一种考虑瞬态效应的散热结构导热路径设计的拓扑优化模型

实际工程中,热载荷多数具有短时和周期性特点,瞬态效应显著。目前的散热结构导热路径设计多基于稳态热传导模型,未考虑瞬态效应。本文提出了一种以区域温度控制函数作为设计目标的瞬态热传导问题的拓扑优化模型,能够实现在整个时间历程上特定区域内最高温度最小。使用伴随变量法,推导了目标函数关于设计变量的敏度计算格式。算例表明,基于本文优化模型获得的散热路径设计与基于稳态热传导模型的结果有明显差别,具有更优的散热性能。因此,时变热荷载下的散热结构构型设计需要考虑瞬态响应的影响。

A topology optimization model for conducting paths design of cooling structures considering transient effect

In practical engineering applications,thermal loads often last for a short time,or appear in a cyclical manner.In these cases,significant transient effects usually occur.However,current conducting paths designs for cooling structures are mostly based on steady-state heat conduction topology optimization method,which does not take into consideration the transient effect.In this paper,a transient heat conduction topology optimization model was proposed,in which the regional temperature control function was taken as the objective function,and the maximum temperature of a specific area through a time duration was minimized.The sensitivities of the objective function with respect to selected design variables are derived based on the adjoint variable method.Numerical examples show that the designs obtained based on the proposed model are significantly superior to those obtained by the steady heat conduction based model with enhanced thermal dissipation,thus proving that it is necessary to include the transient effect in designing the conducting paths.