate | |
| 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 | m_flow_der | 1st derivative of mass flow rate | |
| Real | m_flow_der2 | 2nd derivative of mass flow rate |
Outputs
| Type | Name | Default | Description |
|---|---|---|---|
| Real | dp_der2 | 2nd derivative of pressure difference |
Revisions
-
October 22, 2026, by Martin Sjölund:
First implementation.
This is for Buildings, #4798.