Abstract
Boundary layer transition is a hot research topic in fluid mechanics and aerospace engineering. In low-speed flows, two-dimensional Tollmien-Schlichting (T-S) waves always dominate the flow instability, which has been modeled by Coder and Maughmer from 2013. However, in supersonic flows, three-dimensional oblique Tollmien-Schlichting waves become dominant in flow instability. Inspired by Coder and Maughmer’s NTS amplification factor transport equation for two-dimensional Tollmien-Schlichting waves in low-speed flows and Kroo and Sturdza’s linear stability theory (LST) analysis results for oblique Tollmien-Schlichting waves in supersonic flows, a new amplification factor transport equation for oblique Tollmien-Schlichting waves has been developed based on LST. The compressible Falkner-Skan similarity equations are introduced to build the relationships between nonlocal variables and local variables so that all the variables used in the present model can be calculated using local variables. Applications of this new transport equation to the flows over supersonic flat plate, 3% thick biconvex airfoil, and one modified supersonic laminar airfoil show promising results compared with the standard LST analysis results.
Highlights
Since laminar flow has less drag than turbulent flow, laminar flow design technology has been a research hotspot in energy conservation of the green aviation [1]
Inspired by Coder and Maughmer’s NTS amplification factor transport equation for twodimensional Tollmien-Schlichting waves in low-speed flows and Kroo and Sturdza’s linear stability theory (LST) analysis results for oblique Tollmien-Schlichting waves in supersonic flows, a new amplification factor transport equation for oblique Tollmien-Schlichting waves has been developed based on LST
One is the local transition models established by experimental data and stability analysis results, such as Menter et al.’s γ − Reθt correlation-based transition model [2,3,4], Walters et al.’s k‐kL‐ω model based on laminar kinetic energy mechanism [5, 6], Fu and Wang’s k‐ω‐γ transition model for high-speed flows [7], and Xu et al.’s physical mode-based transition models [8,9,10,11]
Summary
Since laminar flow has less drag than turbulent flow, laminar flow design technology has been a research hotspot in energy conservation of the green aviation [1]. One is the local transition models established by experimental data and stability analysis results, such as Menter et al.’s γ − Reθt correlation-based transition model [2,3,4], Walters et al.’s k‐kL‐ω model based on laminar kinetic energy mechanism [5, 6], Fu and Wang’s k‐ω‐γ transition model for high-speed flows [7], and Xu et al.’s physical mode-based transition models [8,9,10,11] These models play an important role to predict transition for three-dimensional complex aerodynamic flows. Based on Drela’s idea, Coder and Maughmer [21] established an amplification factor transport equation to solve the amplification factor based on the approximate envelope method, which was extended using new local pressure gradient parameters [22, 23] recently This transition model can predict the two-dimensional Tollmien-Schlichting (T-S) instabilities and laminar separation bubble- (LSB-) induced transition in low-speed flows. Since a suitable critical value of amplification factor can be found in the flows below Mach number 3.0 using Mack’s relations [14, 26, 27] with freestream turbulence intensity, the present work is very valuable and meaningful for natural laminar flow (NLF) optimizations of supersonic airfoils and wings
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