Consistent initialization of system of differential-algebraic equations for dynamic simulation of centrifugal chillers

For simulation of centrifugal chiller system with differential algebraic equations, consistent initial conditions are difficult to obtain due to the two-phase refrigerant cycle and the connections between several components. Existing rigorous initialization methods are not suitable for the particular problems in centrifugal chiller simulation, such as the surge instability. In this paper, the dynamic model of a water-cooled centrifugal chiller is developed in Modelica with Dymola and the TLK/IfT Library (TIL). A preprocessing scheme and a direct initialization method are proposed for the consistent initialization of chiller DAE system. Simulation results have shown the effectiveness of the proposed modelling framework and the initialization method.

[1]  Derk J. Swider,et al.  A comparison of empirically based steady-state models for vapor-compression liquid chillers , 2003 .

[2]  P. Bansal,et al.  Steady-state model of centrifugal liquid chillers , 1998 .

[3]  N. Watson,et al.  Turbocharging the internal combustion engine , 1982 .

[4]  T. Kármán,et al.  Turbulence and Skin Friction , 1934 .

[5]  V. K. Dhir,et al.  Laminar Film Condensation on Plane and Axisymmetric Bodies in Nonuniform Gravity , 1971 .

[6]  Wilhelm Tegethoff,et al.  Modelling of heat pumps with an object-oriented model library for thermodynamic systems , 2010 .

[7]  E. A. Parr Industrial control handbook , 1986 .

[8]  André Bontemps,et al.  Experimental study and modelling of heat transfer during condensation of pure fluid and binary mixture on a bundle of horizontal finned tubes , 2003 .

[9]  Gintaras V. Reklaitis,et al.  Dynamic simulation of multicomponent batch rectification with chemical reactions , 1986 .

[10]  Asfaw Beyene,et al.  Conventional chiller performances simulation and field data , 1994 .

[11]  M. A. Akanbi,et al.  Numerical solution of initial value problems in differential - algebraic equations , 2005 .

[12]  C. W. Gear,et al.  Approximation methods for the consistent initialization of differential-algebraic equations , 1988 .

[13]  M. Gerdts Direct Shooting Method for the Numerical Solution of Higher-Index DAE Optimal Control Problems , 2003 .

[14]  Karl Johan Åström,et al.  Evolution of Continuous-Time Modeling and Simulation , 1998, ESM.

[15]  Donald Q. Kern,et al.  Mathematical development of tube loading in horizontal condensers , 1958 .

[16]  Barbara Pfeffer,et al.  Refrigeration and Air Conditioning , 1982 .

[17]  採編典藏組 Society for Industrial and Applied Mathematics(SIAM) , 2008 .

[18]  Ron Sacks-Davis,et al.  An Alternative Implementation of Variable Step-Size Multistep Formulas for Stiff ODEs , 1980, TOMS.

[19]  Lorenz T. Biegler,et al.  A Successive Linear Programming Approach for Initialization and Reinitialization after Discontinuities of Differential-Algebraic Equations , 1998, SIAM J. Sci. Comput..

[20]  Wolfgang Marquardt,et al.  Getting around consistent initialization of DAE systems , 1997 .

[21]  Shan K. Wang,et al.  Handbook of Air Conditioning and Refrigeration , 1993 .

[22]  Jan Tommy Gravdahl,et al.  Modelling and Control of Surge for a Centrifugal Compressor with Non-Constant Speed , 1999 .

[23]  Jan Tommy Gravdahl,et al.  Modeling and Control of Surge and Rotating Stall in Compressors , 1998 .

[24]  Edward M. Greitzer,et al.  Surge and Rotating Stall in Axial Flow Compressors—Part I: Theoretical Compression System Model , 1976 .

[25]  Linda R. Petzold,et al.  Numerical solution of initial-value problems in differential-algebraic equations , 1996, Classics in applied mathematics.

[26]  Kim Choon Ng,et al.  Predictive and diagnostic methods for centrifugal chillers , 2008 .

[27]  Jonas Eborn,et al.  Chemical Reaction Modeling with ThermoFluid/MF and MultiFlash , 2002 .

[28]  Evaristo C. Biscaia,et al.  Direct methods for consistent initialization of DAE systems , 2001 .

[29]  Satyam Bendapudi,et al.  Development and evaluation of modeling approaches for transients in centrifugal chillers , 2004 .

[30]  Evaristo C. Biscaia,et al.  Heuristic optimization for consistent initialization of DAEs , 2000 .

[31]  Wolfgang Marquardt,et al.  Computing consistent initial conditions for differential-algebraic equations , 1992 .

[32]  James E. Braun,et al.  A comparison of moving-boundary and finite-volume formulations for transients in centrifugal chillers , 2008 .

[33]  Perry Y. Li,et al.  A new explicit equation for accurate friction factor calculation of smooth pipes , 2011 .

[34]  T. B. Ferguson The centrifugal compressor stage , 1963 .

[35]  R. C. Pampreen Small Turbomachinery Compressor and Fan Aerodynamics , 1973 .

[36]  Uri M. Ascher,et al.  Computer methods for ordinary differential equations and differential-algebraic equations , 1998 .

[37]  William A. Beckman,et al.  Models for variable-speed centrifugal chillers , 1987 .

[38]  R. Shah,et al.  Handbook of single-phase convective heat transfer , 1987 .

[39]  K. Hansen,et al.  Experimental and Theoretical Study of Surge in a Small Centrifugal Compressor , 1981 .

[40]  A. Weise Dr. Ludwig Prandtl (Prof. a. d. Univ. Göttingen), Führer durch die Strömungslehre. 3. Aufl., 407 S. Braunschweig 1949. Fr. Vieweg u. Sohn. Preis geb. 16, ‐DM , 1950 .

[41]  Peter Fritzson,et al.  Principles of Object-Oriented Modeling and Simulation with Modelica 3.3: A Cyber-Physical Approach , 2014 .

[42]  M. M. Chen,et al.  An Analytical Study of Laminar Film Condensation: Part 2—Single and Multiple Horizontal Tubes , 1961 .

[43]  Jan Tommy Gravdahl,et al.  Drive torque actuation in active surge control of centrifugal compressors , 2002, Autom..

[44]  Christof Büskens,et al.  Consistent Initialization of Sensitivity Matrices for a Class of Parametric DAE Systems , 2002 .

[45]  R. F. Sincovec,et al.  Analysis of descriptor systems using numerical algorithms , 1981 .

[46]  Jan Tommy Gravdahl,et al.  Compressor Surge and Rotating Stall: Modeling and Control , 1998 .

[47]  Edward M. Greitzer,et al.  Surge Dynamics in a Free-Spool Centrifugal Compressor System , 1991 .

[48]  Michael Wetter Modelica-based Modeling and Simulation to Support Research and Development in Building Energy and Control Systems , 2010 .

[49]  L. Petzold Differential/Algebraic Equations are not ODE's , 1982 .

[50]  André Bontemps,et al.  Condensation heat transfer of a pure fluid and binary mixture outside a bundle of smooth horizontal tubes. Comparison of experimental results and a classical model , 2001 .

[51]  V. Gnielinski New equations for heat and mass transfer in turbulent pipe and channel flow , 1976 .

[52]  Jeffrey M. Gordon,et al.  Centrifugal chillers: Thermodynamic modelling and a diagnostic case study , 1995 .

[53]  Hilding Elmqvist,et al.  Physical system modeling with Modelica , 1998 .

[54]  Wilhelm Tegethoff,et al.  Effects of Tool Coupling on Transient Simulation of a Mobile Air-Conditioning Cycle , 2009 .

[55]  C. Pantelides The consistent intialization of differential-algebraic systems , 1988 .

[56]  Itaru Michiyoshi,et al.  Heat Transfer in Condensation , 1962 .