OVERVIEW ON MODELING OF THERMO-FLUID SYSTEMS
41 process known as model deduction. Most techniques, however, begin with excessively complex models and then reduce them until they become proper.
Usually the approach that should be followed in the application of proper modelling techniques to energy systems simplify a given model by eliminating less energetic components, while trying to minimize the effect of the elimination on the overall energy flow according to a reduction procedure. In many circumstances, it may also be possible to simplify a given model and thus make it proper not only by reducing or eliminating its various submodels but also by simplifying the interconnections between these submodels. Such model structure simplification includes simplifying a model by lumping its coupled inertias, partitioning its weakly coupled subsystems, or simplifying its mathematical representation without loss of accuracy.
It can eventually be noted that the dynamic models proposed and described within this Thesis, if intended for system design, might be used also for long term simulation of the designed system.
While the dynamic models realized are specifically developed to assess new arrangements within complex energy systems in order to have a tool that help predicting the transient behaviour in off design operating conditions and for control design, it is quite common that these systems in real world will be operated very often under steady state conditions or with high time constant transients.
To this extent a detailed dynamical model might be too accurate for the scope, the computation might be too demanding and the modelling approach would thus result improper.
In this sense the dynamic model of the newly designed system setup can also be used to derive characteristic maps that define the different and possible steady state operating conditions and these maps can be eventually introduced within a code where the main energy fluxes of the system may be evaluated, for example on hourly bases, hence recurring to a queasy steady simulation.
CHAPTER TWO
42
Refernces
1 Curlett P., Felder J.L., Object-Oriented Approach for Gas Turbine Engine Simulation, NASA-TM-106970. Lewis Research Center, National Aeronautics and Space Administration, Cleveland, OH, 1995.
2 Doebelin E.O., System Dynamics – Modeling, Analysis, Simulation, Design, Marcel Dekker Inc., 1998.
3 Karnopp D.C., Margolis D.L., Rosenberg R.C., System Dynamics: modeling and simulation of Mechatronic Systems. New York: John Wiley & Sons Inc., 2000.
4 Guzzella L., Onder C.H., Introduction to Modelling and Control of Internal Combustion Engine Systems, Springer, 2004.
5 Moskwa J.J., Munns S.A., Rubin Z. J., The Development of Vehicular Powertrain System Modeling Methodologies: Philosophy and Implementation. SAE Technical Paper 971089.
6 Ali M., Moskwa J.J., Developing a Generalized Modular Structure for Dynamic Engine Simulation. SAE Technical Paper 2002-01-0202.
7 Canova M., Fluid Systems Dynamics Modeling for Control: Internal Combustion Engines Case Studies, Ph. D Thesis, Industrial Engineering Department, University of Parma, Italy 2006.
8 Shapiro A.H., The dynamics and thermodynamics of compressible fluid flow, Vol I., The Ronald Press Company, New York, 1953.
9 Vaja I., Modellazione e simulazione finalizzate al controllo di una centrale solare termoelettrica a collettori parabolici lineari: il progetto “Archimede”. Master Thesis, Industrial Engineering Department, University of Parma, 2007 (in Italin), sponsored by ENEA.
10 Menta B., Studio tecnico-economico e simulazione di un impianto cogenerativo applicato ad un complesso scolastico. Master Thesis, Industrial Engineering Department, University of Parma, Italy, 2006 (in Italian).
11 Salati L., Studio di fattibilità e valutazione tecnico-economica di un impianto cogenerativo a biomassa applicato ad un complesso agrituristico. Master Thesis, Industrial Engineering Department, University of Parma, Italy, 2006 (in Italian).
12 Favaro V., Simulazione del comportamento di un edificio a basso consumo di energia:
confronto tra diverse soluzioni impiantistiche. Master Thesis, Industrial Engineering Department, University of Parma, Italy, 2007 (in Italian).
13 Augenti C., Gambarotta A., Pagliarini G., Rainieri S., Vaja I., Economic feasability analysis of a CCHP system in a tertiary sector application. ASME-ATI Conference, Milano 2006.
14 Vaja I., Augenti C., Gambarotta A., Pagliarini G., Rainieri S., Aspetti economici di un impianto trigenerativo applicato al settore terziario. 61° Congresso Nazionale ATI, Perugia – Italia 12-15 settembre 2006. (in Italian).
OVERVIEW ON MODELING OF THERMO-FLUID SYSTEMS
43 15 Elmqvist H., Mattsson S.E., An introduction to the physical modeling language Modelica,
Proceedings of the 9th European Simulation Symposium, ESS'97, Oct 19-23, Passau, Germany, 1997
16 Pfafferott T., Schmitz G., Modelling and transient simulation of CO2-refrigeration systems with Modelica, International Journal of Refrigeration 27 pp.42–52, 2004.
17 Miche M., Lafossas F.A., Guillemin J., Enhanced Phenomenological Modelling of Conventional and HCCI Diesel Combustion using Algorithms for Automatic Calibration.
SAE Paper 2007-24-0036, ICE 2007, Capri, Naples, Sept. 16-20, 2007.
18 Izenbrandt J., Goudappel E., Simulation of the AVV 1 cycle with GateCycle, ECOS 2003 conference, Copenhagen Denmark, Jun.30-Jul.2, 2003.
19 Falcone C., Utilizzo delle biomasse per la produzione di energia elettrica: studio di fattibilità di un impianto per la combustione di pollina, Master Thesis, Industrial Engineering Department, University of Parma, Italy, 2007 (in Italian).
20 Moita R. D., Matos H. A., Fernandes C., Nunes C. P., Prior J. M., Dynamic modelling and simulation of a cogeneration system integrated with a salt recrystallization process, , Computers and Chemical Engineering 29 (2005) 1491–1505.
21 Cennerilli S., Sciubba E., Application of the CAMEL process simulator to the dynamic simulation of gas turbines, Energy Conversion and Management 48 (2007) 2792–2801.
22 Cennerilli S., Fiorini P., Sciubba E., Application of the Camel process simulator to the dynamic simulation of gas turbines, ECOS 2006 Proceedings, Vol. 1, pp. 355-363.
23 Traverso A., TRANSEO: A New Simulation Tool for Transient Analysis of Innovative Energy Systems, Ph.D. Thesis, TPG-DiMSET, University of Genova, Italy, 2004.
24 Ersal T., Faty H.K., Rideout D.G., Louca L.S., Stein J.L., A review of proper modelling techniques, Journal of Dynamic Systems, Measurement, and Control, vol. 130, Nov. 2008.
25 Gonzalez-Bustamante J.A., Sala J.M., Lopez-Gonzalez L.M., Mıguez J.L., Flores I., Modelling and dynamic simulation of processes with ‘MATLAB’. An application of a natural gas installation in a power plant, Energy 32 (2007) 1271–1282.
26 Curlett P., Felder J.L., Object-Oriented Approach for Gas Turbine Engine Simulation, NASA-TM-106970, Lewis Research Center, National Aeronautics and Space Administration, Cleveland, OH, 1995.
27 Falchetta M., Gambarotta A., Vaja I., Cucumo M., Manfredi C., Modeling and simulation of the thermo and fluid dynamics of the “Archimede Project” solar power station, ECOS 2006 Int. Conference, Creta – Greece 12-14 Lug. 2006.
28 Karcanias, Modeling and simulation in technological and emerging fields: emerging challenges, Sim-Serv Conference, Modeling and Simulations: Challenges, Oct. 2004 29 Ersal T., Faty H.K., Rideout D.G., Louca L.S., Stein J.L., A review of proper modelling
techniques, Journal of Dynamic Systems, Measurement, and Control, Nov. 2008, vol. 130.
CHAPTER TWO
44
3
A L IBRARY OF M ODELS FOR THE D YNAMIC S IMULATION OF E NERGY S YSTEMS
The present Chapter reports a collection of components that have been realized during this Ph.D work at the Industrial Engineering Department of the University of Parma.
All the proposed models have been developed with the common characteristic of being flexible, fast scalable and suitable to be used to build up full dynamic models of complex and advanced energy conversion systems, some example of which will be presented in the next Chapters.
Not for all the components, however, the dynamic behaviour has been considered: for some energy systems elements, classified as ‘not state determined’, dynamic phenomena have been neglected leading to the realization of quasi-steady components. The dynamics of the whole plants will be simulated by the
‘state determined’ components, intended as those elements where some sort of storage is possible (of energy, mass, momentum etc.). The cause-effect approach used to create the complete model will lead to alternating the ‘not state determined’ elements with ‘state determined’ elements, favouring the numerical stability of the complete mathematical models since algebraic loops are in most of the cases avoided.
The scalability and flexibility of the component models are considered as fundamental requirements in the modelling activity, since it is author’s belief that each model should be promptly and easily used in a wide range of situations with different design (i.e. size) and considering different working fluids. An analysis of the dialog windows created for each component and reported in the following Paragraphs reveals in fact that many parameters are required to configure precisely the component according to the application.
To be noted that the modeling approaches here applied to the different components of interest are not unique and that many other techniques may be followed but the one proposed here are those that have been believed to be the most appropriate case to case.
To be noted that the modeling approaches applied in the work are not the only possible, since other techniques may be used: the solutions proposed here are those that are thought to be the most appropriate for the scope.
C HAPTER
T HREE
CHAPTER THREE
46
Nomenclature
cp Specific heat at constant pressure [J/kg K]
cv Specific heat at constant volume [J/kg K]
d Diameter [m]
f Friction factor [-]
0
g f Free Gibbs energy molar at standard conditions [kJ/kmol]
h Specific enthalpy [kJ/kg]
h Molar enthalpy [kJ/kmol]
k Thermal conductivity [W/mK]
m Mass [kg] – Polytrophic exponent [-]
m Mass flow rate [kg/s]
q Heat transfer rate [W]
q’ Heat transfer rate per unit length [W/m]
q’’ Heat Flux [W/m2] s Specific Entropy [kJ/kg K]
t Time [s] - Thickness [m]
u Speed [m/s] –Specific internal energy [J/kg]
u Molar internal energy [kJ/kmol]
x Vapour mass fraction [-]
A Area [m2] Bi Biot number [-]
Dh Hydraulic diameter [m]
J Inertia [kg m2] Ja Jacob number [-]
L Length [m]
Nu Nusselt number [-]
P Power [kW]
Pr Prandtl number [-]
Re Reynolds number [-]
S Surface area [m2] T Temperature [K]
U Heat exchange coefficient [W/m2K]
X Molar fraction Xtt Martinell Factor [-]
Greek symbols
α Convection heat transfer coefficient [W/m2K] – Air fuel mass ratio [-]
ε Emissivity[-], Relative error [-], Turbine pressure ratio [-]
σ Stefan-Boltzmann constant [-]
η Efficiency [-]
θ Crank angle µ Viscosity [kg/s m]
τ Torque [Nm]
φ Air fuel equivalence ratio [-]
ω Angular speed [rad/s]
φ
Abbreviations and subscripts
a Air
abs Absolute avg Average b Burning cond Conduction conv Convection
cr Critical df Dumping factor exp Experimental
f Fluid, Fin, Fuel h Hydraulic i Insulation irr Irradiation in Inlet m Mechanical
bmip Brake mean indicated pressure mod Model
n Nominal l Liquid out Outlet p Pipe prod Products
rad Radiative react Reactants t Thermal tf Transfer fluid v Vapour x Axial abscissa y Longitudinal abscissa w Wind, Wall, Water C Compressor CC Combustion Chamber
F Fuel
HTF Heat transfer fluid ICE Internal Combustion Engine MGT Micro Gas Turbine
N Negative
ORC Organic Rankine Cycle P Positive, Pump R Reduced
S Sun
T Turbine