Planar turbulent wakes under pressure gradient: Integral and self-similarity analyses

Journal Article · 24 April 2023 · Physics of Fluids

DOI: https://doi.org/10.1063/5.0149652 · OSTI ID:2008295

Wei, Tie  ^[1]; Liu, Xiaofeng  ^[2]; Li, Zhaorui  ^[3]; Livescu, Daniel  ^[4]

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1. New Mexico Institute of Mining and Technology, Socorro, NM (United States)
2. San Diego State University, CA (United States)
3. Texas A&M University-Corpus Christi, TX (United States)
4. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

By using a combination of integral and self-similarity analyses, the generalized analytical solutions for the mean transverse velocity and Reynolds shear stress are rigorously derived for the first time for the far field of planar turbulent wakes under arbitrary pressure gradients. Specifically, by assuming self-similarity for the mean axial velocity, the analytical formulation for the mean transverse velocity is obtained from the integral of the mean continuity equation, and the analytical formulation for the Reynolds shear stress is obtained from the integral of the momentum equation. The generalized analytical formulations for the mean transverse velocity and Reynolds shear stress consist of multiple components, each with its unique scale and physical mechanism. In the zero pressure gradient limit, the generalized formulations recover the single-scale equations reported by Wei, Liu, and Livescu. Furthermore, simpler approximate formulations for the mean transverse velocity and Reynolds shear stress are also obtained, and show excellent agreement with the experimental measurements. Here, the findings provide new insights into the properties of planar turbulent wakes under pressure gradients, filling some long-standing gaps in the existing literature.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE Laboratory Directed Research and Development (LDRD) Program
• Grant/Contract Number: 89233218CNA000001
• OSTI ID: 2008295
• Report Number(s): LA-UR--23-25199
• Journal Information: Physics of Fluids, Journal Name: Physics of Fluids Journal Issue: 4 Vol. 35; ISSN 1070-6631
• Publisher: American Institute of Physics (AIP)Copyright Statement
• Country of Publication: United States
• Language: English