CompressorGas L1 affinity
Created Thursday 20 March 2014
An analytic model for a gas compressor featuring static conservation of mass, energy and momentum with an isentropic correlation and an implemented affinity law to regard part load behaviour as correlation between volume flow,pressure ratio and shaft speed.
1. Purpose of Model
The model is used to simulate a simple compressor with constant isentropic efficiency but part load behaviour of the volume flow rate depending on the pressure ratio and shaft speed. Furthermore, the model should be used if the behaviour of the attached mechanical and electrical equipment is of interest.
2. Level of Detail, Physical Effects Considered and Physical Insight
2.1 Level of Detail
Referring to Brunnemann et al. [1], this model refers to the level of detail L1 because the system is modelled in an phenomenological manner, without calculating state equations. The model is of the flow model type. However, conservation of mass and energy is granted.
2.2 Physical Effects Considered
- Conservation of Mass (in steady state)
- Conservation of Momentum (in steady state)
- Conservation of Energy (in steady state)
- Hydraulic Efficiency
2.3 Level of Insight
- all balance equations are considered in a steady-state manner
- all efficiencies are considered constant
3. Limits of Validity
- Backflow and zero mass flow is not supported.
- Flow velocity differences small.
- Difference between the heights of the ports small.
4. Interfaces
4.1 Physical Connectors
Basics:Interfaces:GasPortIn inlet
Basics:Interfaces:GasPortOut outlet
- Mechanical port for:
- Torque [Nm]
- Absolute rotation angle [rad]
4.2 Medium Models
- Medium models of the gas mixture type are supported.
5. Nomenclature
6. Governing Equations
In general the derived dynamical equations for the model consider the balance of certain properties like: mass, energy and momentum. For the model, mechanical and hydraulic efficiency of the compressor are used.
6.1 System Description and General model approach
The derived dynamical equations for the model are balances of mass, energy and momentum considering the isentropic efficiencies. There are no transient state variables defined, i.e. the model equations are purely algebraic.
6.2 Governing Model Equations
Energy Conservation
The difference in the specific enthalpy between in- and outlet is:
And the energy balance of the fluid is calculated as follows:
The shaft power regarding mechanical losses is calculated as:
The difference in the specific enthalpy along the compressor is calculated with the following isentropic expression:
by the use of the isentropic exponent 
which is used as mean value between in and outlet. The model here uses pseudostates of the isentropic exponent at in an outlet to reduce the equation system.
The maximum values for the volume flow rate and the pressure ratio are defined by the following equations depending on the shaft speed:
And 
is calculated accordingly:
Note that user shall use in order to capture property chanage at the inlet which modifies the hydraulic characteristic according to affinity law.
The correlation between actual volume flow rate and pressure ratio is given by the following equation:
Please note that the backflow definition of the stream variable T_in is a dummy value since backflow is not supported.
Mass Conservation
A constant fluid mass flow is assumed:
Momentum Conservation
Balance of stationary momentum is used to model the pressure changes at the outlet port of the compressor
Mechanics
The mechanical connector (shaft) can be dedicated whether to be used or not via the parameter useMechanicalPort.
a) mechanical port is used
If the shaft is activated then a dynamic torque balance is evaluated:
where the shafts acceleration may be zero (useSteadyTorque = true) or defined as follows:
b) mechanical port is NOT used
If the mechanical port is deactivated the parameter rpm_fixed is used to define the rotational speed and the shaft angle is set to zero.
Hydraulics
The volume flow rate trough the system is calculated with the inlet density
Chemistry
No chemical reaction is considered.
Summary
A summary is available including the following:
- an outline record:
- and two records of type FlangeGas named inlet and outlet
7. Remarks for Usage
- Stationary flow.
- Compressible flow.
- No backflow, no zero flow
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
Date - Version - Description of changes - author/revisor
25.06.2014 - v0.1 - initial implementation of the model - Lasse Nielsen, TLK-Thermo GmbH
Backlinks: ClaRa:A User Guide:Revisions:v1.4.1