Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session L11: Convection and BuoyancyDriven Flows: Turbulence 
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Chair: Najmeh Foroozani, The Abdus Salam ICTP Room: 111 
Monday, November 23, 2015 4:05PM  4:18PM 
L11.00001: Reorientations of the large scale flow in turbulent convection with cubic confinement Najmeh Foroozani, Joseph Niemela, Vincenzo Armenio, Katepalli Sreenivasan Largeeddy simulations (LES) of turbulent RayleighB\'{e}nard convection were conducted with a fluid of Prandtl number $Pr=0.7$ in a fully three dimensional cubic confinement of characteristic widthtoheight aspect ratio unity for $Ra$ = $10^6$ and $10^8$. The model solves the unsteady NavierStokes equations under the Boussinesq approximation, using a dynamic Smagorinsky model with a Lagrangian averaging technique for the subgrid scale terms. Under fully developed conditions the flow topology is characterized by a large scale circulation (LSC) or mean wind developing in a plane containing one of the diagonals of the cell, while two counterrotating vortices develop in the other diagonal plane, resulting in inflow at the midplane. This flow structure is not stable in time, undergoing nonperiodic reorientation or switching between the two diagonal planes. The timeinterval over which the flow maintains a particular orientation is not constant. We contrast the threedimensional timeaveraged flow structures with single point measurements (timeseries) to shed light on the dynamics of the reorientations. We observe that as $Ra$ increases the LSC becomes more robust and attains a more squarishlike shape. [Preview Abstract] 
Monday, November 23, 2015 4:18PM  4:31PM 
L11.00002: Azimuthal diffusion of the largescale circulation of turbulent RayleightB\'enard convection Xiaozhou He, Dennis P. M. van Gils, Eberhard Bodenschatz, Guenter Ahlers We present measurements of the azimuthal orientation $\theta_0(t)$ of the largescale circulation (LSC) of turbulent RayleightB\'enard convection. The sample was a cylinder with height and diameter equal to 1.12 m. We used compressed SF$_6$ gas at pressures up to 19 bars as the fluid. The measurements covered the Rayleighnumber range $10^{12} \leq Ra \leq 10^{14}$ at a Prandtl number $Pr \simeq 0.80$. We found that the preferred orientation of the LSC upflow was aligned to the West, consistent with Earth's Coriolis force. The LSC azimuthal dynamics was diffusive, driven by the smallscale turbulent fluctuations. For $Ra\leq 10^{13}$ the Reynolds number $Re^{\dot{\theta}}$ based on the azimuthal diffusivity had a $Ra$ dependence similar to that seen for $10^{9} \leq Ra \leq 10^{11}$ and $Pr=4.38$. The $Pr$ dependence $Re^{\dot{\theta}} \propto Pr^{\alpha}$ with $\alpha \simeq 1.2$ was the same as that found for the Reynolds number based on the rootmeansquare fluctuation velocity in the interior bulk flow. For $Ra = Ra^*_1 \simeq 2\times10^{13}$ $Re^{\dot{\theta}}$ showed the ultimatestate transition and for $Ra \geq Ra^*_2 \simeq 8\times10^{13}$ it had a $Ra$ dependence with an exponent of $0.40 \pm 0.02$. [Preview Abstract] 
Monday, November 23, 2015 4:31PM  4:44PM 
L11.00003: Fluctuations of entropy production rate in turbulent thermal convection Francesco Zonta, Sergio Chibbaro We use Direct Numerical Simulation (DNS) to compute the entropy production rate ($\sigma$) in turbulent thermal convection. The overall entropy production rate is measured injecting a large number of pointwise lagrangian tracers within the flow and simultaneously sampling velocity and temperature fields along the tracers trajectory. For an isolated system, classical thermodynamics prescribes that $\sigma$ always increases until equilibrium. However, we show here that the entropy production rate is characterized by large fluctuations and becomes often negative. We also discuss the fluctuations of $\sigma$ averaged over a time lag $\tau$ in the framework of the fluctuation theorem. [Preview Abstract] 
Monday, November 23, 2015 4:44PM  4:57PM 
L11.00004: Quantifying RayleighBenard convection via a symmetry approach HongYue Zou, Xi Chen, Yun Bao, Fazle Hussain, ZhenSu She We apply our recent symmetrybased theory of wall bounded turbulent flow  WBT  (i.e. channel, pipe and TBL) to study turbulent RayleighBenard convection (RBC), which yields a multilayer description of both mean velocity and temperature profile in the vertical direction. Close analogy to the WBT is developed in terms of two order functions, i.e. a momentum stress length function and a thermal diffusion function. Using the multilayer formulas, the predictions are in quantitative agreement with DNS and experimental data for the Rayleighnumber (\textit{Ra}) covering seven decades. In particular, a thermal buffer layer is predicted in accordance with previously postulated mixing zone which follows a \textit{Ra}$^{1/7}$ scaling. Recently observed logarithmic profile of the mean temperature is reproduced, and the Radependence of the log profile is explained. The nonhomogenous effects in the horizontal direction of the RBC cell are also characterized by slight variations of the multilayer parameters (i.e. layer thicknesses), influenced by the plumes and corner vortex in the flow. Thus, the turbulent RBC shares a similar multilayer structure with the canonical wallbounded flows whose mean profiles are quantified here for the first time. [Preview Abstract] 
Monday, November 23, 2015 4:57PM  5:10PM 
L11.00005: Forced Convection from Square Cylinder Placed Near a Wall Using Variable Resolution Turbulence Modelling Pritanshu Ranjan, Anupam Dewan The effect of wall proximity on flow and heat transfer around a square cylinder placed inside a channel is numerically investigated. This flow configuration is a fundamental problem and is widely encountered in several engineering applications. The presence of wall close to the cylinder can alter the shedding process and this in turn can affect the thermal transport in the wake region. Many researchers have studied this phenomenon experimentally but the heat transfer characteristics around a square cylinder placed inside a channel still remain an open question. We present here an insight into this problem. The simulations were carried out for a Reynolds number of 37,000 (based on cylinder diameter, D) and as a function of gap height, G/D, at different blockage ratios. A variable resolution modelling approach (PANS SST k$\omega$ model) was used to study turbulence structures. The results are presented in terms of pressure coefficient, drag coefficient, thermal fluctuations and local and average Nusselt number (Nu). The results obtained showed that, for $G/D < 0.5$ very weak shedding process at random time intervals occurs suggesting the suppression of vortex shedding due to wall. Thus, the local and average Nu decrease as the cylinder is moved towards wall at all blockage ratios. [Preview Abstract] 
Monday, November 23, 2015 5:10PM  5:23PM 
L11.00006: An analysis of spatially varying turbulent Prandtl number in a flow with local acceleration and deceleration Eunbum Jung, Wook Lee, Seongwon Kang, Gianluca Iaccarino The turbulent Prandtl number (Pr$_{t}$) is an important parameter in turbulent flows used in many engineering models for heat transfer. In the present study, spatial variation of Pr$_{t}$ in a wallbounded turbulent flow is investigated using DNS. We derived a form of Pr$_{t}$ applicable to a general flow configuration, using the leastsquare method in a manner consistent with the turbulent viscosity model in LES. For a flow subject to local acceleration and deceleration induced by the wall geometry, we performed a parametric study for the Reynolds number, Prandtl number and a geometric factor using DNS. A comparison of the data from DNS and RANS with a constant Pr$_{t}$ indicates the potential of improved RANS predictions using the present variable Pr$_{t}$ subject to the local flow field. Also, it is observed that the local pressure gradient has an important effect on the Pr$_{t}$ field. From the flow statistics, a few flow variables showing higher correlations with Pr$_{t}$ are identified. An elementary model for Pr$_{t}$ is devised, and used for RANS prediction producing a more accurate prediction of the heat transfer rate. [Preview Abstract] 
Monday, November 23, 2015 5:23PM  5:36PM 
L11.00007: Effects of Natural Convection on the NearWall Turbulence in Unstably Stratified Turbulent Channel Flows Samir Sid, Vincent Terrapon, Yves Dubief Results of direct numerical simulation of turbulent channel flows under unstable stratification are reported. Two Reynolds number are considered: $\mathrm{Re}_\tau = 180, 395$ and the Rayleigh number ranges between $\mathrm{Ra} = [10^6  10^9]$. The Prandtl number is set to 1. The channel is periodic in both streamwise and spanwise directions and nonslip/isothermal boundary conditions are imposed at the walls. The temperature difference between the walls is set so that the stratification is unstable and the coupling between temperature and momentum is achieved using the Boussinesq approximation. The dependency of the typical large scale convective structures on both Reynolds and Rayleigh numbers are investigated through cross flow sectional statistics and instantaneous flow field visualizations. Moreover, the effects of the natural convection on the coherent structures associated to the cycle of wallbounded turbulence (Jimenez, \textit{et al.} JFM 1999), namely velocity streaks and streamwise vortices, are examined. Finally, macroscopic quantities such as friction coefficient and Nusselt number are reported as a function of the Rayleigh number and are compared for both Reynolds numbers. [Preview Abstract] 
Monday, November 23, 2015 5:36PM  5:49PM 
L11.00008: Thermal Convection From a Minimal Flow Unit to a Wide Fluid Layer Curtis Hamman, Parviz Moin The computations of the ``minimal channel'' by Jim\'enez \& Moin (1991, JFM) provided a conceptual framework and building block from which to study the structure of nearwall turbulence driven by mean shear. Mean buoyancy, on the other hand, can sustain a vigorous field of very large eddies whose horizontal extent can extend across many full channel heights. We examine the extent to which a flow model consisting of a finite periodic array of such structures can successfully predict certain turbulence statistics in thermal convection with and without a mean flow in very largeaspect ratio channels. [Preview Abstract] 
Monday, November 23, 2015 5:49PM  6:02PM 
L11.00009: Largeeddy simulation of bubbledriven plume in stably stratified flow. Di Yang, Bicheng Chen, Scott Socolofsky, Marcelo Chamecki, Charles Meneveau The interaction between a bubbledriven plume and stratified water column plays a vital role in many environmental and engineering applications. As the bubbles are released from a localized source, they induce a positive buoyancy flux that generates an upward plume. As the plume rises, it entrains ambient water, and when the plume rises to a higher elevation where the stratificationinduced negative buoyancy is sufficient, a considerable fraction of the entrained fluid detrains, or peels, to form a downward outer plume and a lateral intrusion layer. In the case of multiphase plumes, the intrusion layer may also trap weakly buoyant particles (e.g., oil droplets in the case of a subsea accidental blowout). In this study, the complex plume dynamics is studied using largeeddy simulation (LES), with the flow field simulated by hybrid pseudospectral/finitedifference scheme, and the bubble and dye concentration fields simulated by finitevolume scheme. The spatial and temporal characteristics of the buoyant plume are studied, with a focus on the effects of different bubble buoyancy levels. The LES data provide useful mean plume statistics for evaluating the accuracy of 1D engineering models for entrainment and peeling fluxes. Based on the insights learned from the LES, a new continuous peeling model is developed and tested. [Preview Abstract] 
Monday, November 23, 2015 6:02PM  6:15PM 
L11.00010: Energy spectrum of stablystratified and convective turbulent flows Mahendra Verma, Abhishek Kumar In the inertial range of fluid turbulence, the energy flux is constant, while the energy spectrum scales as $k^{5/3}$ ($k$=wavenumber). The buoyancy however could change the phenomenology dramatically. Bolgiano and Obukhov (1959) had conjectured that stably stratified flows (as in atmosphere) exhibits a decrease in the energy flux as $k^{4/5}$ due to the conversion of kinetic energy to the potential energy, consequently, the energy spectrum scales as $k^{11/5}$. We show using detailed numerical analysis that the stably stratified flows indeed exhibit $k^{11/5}$ energy spectrum for Froude numbers Fr near unity. The flow becomes anisotropic for small Froude numbers. For weaker buoyancy (large Fr), the kinetic energy follows Kolmogorov's spectrum with a constant energy flux. However, in convective turbulence, the energy flux is a nondecreasing function of wavenumber since the buoyancy feeds positively into the kinetic energy. Hence, the kinetic energy spectrum is Kolmogorovlike ($k^{5/3}$) or shallower.\footnote{A. Kumar, A. G. Chatterjee, and M. K. Verma, PRE, {\bf 90}, 023016 (2014)} We also demonstrate the above scaling using a shell model of buoyancydriven turbulence.\footnote{A. Kumar and M. K. Verma, PRE, {\bf 91}, 053005 (2015)} [Preview Abstract] 

L11.00011: ABSTRACT WITHDRAWN 
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