以有限體積法計算任意截面形狀流道內完全發展層流場

Computation of Fully Developed Laminar Flow in Ducts with Arbitrary Cross Section Shape Using a Finite Volume Method

傅煜平(Yu-Ping Fu)

指導教授 ： 趙修武

中原大學/工學院/機械工程研究所/碩士(2004年)

https://doi.org/10.6840/cycu200400690

摘要

本研究運用數值模擬方式來探討任意截面流道內完全發展層流場，同時比較數值模擬方法與理論計算結果之差異性。本研究透過水力直徑100 m不同幾何結構形狀流道探討流體壓降現象，並藉由理論與數值分析結果，以了解並探討其摩擦因子、平均流速與最大流速對形狀參數之間的關係。本研究以有限體積法為基礎，將計算空間以非結構性三角形網格離散，求解控制方程式。假設管內的層流場為穩態，為不可壓縮且忽略重力，分析牛頓流體與非牛頓流體，在不同截面形狀之管道的數值模擬，並探討其摩擦因子、平均流速與最大流速對幾何形狀參數之間的關係，本研究的數值結果與理論值比較，發現有良好的一致性。

關鍵字

有限體積法 ； 非結構性網格 ； 截面形狀 ； 摩擦因子

並列摘要

This thesis investigated the fully developed laminar flow in ducts with arbitrary cross section shape using a numerical approach. The numerical results were then compared with available analytical solutions. The fully developed flow field in ducts with hydraulic diameter 100μm was computed to study the relationship among the friction factor, the mean laminar flow velocity and the maximum flow velocity value and the geometrical parameters. The governing equations were discretized with triangular cells using a finite volume method with an unstructured grid arrangement. The steady incompressible laminar flow was computed for Newtonian and Non-Newtonian fluids in arbitrary ducts under the assumption of fully developed flow. The numerical results were found to be in good agreement with the analytical solutions.

並列關鍵字

Finite Volume Method ； Unstructiured Grid. ； Cross Section Shape ； Friction Factor

參考文獻

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