大吸附雷諾數下脹-縮壁面管道非穩態流動漸近求解

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Asymptotic solution for unsteady flow in expanding or contracting channels with large suction Reynolds

1. School of Applied Science, University of Science and Technology Beijing, Beijing 100083, China;
2. School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China;
3. Chemical Defense Institute of PLA, Beijing 102205, China

摘要: 研究了大吸附雷諾數下,可滲透、膨脹或收縮的半無限長管道中的層流流動.采用自相似理論,把描述該模型的Navier-Stokes方程轉化成一個四階的非線性微分方程.應用奇異攝動方法,對該方程進行漸近求解.分析了不同的膨脹系數、吸附雷諾數對管道流動的影響.壁面收縮時,邊界層變薄;壁面膨脹時,邊界層變厚;當膨脹率與雷諾數之比大于1時,管道流動出現回流.
- 非穩態流 /
- 管道流動 /
- 膨脹與收縮壁面 /
- 漸近解
Abstract: An incompressible laminar flow in a semi-infinite porous channel with expanding or contracting wails is considered. Following the self-similarity transformation, the Navier-Stokes equations are reduced to a fourth-order non-linear differential equation. The resulting equation is then solved asymptotically for large suction Reynolds number. The influences of expansion rate and Reynolds number on the fluid are obtained. When the wall contracts, the boundary layer becomes thinner; and when the wall expands, the boundary layer becomes thicker. It appears that flow reversal begins when the ratio of expansion rate to suction Reynolds number exceeds 1.
- unsteady flow /
- pipe flow /
- expanding or contracting wall /
- asymptotic solution