Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session D11: Rotating Flows II |
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Chair: Zvi Rusak, Rensselaer Polytechnic Institute Room: 3007 |
Sunday, November 23, 2014 2:15PM - 2:28PM |
D11.00001: Effect of sinusoidal perturbation of the inner cylinder on the stability criteria in a wide gap Taylor-Couette flow Krishnashis Chatterjee, Anne Staples The effects of sinusoidal perturbations of the inner cylinder radius in the axial direction in a Taylor-Couette flow apparatus are studied. The base flow solution in the apparatus is derived and then linear stability analysis is performed using the wide gap approximation. The stability criteria are established based on the critical Taylor numbers which mark the transition from the purely circular base flow to the Taylor Vortex flow regime. The effects of varying the forcing wavelength and modulation amplitude on the stability criteria are investigated. The studies are conducted for different instability wave numbers and inner and outer cylinder rotational velocity combinations. The results are compared with those obtained in the same apparatus using a narrow gap assumption, and with the classical Taylor-Couette case. [Preview Abstract] |
Sunday, November 23, 2014 2:28PM - 2:41PM |
D11.00002: DNS study on the turbulence statistics of the Taylor-Couette flow in the Reynolds numbers near the torque transition Kousuke Osawa, Yoshitsugu Naka, Naoya Fukushima, Masayasu Shimura, Mamoru Tanahashi The Taylor-Couette flow has been investigated extensively because of its significance in a wide range of engineering applications. In the present study, direct numerical simulations (DNS) have been performed to clarify the characteristics of turbulence statistics of Taylor-Couette flow in $Re$ from 8000 to 20000 where the torque scaling changes according to the Wendt's empirical formula. Although the flow structures show the existence of the Taylor vortex, the fine scale structures become more pronounced in higher Reynolds numbers. The velocity fluctuations are decomposed into the contribution of Taylor vortex and the remaining turbulent component. A distinct Reynolds number dependence is observed for the turbulence components in the circumferential velocity fluctuation and the Reynolds shear stress while those of the wall normal and the axial velocity fluctuations are insensitive to the Reynolds number change. The budget of the transport equation of the Reynolds stress is evaluated, and the balance of the Reynolds shear stress indicates the Reynolds number dependence in the redistribution and pressure-diffusion terms. This may explain the Reynolds number dependence in the relative contribution of the Taylor vortex and the turbulence components of the Reynolds shear stress. [Preview Abstract] |
Sunday, November 23, 2014 2:41PM - 2:54PM |
D11.00003: ABSTRACT WITHDRAWN |
(Author Not Attending)
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D11.00004: Axially localized states in Taylor Couette flows Jose M. Lopez, Francisco Marques We present numerical simulations of the flow in a Taylor Couette system with the inner cylinder rotating and aspect ratio $\Gamma$ restricted to $0.86 < \frac{\Gamma}{N} < 0.95$, being $N$ the number of Taylor vortices. For these values a complex experimental bifurcation scenario has been reported. The transition from wavy vortex flow (WVF) to a very low frequency mode \mbox{\it VLF} happens via an axisymmetric eigenfunction. The \mbox{\it VLF} plays an essential role in the dynamics, leading to chaos through a two-tori period-doubling route. This chaotic regime vanishes with further increase in $Re$ and gives rise to a new flow regime \mbox{\it ALS} characterized by the existence of large jet oscillations localized in some pairs of vortices. The aim of this numerical study is to extend the available information on \mbox{\it ALS} by means of a detailed exploration of the parameter space in which it occurs. Frequency analysis from time series simultaneously recorded at several points of the domain has been applied to identify the different transitions taking place. The \mbox{\it VLF} occurs in a wide range of control parameters and its interaction with the axially localized states is crucial is most transitions, either between different \mbox{\it ALS} or to the chaotic regime. [Preview Abstract] |
Sunday, November 23, 2014 3:07PM - 3:20PM |
D11.00005: Precession of a rapidly rotating cylinder flow: traverse through resonance Juan Lopez, Francisco Marques The flow in a rapidly rotating cylinder that is titled and also rotating around another axis can undergo sudden transitions to turbulence. Experimental observations of this have been associated with triadic resonances. The experimental and theoretical results are well-established in the literature, but there remains a lack of understanding of the physical mechanisms at play in the sudden transition from laminar to turbulent flow with very small variations in the governing parameters. Here, we present direct numerical simulations of a traverse in parameter space through an isolated resonance, and describe in detail the bifurcations involved in the sudden transition. [Preview Abstract] |
Sunday, November 23, 2014 3:20PM - 3:33PM |
D11.00006: Instabilities of the sidewall boundary layer in a rapidly rotating split cylinder Paloma Gutierrez-Castillo, Juan Lopez The flow in a rapidly rotating cylinder is studied numerically. The cylinder is split in two with the top rotating slightly faster than the half. The interior basic state is in solid-body rotation with the mean rotation rate. Differential rotation drives boundary layers on the sidewall, and the top and bottom endwalls drive fluid into the sidewall layer. The basic state loses stability to three-dimensional perturbations when both the mean rotation and differential rotation increase. Then, the sidewall boundary layer and the corner flow in the slower half undergo a number of instabilities. These include slow low-azimuthal-wavenumber modes whose frequencies excite inertial waves in the interior as well as fast high-azimuthal-wavenumber modes whose impact is contained in the sidewall boundary layer region. Some of these high azimuthal-wavenumber modes have a complicated behavior with pairs of Gortler vortices present in the bottom corner of the cylinder. The behavior becomes even more complicated with mixed modes with interacting low and high azimuthal wavenumbers, and nonlinear competition due to Eckhaus instabilities and mode interactions. [Preview Abstract] |
Sunday, November 23, 2014 3:33PM - 3:46PM |
D11.00007: On the nonlinear stability of the circular Couette flow to viscous axisymmetric perturbations Pun Wong Yau, Shixiao Wang, Zvi Rusak An axisymmetric viscous nonlinear stability analysis of the circular Couette flow to any finite amplitude perturbation is developed. The analysis is based on investigating the reduced Arnol'd energy-Casimir function $A_{rd}$, which consists of the sum of the total kinetic energy of the flow $E$ and the Casimir circulation dependent function $C_S$, i.e. $A_{rd}=E+C_S$. In this case, $\Delta A_{rd}$ is used as a Lyapunov function, which represents the difference between the reduced Arnol'd function at a later time $t$ and the corresponding base flow value. The requirement for the temporal decay of $\Delta A_{rd}$ leads to two novel conditions for the nonlinear stability of this steady flow against axisymmetric viscous perturbations of any finite amplitude. We also establish for the very first time a definite nonlinear stability region in terms of the operational parameters for the circular Couette flow. Once the flow is nonlinearly stable and stays axisymmetric, it always decays asymptotically to a unique steady state defined by the rotating cylinders. The results from this research shed a new fundamental physical insight into a classical flow problem that was studied for many decades. [Preview Abstract] |
Sunday, November 23, 2014 3:46PM - 3:59PM |
D11.00008: At what spatio-temporal scales can inertial waves be found in rotating turbulence? Pierre-Philippe Cortet, Antoine Campagne, Basile Gallet, Fr\'{e}d\'{e}ric Moisy We present a spatio-temporal analysis of a statistically stationary rotating turbulence experiments aiming to extract a statistical signature of inertial waves and to determine at what scales and frequencies these waves can be detected. This analysis is performed from two-point correlations of temporal Fourier transform of the velocity fields time series obtained from stereoscopic PIV measurements in the rotating frame. From this data, it is possible to quantify the degree of anisotropy of turbulence due to global rotation both as a function of angular frequency $\omega$ and spatial scale normal to the rotation axis $r_\perp$. This frequency and scale dependent anisotropy is found compatible with the dispersion relation of inertial waves, provided that a weak non-linearity condition is satisfied in terms of a properly defined Rossby number dependant on the spatio-temporal scale ($\omega$,$r_\perp$). [Preview Abstract] |
Sunday, November 23, 2014 3:59PM - 4:12PM |
D11.00009: On the development of lift and drag in a rotating and translating cylinder Antonio Martin-Alcantara, Enrique Sanmiguel-Rojas, Ramon Fernandez-Feria The two-dimensional flow around a rotating cylinder is investigated numerically using a vorticity forces formulation with the aim of analyzing the flow structures, and their evolutions, that contribute to the lift and drag forces on the cylinder. The Reynolds number, based on the cylinder diameter and steady free-stream speed, considered is $Re=200$, while the non-dimensional rotation rate (ratio of the surface speed and free-stream speed) selected were $\alpha=1$ and $3$. For $\alpha=1$ the wake behind the cylinder for the fully developed flow is oscillatory due to vortex shedding, and so are the lift and drag forces. For $\alpha=3$ the fully developed flow is steady with constant (high) lift and (low) drag. Each of these cases is considered in two different transient problems, one with angular acceleration of the cylinder and constant speed, and the other one with translating acceleration of the cylinder and constant rotation. Special attention is paid to explaining the mechanisms of vortex shedding suppression for high rotation (when $\alpha=3$) and its relation to the mechanisms by which the lift is enhanced and the drag is almost suppressed when the fully developed flow is reached. [Preview Abstract] |
Sunday, November 23, 2014 4:12PM - 4:25PM |
D11.00010: Robustness of point vortex equilibria in the vicinity of a Kasper Wing Rhodri Nelson, Takashi Sakajo The concept of the Kapser Wing was introduced by Witold Kasper in the early 1970's. His design proposed to add additional ``flaps'' or auxiliary aerofoils close to the main aerofoil to control the feeding and shedding of vortices in the vicinity of the wing - the aim being to ``trap'' a vortex above the main aerofoil thus resulting in an increased lift being experienced. In this study, equilibira consisting of a single point vortex in the presence of an idealised Kapser Wing (modelled as three thin plates) are computed. A background potential flow at an angle attack $\chi$ to to the main plate is also present. A range of auxiliary plate configurations is considered and the lift of the system computed. It is seen that the lift experienced by the main plate is ``sensitive'' to the placement of the auxiliary plates and can be enhanced in comparison to the single plate case (previously considered by Saffman and Sheffield, 1977). The linear stability and non-linear time evolution of the Kasper Wing system is then compared to that of the single plate system. It is seen that the presence of the auxiliary plates, in general, result in a larger range of ``useful' neutrally stable equilibria (according to linear theory) and and can increase the non-linear robustness of the system. [Preview Abstract] |
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