Criterion for the laminar-turbulent transition onset in a compressible boundary layer

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Abstract

A criterion of the laminar-turbulent transition onset in a compressible boundary-layer flow is formulated on the base of Liepmann’ assumption according to which the critical condition is reached where the Reynolds stress (caused by the laminar oscillations) becomes equal to the shear stress of the base (undisturbed) flow. Comparison with known results of direct numerical simulations of disturbances propagating in the non-gradient boundary layers on flat plates and sharp cones at zero angle of attack showed that the criterion works well in a wide range of local Mach numbers (0 < Me < 7) for different mechanisms of the nonlinear breakdown of unstable waves.

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About the authors

I. V. Egorov

The Central Aerohydrodynamic Institute named after Proffesor N.E. Zhukovsky; Moscow Institute of Physics and Technology (National Research University)

Author for correspondence.
Email: ivan.egorov@tsagi.ru

Corresponding Member of the RAS

Russian Federation, Zhukovsky, Moscow Region; Dolgoprudny, Moscow Region

A. V. Fedorov

Moscow Institute of Physics and Technology (National Research University)

Email: ivan.egorov@tsagi.ru
Russian Federation, Dolgoprudny, Moscow Region

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Supplementary files

Supplementary Files
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2. Fig. 1. Flow diagram and coordinate system.

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3. Fig. 2. Temperature profiles T(y) (1) and velocity u(y) (2) of the undisturbed flow, as well as the Reynolds stress modulus ︱τ︱=0.5ρ︱urvr + uivi︱(3) and longitudinal velocity  ︱û︱(4) for the case of [22] (see Table 1). The dashed line corresponds to the critical point yc. The eigenfunction is normalized by the condition: the pressure disturbance on the wall, referred to the static pressure, is equal to pw/pe = 1.

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4. Fig. 3. Critical coefficient Acr (Me) and its average value.

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