Predictor-corrector algorithm for solving quasi-separated-flow and transient distributed-parameter model for heat exchangers

Abstract

The successive sub〈stitution (SS) method is a suitable approach to solving the transient distributed-parameter model for heat exchangers. However, this method must be enhanced because its convergence heavily depends on the iterative initial pressure. When the iterative initial pressure is improperly assigned, the calculated flow rates become negative values, causing the state parameters to exhibit negative values as well. Therefore, a predictor-corrector algorithm (PCA) is proposed to improve the convergence of the SS method. A predictor is developed to determine an appropriate iterative initial pressure. Total fluid mass is adopted as the convergence criterion of pressure iteration instead of outlet flow rate as is done in the SS method. Convergence analysis and case study of the PCA and SS method are conducted, which show that the PCA has better convergence than the SS method under the same working conditions.

Keywords

algorithm / convergence / heat exchanger / modeling / transient

References

[1] Wedekind G L, Stoecker W F. Transient response of the mixture-vapor transition point in horizontal evaporating flow, ASHRAE Transactions, 1966, 72(II): IV.2.1–IV.2.15

[2] Chi J, Didion D. A simulation model of the transient performance of a heat pump, International Journal of Refrigeration, 1982, 5(3): 176–184

[3] Fu L, Ding G L, Zhang C L. Dynamic simulation of air-to-water dual-mode heat pump with screw compressor. Applied Thermal Engineering, 2003, 23(13): 1629–1645

[4] Pettit N B O L, Willatzen M, Plong-Sørensen L. A general dynamic simulation model for evaporators and condensers in refrigeration part II: simulation and control of an evaporator. International Journal of Refrigeration, 1998, 21(5): 404–414

[5] Zhang W J, Zhang C L. A generalized moving-boundary model for transient simulation of dry-expansion evaporators under larger disturbances. International Journal of Refrigeration, 2006, 29(7): 1119–1127

[6] Nyers J, Stoyan G. A dynamic model adequate for controlling the evaporator of a heat pump. International Journal of Refrigeration, 1994, 17(2): 101–108

[7] Jia X, Tso C P, Chia P K, Jolly P. A distributed model for prediction of the transient response of an evaporator. International Journal of Refrigeration, 1995, 18(5): 336–342

[8] Aprea C, Renno C. An air cooled tune-fin evaporator model for an expansion valve control law. Mathematical and Computer Modeling, 1999, 30(7–8): 135–146

[9] Wang C C. A numerical method for thermally non-equilibrium condensing flow in a double-pipe condenser. Applied Thermal Engineering, 1997, 17(7): 647–660

[10] Wang H, Touber S. Distributed and non-steady-state modeling of an air cooler. International Journal of Refrigeration, 1991, 14(2): 98–111

[11] Jia X, Tso C P, Jolly P, Wong Y W. Distributed steady and dynamic modeling of dry-expansion evaporators. International Journal of Refrigeration, 1999, 22(2): 126–136

[12] Tso C P, Cheng Y C, Lai A C K. Dynamic behavior of a direct expansion evaporator under frosting condition Part I. Distributed model. International Journal of Refrigeration, 2006, 29(4): 611–623

[13] Koury R N N, Machado L, Ismail K A R. Numerical simulation of a variable speed refrigeration system. International Journal of Refrigeration, 2001, 24(2): 192–200

[14] Mithraratne P, Wijeysundera N E, Bong T Y. Dynamic simulation of a thermostatically controlled counter-flow evaporator. International Journal of Refrigeration, 2000, 23(3): 174–189

[15] Mithraratne P, Wijeysundera N E. An experimental and numerical study of the dynamic behavior of a counter-flow evaporator. International Journal of Refrigeration, 2001, 24(6): 554–565

[16] Jiang H B, Radermacher R. A distributed model of a space heat pump under transient conditions. International Journal of Energy Research, 2003, 27(2): 145–160

[17] Rice C K. The effect of void fraction correlation and heat flux assumption on refrigerant charge inventory predictors. ASHRAE Transactions, 1987, 93(part 1): 341–367

[18] Ding G L. Recent developments in simulation techniques for vapour-compression refrigeration systems. International Journal of Refrigeration, 2007, 30(7): 1119–1133

[19] Ding G L. Dynamic simulation and optimization of small refrigeration equipments. Dissertation for the Doctoral Degree. Shanghai: Shanghai Jiao Tong University, 1993, 45–67

[20] Gungor K E, Winterton, R H S. A general correlation for flow boiling in tubes and annuli. International Journal of Heat Mass Transfer, 1986, 29(3): 351–358

[21] Ding G L, Wu Z G, Liu J, Inagaki T, Wang K J, Fukaya M. An implicit curve-fitting method for fast calculation of thermal properties of pure and mixed refrigerants. International Journal of Refrigeration, 2005, 28(6): 921–932

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg