The compressible Görtler problem in two-dimensional boundary layers

Dando, Andrew; Seddougui, Sharon O.

doi:10.1093/imamat/51.1.27

Cited by 19 publications

(18 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This work was later modified by Wadey (1992) through a new set of improved initial conditions, but receptivity was still not introduced. The eigenvalue approach with vanishing perturbations in the free stream was also adopted by Dando & Seddougui (1993) to study compressible Görtler vortices. From these early theories it was first noticed that increasing the Mach number leads to a more stable flow and to a shift of the vortices away from the wall.…”

Section: Compressible Görtler Vorticesmentioning

confidence: 99%

Compressible unsteady Görtler vortices subject to free-stream vortical disturbances

Viaro

Riccó

2019

J. Fluid Mech.

View full text Add to dashboard Cite

The perturbations triggered by free-stream vortical disturbances in compressible boundary layers developing over concave walls are studied numerically and through asymptotic methods. We employ an asymptotic framework based on the limit of high Görtler number, the scaled parameter defining the centrifugal effects; we use an eigenvalue formulation where the free-stream forcing is neglected; and we solve the receptivity problem by integrating the compressible boundary-region equations complemented by appropriate initial and boundary conditions that synthesize the influence of the free-stream vortical flow. Near the leading edge, the boundary-layer perturbations develop as thermal Klebanoff modes and, when centrifugal effects become influential, these modes turn into thermal Görtler vortices, i.e. streamwise rolls characterized by intense velocity and temperature perturbations. The high-Görtler-number asymptotic analysis reveals the condition for which the Görtler vortices start to grow. The Mach number is destabilizing when the spanwise diffusion is negligible and stabilizing when the boundary-layer thickness is comparable with the spanwise wavelength of the vortices. When the Görtler number is large, the theoretical analysis also shows that the vortices move towards the wall as the Mach number increases. These results are confirmed by the receptivity analysis, which additionally clarifies that the temperature perturbations respond to this reversed behaviour further downstream than the velocity perturbations. A matched-asymptotic composite profile, found by combining the inviscid core solution and the near-wall viscous solution, agrees well with the receptivity profile sufficiently downstream and at high Görtler number. The Görtler vortices tend to move towards the boundary-layer core when the flow is more stable, i.e. as the frequency or the Mach number increase, or when the curvature decreases. As a consequence, a region of unperturbed flow is generated near the wall. We also find that the streamwise length scale of the boundary-layer perturbations is always smaller than the free-stream streamwise wavelength. During the initial development of the vortices, only the receptivity calculations are accurate. At streamwise locations where the free-stream disturbances have fully decayed, the growth rate and wavelength are computed with sufficient accuracy by the eigenvalue analysis, although the correct amplitude and evolution of the Görtler vortices can only be determined by the receptivity calculations. It is further proved that the eigenvalue predictions of the growth rate and wavenumber worsen as the Mach number increases as these quantities show a dependence on the wall-normal direction. We conclude by qualitatively comparing our results with the direct numerical simulations available in the literature.

show abstract

Section: Compressible Görtler Vorticesmentioning

confidence: 99%

Compressible unsteady Görtler vortices subject to free-stream vortical disturbances

Viaro

Riccó

2019

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…It was illustrated that in addition to the conventional Görtler modes in the incompressible flows, there exists the trapped-layer modes [33,34] in compressible boundary layers. The conventional Görtler modes have their disturbances concentrated close to the boundary layer wall, and are hence called the wall-layer modes (mode W).…”

Section: Introductionmentioning

confidence: 99%

Study of the Discrete Spectrum in a Mach 4.5 Görtler Flow

Ren

2014

Flow Turbulence Combust

View full text Add to dashboard Cite

Evolution of the discrete spectrum in the Ma = 4.5 boundary layer is studied with LST and PSE approaches. Both two-dimensional (2-D) and three-dimensional (3-D) disturbances are considered with streamwise curvature effects. The concave curvature shows a destabilizing effect on the 2-D second/third mode when the fast mode (mode F (1) , mode F (2) ...) synchronizes with the slow mode (mode S). The spectrum branching in the synchronization between the mode F (2) and mode S is also observed. The increase in the spanwise wavenumber(3-D disturbances), on the other hand, suppresses the synchronization between mode F and mode S and reduces the growth rate of the unstable mode. With regard to the 3-D disturbances subjecting to the concave curvature, the mode S originating from the slow acoustic wave amounts to the unsteady Görtler mode while the quasi-steady Görtler mode emanates from the continuous spectrum of the vorticity/entropy wave.

show abstract

“…The linear Görtler instability for a compressible flow over a curved boundary layer was investigated by Dando and Seddougui, 21 and it was shown that the modes with O͑1͒ scaled wave numbers in flows characterized by large Görtler numbers would develop over short streamwise length scales and the behavior of the modes are governed by an inviscid equation. To study the behavior of the referred inviscid modes for our problem, the disturbance quantities Ǔ , V , W , Ť , and P have growth rate in the streamwise direction G 1/2 ␤ and are expanded as …”

Section: A the Inviscid Modesmentioning

confidence: 99%

Centrifugal instabilities in curved compressible wakes

Stephen

2009

Physics of Fluids

View full text Add to dashboard Cite

This investigation is concerned with the linear development of Görtler vortices in the high-Reynolds-number laminar compressible wake behind a flat plate which is aligned with the centerline of a curved mixing-layer system. The Görtler modes were previously found to exist within curved compressible mixing layers by Owen et al. ͓Phys. Fluids 8, 2506 ͑1997͔͒. This study extends that investigation and demonstrates the effect a wake has on the growth rate and location of such modes. The investigations were made by examining the growth rate and the location of the Görtler modes in the limit of large Görtler number and high wave number within the wake-dominated curved compressible mixing-layer systems based on three wake flow models. An analytic Gaussian wake profile is first used to model the behavior of the basic flow within the mixing layer at the trailing edge of the splitter plate. It is found that the wake has an amplification effect on the growth of the Görtler instability within the concavely curved or "unstably" curved compressible mixing layers. It is also found that within the convexly curved or "stably" curved compressible mixing layers wake modes can occur that behave differently to the "thermal modes," which were previously found within the plain curved compressible system by Owen et al. Another analytic composite model which has some practical applications is then used to predict the behavior of the modes within the systems. Solutions from a numerical wake flow model have been compared with the predictions based on the analytic wake flow models.

show abstract

The compressible Görtler problem in two-dimensional boundary layers

Cited by 19 publications

References 0 publications

Compressible unsteady Görtler vortices subject to free-stream vortical disturbances

Compressible unsteady Görtler vortices subject to free-stream vortical disturbances

Study of the Discrete Spectrum in a Mach 4.5 Görtler Flow

Centrifugal instabilities in curved compressible wakes

Contact Info

Product

Resources

About