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首页> 外文期刊>Journal of Micromechanics and Microengineering >Numerical method for predicting three-dimensional steady compressible flow in long microchannels
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Numerical method for predicting three-dimensional steady compressible flow in long microchannels

机译：预测长微通道三维可压缩稳定流动的数值方法

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摘要

Numerical results available in the literature for microchannel flow are either for incompressible flow or for two-dimensional compressible flow. Three-dimensional simulations are limited to very short channels due to the long computational time and large memory required. This study develops an efficient three-dimensional numerical procedure to calculate steady compressible flow in long microchannels, which has not previously been reported in the literature. The proposed numerical procedure solves the reduced compressible Navier-Stokes equations, which do not model the entrance region accurately, but this region is small for the long microchannels studied in this paper. The major advantage of the present numerical procedure is its fast speed due to the parabolic character of the governing equations. An efficient space marching algorithm is adopted to solve the governing equations. It is at least two to three orders of magnitude faster than the full Navier-Stokes simulation. This is because the unsteady Navier-Stokes equations are a mixed set of hyperbolic-parabolic equations that are integrated in time until a steady state solution is reached. This procedure is inefficient because of its time marching procedure. The calculated mass flow rate and pressure distribution were compared with a known analytical solution for a two-dimensional microchannel flow and experimental data. The agreement was very good. The slip effect plays an important role in the friction characteristic of microchannel flows. This effect was investigated for three-dimensional microchannel flows. The effect of channel aspect ratio on the friction characteristic was also studied. The present numerical procedure is an efficient and accurate tool in studying steady compressible flow in long microchannels.
机译：文献中可用于微通道流动的数值结果是不可压缩的流动或二维可压缩的流动。由于需要较长的计算时间和所需的大量内存，因此三维仿真仅限于非常短的通道。这项研究开发了一种有效的三维数值程序来计算长微通道中的稳定可压缩流量，这在文献中以前没有报道过。所提出的数值程序解决了简化的可压缩Navier-Stokes方程，该方程不能精确地模拟入口区域，但是对于本文研究的长微通道来说，该区域很小。本数值程序的主要优点是其速度快，这归因于控制方程的抛物线特性。采用一种有效的空间行进算法求解控制方程。它比完整的Navier-Stokes仿真至少快两到三个数量级。这是因为非稳态Navier-Stokes方程是双曲线-抛物线方程的混合集合，它们在时间上一直积分到达到稳态解。该过程由于其时间行进过程而效率低下。将计算出的质量流量和压力分布与二维微通道流动和实验数据的已知分析解决方案进行比较。协议很好。滑移效应在微通道流的摩擦特性中起着重要作用。对于三维微通道流，研究了这种效果。还研究了通道长宽比对摩擦特性的影响。本数值程序是研究长微通道中稳定可压缩流动的有效且准确的工具。

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