Elevated low-frequency free-stream vortical disturbances eliminate boundary-layer separation
File(s)
Accepted version
Author(s)
Xu, Dongdong
Wu, Xuesong
Type
Journal Article
Abstract
steady two-dimensional boundary layer subject to an adverse streamwise pressure gradient usually separates. In this paper, we investigate how free-stream vortical disturbances (FSVD) of moderate level prevent the separation in such a boundary layer over a plate or concave wall. The focus is on physically realisable FSVD with sufficiently long wavelength (low frequency) as they have the most significant impact on the boundary layer. The FSVD intensity ϵ
is taken to be small but nevertheless strong enough that the streaks or Görtler vortices generated in the boundary layer are fully nonlinear and can alter the mean-flow profile by an order-one amount. The excitation and evolution of streaks and Görtler vortices are governed by the nonlinear unsteady boundary-region equations supplemented by appropriate initial (upstream) and boundary (far-field) conditions, which describe appropriately the action of FSVD on the boundary layer. The flow variables are decomposed into two parts: the steady spanwise-averaged and the unsteady or spanwise-varying components. These two parts are coupled and are computed simultaneously. Numerical results show that the separation is eliminated when the FSVD level exceeds a critical intensity ϵc
. It is inferred that the strong nonlinear mean-flow distortion associated with the nonlinear streaks or Görtler vortices prevents the separation. The critical FSVD intensity ϵc
depends on the streamwise curvature, the pressure gradient and the frequency of FSVD. The value of ϵc
decreases significantly with the Görtler number, indicating that concave curvature inhibits separation. A higher ϵc
is required to prevent the separation in the case of stronger adverse pressure gradient. Interestingly, unsteady FSVD with low frequencies are found to be more effective than steady ones in suppressing the separation.
is taken to be small but nevertheless strong enough that the streaks or Görtler vortices generated in the boundary layer are fully nonlinear and can alter the mean-flow profile by an order-one amount. The excitation and evolution of streaks and Görtler vortices are governed by the nonlinear unsteady boundary-region equations supplemented by appropriate initial (upstream) and boundary (far-field) conditions, which describe appropriately the action of FSVD on the boundary layer. The flow variables are decomposed into two parts: the steady spanwise-averaged and the unsteady or spanwise-varying components. These two parts are coupled and are computed simultaneously. Numerical results show that the separation is eliminated when the FSVD level exceeds a critical intensity ϵc
. It is inferred that the strong nonlinear mean-flow distortion associated with the nonlinear streaks or Görtler vortices prevents the separation. The critical FSVD intensity ϵc
depends on the streamwise curvature, the pressure gradient and the frequency of FSVD. The value of ϵc
decreases significantly with the Görtler number, indicating that concave curvature inhibits separation. A higher ϵc
is required to prevent the separation in the case of stronger adverse pressure gradient. Interestingly, unsteady FSVD with low frequencies are found to be more effective than steady ones in suppressing the separation.
Date Issued
2021-08-10
Date Acceptance
2021-06-01
Citation
Journal of Fluid Mechanics, 2021, 920
ISSN
0022-1120
Publisher
Cambridge University Press
Journal / Book Title
Journal of Fluid Mechanics
Volume
920
Copyright Statement
Copyright © 2021 Cambridge University Press. This article has been published in a revised form in Journal of Fluid Mechanics https://doi.org/10.1017/jfm.2021.441. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works.
Identifier
https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000658784200001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=a2bf6146997ec60c407a63945d4e92bb
Subjects
ACTIVE FLOW-CONTROL
boundary layer receptivity
boundary layer separation
boundary layer stability
BUBBLES
DIRECT NUMERICAL SIMULATIONS
DYNAMIC ROUGHNESS ELEMENTS
INSTABILITY
LAMINAR
Mechanics
Physical Sciences
Physics
Physics, Fluids & Plasmas
Science & Technology
STEADY
Technology
TRANSITION
TURBULENCE INTENSITY
UNSTEADY GORTLER VORTICES
Publication Status
Published
Article Number
ARTN A14
Date Publish Online
2021-06-08