Three-Dimensional Numerical Simulation of Görtler Vortices in Hypersonic Compression Ramp

2013 ◽  
Author(s):  
Yuya Ohmichi ◽  
Kojiro Suzuki
Keyword(s):  
Numerical Simulation ◽  
Three Dimensional ◽  
Görtler Vortices ◽  
Compression Ramp ◽  
Gortler Vortices

Visualization of transition

1969 ◽  
Vol 38 (3) ◽  
pp. 473-480 ◽  
Author(s):  
F. X. Wortmann
Keyword(s):  
Boundary Layer ◽  
Experimental Study ◽  
Flow Visualization ◽  
Three Dimensional ◽  
Vortex Pair ◽  
Instability Mode ◽  
Vortex Pattern ◽  
Görtler Vortices ◽  
Instability Modes ◽  
Gortler Vortices

In an experimental study the development of transition downstream of Görtler vortices was investigated. With the tellurium method it was possible to distinguish beyond the Görtler vortices to successive instability modes. The first deforms the vortex pattern in a steady way and produces between each vortex pair boundary-layer profiles with two points of inflexion. When this has been established another instability mode starts, consisting of regular three-dimensional oscillations. By detailed flow visualization a nearly complete picture of the different flow patterns can be obtained.

The onset of three-dimensionality and time-dependence in Görtler vortices: neutrally stable wavy modes

1990 ◽  
Vol 220 ◽  
pp. 661-672 ◽  
Author(s):  
Andrew P. Bassom ◽  
Sharon O. Seddougui
Keyword(s):  
Boundary Layer ◽  
Time Dependence ◽  
Large Amplitude ◽  
Three Dimensional ◽  
Three Dimensional Flow ◽  
Numerical Work ◽  
Linear Ordinary Differential Equations ◽  
Görtler Vortices ◽  
Nonlinear Version ◽  
Gortler Vortices

Recently Hall & Seddougui (1989) considered the secondary instability of large-amplitude Görtler vortices in a growing boundary layer into a three-dimensional flow with wavy vortex boundaries. They obtained a pair of coupled, linear ordinary differential equations for this instability which constituted an eigenproblem for the wavelength and frequency of this wavy mode. In the course of investigating the nonlinear version of this problem (Seddougui & Bassom 1990), we have found that the numerical work of Hall & Seddougui (1989) is incomplete; this deficiency is rectified here. In particular, we find that many neutrally stable modes are possible; we derive the properties of such modes in a high-wavenumber limit and show that the combination of the results of Hall & Seddougui and our modifications lead to conclusions which are consistent with the available experimental observations.

Heat transfer enhancement via Görtler flow with spatial numerical simulation

2017 ◽  
Vol 27 (1) ◽  
pp. 189-209 ◽  
Author(s):  
Vinicius Malatesta ◽  
Josuel Kruppa Rogenski ◽  
Leandro Franco de Souza
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Boundary Layer ◽  
Numerical Method ◽  
Layer Structure ◽  
Heat Transfer Process ◽  
Content Type ◽  
Transfer Rates ◽  
Görtler Vortices ◽  
Gortler Vortices

Purpose The centrifugal instability mechanism of boundary layers over concave surfaces is responsible for the development of quasi-periodic, counter-rotating vortices aligned in a streamwise direction known as Görtler vortices. By distorting the boundary layer structure in both the spanwise and the wall-normal directions, Görtler vortices may modify heat transfer rates. The purpose of this study is to conduct spatial numerical simulation experiments based on a vorticity–velocity formulation of the incompressible Navier–Stokes system of equations to quantify the role of the transition in the heat transfer process. Design/methodology/approach Experiments are conducted using an in-house, parallel, message-passing code. Compact finite difference approximations and a spectral method are used to approximate spatial derivatives. A fourth-order Runge–Kutta method is adopted for time integration. The Poisson equation is solved using a geometric multigrid method. Findings Results show that the numerical method can capture the physics of transitional flows over concave geometries. They also show that the heat transfer rates in the late stages of the transition may be greater than those for either laminar or turbulent ones. Originality/value The numerical method can be considered as a robust alternative to investigate heat transfer properties in transitional boundary layer flows over concave surfaces.

Direct numerical simulation of turbulent Taylor–Couette flow

2007 ◽  
Vol 587 ◽  
pp. 373-393 ◽  
Author(s):  
S. DONG
Keyword(s):  
Couette Flow ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Taylor Vortex ◽  
Görtler Vortices ◽  
Tilting Angle ◽  
Taylor Couette ◽  
Gortler Vortices ◽  
Taylor Couette Flow

We investigate the dynamical and statistical features of turbulent Taylor–Couette flow (for a radius ratio 0.5) through three-dimensional direct numerical simulations (DNS) at Reynolds numbers ranging from 1000 to 8000. We show that in three-dimensional space the Görtler vortices are randomly distributed in banded regions on the wall, concentrating at the outflow boundaries of Taylor vortex cells, which spread over the entirecylinder surface with increasing Reynolds number. Görtler vortices cause streaky structures that form herringbone-like patterns near the wall. For the Reynolds numbers studied here, the average axial spacing of the streaks is approximately 100 viscous wall units, and the average tilting angle ranges from 16° to 20°. Simulationresults have been compared to the experimental data in the literature, and the flow dynamics and statistics are discussed in detail.

Primary and secondary instabilities of the asymptotic suction boundary layer on a curved plate

1995 ◽  
Vol 283 ◽  
pp. 249-272 ◽  
Author(s):  
Daniel S. Park ◽  
Patrick Huerre
Keyword(s):  
Boundary Layer ◽  
Velocity Profile ◽  
Three Dimensional ◽  
Vertical Direction ◽  
Secondary Instability ◽  
Spanwise Direction ◽  
Görtler Vortices ◽  
Gortler Vortices ◽  
Secondary Instabilities ◽  
Asymptotic Suction

The temporal growth of Görtler vortices and the associated secondary instability mechanisms are investigated numerically in the case of an asymptotic suction boundary layer on a curved plate. Highly inflectional velocity profiles are generated in both the spanwise and vertical directions. The inflectional velocity profile develops earlier in the spanwise direction. There exist two distinct modes of instability that eventually lead to the breakdown of Görtler vortices: the sinuous mode and the varicose mode. The temporal secondary instability analysis of the three-dimensional inflectional velocity profile reveals that the sinuous mode becomes unstable earlier than the varicose mode. The sinuous mode is shown to be primarily related to shear in the spanwise direction, ∂U/∂z, and the varicose mode to shear in the vertical direction, ∂U/∂y.

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