间冷式电冰箱箱体的Z传递函数模型(Ⅰ)——数学方法

Z-transfer Function Model for Cabinet of Indirect Cooling Household Refrigerator(Ⅰ)——Principle

为了在间冷式冰箱动态仿真中较快地计算箱内空气温度变化,提出基于Z传递函数计算箱内空气温度的方法。首先采用状态空间方程描述三种边界条件下的单个箱壁动态传热过程,并通过Leverrier-Faddeeva算法求得三种边界条件下单个箱壁的Z传递函数;其次,由单个箱壁的Z传递函数计算得到整个箱室的Z传递函数;最后利用整个箱室的Z传递函数,可求得每一时刻的箱内空气温度的代数关系式。提出的计算方法可避免每个时刻对于箱体传热动态方程的求解,节省仿真时间。

In order to simulate the air temperature variation inside an indirect cooling household refrigerator quickly,a Z-transfer function based model for the cabinet of indirect cooling household refrigerator was proposed.In application of the new model,firstly,state space equations for heat transfer through any cabinet wall under three kinds of boundary conditions were built up,and Leverrier-Faddeeva method was employed to calculate the Z-transfer function for each wall;secondly,the total Z-transfer function for a single compartment cabinet was obtained based on the Z-transfer functions of cabinet walls of the compartment;lastly,the equations used to calculate the air temperature inside the compartment based on the Z-transfer function for the single compartment cabinet were given.In simulating the air temperature inside the compartment with the new model,it is avoided to solve differential equations for dynamic heat transfer through cabinet walls at every moment,and so the computation time can be saved a lot.