Applications of EPSE method for predicting crossflow instability in swept-wing boundary layers

The nth-order expansion of the parabolized stability equation （EPSEn） is obtained from the Taylor expansion of the linear parabolized stability equation （LPSE） in the streamwise direction. The EPSE together with the homogeneous boundary conditions forms a local eigenvalue problem, in which the streamwise variations of the mean flow and the disturbance shape function are considered. The first-order EPSE （EPSE1） and the second-order EPSE （EPSE2） are used to study the crossflow instability in the swept NLF（2）-0415 wing boundary layer. The non-parallelism degree of the boundary layer is strong. Compared with the growth rates predicted by the linear stability theory （LST）, the results given by the EPSE1 and EPSE2 agree well with those given by the LPSE. In particular, the results given by the EPSE2 are almost the same as those given by the LPSE. The prediction of the EPSE1 is more accurate than the prediction of the LST, and is more efficient than the predictions of the EPSE2 and LPSE. Therefore, the EPSE1 is an efficient ey prediction tool for the crossflow instability in swept-wing boundary-layer flows.

Improved local amplification factor transport equation for stationary crossflow instability in subsonic and transonic flows

Transition prediction is a hot research topic of fluid mechanics.For subsonic and transonic aerodynamic flows,e^(N) method based on Linear Stability Theory(LST)is usually adopted reliably to predict transition.In 2013,Coder and Maughmer established a transport equation for Tollmien-Schlichting(T-S)instability so that the e^(N) method can be applied to general Reynolds-Average-Navier-Stokes(RANS)solvers conveniently.However,this equation focuses on T-S instability,and is invalid for crossflow instability induced transition which plays a crucial role in flow instability of three-dimensional boundary layers.Subsequently,a transport equation for crossflow instability was developed in 2016,which is restricted to wing-like geometries.Then,in 2019,this model was extended to arbitrarily shaped geometries based on local variables.However,there are too many tedious functions and parameters in this version,and it can only be used for incompressible flows.Hence,in this paper,after a large amount of LST analyses and parameter optimization,an improved version for subsonic and transonic boundary layers is built.The present improved model is more robust and more concise,and it can be applied widely in aeronautical flows,which has great engineering application value and significance.An extensive validation study for this improved transition model will be performed.

Experimental study on hypersonic crossflow instability over a swept flat plate by flow visualization

An experimental study on the traveling crossflow instability over a 60∘swept flat plate was conducted.The Mach number is 6,the angle of attack of the model is 5∘.The traveling crossflow waves and the secondary instability of the traveling crossflow waves were visualized by nano-tracer-based planar laser scattering(NPLS)technique.In the spanwise NPLS images,the traveling crossflow waves appeared as regular strikes,and the secondary instability appeared as small eddies attached to strikes.The wavelet transform was used to study the wavelength contents of the traveling crossflow waves.The most amplified wavelength is stable before the secondary instability happening,which is around 12 mm at Re_(∞)=3.45×10^(6)m^(−1).Besides,the Reynolds number effects on the boundary layer transition and traveling crossflow instability were discussed.

Transition study of 3D aerodynamic configures using improved transport equations modeling

As boundary layer transition plays an important role in aerodynamic drag prediction, the proposal and study of transition prediction methods simulating the complex flow phenomena are prerequisite for aerodynamic design. In this paper, with the application of the linear stability theory based on amplification factor transport transition equations on the two-equation shear stress transport (SST) eddy-viscosity model, a new method, the SST-NTS-NCF model, is yielded. The new amplification factor transport equation for the crossflow instability induced transition is proposed to add to the NTS equation proposed by Coder, which simulates Tollmien-Schlichting wave transition. The turbulent kinetic energy equation is modified by introducing a new source term that simulates the transition process without the intermittency factor equation. Finally, coupled with these two amplification factor transport equations and SST turbulence model, a four-equation transition turbulence model is built. Comparisons between predictions using the new model and wind-tunnel experiments of NACA64(2) A015, NLF(2)-0415 and ONERA-D infinite swept wing and ONERAM6 swept wing validate the predictive quality of the new SST-NTS-NCF model. (C) 2016 Chinese Society of Aeronautics and Astronautics. Production and hosting by Elsevier Ltd.

Analysis of the secondary instability of the incompressible flows over a swept wing

The crossflow instability of a three-dimensional (3-D) boundary layer is an important factor which affects the transition over a swept-wing.In this report,the primary instability of the incompressible flow over a swept wing is investigated by solving nonlinear parabolized stability equations (NPSE).The Floquet theory is applied to study the dependence of the secondary and high-frequency instabilities on curvature,Reynolds number and angle of swept (AOS).The computational results show that the curvature in the present case has no significant effect on the secondary instabilities.It is generally believed that the secondary instability growth rate increases with the magnitude of the nonlinear mode of crossflow vortex.But,at a certain state,when the Reynolds number is 3.2 million,we find that the secondary instability growth rate becomes smaller even when the magnitude of the nonlinear mode of the crossflow vortex is larger.The effect of the angle of swept at 35,45 and 55 degrees,respectively,is also studied in the framework of the secondary linear stability theory.Larger angles of swept tend to decrease the spanwise spacing of the crossflow vortices,which correspondingly helps the stimulation of 'z' mode.

Secondary instability control of compressible flow by suction for a swept wing

The crossflow instability of a three-dimensional boundary layer is a main factor affecting the transition around the swept-wing.The three-dimensional boundary layer flow affected by the saturated crossflow vortex is very sensitive to the high frequency disturbances,which foreshadows that the swept wing flow transition will happen.The primary instability of the compressible flow over a swept wing is investigated with nonlinear parabolized stability equations (NPSE).The Floquet theory is then applied to the analysis of the influence of localized steady suction on the secondary instability of crossflow vortex.The results show that suction can significantly suppress the growth of the crossflow mode as well as the secondary instability modes.

Wall pressure beneath a transitional hypersonic boundary layer over an inclined straight circular cone

Properties of wall pressure beneath a transitional hypersonic boundary layer over a 7°half-angle blunt cone at angle of attack 6°are studied by Direct Numerical Simulation.The wall pressure has two distinct frequency peaks.The low-frequency peak with f≈10−50 kHz is very likely the unsteady crossflow mode based on its convection direction,i.e.along the axial direction and towards the windward symmetry ray.Highfrequency peaks are roughly proportional to the local boundary layer thickness.Along the trajectories of stationary crossflow vortices,the location of intense high-frequency wall pressure moves from the bottom of trough where the boundary layer is thin to the bottom of shoulder where the boundary layer is thick.By comparing the pressure field with that inside a high-speed transitional swept-wing boundary layer dominated by the z-type secondary crossflow mode,we found that the high-frequency signal originates from the Mack mode and evolves into the secondary crossflow instability.