Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session H10: Convection and Buoyancy Driven Flows: Theory I 
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Sponsoring Units: DFD GPC Chair: Olga Shishkina, Max Planck Institute for Dynamics and SelfOrganization Room: B118119 
Monday, November 21, 2016 10:40AM  10:53AM 
H10.00001: Hydrodynamic stability in the presence of a stochastic source: convection as a case study Jared Whitehead, Juraj Foldes, Nathan GlattHoltz, Geordie Richards We quantify the stability of a conductive state in RayleighBenard convection when the fluid is driven not only by an enforced temperature gradient, but also by a mean zero stochastic (in time) internal heat source, a modeled system applicable to situations such as convection in stars, nuclear reactors, and the earth's mantle. We explore the effects of such a mean zero forcing on the onset of convection. The methods applied to the convection problem here, are applicable to any other question of hydrodynamic stability where a stochastic forcing is present. [Preview Abstract] 
Monday, November 21, 2016 10:53AM  11:06AM 
H10.00002: Temperature variance profiles of turbulent thermal convection at high Rayleigh numbers Xiaozhou He, Eberhard Bodenschatz, Guenter Ahlers We present measurements of the Nusselt number $Nu$, and of the temperature variance $\sigma^2$ as a function of vertical position $z$, in turbulent RayleighB\'enard convection of two cylindrical samples with aspect ratios (diameter D/height L) $\Gamma = 0.50$ and $0.33$. Both samples had $D = 1.12$ m but different $L$. We used compressed SF$_6$ gas at pressures up to 19 bars as the fluid. The measurements covered the Rayleighnumber range $10^{13} < Ra < 5 \times 10^{15}$ at a Prandtl number $Pr \simeq 0.80$. Near the side wall we found that $\sigma^2$ is independent of $Ra$ when plotted as a function of $z/\lambda$ where $\lambda \equiv L/(2Nu)$ is a thermal boundarylayer thickness. The profiles $\sigma^2(z/\lambda)$ for the two $\Gamma$ values overlapped and followed a logarithmic function for $20 \alt z/\lambda \alt 120$. With the observed ``1"scaling of the temperature power spectra and on the basis of the PerryTownsend similarity hypothesis, we derived a fitting function $\sigma^2 = p_1\ln(z/\lambda) + p_2 + p_3(z/\lambda)^{0.5}$ which describes the $\sigma^2$ data up to $z/\lambda \simeq 1500$. [Preview Abstract] 
Monday, November 21, 2016 11:06AM  11:19AM 
H10.00003: Measured temperature fluctuations and Reynolds number in turbulent RayleighB\'enard convection with varying roughness size Yichao Xie, Keqing Xia We present measurements of the temperature fluctuations $\sigma_T$ and of the Reynolds number Re in turbulent RayleighB\'enard convection in cylindrical cell with pyramidshaped rough top and bottom plates. To study the effects of roughness size, we varied a roughness parameter $\lambda$, defined as a single roughness height h (kept at a constant of 8 mm) over its base width d, from 0.5 to 4.0. Fluorinert Liquid FC770 was used as the working fluid with the Rayleigh number Ra varying from $4.49 \times 10^{9}$ to $9.94 \times 10^{10}$ and Prandtl number Pr kept at 23.34. It is found that $\sigma_T$ in both cell center and sidewall increases dramatically with $\lambda$. The scaling exponent of the normalized $\sigma_T$ with respect to $Ra$ increases from $0.16$ to $0.09$ at cell center and $0.23$ to $0.08$ near sidewall when $\lambda$ is increased from $0.5$ to $4.0$. The Reynolds number $Re$ based on the circulation time of the largescale circulation (LSC) also increases with $\lambda$, suggesting a faster LSC. The scaling exponent of $Re$ with respect to $Ra$ increases from 0.47 to 0.55 with $\lambda$ increased from $0.5$ to $4.0$. The study reveals that the flow and temperature fluctuations are very sensitive to the perturbation induced by rough plate with vary $\lambda$. [Preview Abstract] 
Monday, November 21, 2016 11:19AM  11:32AM 
H10.00004: Scaling Analysis of Temperature Variability Between a Rotating Cylinder and a Turbulent Buoyant Jet Caelan Lapointe, Nicholas T. Wimer, Torrey R.S. Hayden, Jason D. Christopher, Gregory B. Rieker, Peter E. Hamlington Vortex shedding from a cylinder is a canonical problem in fluid dynamics and is a phenomenon whose behavior is well documented for a wide range of Reynolds numbers. Industrial processes, by contrast, often have many moving parts that may also be exposed to high temperatures, resulting in highly complex flow fields. This complexity can, in turn, introduce velocity and temperature variations that may be undesirable for a particular industrial process. In this study, we specifically seek to understand and parameterize temperature variability between a rotating cylinder and a hightemperature turbulent buoyant jet. The relevance of this configuration for industrial processing is outlined, and velocity and temperature fields between the jet and cylinder are obtained using large eddy simulations (LES). In the LES, key parameters such as the angular velocity and diameter of the cylinder, the dimensions, velocity, and temperature of the turbulent buoyant jet, and the distance between the cylinder and the jet are varied. The resulting LES results are then used to develop scaling relationships between temperature variance near the cylinder and other problem parameters. Such scaling relations will be highly beneficial for the estimation of temperature variations in industrial applications. [Preview Abstract] 
Monday, November 21, 2016 11:32AM  11:45AM 
H10.00005: Temperature fluctuation in RayleighB\'enard convection: Logarithmic vs powerlaw$^1$ YuHao He, KeQing Xia We present an experimental measurement of the rms temperature ($\sigma_T$) profile in two regions inside a large aspect ratio ($\Gamma=4.2$) rectangular RayleighB\'enard convection cell. The Rayleigh number ($Ra$) is from $3.2 \times 10^7$ to $1.9 \times 10^8$ at fixed Prandtl number ($Pr=4.34$). It is found that, in one region, where the boundary layer is sheared by a largescale wind, $\sigma_T$ versus the distance ($z$) above the bottom plate, obeys power law over one decade, whereas in another region, where plumes concentrate and move upward (plumeejection region), the profile of $\sigma_T$ has a logarithmic dependence on $z$. When normalized by a typical temperature scale $\theta_*$, the profiles of $\sigma_T$ at different Rayleigh numbers collapse onto a single curve, indicating a university of $\sigma_T$ profile with respect to $Ra$. 1. This work is supported by the Hong Kong Research Grant Council under grant number N\_CUHK437/15. [Preview Abstract] 
Monday, November 21, 2016 11:45AM  11:58AM 
H10.00006: The scaling transition between Nu number and boundary thickness in RB convection HongYue Zou, Xi Chen, ZhenSu She A quantitative theory is developed for the vertical mean temperature profile (MTP) and mean velocity profile (MVP) in turbulent RayleighBenard convection(RBC), which explains the experimental and numerical observations of logarithmic law in MTP and the coefficient A varying along the Ra. Based on a new meanfield approach via symmetry analysis to wallbounded turbulent flows£¬it yields accurate scaling of the sublayer buffer layer and loglayer over a wide range of Rayleigh number£¬and gives an explanation of their physical mechanism. In particular, based on the scaling of multilayer thickness for mean temperature and velocity, we first prove that the coefficient A follows a 0.121 scaling, which agrees well with the experimental data, and the scaling transition of Nu from 1/3 to 0.38 is due to the thickness variation of the multilayer. The new explanation of mean temperature logarithmic law is that the effect of inverse pressure gradient (LSC) driving the plume to side wall, which yields the similarity between vertical temperature transport and vertical momentum. [Preview Abstract] 
Monday, November 21, 2016 11:58AM  12:11PM 
H10.00007: Adjoint analyses of enhanced solidification for shape optimization in conjugate heat transfer problem Kenichi Morimoto, Hidenori Kinoshita, Yuji Suzuki In the present study, an adjointbased shapeoptimization method has been developed for designing extended heat transfer surfaces in conjugate heat transfer problems. Here we specifically consider heat conductiondominated solidification problem under different thermal boundary conditions: (i) the isothermal condition, and (ii) the conjugate condition with thermal coupling between the solidified liquid and the solid wall inside the domain bounded by the extended heat transfer surface. In the present shapeoptimization scheme, extended heat transfer surfaces are successively refined in a local way based on the variational information of a cost functional with respect to the shape modification. In the computation of the developed scheme, a meshless method is employed for dealing with the complex boundary shape. For highresolution analyses with boundaryfitted node arrangement, we have introduced a bubblemesh method combined with a highefficiency algorithm for searching neighboring bubbles within a cutoff distance. The present technique can be easily applied to convection problems including high Reynolds number flow. We demonstrate, for the isothermal boundary condition, that the present optimization leads to treelike fin shapes, which achieve the temperature field with global similarity for different initial fin shapes. We will also show the computational results for the conjugate condition, which would regularize the present optimization due to the finefficiency effect. [Preview Abstract] 
Monday, November 21, 2016 12:11PM  12:24PM 
H10.00008: Boundary layer fluctuations and their effects on mean and variance temperature profiles in turbulent RayleighB{\'e}nard convection Yin Wang, Xiaozhou He, Penger Tong We report simultaneous measurements of the mean temperature profile $\theta(z)$ and temperature variance profile $\eta(z)$ near the lower conducting plate of a specially designed quasitwodimensional cell for turbulent RayleighB{\'e}nard convection. The measured $\theta(z)$ is found to have a universal scaling form $\theta(z/\delta)$ with varying thermal boundary layer (BL) thickness $\delta$, and its functional form agrees well with the recently derived BL equation by Shishkina et al. The measured $\eta(z)$, on the other hand, is found to have a scaling form $\eta(z/\delta)$ only in the nearwall region with $z/\delta < 2$. Based on the experimental findings, we derive a new BL equation for $\eta(z/\delta)$, which is in good agreement with the experimental results. The new BL equations thus provide a common framework for understanding the effect of BL fluctuations. *This work was supported by the Research Grants Council of Hong Kong SAR and by the China Thousand Young Talents Program. [Preview Abstract] 
Monday, November 21, 2016 12:24PM  12:37PM 
H10.00009: Heat and momentum transport scalings in vertical convection Olga Shishkina For vertical convection, where a fluid is confined between two differently heated isothermal vertical walls, we investigate the heat and momentum transport, which are measured, respectively, by the Nusselt number $Nu$ and the Reynolds number $Re$. For laminar vertical convection we derive analytically the dependence of $Re$ and $Nu$ on the Rayleigh number $Ra$ and the Prandtl number $Pr$ from our boundary layer equations and find two different scaling regimes: $Nu\sim~Pr^{1/4}Ra^{1/4}$, $Re\sim~Pr^{1/2}Ra^{1/2}$ for $Pr\ll1$ and $Nu\sim~Pr^{0}Ra^{1/4}$, $Re\sim~Pr^{1}Ra^{1/2}$ for $Pr\gg1$. Direct numerical simulations for $Ra$ from $10^5$ to $10^{10}$ and $Pr$ from 0.01 to 30 are in excellent ageement with our theoretical findings and show that the transition between the regimes takes place for $Pr$ around 0.1. We summarize the results from Shishkina, Phys. Rev. E 93 (2016) 051102R and present new theoretical and numerical results for transitional and turbulent vertical convection. [Preview Abstract] 
(Author Not Attending)

H10.00010: Gravity current jump conditions, revisited Marius Ungarish, Andrew J Hogg Consider the flow of a highReynoldsnumber gravity current of density $\rho_c$ in an ambient fluid of density $\rho_a$ in a horizontal channel $z \in [0,H]$, with gravity in $z$ direction. The motion is often modeled by a twolayer formulation which displays jumps (shocks) in the height of the interface, in particular at the leading front of the dense layer. Various theoretical models have been advanced to predict the dimensionless speed of the jump, $Fr=U/\sqrt{g' h}$; $g', h$ are reduced gravity and jump height. We revisit this problem and using the NavierStokes equations, integrated over a control volume embedding the jump, derive balances of mass and momentum fluxes. We focus on understanding the closures needed to complete this model and we show the vital need to understand the pressure head losses over the jump, which we show can be related to the vorticity fluxes at the boundaries of the control volume. Our formulation leads to two governing equations for three dimensionless quantities. Closure requires one further assumption, depending on which we demonstrate that previous models for gravity current fronts and internal bores can be recovered. This analysis yield new insights into existing results, and also provides constraints for potential new formulae. [Preview Abstract] 
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