Coupled numerical and theoretical study of the flow transition between a rotating and a stationary disk (original) (raw)
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Comptes Rendus Mécanique, 2002
Both theoretical linear stability analysis and direct numerical simulation are performed to study the transition flow between a stationary and a rotating disc. This paper concerns threedimensional spiral and annular patterns computed with a high-order (spectral) numerical method and related to Bödewadt layer instabilities. The characteristic parameters of these boundary layer patterns are compared to the theoretical results and interpreted in terms of type I and type II generic instabilities. Moreover, the absolute instability regions are also theoretically identified and the critical Reynolds numbers of the convective/absolute transition in both layers are given. To cite this article: E. Tuliska-Sznitko et al., C. R. Mecanique 330 (2002) 91-99. 2002 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS fluid mechanics / instability and transition in rotating flows / convective and absolute instability / direct numerical simulation / linear stability analysis Sur la nature des instabilités de couche limite dans un écoulement entre un disque fixe et un disque tournant Résumé La transition d'un écoulement inter-disques de type rotor-stator est étudiée au moyen de la simulation numérique directe et de l'analyse linéaire de stabilité, en utilisant des approximations spectrales. Ce papier est consacré à l'analyse des structures annulaires et spirales obtenues par une méthode numérique tridimensionnelle dans la couche limite de Bödewadt. Les paramètres caractéristiques de ces structures sont comparés aux résultats théoriques et interprétés en termes d'instabilités de type I et II. De plus, les régions absolument instables sont identifiées théoriquement et les nombres de Reynolds critiques à la transition convectif/absolu sont déterminés dans les deux couches de Bödewadt et d'Ekman. Pour citer cet article : E. Tuliska-Sznitko et al., C. R. Mecanique 330 (2002) 91-99. 2002 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS mécanique des fluides / instabilité et transition dans un écoulement en rotation / instabilité convective et absolue / simulation numérique directe / analyse linéaire de stabilité (P. Bontoux). 2002 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS. Tous droits réservés S 1631-0721(02) 01 4 32 -8 /FLA
2001
The purpose of this article is the direct numerical simulation (DNS) of the complex phenomena that precede the transition to turbulence inside a cavity subjected to rotation. The configurations of cylindrical cavities subjected to a radial throughflow or to a differential rotation of the walls are relevant to rotating machinery devices. At a high rotation rate, the DNS exhibits instability patterns arising inside the thin layers close to the disks. The efficient spectral solver is based on a Chebyshev-Fourier approximation. For large aspect ratio and at high Reynolds number, an instability occurs inside the Ekman and B?dewadt layers in the form of annular and spiral vortices that are characteristic of type I and type II instabilities.
Stability, transition and turbulence in rotating cavities
Billerica, MA: WIT Press, …, 2005
This chapter reviews striking features of boundary-layer instabilities induced by different mechanisms and related to transition to turbulence in rotating flows with walls. Besides its fundamental importance as a three-dimensional prototype flow, confined flow between rotating discs has been extensively examined because of its relevance to many industrial applications such as turbomachinery and engineering processes. Many studies using stability analyses and experiments have been devoted to the onset of unstable waves and to the mechanisms associated with them. Here, we focus on how numerical investigations may provide insights and complement experimental data and analytical results by providing the full velocity field in well-controlled flows within idealized configurations. Rotor-stator and rotating cavity with radial throughflow are investigated. At a critical rotation rate, axisymmetric and/or three-dimensional structures appear in the Bödewadt and Ekman layers. All features of the transitions in these rotating cavities are documented. A comparison of the wave numbers, frequencies, and phase velocities of the instabilities with available theoretical and experimental results shows that both Type II (or A) and Type I (or B) instabilities appear, depending on flow and geometric control parameters. Interesting patterns exhibiting the coexistence of circular and spiral waves are found under certain conditions.
Experimental investigation of absolute instability of a rotating-disk boundary layer
Journal of Fluid Mechanics, 2006
A series of experiments were performed to study the absolute instability of Type I travelling crossflow modes in the boundary layer on a smooth disk rotating at constant speed. The basic flow agreed with analytic theory, and the growth of natural disturbances matched linear theory predictions. Controlled temporal disturbances were introduced by a short-duration air pulse from a hypodermic tube located above the disk and outside the boundary layer. The air pulse was positioned just outboard of the linear-theory critical radius for Type I crossflow modes. A hot-wire sensor primarily sensitive to the azimuthal velocity component, was positioned at different spatial (r, θ) locations on the disk to document the growth of disturbances produced by the air pulses. Ensemble averages conditioned on the air pulses revealed wave packets that evolved in time and space. Two amplitudes of air pulses were used. The lower amplitude was verified to produced wave packets with linear amplitude characteristics. The space-time evolution of the leading and trailing edges of the wave packets were followed past the critical radius for the absolute instability, r c A. With the lower amplitudes, the spreading of the disturbance wave packets did not continue to grow in time as r c A was approached. Rather, the spreading of the trailing edge of the wave packet decelerated and asymptotically approached a constant. This result supports previous linear DNS simulations where it was concluded that the absolute instability does not produce a global mode and that linear disturbance wave packets are dominated by the convective instability. The larger-amplitude disturbances were found to produce larger temporal spreading of the wave packets. This was accompanied by a sharp growth in the wave packet amplitude past r c A. Explanations for this are discussed.
Secondary instability in rotating-disk flow
Journal of Fluid Mechanics, 1992
Primary instability of the three-dimensional boundary layer on a rotating disk introduces periodic modulation of the mean flow in the form of stationary crossflow vortices. Here we study the stability of this modulated mean flow with respect to secondary disturbances. These secondary disturbances are found to have quite large growth rates compared to primary disturbances. Both fundamental and subharmonic resonance cases are considered and their corresponding results indicate that the growth rate and the frequency of the secondary instability are insensitive to the exact nature of the resonance condition. The threshold primary stationary crossflow vortex amplitude for secondary instability found in this three-dimensional incompressible boundary layer is significantly larger than that for a two-dimensional boundary layer which is subjected to Tollmien–Schlichting instability. The secondary instability results in a pair of travelling counter-rotating vortices, tilted up and oriented at...
The instability of the boundary layer over a disk rotating in an enforced axial flow
Physics of Fluids, 2011
We consider the convective instability of stationary and traveling modes within the boundary layer over a disk rotating in a uniform axial flow. Complementary numerical and high Reynolds number asymptotic analyses are presented. Stationary and traveling modes of type I (crossflow) and type II (streamline curvature) are found to exist within the boundary layer at all axial flow rates considered. For low to moderate axial flows, slowly-traveling type I modes are found to be the most amplified and quickly-traveling type II modes are found to have the lower critical Reynolds numbers. However, nearstationary type I modes are expected to be selected due to a balance being struck between onset and amplification. Axial flow is seen to stabilize the boundary layer by increasing the critical Reynolds numbers and reducing amplification rates of both modes. However, the relative importance of type II modes increases with axial flow and they are therefore expected to dominate for sufficiently high rates. The application to chemical vapour deposition (CVD) reactors is considered.
Transient growth and instability in rotating boundary layers
2004
The three-dimensional temporal instability of rotating boundary layer flows is investigated by computing classical normal modes as well as by evaluating the transient growth of optimal disturbances. The flows examined are the rotating Blasius (RB) and the rotating asymptotic suction layers (RAS), with the rotation axis normal to the basic flow plane. In agreement with an inviscid criterion, streamwise unstable modes are found in both flow cases for anti-cyclonic rotation: at high Reynolds numbers, one obtains the Rossby number unstable range 0<1/Ro<0.57 for RB, or 0<1/Ro<1 for RAS. Critical Reynolds and Rossby numbers are also determined in both instances. Moreover the dependence of transient growth with respect to wavenumbers, Rossby and Reynolds numbers is presented for both cyclonic and anti-cyclonic régimes. In particular, the peak transient growth is computed for a wide range of parameter values within the cyclonic regime and is shown to be reduced by rotation. A sc...
Formation of Turbulent Vortex Breakdown: Intermittency, Criticality, and Global Instability
AIAA Journal, 2012
and the bifurcation to a global spiral mode in turbulent swirling jets. The different flow states that evolve at incrementally increasing swirl are characterized by means of time-resolved stereo PIV measurements in conjunction with post-processing tools, including Fourier analysis and proper orthogonal decomposition. Vortex breakdown occurs first intermittently, accompanied by strong axial oscillations. By further increasing the swirl, vortex breakdown stabilizes and a region of reversed flow appears in the mean flow. This region grows linearly with increasing swirl until the flow undergoes a supercritical Hopf bifurcation to a global single-helical mode and vortex breakdown becomes spiral shaped. The appearance of an internal stagnation point is accompanied by a supercritical-to-subcritical transition of the inflow profiles, in accordance to Benjamin's inviscid theory [1]. This critical swirl number is found to be smaller than the one for the supercritical Hopf bifurcation. The observed mean flow sequence compares well with the transient formation of spiral vortex breakdown in laminar swirling jets as reported by Brücker & Althaus[2], Liang & Maxworthy[3] and Ruith et al.[4]. The present experiment is properly scaled by the swirl number based on the axial momentum flux when omitting the commonly used boundary layer approximations.