In the design of flow geometries consisting of channels such as high-temperature gas heat exchangers, a great number of design parameters can be chosen, why solving the turbulent Reynolds Averaged Navier-Stokes (RANS) equations by CFD coupled with other physics can become computational demanding. Therefore, we here propose a method for a significant reduction of computational resources and consequent high speed. This is done by using the less computational demanding Darcy’s Law (DL) to approximate the laminar and turbulent flows in channels with circular and arbitrary cross-sections. To obtain the right velocity profile, an artificial permeability variation across the cross-section of the channel is determined. This is obtained based on the analogy of the DL and Darcy–Weisbach equation (DW). Results demonstrate that the DL approximations predict velocities and pressures distributions from the laminar and turbulent flows in the channels with circular and arbitrary cross-sections very well. At the same time, the models with DL approximations reduce the runtime up to ~40 times as compared to RANS, and improve the stability and convergence of the model. Lastly, a cross-flow heat exchanger is studied as an application of the DL approximations.

在由通道（例如高温气体热交换器）组成的流动几何结构的设计中，可以选择大量的设计参数，为什么通过CFD与其他物理方法结合来​​求解湍流的雷诺平均Navier-Stokes（RANS）方程成为计算问题苛刻。因此，我们在这里提出一种用于显着减少计算资源并进而提高速度的方法。这是通过使用较少计算要求的达西定律（DL）来近似估算圆形和任意横截面通道中的层流和湍流。为了获得正确的速度分布，确定通道横截面的人为渗透率变化。这是根据DL和Darcy-Weisbach方程（DW）的类比得出的。结果表明，DL近似可以很好地预测圆形和任意横截面通道中层流和湍流的速度和压力分布。同时，与RANS相比，具有DL逼近的模型将运行时间减少了约40倍，并提高了模型的稳定性和收敛性。最后，研究了横流式换热器作为DL近似的应用。