Linearization of Turbulent Boundary-Layer Equations with an Interactiong Boundary Condition

包含一交互作用邊界條件之紊流邊界層方程式線性化

張鴻明(H.M. Jang)

《華岡工程學報》 9期 (1995/07) Pp. 141-156

https://doi.org/10.29987/CCUHKJE.199507.0009

摘要

在數值模擬含有分離點之邊界層流場時，欲使計算該流場方式之數值解的過程中免於在該分離點處出現異常解且可使計算持續超過迥流區，賦于該方程式一個位於邊界層外緣之交互作用邊界條件即可達成此一目的。該交互作用邊界條件係基於物體外圍勢流所施予物體表面之壓力分佈再適當計上因邊界層存在對該壓力分佈的影響量。因此，該邊界條件深受邊界層數值解之影響，反之亦然。結果，若要有高效率的計算過程該邊界條件必須被線性化後與該流場方程式聯立解出。本文主要探討將可計算含有迥流區的紊流邊界層統禦方程式和其交互作用邊界條件完全線性化成可用邊框矩陣法(Full Bordering Algorithm)求解的過程中所面對的問題以及導出其相應之線性方程式。

並列摘要

Numerical simulation of the boundary-layer flow by using the boundary-layer equations and an imposed edge condition inevitably encounters a difficulty when the flow tends to separate from the surface. For avoiding this numerical difficulty and ensuring a successful computation over the recirculating region, an interacting boundary-layer edge condition may be employed to substitute that imposed one. This interacting boundary-layer edge condition is based on the pressure distribution imposed on the body surface by its outer inviscid flow and also includes a correction that properly takes the boundary-layer's own effects into account. Consequently, the boundary-layer equations and their interacting edge condition are mutually coupled and the full linearization of both of them is essential to obtain an efficient computational procedure. Therefore this study focuses on the full linearization of the two-dimensional turbulent boundary-layer equations and their interacting edge condition; some strategies associate with it are also discussed.