QuadraticFlowFunction

Created Monday 08 July 2013
This model provides a nonlinear pressure drop model for compressible flows using a flow function derived from ideal gas approaches, Mass flow rate through the vessel depends on the opening, the inlet density and the pressure difference. The flow resistance is defined by a user given zeta value or the valve area and the outflow number. Please note, this model does not support two-phase flow.

1. Purpose of Model

The model can be used for introducing pressure loss effects (either due to physical or numerical motivation), when the inlet density of the vessel may vary considerably over time and choked flow may occur. Since the model neglects changes in kinetic energy it implies either small density changes or adapted flange geometry. It is possible to use the valve as a check valve, for example to avoid back flows. Since the model takes inlet density into account it is considered less robust than e.g. Components:VolumesValvesFittings:Valves:Fundamentals:LinearNominalPoint and Components:VolumesValvesFittings:Valves:Fundamentals:QuadraticKvs but shows a more realistic behaviour when it comes to density variations in the upstream components and choked flow conditions. This model will give smaller mass flow rates than Quadratic EN60534 compressible.

2. Level of Detail and Physical Effects Considered


2.1 Level of Detail

Referring to Brunnemann et al. [1], this model refers to the level of detail L1 because no spatially discretisation is featured

2.2 Physical Effects Considered

3. Limits of Validity


4. Interfaces

the calculated mass flow rate is accessed via
inlet.m_flow = pressureLoss.m_flow
in the superordinate valve model

5. Nomenclature


6. Governing Equations


The mass flow rate correlates with the pressure difference for valve definition by zeta-value as follows:

The mass flow rate correlates with the pressure difference for valve definition by cross sectional area and outflow number as follows:

The outflow function is calculated as follows:

7. Remarks for Usage


The outflow number gives a measure of the real behaviour of the valve compared to an ideal nozzle. It descibes the ratio of measured outflow to theoretical outlfow of an ideal nozzle, i.e. a value of 1 refers to an ideal nozzle. Usually its value is given by the manufacturer. So far only a fixed value can be given. However, it can depend on pressure ratio and valve opening. A typical value of a safety valve for vapour and gases is . Values for liquids for identical valves with the same opening are 35% lower [3].
For burst disks the following values hold according to [4]:
Borda type orifice (short tube is at upstream):
for gas and vapour
for liquids
Short tube (downstream) or sharp edged orifice:
for gas and vapour
for liquids
Short tube (downstream) with rounded edges or round edged orifice:
for gas, vapour and liquids

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
[2] Walter Wagner: "Regelarmaturen", ISBN 3-8023-15664-2, Vogel Buchverlag, Germany, 1996.

[3] Lutz Friedel: "Strömungstechnische Auslegung der Entlastungseinrichtung für druckführende Anlagenteile", 1998

[4] Schweizerischer Verein für technische Inspektionen: "Technische Regeln Armaturen und Ausrüstung Berstsicherungen", 2007

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


Backlinks: ClaRa:Components:VolumesValvesFittings:Fittings:SprayInjectorVLE L3 ClaRa:Components:VolumesValvesFittings:Fittings:SprayInjectorVLE L3 advanced ClaRa:Components:VolumesValvesFittings:Valves:GenericValveGas L1 ClaRa:Components:VolumesValvesFittings:Valves:GenericValveVLE L1 ClaRa:Components:VolumesValvesFittings:Valves:ValveFuelFlueGas L1