.AixLib.Fluid.FixedResistances.PressureDrop

Information

Model of a flow resistance with a fixed flow coefficient. The mass flow rate is

ṁ = k √Δp,

where k is a constant and Δp is the pressure drop. The constant k is equal to k=m_flow_nominal/sqrt(dp_nominal), where m_flow_nominal and dp_nominal are parameters.

Assumptions

In the region abs(m_flow) < m_flow_turbulent, the square root is replaced by a differentiable function with finite slope. The value of m_flow_turbulent is computed as m_flow_turbulent = deltaM * abs(m_flow_nominal), where deltaM=0.3 and m_flow_nominal are parameters that can be set by the user.

The figure below shows the pressure drop for the parameters m_flow_nominal=5 kg/s, dp_nominal=10 Pa and deltaM=0.3.

Important parameters

The parameter from_dp is used to determine whether the mass flow rate is computed as a function of the pressure drop (if from_dp=true), or vice versa. This setting can affect the size of the nonlinear system of equations.

If the parameter linearized is set to true, then the pressure drop is computed as a linear function of the mass flow rate.

Setting allowFlowReversal=false can lead to simpler equations. However, this should only be set to false if one can guarantee that the flow never reverses its direction. This can be difficult to guarantee, as pressure imbalance after the initialization, or due to medium expansion and contraction, can lead to reverse flow.

If the parameter show_T is set to true, then the model will compute the temperature at its ports. Note that this can lead to state events when the mass flow rate approaches zero, which can increase computing time.

Notes

For more detailed models that compute the actual flow friction, models from the package Modelica.Fluid can be used and combined with models from the AixLib library.

For a model that uses the hydraulic parameter and flow velocity at nominal conditions as a parameter, use AixLib.Fluid.FixedResistances.HydraulicDiameter.

Implementation

The pressure drop is computed by calling a function in the package AixLib.Fluid.BaseClasses.FlowModels, This package contains regularized implementations of the equation

ṁ = sign(Δp) k √ Δp  

and its inverse function.

To decouple the energy equation from the mass equations, the pressure drop is a function of the mass flow rate, and not the volume flow rate. This leads to simpler equations.

Revisions

• September 21, 2018, by Michael Wetter:
  Decrease value of deltaM(min=...) attribute. See #1026.
• February 3, 2018, by Filip Jorissen:
  Revised implementation of pressure drop equation such that it depends on from_dp when linearized=true. See #884.
• December 1, 2016, by Michael Wetter:
  Simplified model by removing the geometry dependent parameters into the new model AixLib.Fluid.FixedResistances.HydraulicDiameter.
• November 23, 2016, by Filip Jorissen:
  Removed dp_nominal and m_flow_nominal labels from icon.
• October 14, 2016, by Michael Wetter:
  Updated comment for parameter use_dh.
• November 26, 2014, by Michael Wetter:
  Added the required annotation(Evaluate=true) so that the system of nonlinear equations in AixLib.Fluid.FixedResistances.Validation.PressureDropsExplicit remains the same.
• November 20, 2014, by Michael Wetter:
  Rewrote the warning message using an assert with AssertionLevel.warning as this is the proper way to write warnings in Modelica.
• August 5, 2014, by Michael Wetter:
  Corrected error in documentation of computation of k.
• May 29, 2014, by Michael Wetter:
  Removed undesirable annotation Evaluate=true.
• October 8, 2013, by Michael Wetter:
  Removed parameter show_V_flow.
• December 14, 2012 by Michael Wetter:
  Renamed protected parameters for consistency with the naming conventions.
• January 16, 2012 by Michael Wetter:
  To simplify object inheritance tree, revised base classes AixLib.Fluid.BaseClasses.PartialResistance, AixLib.Fluid.Actuators.BaseClasses.PartialTwoWayValve, AixLib.Fluid.Actuators.BaseClasses.PartialDamperExponential, AixLib.Fluid.Actuators.BaseClasses.PartialActuator and model AixLib.Fluid.FixedResistances.PressureDrop.
• May 30, 2008 by Michael Wetter:
  Added parameters use_dh and deltaM for easier parameterization.
• July 20, 2007 by Michael Wetter:
  First implementation.