PumpVLE L1 simple
Created Tuesday 11 December 2012
An analytic model for a pump featuring static conservation of mass, energy and momentum. Here the fluid is considered to be incompressible. Thus, the hydraulic characteristics of the pump are modelled taking a constant density into account. The effect of strongly reduced flow rates when steam is drawn into the inlet at constant rotational speed and pressure difference is caught qualitatively. The model is singular at zero mass flow rates.
1. Purpose of Model
The model is appropriate when the time behaviour of the flow rate and outlet states of a pump depending on drive power and pressure difference is required and if the behaviour of the attached mechanical and electrical equipment is not of interest. If unusual operation (including failure with backflow or zero flow) or the behaviour of attached equipment is of interest, use PumpVLE L1 affinity.
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 Linear Momentum (in steady state)
- Conservation of Energy (in steady state)
- Mechanical Efficiency
- 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.
- Incompressible Flow.
4. Interfaces
4.1 Physical Connectors
- Inlet and outlet connectors combined for:
- Mass flow rate in the connection ports [kg/s]
- Thermodynamic pressure in the connection ports [Pa]
- Specific thermodynamic enthalpy close to the connection ports [J/kg]
- Medium properties at the ports.
- Driving power of the pump's shaft. [W]
4.2 Medium Models
- Medium models of the Vapour-Liquid-Equilibrium (VLE) 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 pump 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 mechanic and hydraulic efficiencies. There are no transient state variables defined, i.e. the model equations are purely algebraic.
6.2 Governing Model Equations
Energy Conservation
The constant energy balance of the pump reads
where the hydraulic power of the shaft given by the (constant) hydraulic and mechanic efficiency and the given drive power:
and where 
is a numerical factor for computational stability.
Please note that the backflow definition of the stream variable 
is a dummy value since backflow is not supported.
Mass Conservation
A constant fluid mass is assumed, which yields
Momentum Conservation
Balance of stationary momentum is used to model the pressure changes at the outlet port of the pump,
Hydraulics
The volume flow rate trough the system is related to the inlet mass flow rate and inlet density.
Note that the combination of equation (3) and (5) imply constant density over the pump which may lead to errors of approx. 5 % for high pressure differences (and water as fluid).
Chemistry
No chemical reaction is considered.
Summary
A summary is available including the following:
- an outline record:
- and two records of type FlangeVLE named inlet and outlet
7. Remarks for Usage
- no backflow supported
- model is singular at Δp = 0 giving infinte volume 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
- 2011-Nov-02 - v0.0 - Initial implementation- F. Gottelt, XRG Simulation GmbH
- 2012-Apr.-17 - v0.1 - Avoid devision by zero Delta_p - F.Gottelt, XRG Simulation GmbH
- 2013-Mar-19 - v0.2 - introduced summary, revised nomenclature - F. Gottelt, XRG Simulation GmbH
- 2017-Dec-08 - v0.3 - minor changes to summary and nomencalture, implemented visualiser - F.Gottelt, XRG Simulation GmbH
Backlinks: ClaRa:A User Guide:Revisions:v1.0.1 ClaRa:Components:TurboMachines:Compressors:CompressorVLE L1 simple ClaRa:Components:TurboMachines:Pumps:PumpVLE L1 affinity