Passive scalar mixing near turbulent/non-turbulent interface in compressible turbulent boundary layers

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X. Zhang, T. Watanabe, K. Nagata
Passive scalar mixing near turbulent/non-turbulent interface in compressible turbulent boundary layers
Physica Scripta 94(4) 044002 2019

Accepted manuscript is available here. 
This version is free to view and download for private research and study only. 

This article may be found at https://doi.org/10.1088/1402-4896/aafbdf.

Abstract

Direct numerical simulations for compressible temporally evolving turbulent boundary layers (TBLs) at Mach numbers of M = 0.8 and 1.6 are preformed up to the Reynolds number based on the momentum thickness Reθ ≈ 2200 to investigate a passive scalar field near the turbulent/non-turbulent interface (TNTI) layer that is formed at the edge of the TBLs. The passive scalar is diffused from the wall in the TBLs developing on the moving wall at constant speed. The outer edge of the TNTI layer detected by an isosurface of vorticity magnitude and passive scalar are compared by visualization, and it is shown that the passive scalar can be used for detecting the TNTI layer in compressible boundary layers. Conditional statistics are calculated as a function of the distance from the outer edge of the TNTI layer. The mean thicknesses of the TNTI layer, viscous superlayer (VSL), and turbulent sublayer (TSL), is about 15ηI, 4ηI, and 11ηI, respectively (ηI: Kolmogorov length scale in the turbulent core region near the TNTI layer). The conditional mean profiles of scalar dissipation rate have a large peak near the boundary between the VSL and TSL, where the fluid with a low scalar value locally entrained from non-turbulent region encounters the turbulent fluid with a higher scalar value. The scalar dissipation rate near the TNTI depends on the TNTI orientation: it is larger near the TNTI facing the downstream direction with respective to the mean flow in the boundary layer (leading edge). This is partially explained by the dependence of the production rate of passive scalar gradient. The conditional mean production rate of the scalar dissipation rate near the leading edge is as large as in the turbulent core region while it is close to the non-turbulent value when the TNTI faces the upstream region (trailing edge).

日本語訳 (DeepL翻訳)

圧縮性乱流境界層における乱流・非乱流界面近傍のパッシブスカラー混合現象

マッハ数0.8と1.6の圧縮性時間発展型乱流境界層(TBL)の直接数値シミュレーションを運動量厚Reθ≈2200に基づくレイノルズ数まで行い、TBLの端にできる乱流/非乱流境界層（TNTI）付近のパッシブスカラー場について調べる。受動スカラーは、一定速度で移動する壁面上に形成されるTBLにおいて壁面から拡散される。渦度等値面とパッシブスカラーで検出したTNTI層外縁を可視化して比較し、パッシブスカラーが圧縮性境界層におけるTNTI層の検出に利用できることを示す。TNTI層の外縁からの距離の関数として、条件付き統計量を計算した。TNTI層、粘性上層(VSL)、乱流下層(TSL)の平均厚さは、それぞれ約15ηI, 4ηI, 11ηI (ηI：TNTI層付近の乱流中心領域のコルモゴロフ長さスケール)であった。スカラー散逸率の条件付き平均分布はVSLとTSLの境界付近に大きなピークを持つが，これは非乱領域から局所的に巻き込まれたスカラー値の低い流体が，スカラー値の高い乱流に遭遇するためである．TNTI近傍のスカラー散逸率はTNTIの向きに依存し、境界層内の平均流（前縁）に対して、下流方向を向いたTNTI近傍で大きくなる。これは受動的スカラー勾配の生成率の依存性によって部分的に説明される。スカラー散逸率の条件付き平均生成率は、前縁付近では乱流コア領域と同程度に大きく、TNTIが上流側（後縁）を向いている場合は非乱流に近い値となることがわかった。

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