Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session NM: Instability: Rayleigh-Taylor and Taylor-Couette |
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Chair: Greg Burton, Lawrence Livermore National Laboratory Room: Salt Palace Convention Center 251 A |
Tuesday, November 20, 2007 11:35AM - 11:48AM |
NM.00001: Investigation of Turbulence Dynamics in a Very Large Reynolds Number Rayleigh-Taylor Mixing Layer Using Direct Numerical Simulation Data Gregory Burton, Oleg Schilling Classical gradient-diffusion models of turbulent transport in Rayleigh-Taylor instability-induced mixing are assessed using data from the Cabot and Cook [Nat. Phys. \textbf{2}, 562] $3072^3$ direct numerical simulation (DNS) attaining a Reynolds number of $\sim 32,000$. Mean and fluctuating fields, defined from spatial averages over the two periodic directions of the DNS, are used to construct the profiles across the mixing layer of the terms in the turbulent kinetic energy and turbulent kinetic energy dissipation rate transport equations. The unclosed terms are then compared a priori with the corresponding terms modeled using the gradient-diffusion approximation to assess the validity of this approximation at very large Reynolds numbers. In addition, optimized turbulent Schmidt numbers appearing in the closures are obtained by correlating the unclosed and closed model terms. [Preview Abstract] |
Tuesday, November 20, 2007 11:48AM - 12:01PM |
NM.00002: Evaluation of Turbulence Mix Model Constants for Low Atwood Number Rayleigh-Taylor Flows Arindam Banerjee, Robert A. Gore, Malcolm J. Andrews Progress on evaluation of turbulence mix model constants for the \textit{$\kappa $}-\textit{$\varepsilon $} and BHR mix models will be presented. Our detailed measurements of Rayleigh-Taylor (RT) mixing at low Atwood number ($A_{t}$ = 0.04) in the Texas A{\&}M air-helium gas channel facility has allowed us to evaluate several mix model constants used in the \textit{$\kappa$}-\textit{$\varepsilon $} and BHR models. We have measured the various terms allowing us to compute (measure) the model constant C$_{\mu}$. The measured value of C$_{\mu}$ is 0.3, significantly higher that the usual value of 0.09 assigned for shear flows. In addition, model constants are evaluated based on a self similar analytical solution using top-hat and parabolic profiles, and then compared with a detailed one-dimensional transient numerical solution. Various assumptions at the low Atwood limit that have been used for evaluating the various model constants will be discussed. [Preview Abstract] |
Tuesday, November 20, 2007 12:01PM - 12:14PM |
NM.00003: Progress with Molecular Mixing Measurements {\&} High Atwood Number Experiments at Texas A{\&}M University Malcolm J. Andrews, Wayne N. Kraft, Nicholas J. Mueschke Current progress with high Schmidt number molecular mixing measurements in a small Atwood number water channel facility is reported. In the experiments, the pH of the heavy (salt) and light (fresh) water streams is controlled by adding acid or alkali to each stream. As the two streams molecularly mix, the chemical reaction between the acid and alkali is marked by a phenolphthalein chemical indicator, which is imaged under backlit conditions. The current high Schmidt number ($\sim $700) experiments have resulted in low measures of molecular mixing as compared with previous experiments and simulations at moderate Schmidt numbers. In addition, progress with measurements at high Atwood numbers ($\sim $0.6) in a gas channel facility using helium and air is also reported. Instantaneous velocity and density measurements inside the mixing layer are obtained using a novel combined hot-wire / cold-wire anemometry technique, where temperature is used as a fluid marker. This technique provides detailed simultaneous velocity and density measurements which allows for determination of velocity and density variances, velocity-density cross-correlations, and their spectra. [Preview Abstract] |
Tuesday, November 20, 2007 12:14PM - 12:27PM |
NM.00004: Variable density mixing in buoyancy driven turbulence Daniel Livescu, Ray Ristorcelli The homogenization of a heterogeneous mixture of two pure fluids with different densities by molecular diffusion and stirring induced by buoyancy generated motions, as occurs in the Rayleigh-Taylor instability, is studied using Direct Numerical Simulations. The Schmidt number, $Sc$, is varied by a factor of twenty, $0.1 \le Sc \le 2.0$, and the Atwood number, $A$, a factor of ten, $0.05 \le A \le 0.5$. Important differences between the mixing in a variable density (VD) fluid, as compared to a Boussinesq fluid, are observed. The pure heavy fluid mixes more slowly than the pure light fluid: an initially symmetric double delta density PDF is rapidly skewed and, only at long times and low density fluctuations, it relaxes to a Gaussian-like PDF. Diverse mix metrics and their dependence on $A$, $Re$, and $Sc$ are used to examine the homogenization of the two fluids. In particular, it is shown that the specific volume density covariance is a better measure of the mixing state than the density variance for VD flows, as it directly appears in the dynamical equations. The usual mix parameter $\theta$ is mathematically related to the variance of the excess reactant of a hypothetically fast chemical reaction. Analytic expressions and bounds relating $\theta$ and the normalized product, $\Xi$, are derived. In general, no usual mix measure can predict the amount of pure or mixed fluid in the flow, however bounds on the fluid composition, using low order moments of the density PDF, can be derived. [Preview Abstract] |
Tuesday, November 20, 2007 12:27PM - 12:40PM |
NM.00005: Local measurements of turbulent angular momentum transport in Taylor-Couette flow. Michael Burin, Ethan Schartman, Hantao Ji We report on velocity fluctuations and the fluctuation-driven radial transport of angular momentum in turbulent wide-gap Taylor-Couette flow (2x10$^{3}<$ \textit{Re} $<$2x10$^{5})$. Fluctuation r.m.s. levels and the mean specific angular momentum are found to be nearly constant over radius, in accordance with previous studies featuring narrower gaps. Synchronized dual beam Laser Doppler Velocimetry (2D LDV) is used to directly measure the \textit{r-$\theta $} Reynolds stress component, revealing an approximate power-law scaling in the non-dimensional angular momentum transport: $G \quad \propto $ \textit{Re}$^{1.77\pm 0.07}$. The local exponent between 1.7 and 1.8 confirms previous measurements of torque in similar flows at high Reynolds numbers; its constancy over two decades differs from previous work however, and is attributed to the wide-gap geometry of our apparatus (ratio of cylinder radii $\eta \sim $ 0.35). 2D LDV allows for decomposition of the turbulent transport to assess the relative roles of fluctuation intensity and cross-correlation. We find that the increasing transport with \textit{Re} is solely due to intensifying fluctuations; changes in cross-correlation for these Reynolds numbers are insignificant. [Preview Abstract] |
Tuesday, November 20, 2007 12:40PM - 12:53PM |
NM.00006: Hydromagnetic Taylor-Couette Experiments in Liquid Sodium Daniel Zimmerman, Barbara Brawn, Daniel Lathrop We present results from experiments in liquid sodium flow between a stationary 30cm diameter stainless steel cylinder and a rotating 15cm diameter copper plated aluminum cylinder, both 30cm long. The inner cylinder is driven at an angular frequency $\Omega$ to access a range of magnetic Reynolds number $R_m = \frac{\Omega R_{i}\L_{gap}}{\eta}$ between 0.9 and 13 and an axial magnetic field $B_0$ is applied achieving an interaction parameter (Stuart number) $N = \frac{B_0^2 L_{gap}}{\rho\mu_0\eta \Omega R_i}$ between about 0.02 and 14. Hall probe array measurements of induced magnetic field and ultrasound measurements of velocity show significant influence of the applied magnetic field on the turbulent basic flow. This includes the emergence of coherent oscillations in both the induced magnetic field and velocities in some regions of parameter space. Understanding the interplay between magnetic fields and flows of conducting liquids in this geometry has broader applicability to astrophysical problems such as flow in accretion disks. [Preview Abstract] |
Tuesday, November 20, 2007 12:53PM - 1:06PM |
NM.00007: Mode competition in modulated Taylor-Couette flow Marc Avila, Michael J. Belisle, Juan M. Lopez, Francisco Marques, William S. Saric The effects of harmonically oscillating the inner cylinder about a zero mean rotation in a Taylor-Couette flow are investigated experimentally and numerically. The resulting time-modulated circular Couette flow possesses an involutive spatio-temporal symmetry which gives rise to two distinct modulated Taylor vortex flows. These flows are born at synchronous bifurcations, have the same spatial symmetries, but are characterized by different spatio-temporal symmetries and axial wavenumber. Mode competition between these two states has been investigated in the neighborhood where they bifurcate simultaneously. In the idealized numerical model, the two flows have been found to coexist and be stable in a narrow region of parameter space. However in the physical experiment neither state has been observed in the coexistence region. Instead, we empirically observe noise-sustained modes whose axial wavenumber varies as a function of time. [Preview Abstract] |
Tuesday, November 20, 2007 1:06PM - 1:19PM |
NM.00008: Detecting the Normal Modes of Instability in Rotating Couette Flow of He II Howard Snyder Several attempts have been make to verify the HVBK equations of He II using the Couette double cylinder experiment. Calculations show that the critical Reynolds number and wave number rapidly approach zero as the temperature is lowered from the lambda-temperature. The wavelength of Taylor cells is predicted to be longer than any reported apparatus when the temperature is below 2.05 K. Yet, all the experimental data have breaks in plots of the torque or attenuation of second sound vs. the Reynolds number. This data spans a large range of parameter space. The breaks occur at the calculated Reynolds number when the calculated wavelength is somewhat shorter than the apparatus i.e. near the lambda temperature. The observed breaks at lower temperatures, down to 1.2 K, are unexplained. We present a method of analyzing second sound resonances that will help solve the problem. If sufficient data is available, the method will verify or reject an assumed form of the disturbance. The analysis is based on a publication of the author in which the propagation of waves in uniformly rotating He II is described. Those procedures are generalized so that they apply to Couette flow. The slopes of the curves of second sound attenuation vs. Reynolds number are calculated for a range of normal modes of both second sound and Taylor cells. The slopes are also calculated below the break points so that end effects can be measured. [Preview Abstract] |
Tuesday, November 20, 2007 1:19PM - 1:32PM |
NM.00009: Experimental analysis of the Strato-rotational Instability in a cylindrical Couette flow Patrice Le Gal, Michael Le Bars This study is devoted to the experimental analysis of the Strato-Rotational Instability (SRI). This instability affects the classical cylindrical Couette flow when the fluid is stably stratified in the axial direction. In agreement with recent theoretical and numerical analyses, we describe for the first time in detail the destabilization of the stratified flow below the Rayleigh line (i.e. the stability threshold without stratification). We confirm that the unstable modes of the SRI are non axisymmetric, oscillatory, and take place as soon as the azimuthal linear velocity decreases along the radial direction. This new instability is relevant for accretion disks. [Preview Abstract] |
Tuesday, November 20, 2007 1:32PM - 1:45PM |
NM.00010: Radial Temperature gradient effects on the Taylor-Couette flow stability Innocent Mutabazi, Valerie Lepiller, Arnaud Prigent, Kyung-Soo Yang A radial temperature gradient imposed on the vertical Taylor-Couette system induces an axial flow that modifies the flow stability. The flow is ascending near the hot cylindrical wall while it is descending near the cold one [1]. For a flow setup with a large aspect-ratio $\Gamma = 114$ and a radius ratio $\eta=0.8$, the stability depends on the Taylor number $Ta$ related to the rotation of the inner cylinder and on the Grashof number $Gr$ related to the radial temperature gradient. We have shown that for small values of $Gr$, a convective instability is followed by an absolute instability both leading to traveling inclined vortices at $Ta_c$. For large values of $Gr$, the onset leads to an absolute instablilty with large traveling inclined vortices filling the whole system. We have established a state diagram in the parameter space $Gr,Ta$. The spatio-temporal properties of the different patterns observed in this parameter space are described. In particular we have found that the temperature gradient increases the size of vortices. The thermal effects disappear for large values for a value of the Richardson number $Ri=0.33$. Numerical simulations of the corresponding Boussinesq-Oberbeck equations provide results in a good agreement with experiments. [Preview Abstract] |
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