Abstract An increasing number of technologies require prediction of unsteady forced convection in porous media when the inlet flow is unsteady. To gain further insight into this problem, the unsteady equations of continuity, Navier Stokes and energy are solved within the pores formed by several cylindrical flow obstacles. The system is modulated by sine waves superimposed on the inlet flow velocity, and the spatio-temporal responses of the flow and temperature fields are calculated. The results are then utilised to assess the linearity of the thermal response represented by the Nusselt number on the obstacles. It is shown that for linear cases, a transfer function can be devised for predicting the dynamic response of the Nusselt number. It is further argued that such a transfer function can be approximated by a classic low-pass filter which resembles the average response of the individual obstacles. This indicates that there exists a frequency threshold above which the thermal system is essentially insensitive to flow modulations. The results also show that changes in Reynolds number and porosity of the medium can push the dynamic response of the system towards non-linearity. Yet, there appears to be no monotonic change in the linearity of the response with respect to the Reynolds number and porosity. In general, it is found that for low Reynolds numbers, the dynamics of heat convection can be predicted decently by taking a transfer function approach. The findings of this study can enable further understanding of unsteady forced convection in porous media subject to time-varying inlet flows.

中文翻译：

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多孔介质中强制对流对入口流量调制的动态响应的孔隙尺度评估

摘要 越来越多的技术需要在入口流动不稳定时预测多孔介质中的非定常强制对流。为了进一步了解这个问题，在由几个圆柱形流动障碍物形成的孔隙内求解了连续性、纳维斯托克斯和能量的非定常方程。该系统由叠加在入口流速上的正弦波调制，并计算流场和温度场的时空响应。然后利用结果来评估由障碍物上的努塞尔数表示的热响应的线性度。结果表明，对于线性情况，可以设计一个传递函数来预测 Nusselt 数的动态响应。还有人认为，这样的传递函数可以通过经典的低通滤波器来近似，该滤波器类似于单个障碍物的平均响应。这表明存在一个频率阈值，高于该阈值热系统基本上对流量调制不敏感。结果还表明，雷诺数和介质孔隙率的变化可以将系统的动态响应推向非线性。然而，相对于雷诺数和孔隙率的响应线性似乎没有单调变化。通常，发现对于低雷诺数，可以通过采用传递函数方法来适当地预测热对流的动力学。