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QuadraticNominalPoint L4

Created Monday 05 October 2015

A quadratic pressure drop model - depending of nominal values of pressure difference and mass flow rate and the square root of the actual pressure difference

1. Purpose of Model

This model is appropriate if a pressure drop due to friction, depending on the load is needed (either due to numerical or technical reasons). The model is parametrized by choosing a nominal load point and the corresponding pressure loss. The quadratic correlation is valid for turbulent flow in rough conduits. Thus, huge changes from nominal point can be calculated properly (as long as no change in flow regime occurs).

2. Physical Insight

This replaceable model is compatible to models of level of detail L4 according to Brunnemann et al. [1] since the friction losses are lumped over the component. The model is regularised around zero, to avoid numerical instability in that point.

3. Limits of Validity

• no supercritical flow conditions are supported
• no significant changes of inlet density over time
• no changes in flow regime (to laminar or transitional flow regime)

4. Interfaces

The model communicates via outer models and records. Thus, it expects to have:

• an outer record named iCom as defined in Basics:Records:IComBase L3
• an outer model named geo as defined Fundamentals:Geometry:GenericGeometry

5. Nomenclature

6. Governing Equations

This pressure loss model bases on the QuadraticPressureLoss_L2 model.


* is regularised for values below via Basics:Functions:ThermoRoot function. The pressure coefficient is the definite quantity for the pressure loss model. Therefore, it is distributed over the component according to the flow model discretization array . The user can choose between four different flow models for this pressure loss model. This results in four cases:
(1) no pressure loss at inlet, no pressure loss at outlet
(2) no pressure loss at inlet, pressure loss at outlet
(3) pressure loss at inlet, no pressure loss at outlet
(4) pressure loss at inlet, pressure loss at outlet
See Basic Concepts of Modelling:Pressure Loss L4 Volumes for a detailed description of the idea behind the different flow models.

7. Remarks for Usage

• The model should be used if huge changes in the load can be expected. The model bases on the quadratic correlation of mass flow rate to pressure loss. Thus, the accuracy in load points which differ significantly from the nominal point is better than in the LinearPressureLoss L4 model.
• If changes in the density are expected the density dependent pressure loss model VLE PL:QuadraticNominalPoint L4 should be used.

8. Validation

-

9. References

[1] Johannes Brunnemann and Friedrich Gottelt, Kai Wellner, Ala Renz, André Thüring, Volker Röder, Christoph Hasenbein, Christian Schulze, Gerhard Schmitz, Jörg Eiden: "Status of ClaRaCCS: Modelling and Simulation of Coal-Fired Power Plants with CO2 capture", 9th Modelica Conference, Munich, Germany, 2012

10. Authorship and Copyright Statement for original (initial) Contribution

Author:
DYNCAP/DYNSTART development team, Copyright 2011 - 2022.
Remarks:
This component was developed during DYNCAP/DYNSTART projects.
Acknowledgements:
ClaRa originated from the collaborative research projects DYNCAP and DYNSTART. Both research projects were supported by the German Federal Ministry for Economic Affairs and Energy (FKZ 03ET2009 and FKZ 03ET7060).
CLA:
The author(s) have agreed to ClaRa CLA, version 1.0. See https://claralib.com/pdf/CLA.pdf
By agreeing to ClaRa CLA, version 1.0 the author has granted the ClaRa development team a permanent right to use and modify his initial contribution as well as to publish it or its modified versions under the 3-clause BSD License.

11. Version History

• 2012 - v 0.1 - initial implementation - Friedrich Gottelt, XRG Simulation

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