Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session Q34: Stratified Flows and Thermal Instabilities |
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Chair: Colm-Cille Caulfield, University of Cambridge Room: Georgia World Congress Center B406 |
Tuesday, November 20, 2018 12:50PM - 1:03PM |
Q34.00001: Layer formation and relaminarisation in plane Couette flow with spanwise stratification C. P. Caulfield, D. Lucas, R. R. Kerswell We investigate the dynamics of stably-stratified plane Couette flow at high Reynolds number with gravity oriented in the spanwise direction. We observe near-wall layering and associated new mean flows in the form of large scale spanwise-flattened streamwise rolls. The layers exhibit the expected buoyancy scaling l_{z} ~ U/N where U is a typical horizontal velocity scale and N is the buoyancy frequency. We associate the new coherent structures with a stratified modification of the well-known large scale secondary flow in (unstratified) plane Couette flow and find that the possibility of the transition to sustained turbulence is controlled by the relative size of this buoyancy scale to the spanwise spacing of the streaks. |
Tuesday, November 20, 2018 1:03PM - 1:16PM |
Q34.00002: The linear instability of the stratified plane Couette flow Michael Le Bars, Giulio Facchini, Benjamin Favier, Patrice Le Gal, Meng Wang We present the stability analysis of a plane Couette flow, stably stratified in the vertical direction orthogonally to the horizontal shear. We first perform the linear stability analysis of the flow in a confined domain in the cross-stream direction. The flow becomes unstable when shear and stratification are of the same order (i.e. Fr~1) and above a moderate value of the Reynolds number Re~700. The instability results from a resonance mechanism already known in the context of channel flows, e.g. in the non-stratified plane Couette flow in shallow water. The result is confirmed by fully nonlinear direct numerical simulations. We also report the study of a laboratory flow generated by a transparent belt entrained by two vertical cylinders and immersed in a tank filled with salty water linearly stratified in density. We observe the emergence of a robust spatio-temporal pattern close to the threshold indicated by linear analysis, and explore the accessible part of the stability diagram. With the support of numerical simulations, we conclude that the observed pattern is a signature of the same instability predicted by the linear theory, although modified due to streamwise confinement. |
Tuesday, November 20, 2018 1:16PM - 1:29PM |
Q34.00003: Linear instability analysis of the onset of thermal convection in an Ekman Couette-flow Ruben Avila, Diana Perez The onset of thermal convection of a Boussinesq fluid in a plane layer with rotation and shear is investigated. The boundaries of the layer are parallel to the x-y plane of the Cartesian coordinate system. The layer rotates at a constant angular velocity around the z axis. The fluid layer is sheared by moving the lower and upper boundaries parallel to themselves with constant velocity -U and U respectively. The temperature of the lower boundary is higher than the temperature of the upper boundary. Due to the physical situation, the basic state of the system has a linear temperature profile and a two dimensional Ekman-Couette flow. The Orr-Sommerfeld type equations for the perturbations of the vertical velocity, temperature and vorticity, are formulated in terms of the six parameters (the wave number, the angle of the steady convective rolls, and the Rayleigh, Taylor, Reynolds and Prandtl numbers) that govern the system under investigation. The linear stability equations are solved by using the Tau-Chebyshev spectral numerical method, taking into account no slip boundary conditions. We present, for a fluid with Prandtl number equal to 0.7 and at Taylor numbers up to 200, the neutral stability curves for transverse, longitudinal and oblique convective rolls. |
Tuesday, November 20, 2018 1:29PM - 1:42PM |
Q34.00004: Experimental and numerical study of the flow produced in a vertical Taylor-Couette system submitted to a large radial temperature gradient Arnaud Prigent, Clément Savaro, Changwoo Kang, Innocent Mutabazi The Taylor-Couette system has long been studied as a model for the study of the transition to turbulence in closed flows. In realistic situations, it is often necessary to take into account the presence of thermal effects. Here we describe and compare the results of experimental and numerical studies of the water flow produced in a Taylor-Couette system submitted to a large radial temperature gradient. Our system is composed of two vertical coaxial cylinders maintained at different temperatures. The inner cylinder is rotated whereas the outer one is at rest. The flow can be described by Ta, Gr and Pr: the Taylor, Grashof and Prandtl numbers. As soon as a radial temperature gradient is imposed between the cylinders, the flow takes the form of a vertical convective cell. When the inner cylinder starts to rotate, the circular Couette flow is added. Then, when the rotation of the inner cylinder is further increased and the Taylor number reaches a critical value which depends on Gr, this base flow is destabilized and leads to different states. For |Gr|>800, the pattern has a low frequency time modulation. For |Gr|>2500 , as soon as the Taylor number is slightly increased above its critical value, a pattern called solitary wave appears on the background of the modulated spiral. |
Tuesday, November 20, 2018 1:42PM - 1:55PM |
Q34.00005: The Front Condition for Non-Boussinesq Gravity Currents Jim N McElwaine, Nathan Alexander Konopliv, Eckart Heinz Meiburg Many geophysical flows such as powder snow avalanches and turbidity currents are particle-laden gravity currents in which the particles are largely or wholly suspended by fluid turbulence. Despite years of study there is still controversy about the appropriate front condition at high Reynolds number. We describe a theory that reconciles the approaches of von Karman and Benjamin settling the controversy. |
Tuesday, November 20, 2018 1:55PM - 2:08PM |
Q34.00006: Onset of double-diffusive convection in a near-critical fluid Zhan-Chao Hu, Stephen H Davis, Xin-Rong Zhang Near the liquid-vapor critical point, the physical properties of binary fluids exhibit large variations, whose effects on the onset of double-diffusive convection are studied. The physical model is an infinite horizontal layer of near-critical binary fluid bounded by two rigid walls, with Dirichlet boundary conditions for both temperature and concentration. A numerical linear stability analysis is conducted, showing that the vertical symmetry is broken, irregular penetrative instability occurs, and cat’s eye patterns are identified in the fingering and oscillatory regime, respectively. A new parameter Θ is defined which measures how the variations of physical properties influence flow fields. It is seen through numerical simulations that the Boussinesq approximation with constant physical properties has limited applicability, and that the Boussinesq equations with variable properties and density will describe all features seen. This conclusion is based on comparisons with simulations on the fully compressible, variable properties system. |
Tuesday, November 20, 2018 2:08PM - 2:21PM |
Q34.00007: Stably-stratified wall-bounded turbulence Francesco Zonta, Alfredo Soldati Stably-stratified wall-bounded turbulence is commonly encountered in many industrial and natural processes. |
Tuesday, November 20, 2018 2:21PM - 2:34PM |
Q34.00008: Investigation of mean scalar characteristics of vertical buoyant gas plume inside a gas chamber with multiple sensors Sudheer Reddy Bhimireddy, Daniel Brun, Kiran Bhaganagar |
Tuesday, November 20, 2018 2:34PM - 2:47PM |
Q34.00009: Abstract Withdrawn Heat transfer enhancement in free convection systems is a challenge for many industrial processes, such as nuclear reactors cooling, electronic circuits or building's ventilation. The key factor to succeed is to destabilize the thermal boundary layers in order to enhance the temperature gradient at the walls. Most of the published studies concern the effect of thermal perturbations in differentially heated cavities (DHC). In this work, we numerically compare the influence of various configurations of passive actuators positioned at the walls of a DHC such as cylinders, cubes, and arrays of them. The influence of their size and shape is analized. Various Rayleigh numbers (or temperature difference) are considered. These obstacles perturb and promote the transition of the boundary layers. The selected configuration is a DHC with aspect ratio 1:4 (height : width), filled with air (Prandtl number = 0.71). Direct numerical simulations of the three-dimensional incompressible Navier-Stokes-Boussinesq equations, are performed using the spectral element method with a P_{n}-P_{n-2} formulation, with polynomial order 7, written in the open source code Nek5000. |
Tuesday, November 20, 2018 2:47PM - 3:00PM |
Q34.00010: Effect of finite walls thicknesses and thermal conductivities on the Rayleigh convection in a viscoelastic Jeffreys fluid layer Ildebrando Perez-Reyes, Luis Antonio Davalos-Orozco, Nestor Gutierrez-Mendez The problem of thermal convection in a viscoelastic Jeffreys fluid layer is extended to include the fluid layer thickness and that of the walls along with its thermal conductivities. The aim is to show the bridge between two familiar cases of thermal convection: insulating (constant heat flux) and perfect thermal conducting walls (fixed temperature). |
Tuesday, November 20, 2018 3:00PM - 3:13PM |
Q34.00011: Flow instability of natural convection in horizontal annuli under non-Oberbeck-Boussinesq condition Yuhui Cao The hydrodynamic and thermal instabilities in the natural convection in horizontal concentric annuli have been studied extensively under the Oberbeck-Boussinesq (constant-property) assumption. However, the effects of the variable properties on the instabilities of these systems have not been fully understood. In this work, numerical simulations and theoretical analysis are performed to investigate the flow instability under non-Oberbeck-Boussineq conditions for a wide range of the temperature difference ratios and radius ratios. A variable-property-based lattice Boltzmann flux solver is used to account for the total variation in fluid properties. The results demonstrate that the variable property effect and the initial condition effect play important roles in determining the flow pattern, and that the significance of both effects depends strongly and non-monotonically on the temperature difference ratio. |
Tuesday, November 20, 2018 3:13PM - 3:26PM |
Q34.00012: Thin plate fluttering by thermally induced buoyancy effects Tomas Solano, Kourosh Shoele The canonical problem of flow-induced flutter of a thin flexible plate is revisited, with an emphasis on the thermally induced buoyancy effects on the dynamics and thermal characterization of the system. An immersed boundary method is used to simulate mixed convection of a heated 2D inextensible and flexible thin plate. The bending stiffness, Richardson number, and Reynolds number are chosen asthe characteristic parameters of the system. The dynamic and thermal responses of the plate are examinedover a wide range of the characteristic parameters, and it is shownthat the stability boundary growth rate of the flapping dynamics dramatically increases after a particular threshold Richardson number due to the mode switching behavior. The appearance of higher oscillatory modes and a shift in the nodes of the dominant oscillatory mode are found to also be correlated to the observed higher Nusselt numbers. |
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