204 Direct numerical simulation of wave-number selection of Gortler vortex in a concave wall boundary layer

Using direct numerical simulation techniques we investigate transition to turbulence in a boundary-layer flow containing two large-scale counter-rotating vortices with axes aligned in the streamwise direction. The vortices are assumed to have been generated by the Görtler instability mechanism operating in boundary-layer flows over concave walls. Full, three-dimensional Navier–Stokes equations in a natural curvilinear coordinate system for a flow over concave wall are solved by a pseudospectral numerical method. The simulations are initialized with the most unstable mode of the linear stability theory for this flow with its amplitude taken from the experimental measurements of Swearingen & Blackwelder (1987). The evolution of the Görtler vortices for two different spanwise wavenumbers has been investigated. In all cases the development of strong inflexional velocity profiles is observed in both spanwise and vertical directions. The instabilities of these velocity profiles are identified as a primary mechanism of the transition process. The results indicate that the spanwise shear plays a more prominent role in the transition to turbulence than the vertical shear, in agreement with the hypothesis originally proposed by Swearingen & Blackwelder (1987). The following features of the transition, consistent with this hypothesis, were observed. Instability oscillations start in the spanwise direction and are followed later by oscillations in the vertical direction. A two-dimensional linear stability analysis predicts that the maximum growth rates of perturbations associated with the spanwise profiles are greater than those associated with the vertical profiles. Regions of high perturbation velocity correlate well with the regions of high spanwise shear and no obvious correlation with the vertical shear regions is observed. Finally, the analysis of the kinetic energy balance equation reveals that most of the perturbation energy production in the initial stages of transition occurs in the region characterized by large spanwise shear created by the action of the vortices moving low-speed fluid away from the wall. Our results are consistent qualitatively and quantitatively with other experimental, theoretical, and numerical investigations of this flow.

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Quantitative Study of Excitation of Unsteady Görtler Instability Modes in Concave-Wall Boundary Layer by Free-Stream Turbulence

Siberian Journal of Physics ◽

10.54362/1818-7919-2014-9-2-84-94 ◽

2014 ◽

Vol 9 (2) ◽

pp. 84-94

Author(s):

Andrey Ivanov ◽

Yuriy Kachanov ◽

Dmitriy Mischenko

Keyword(s):

Boundary Layer ◽

Physical Phenomenon ◽

Linear Stability Theory ◽

Free Stream Turbulence ◽

Wall Boundary Layer ◽

Wall Boundary ◽

Instability Modes ◽

Concave Wall ◽

Quantitative Characteristics ◽

First Time

The paper is devoted to the first experimental study of distributed excitation of Görtler instability modes due the distributed mechanism of receptivity of a concave-wall boundary layer to streamwise freestream vortices. Experiments are carried out in the following range of problem parameters: Görtler numbers G* = 7,4÷21,3, frequencies f = 15, 20, and 26 Hz (nondimensional frequency parameters are F = 17,04; 22,72 and 29,54), and a broad range of spanwise scales of disturbances z = 8÷24 мм (nondimensional scales are Λ = 149÷774). It is found that this receptivity mechanism is quite efficient and can lead to amplification of unsteady Görtler vortices even in regimes where the boundary layer is linearly stable to these boundary-layer disturbances. Estimations of quantitative characteristics of the investigated physical phenomenon: the complex values of the distributed vortex receptivity coefficients are obtained in the present study for the first time. It is found that examined receptivity mechanism is especially effective for vortices with spanwise wavelengths close to the most dangerous in terms of the linear stability theory. The amplitudes of the receptivity coefficients are found to decrease with the streamwise coordinate

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Direct Numerical Simulation of Turbulent Flow Around a Rotating Circular Cylinder

Journal of Fluids Engineering ◽

10.1115/1.2375133 ◽

2006 ◽

Vol 129 (1) ◽

pp. 40-47 ◽

Cited By ~ 8

Author(s):

Jong-Yeon Hwang ◽

Kyung-Soo Yang ◽

Klaus Bremhorst

Keyword(s):

Numerical Simulation ◽

Boundary Layer ◽

Circular Cylinder ◽

Direct Numerical Simulation ◽

Turbulent Flow ◽

Plane Channel ◽

Outer Region ◽

Wave Number ◽

Boundary Layer Flows ◽

Rotating Circular Cylinder

Turbulent flow around a rotating circular cylinder has numerous applications including wall shear stress and mass-transfer measurement related to the corrosion studies. It is also of interest in the context of flow over convex surfaces where standard turbulence models perform poorly. The main purpose of this paper is to elucidate the basic turbulence mechanism around a rotating cylinder at low Reynolds numbers to provide a better understanding of flow fundamentals. Direct numerical simulation (DNS) has been performed in a reference frame rotating at constant angular velocity with the cylinder. The governing equations are discretized by using a finite-volume method. As for fully developed channel, pipe, and boundary layer flows, a laminar sublayer, buffer layer, and logarithmic outer region were observed. The level of mean velocity is lower in the buffer and outer regions but the logarithmic region still has a slope equal to the inverse of the von Karman constant. Instantaneous flow visualization revealed that the turbulence length scale typically decreases as the Reynolds number increases. Wavelet analysis provided some insight into the dependence of structural characteristics on wave number. The budget of the turbulent kinetic energy was computed and found to be similar to that in plane channel flow as well as in pipe and zero pressure gradient boundary layer flows. Coriolis effects show as an equivalent production for the azimuthal and radial velocity fluctuations leading to their ratio being lowered relative to similar nonrotating boundary layer flows.

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