摘要
The dynamic stability analysis of an irreversible refrigerator working at the minimum power input P for given cooling load R was investigated.An irreversible refrigerator model was established based on coupled differential equations.The global asymptotic stability characteristics were proved by constructing Lyapunov function based on Lyapunov stability theory and analyzed by sketching global phase portraits.The influence of parameters such as initial and operating parameters were studied for different values.It was found that an equilibrium point of nonlinear system was the global stability point,and the temperature of the working fluids converged to the stability value as time t approximated to positive infinite.Besides,numerical integrations were carried out to corroborate the global asymptotic stability properties of the system.Finally,the dynamic stability and the thermodynamic properties of the system were analyzed.It was found that the energetic characteristics and the dynamic stability properties were deteriorated as the dimensionless cooling load R~* and the thermal conductance ratio b increased.
The dynamic stability analysis of an irreversible refrigerator working at the minimum power input P for given cooling load R was investigated. An irreversible refrigerator model was established based on coupled differential equations. The global asymptotic stability characteristics were proved by constructing Lyapunov function based on Lyapunov stability theory and analyzed by sketching global phase portraits. The influence of parameters such as initial and operating parameters were studied for different values. It was found that an equilibrium point of nonlinear system was the global stability point, and the temperature of the working fluids converged to the stability value as time t approximated to positive infinite. Besides, numerical integrations were carried out to corroborate the global asymptotic stability properties of the system. Finally, the dynamic stability and the thermodynamic properties of the system were analyzed. It was found that the energetic characteristics and the dynamic stability properties were deteriorated as the dimensionless cooling load R ＊ and the thermal conductance ratio b increased.
基金
the Fundamental Research Fund for the Central Universities,China(No.2011011302)
National Natural Science Foundation of China(No.51078068)
