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Goldstein, R. J., A. S. Fleischer et P. B. Hogerton. « Electrochemical Mass Transfer at Moderate Rayleigh Numbers ». Journal of Heat Transfer 123, no 5 (20 mars 2001) : 1015–17. http://dx.doi.org/10.1115/1.1392991.
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Martorell, Ingrid, Joan Herrero et Francesc X. Grau. « Natural convection from narrow horizontal plates at moderate Rayleigh numbers ». International Journal of Heat and Mass Transfer 46, no 13 (juin 2003) : 2389–402. http://dx.doi.org/10.1016/s0017-9310(03)00010-3.
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Puigjaner, D., J. Herrero, C. Simó et F. Giralt. « From steady solutions to chaotic flows in a Rayleigh–Bénard problem at moderate Rayleigh numbers ». Physica D : Nonlinear Phenomena 240, no 11 (mai 2011) : 920–34. http://dx.doi.org/10.1016/j.physd.2011.01.007.
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Pallares, J., F. X. Grau et Francesc Giralt. « Flow transitions in laminar Rayleigh–Bénard convection in a cubical cavity at moderate Rayleigh numbers ». International Journal of Heat and Mass Transfer 42, no 4 (février 1999) : 753–69. http://dx.doi.org/10.1016/s0017-9310(98)00192-6.
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Pallares, J., M. P. Arroyo, F. X. Grau et F. Giralt. « Experimental laminar Rayleigh-Bénard convection in a cubical cavity at moderate Rayleigh and Prandtl numbers ». Experiments in Fluids 31, no 2 (1 août 2001) : 208–18. http://dx.doi.org/10.1007/s003480100275.
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Padilla, E. L. M., R. Campregher et A. Silveira-Neto. « NUMERICAL ANALYSIS OF THE NATURAL CONVECTION IN HORIZONTAL ANNULI AT LOW AND MODERATE Ra ». Revista de Engenharia Térmica 5, no 2 (31 décembre 2006) : 58. http://dx.doi.org/10.5380/reterm.v5i2.61852.
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The natural convection at low and moderate Rayleigh numbers (Ra) incylindrical horizontal annuli with imposed temperatures in both surfaces isnumerically studied. This flow inside concentric cylinders classic configuration has a wide range of practical and technological applications, which justifies its growing studies efforts. In this work, the governing equations are discretized by the volume finite technique over a staggered grid, with second-order accuracy in space and time. The flow pattern is presented by several Rayleigh numbers, with an analysis of the heat transfer coefficient and flow properties. Furthermore, a three-dimensional field is shown at a moderate Ra number. The results showed a good agreement with the experimental data.
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Goldstein, H. F., E. Knobloch, I. Mercader et M. Net. « Convection in a rotating cylinder. Part 1 Linear theory for moderate Prandtl numbers ». Journal of Fluid Mechanics 248 (mars 1993) : 583–604. http://dx.doi.org/10.1017/s0022112093000928.
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The onset of convection in a uniformly rotating vertical cylinder of height h and radius d heated from below is studied. For non-zero azimuthal wavenumber the instability is a Hopf bifurcation regardless of the Prandtl number of the fluid, and leads to precessing spiral patterns. The patterns typically precess counter to the rotation direction. Two types of modes are distinguished: the fast modes with relatively high precession velocity whose amplitude peaks near the sidewall, and the slow modes whose amplitude peaks near the centre. For aspect ratios τ ≡ d/h of order one or less the fast modes always set in first as the Rayleigh number increases; for larger aspect ratios the slow modes are preferred provided that the rotation rate is sufficiently slow. The precession velocity of the slow modes vanishes as τ → ∞. Thus it is these modes which provide the connection between the results for a finite-aspect-ratio System and the unbounded layer in which the instability is a steady-state one, except in low Prandtl number fluids.The linear stability problem is solved for several different sets of boundary conditions, and the results compared with recent experiments. Results are presented for Prandtl numbers σ in the range 6.7 ≤ σ ≤ 7.0 as a function of both the rotation rate and the aspect ratio. The results for rigid walls, thermally conducting top and bottom and an insulating sidewall agree well with the measured critical Rayleigh numbers and precession frequencies for water in a τ = 1 cylinder. A conducting sidewall raises the critical Rayleigh number, while free-slip boundary conditions lower it. The difference between the critical Rayleigh numbers with no-slip and free-slip boundaries becomes small for dimensionless rotation rates Ωh2/v ≥ 200, where v is the kinematic viscosity.
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Sameen, A., R. Verzicco et K. R. Sreenivasan. « Non-Boussinesq convection at moderate Rayleigh numbers in low temperature gaseous helium ». Physica Scripta T132 (décembre 2008) : 014053. http://dx.doi.org/10.1088/0031-8949/2008/t132/014053.
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Qureshi, Zafar H., et R. Ahmad. « NATURAL CONVECTION FROM A UNIFORM HEAT FLUX HORIZONTAL CYLINDER AT MODERATE RAYLEIGH NUMBERS ». Numerical Heat Transfer 11, no 2 (février 1987) : 199–212. http://dx.doi.org/10.1080/10407788708913550.
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Qureshi, Zafar, et R. Ahmad. « Natural Convection from a Uniform Heat Flux Horizontal Cylinder at Moderate Rayleigh Numbers ». Numerical Heat Transfer, Part B : Fundamentals 11, no 2 (1987) : 199–212. http://dx.doi.org/10.1080/10407798708552540.
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SILANO, G., K. R. SREENIVASAN et R. VERZICCO. « Numerical simulations of Rayleigh–Bénard convection for Prandtl numbers between 10−1 and 104 and Rayleigh numbers between 105 and 109 ». Journal of Fluid Mechanics 662 (14 septembre 2010) : 409–46. http://dx.doi.org/10.1017/s0022112010003290.
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We summarize the results of an extensive campaign of direct numerical simulations of Rayleigh–Bénard convection at moderate and high Prandtl numbers (10−1 ≤ Pr ≤ 104) and moderate Rayleigh numbers (105 ≤ Ra ≤ 109). The computational domain is a cylindrical cell of aspect ratio Γ = 1/2, with the no-slip condition imposed on all boundaries. By scaling the numerical results, we find that the free-fall velocity should be multiplied by $1/\sqrt{{\it Pr}}$ in order to obtain a more appropriate representation of the large-scale velocity at high Pr. We investigate the Nusselt and the Reynolds number dependences on Ra and Pr, comparing the outcome with previous numerical and experimental results. Depending on Pr, we obtain different power laws of the Nusselt number with respect to Ra, ranging from Ra2/7 for Pr = 1 up to Ra0.31 for Pr = 103. The Nusselt number is independent of Pr. The Reynolds number scales as ${\it Re}\,{\sim}\,\sqrt{{\it Ra}}/{\it Pr}$, neglecting logarithmic corrections. We analyse the global and local features of viscous and thermal boundary layers and their scaling behaviours with respect to Ra and Pr, and with respect to the Reynolds and Péclet numbers. We find that the flow approaches a saturation state when Reynolds number decreases below the critical value, Res ≃ 40. The thermal-boundary-layer thickness increases slightly (instead of decreasing) when the Péclet number increases, because of the moderating influence of the viscous boundary layer. The simulated ranges of Ra and Pr contain steady, periodic and turbulent solutions. A rough estimate of the transition from the steady to the unsteady state is obtained by monitoring the time evolution of the system until it reaches stationary solutions. We find multiple solutions as long-term phenomena at Ra = 108 and Pr = 103, which, however, do not result in significantly different Nusselt numbers. One of these multiple solutions, even if stable over a long time interval, shows a break in the mid-plane symmetry of the temperature profile. We analyse the flow structures through the transitional phases by direct visualizations of the temperature and velocity fields. A wide variety of large-scale circulation and plume structures has been found. The single-roll circulation is characteristic only of the steady and periodic solutions. For other regimes at lower Pr, the mean flow generally consists of two opposite toroidal structures; at higher Pr, the flow is organized in the form of multi-jet structures, extending mostly in the vertical direction. At high Pr, plumes mainly detach from sheet-like structures. The signatures of different large-scale structures are generally well reflected in the data trends with respect to Ra, less in those with respect to Pr.
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Yilmaz, Ilyas. « Parallel direct numerical simulation and analysis of turbulent Rayleigh–Bénard convection at moderate Rayleigh numbers using an efficient algorithm ». Computers & ; Fluids 213 (décembre 2020) : 104754. http://dx.doi.org/10.1016/j.compfluid.2020.104754.
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DYKO, MARK P., KAMBIZ VAFAI et A. KADER MOJTABI. « A numerical and experimental investigation of stability of natural convective flows within a horizontal annulus ». Journal of Fluid Mechanics 381 (25 février 1999) : 27–61. http://dx.doi.org/10.1017/s0022112098002948.
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A numerical and experimental study of buoyancy-driven flow in the annulus between two horizontal coaxial cylinders at Rayleigh numbers approaching and exceeding the critical values is presented. The stability of the flow is investigated using linear theory and the energy method. Theoretical predictions of the critical Rayleigh number for onset of secondary flows are obtained for a wide range of radius ratio R and are verified by comparison with results of previous experimental studies. A subcritical Rayleigh number which provides a necessary condition for global flow stability is also determined. The three-dimensional transient equations of fluid flow and heat transfer are solved to study the manifestation of instabilities within annuli having impermeable endwalls, which are encountered in various applications. For the first time, a thorough examination of the development of spiral vortex secondary flow within a moderate gap annulus and its interaction with the primary flow is performed for air. Simulations are conducted to investigate factors influencing the size and number of post-transitional vortex cells. The evolution of stable three-dimensional flow and temperature fields with increasing Rayleigh number in a large gap annulus is also studied. The distinct flow structures which coexist in the large gap annulus at high Rayleigh numbers preceding transition to oscillatory flow, including transverse vortices at the end walls which have not been previously identified, are established numerically and experimentally. The solutions for the large-gap annulus are compared to those for the moderate-gap case to clarify fundamental differences in behaviour. Heat transfer results in the form of local Nusselt number distributions are presented for both the moderate- and large-gap cases. Results from a series of experiments performed with air to obtain data for validation of the numerical scheme and further information on the flow stability are presented. Additionally, the change from a crescent-shaped flow pattern to a unicellular pattern with centre of rotation at the top of the annulus is investigated numerically and experimentally for a Prandtl number of 100. Excellent agreement between the numerical and experimental results is shown for both Prandtl numbers studied. The present work provides, for the first time, quantitative three-dimensional descriptions of spiral convection within a moderate-gap annulus containing air, flow structures preceding oscillation in a large-gap annulus for air, and unicellular flow development in a large-gap annulus for large Prandtl number fluids.
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Ötügen, M. V., et I. Namer. « Rayleigh scattering temperature measurements in a plane turbulent air jet at moderate Reynolds numbers ». Experiments in Fluids 6, no 7 (janvier 1988) : 461–66. http://dx.doi.org/10.1007/bf00196507.
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Corcione, Massimo. « Interactive free convection from a pair of vertical tube-arrays at moderate Rayleigh numbers ». International Journal of Heat and Mass Transfer 50, no 5-6 (mars 2007) : 1061–74. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2006.07.034.
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CIONI, S., S. CILIBERTO et J. SOMMERIA. « Strongly turbulent Rayleigh–Bénard convection in mercury : comparison with results at moderate Prandtl number ». Journal of Fluid Mechanics 335 (25 mars 1997) : 111–40. http://dx.doi.org/10.1017/s0022112096004491.
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An experimental study of Rayleigh–Bénard convection in the strongly turbulent regime is presented. We report results obtained at low Prandtl number (in mercury, Pr = 0.025), covering a range of Rayleigh numbers 5 × 106 < Ra < 5 × 109, and compare them with results at Pr∼1. The convective chamber consists of a cylindrical cell of aspect ratio 1.Heat flux measurements indicate a regime with Nusselt number increasing as Ra0.26, close to the 2/7 power observed at Pr∼1, but with a smaller prefactor, which contradicts recent theoretical predictions. A transition to a new turbulent regime is suggested for Ra ≃ 2 × 109, with significant increase of the Nusselt number. The formation of a large convective cell in the bulk is revealed by its thermal signature on the bottom and top plates. One frequency of the temperature oscillation is related to the velocity of this convective cell. We then obtain the typical temperature and velocity in the bulk versus the Rayleigh number, and compare them with similar results known for Pr∼1.We review two recent theoretical models, namely the mixing zone model of Castaing et al. (1989), and a model of the turbulent boundary layer by Shraiman & Siggia (1990). We discuss how these models fail at low Prandtl number, and propose modifications for this case. Specific scaling laws for fluids at low Prandtl number are then obtained, providing an interpretation of our experimental results in mercury, as well as extrapolations for other liquid metals.
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Jarvise, Richard A., et Herbert E. Huppert. « Solidification of a binary alloy of variable viscosity from a vertical boundary ». Journal of Fluid Mechanics 303 (25 novembre 1995) : 103–32. http://dx.doi.org/10.1017/s0022112095004198.
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We analyse the complete solidification from a side boundary of a finite volume of a binary alloy. Particular emphasis is placed upon the compositional stratification produced in the solid, the structure of which is determined by the competition between the rates of solidification and of laminar box filling by the fractionated fluid released at the solid/liquid interface. It is demonstrated by scaling arguments that numerical calculations performed at relatively low values of the Rayleigh and Lewis numbers may be used to describe equally well laboratory experiments previously performed at moderate Rayleigh and Lewis numbers and the high-Rayleigh-number, high-lewis-number convective regime expected during the solidification of a large magmatic body, provided that the balance between solidification and laminar box filling is maintained. This balance can be represented by a single dimensionless group of parameters. The boundary-layer analysis is extended to fluids whose viscosity is strongly dependent upon temperature and composition, and an effective viscosity is derived which may be used to describe both the magnitude and pattern of compositional stratification in the solid.
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Feldhusen, Kai, Ralf Deiterding et Claus Wagner. « A dynamically adaptive lattice Boltzmann method for thermal convection problems ». International Journal of Applied Mathematics and Computer Science 26, no 4 (1 décembre 2016) : 735–47. http://dx.doi.org/10.1515/amcs-2016-0051.
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Abstract Utilizing the Boussinesq approximation, a double-population incompressible thermal lattice Boltzmann method (LBM) for forced and natural convection in two and three space dimensions is developed and validated. A block-structured dynamic adaptive mesh refinement (AMR) procedure tailored for the LBM is applied to enable computationally efficient simulations of moderate to high Rayleigh number flows which are characterized by a large scale disparity in boundary layers and free stream flow. As test cases, the analytically accessible problem of a two-dimensional (2D) forced convection flow through two porous plates and the non-Cartesian configuration of a heated rotating cylinder are considered. The objective of the latter is to advance the boundary conditions for an accurate treatment of curved boundaries and to demonstrate the effect on the solution. The effectiveness of the overall approach is demonstrated for the natural convection benchmark of a 2D cavity with differentially heated walls at Rayleigh numbers from 103 up to 108. To demonstrate the benefit of the employed AMR procedure for three-dimensional (3D) problems, results from the natural convection in a cubic cavity at Rayleigh numbers from 103 up to 105 are compared with benchmark results.
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Motsay, R. W., K. E. Anderson et R. P. Behringer. « The onset of convection and turbulence in rectangular layers of normal liquid 4He ». Journal of Fluid Mechanics 189 (avril 1988) : 263–86. http://dx.doi.org/10.1017/s0022112088001004.
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We have carried out high-precision measurements of the heat transport in intermediate-size rectangular layers of convecting normal liquid 4He with Prandtl numbers of 0.52 and 0.70. The containers used for these experiments had horizontal dimensions, in units of the height d, of 13.4 × 5.95 (cell I) and 18.2 × 8.12 (cell II). The slopes N1 of the Nusselt curves were 0.56 and 0.70 respectively for cell I and cell II. These values are significantly lower than predictions for N1 for horizontally unbound layers, but comparable with results obtained in cylindrical containers of liquid helium with roughly the same number of convection rolls. For the two containers, the onset of the first instability after the onset of convection occurred at Rayleigh numbers R1 that were in reasonable quantitative agreement with the predictions of Busse and Clever for the skewed-varicose instability. For both containers, the transition at R1 was characterized by long transients ranging from ∼ 102 to ∼ 103 vertical-thermal-diffusion times. A decrease in the Nusselt number was also observed. As the Rayleigh number was increased above R1, a new steady state evolved and then additional transitions were observed. These transitions occurred at Rayleigh numbers labelled R2, R3,…, with a total of five transitions seen in cell I and a total of three transitions seen for cell II. The transition for each cell at R2 can be related quantitatively to the skewed-varicose instability, and the transition at R3 is associated with an oscillatory instability. For cell II, the time-dependence beginning at R3 persisted to the highest Rayleigh number studied, R = 11.7Rc. However, for container I, two more regimes of time-independent flow were observed; the last of these was at an unexpectedly high Rayleigh number of 6.7Rc. This work extends to lower Prandtl number recent studies made on moderate-size rectangular layers of convecting water and alcohol.
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Wells, Andrew J., J. S. Wettlaufer et Steven A. Orszag. « Nonlinear mushy-layer convection with chimneys : stability and optimal solute fluxes ». Journal of Fluid Mechanics 716 (30 janvier 2013) : 203–27. http://dx.doi.org/10.1017/jfm.2012.541.
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AbstractWe model buoyancy-driven convection with chimneys – channels of zero solid fraction – in a mushy layer formed during directional solidification of a binary alloy in two dimensions. A large suite of numerical simulations is combined with scaling analysis in order to study the parametric dependence of the flow. Stability boundaries are calculated for states of finite-amplitude convection with chimneys, which for a narrow domain can be interpreted in terms of a modified Rayleigh number criterion based on the domain width and mushy-layer permeability. For solidification in a wide domain with multiple chimneys, it has previously been hypothesized that the chimney spacing will adjust to optimize the rate of removal of potential energy from the system. For a wide variety of initial liquid concentration conditions, we consider the detailed flow structure in this optimal state and derive scaling laws for how the flow evolves as the strength of convection increases. For moderate mushy-layer Rayleigh numbers these flow properties support a solute flux that increases linearly with Rayleigh number. This behaviour does not persist indefinitely, however, with porosity-dependent flow saturation resulting in sublinear growth of the solute flux for sufficiently large Rayleigh numbers. Finally, we consider the influence of the porosity dependence of permeability, with a cubic function and a Carman–Kozeny permeability yielding qualitatively similar system dynamics and flow profiles for the optimal states.
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Ruiz, X., J. Pallares et F. X. Grau. « On the accuracy of the interdiffusion measurements at low and moderate Rayleigh numbers. Some computational considerations ». International Journal of Heat and Mass Transfer 53, no 19-20 (septembre 2010) : 3708–20. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2010.04.022.
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Goldstein, M. E., et Pierre Ricco. « Non-localized boundary layer instabilities resulting from leading edge receptivity at moderate supersonic Mach numbers ». Journal of Fluid Mechanics 838 (16 janvier 2018) : 435–77. http://dx.doi.org/10.1017/jfm.2017.889.
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This paper uses matched asymptotic expansions to study the non-localized (which we refer to as global) boundary layer instabilities generated by free-stream acoustic and vortical disturbances at moderate supersonic Mach numbers. The vortical disturbances produce an unsteady boundary layer flow that develops into oblique instability waves with a viscous triple-deck structure in the downstream region. The acoustic disturbances (which for reasons given herein are assumed to have obliqueness angles that are close to a certain critical angle) generate slow boundary layer disturbances which eventually develop into oblique stable disturbances with an inviscid triple-deck structure in a region that lies downstream of the viscous triple-deck region. The paper shows that both the vortically generated instabilities and the acoustically generated oblique disturbances ultimately develop into modified Rayleigh-type instabilities (which can either grow or decay) further downstream.
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Madanan, U., et R. J. Goldstein. « Thermal convection in horizontal rectangular enclosures at moderate Rayleigh numbers : Effect of sidewall conductance and aspect ratio ». International Journal of Heat and Mass Transfer 136 (juin 2019) : 178–85. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2019.02.076.
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Net, Marta, Arantxa Alonso et Juan Sánchez. « From stationary to complex time-dependent flows at moderate Rayleigh numbers in two-dimensional annular thermal convection ». Physics of Fluids 15, no 5 (mai 2003) : 1314–26. http://dx.doi.org/10.1063/1.1565335.
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Shishkina, Olga, Susanne Horn et Sebastian Wagner. « Falkner–Skan boundary layer approximation in Rayleigh–Bénard convection ». Journal of Fluid Mechanics 730 (1 août 2013) : 442–63. http://dx.doi.org/10.1017/jfm.2013.347.
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AbstractTo approximate the velocity and temperature within the boundary layers in turbulent thermal convection at moderate Rayleigh numbers, we consider the Falkner–Skan ansatz, which is a generalization of the Prandtl–Blasius one to a non-zero-pressure-gradient case. This ansatz takes into account the influence of the angle of attack $\beta $ of the large-scale circulation of a fluid inside a convection cell against the heated/cooled horizontal plate. With respect to turbulent Rayleigh–Bénard convection, we derive several theoretical estimates, among them the limiting cases of the temperature profiles for all angles $\beta $, for infinite and for infinitesimal Prandtl numbers $\mathit{Pr}$. Dependences on $\mathit{Pr}$ and $\beta $ of the ratio of the thermal to viscous boundary layers are obtained from the numerical solutions of the boundary layers equations. For particular cases of $\beta $, accurate approximations are developed as functions on $\mathit{Pr}$. The theoretical results are corroborated by our direct numerical simulations for $\mathit{Pr}= 0. 786$ (air) and $\mathit{Pr}= 4. 38$ (water). The angle of attack $\beta $ is estimated based on the information on the locations within the plane of the large-scale circulation where the time-averaged wall shear stress vanishes. For the fluids considered it is found that $\beta \approx 0. 7\mathrm{\pi} $ and the theoretical predictions based on the Falkner–Skan approximation for this $\beta $ leads to better agreement with the DNS results, compared with the Prandtl–Blasius approximation for $\beta = \mathrm{\pi} $.
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Julien, K., S. Legg, J. Mcwilliams et J. Werne. « Rapidly rotating turbulent Rayleigh-Bénard convection ». Journal of Fluid Mechanics 322 (10 septembre 1996) : 243–73. http://dx.doi.org/10.1017/s0022112096002789.
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Turbulent Boussinesq convection under the influence of rapid rotation (i.e. with comparable characteristic rotation and convection timescales) is studied. The transition to turbulence proceeds through a relatively simple bifurcation sequence, starting with unstable convection rolls at moderate Rayleigh (Ra) and Taylor numbers (Ta) and culminating in a state dominated by coherent plume structures at high Ra and Ta. Like non-rotating turbulent convection, the rapidly rotating state exhibits a simple power-law dependence on Ra for all statistical properties of the flow. When the fluid layer is bounded by no-slip surfaces, the convective heat transport (Nu − 1, where Nu is the Nusselt number) exhibits scaling with Ra2/7 similar to non-rotating laboratory experiments. When the boundaries are stress free, the heat transport obeys ‘classical’ scaling (Ra1/3) for a limited range in Ra, then appears to undergo a transition to a different law at Ra ≈ 4 × 107. Important dynamical differences between rotating and non-rotating convection are observed: aside from the (expected) differences in the boundary layers due to Ekman pumping effects, angular momentum conservation forces all plume structures created at flow-convergent sites of the heated and cooled boundaries to spin-up cyclonically; the resulting plume/cyclones undergo strong vortex-vortex interactions which dramatically alter the mean state of the flow and result in a finite background temperature gradient as Ra → ∞, holding Ra/Ta fixed.
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Djebali, Ridha, Mohamed Ammar Abbassi et Ahlem Rouahi. « Conjugate Effects of Buoyancy and Magnetic Field on Heat and Fluid Flow Pattern at Low-to-Moderate Prandtl Numbers ». International Letters of Chemistry, Physics and Astronomy 66 (mai 2016) : 79–95. http://dx.doi.org/10.18052/www.scipress.com/ilcpa.66.79.
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This study aims to present a numerical investigation of unsteady two-dimensional natural convection of an electrically conducting fluid in a square medium under externally imposed magnetic field. A temperature gradient is applied between the two opposing side walls parallel to y-direction, while the floor and ceiling parallel to x-direction are kept adiabatic. The coupled momentum and energy equations associated with the Lorentz ‘decelerating’ force as well as the buoyancy force terms are solved using the single relaxation lattice Boltzmann (LB) approach. The flow is characterized by the Rayleigh number Ra (103-106), the Prandtl number Pr (0.01-10), the Hartman number Ha (0-100) determined by the strength of the imposed magnetic field and its tilt angle from x-axis ranging from 0° to 90°. The changes in the buoyant flow patterns and temperature contours due to the effects of varying the controlling parameters and associated heat transfer are examined. It was found that the developed thermal LB model gives excellent results by comparison with former experimental and numerical findings. Starting from the values 105 of the Rayleigh number Ra and Ha=0, the flow is unsteady multicellular for low Prandtl number typical of liquid metal. Increasing gradually Pr, the flow undergoes transition to steady bicellular. The transition occurs at a threshold value between Pr=0.01 and 0.1. Increasing more the Prandtl number, the flow structure is distorted due to the viscous forces which outweigh the buoyancy forces and a thermal stratification is clearly established. For high Hartman number, the damping effects suppress the unsteady behaviour and results in steady state with extended unicellular pattern in the direction of Lorentz force and the heat transfer rate is reduced considerably.
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Djebali, Ridha, Mohamed Ammar Abbassi et Ahlem Rouahi. « Conjugate Effects of Buoyancy and Magnetic Field on Heat and Fluid Flow Pattern at Low-to-Moderate Prandtl Numbers ». International Letters of Chemistry, Physics and Astronomy 66 (30 mai 2016) : 79–95. http://dx.doi.org/10.56431/p-kh7f3t.
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This study aims to present a numerical investigation of unsteady two-dimensional natural convection of an electrically conducting fluid in a square medium under externally imposed magnetic field. A temperature gradient is applied between the two opposing side walls parallel to y-direction, while the floor and ceiling parallel to x-direction are kept adiabatic. The coupled momentum and energy equations associated with the Lorentz ‘decelerating’ force as well as the buoyancy force terms are solved using the single relaxation lattice Boltzmann (LB) approach. The flow is characterized by the Rayleigh number Ra (103-106), the Prandtl number Pr (0.01-10), the Hartman number Ha (0-100) determined by the strength of the imposed magnetic field and its tilt angle from x-axis ranging from 0° to 90°. The changes in the buoyant flow patterns and temperature contours due to the effects of varying the controlling parameters and associated heat transfer are examined. It was found that the developed thermal LB model gives excellent results by comparison with former experimental and numerical findings. Starting from the values 105 of the Rayleigh number Ra and Ha=0, the flow is unsteady multicellular for low Prandtl number typical of liquid metal. Increasing gradually Pr, the flow undergoes transition to steady bicellular. The transition occurs at a threshold value between Pr=0.01 and 0.1. Increasing more the Prandtl number, the flow structure is distorted due to the viscous forces which outweigh the buoyancy forces and a thermal stratification is clearly established. For high Hartman number, the damping effects suppress the unsteady behaviour and results in steady state with extended unicellular pattern in the direction of Lorentz force and the heat transfer rate is reduced considerably.
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Ng, Chong Shen, Andrew Ooi, Detlef Lohse et Daniel Chung. « Bulk scaling in wall-bounded and homogeneous vertical natural convection ». Journal of Fluid Mechanics 841 (1 mars 2018) : 825–50. http://dx.doi.org/10.1017/jfm.2018.102.
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Previous numerical studies on homogeneous Rayleigh–Bénard convection, which is Rayleigh–Bénard convection (RBC) without walls, and therefore without boundary layers, have revealed a scaling regime that is consistent with theoretical predictions of bulk-dominated thermal convection. In this so-called asymptotic regime, previous studies have predicted that the Nusselt number ($\mathit{Nu}$) and the Reynolds number ($\mathit{Re}$) vary with the Rayleigh number ($\mathit{Ra}$) according to $\mathit{Nu}\sim \mathit{Ra}^{1/2}$ and $\mathit{Re}\sim \mathit{Ra}^{1/2}$ at small Prandtl numbers ($\mathit{Pr}$). In this study, we consider a flow that is similar to RBC but with the direction of temperature gradient perpendicular to gravity instead of parallel to it; we refer to this configuration as vertical natural convection (VC). Since the direction of the temperature gradient is different in VC, there is no exact relation for the average kinetic dissipation rate, which makes it necessary to explore alternative definitions for $\mathit{Nu}$, $\mathit{Re}$ and $\mathit{Ra}$ and to find physical arguments for closure, rather than making use of the exact relation between $\mathit{Nu}$ and the dissipation rates as in RBC. Once we remove the walls from VC to obtain the homogeneous set-up, we find that the aforementioned $1/2$-power-law scaling is present, similar to the case of homogeneous RBC. When focusing on the bulk, we find that the Nusselt and Reynolds numbers in the bulk of VC too exhibit the $1/2$-power-law scaling. These results suggest that the $1/2$-power-law scaling may even be found at lower Rayleigh numbers if the appropriate quantities in the turbulent bulk flow are employed for the definitions of $\mathit{Ra}$, $\mathit{Re}$ and $\mathit{Nu}$. From a stability perspective, at low- to moderate-$\mathit{Ra}$, we find that the time evolution of the Nusselt number for homogenous vertical natural convection is unsteady, which is consistent with the nature of the elevator modes reported in previous studies on homogeneous RBC.
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Chaabane, Raoudha, Annunziata D’Orazio, Abdelmajid Jemni, Arash Karimipour et Ramin Ranjbarzadeh. « Convection Inside Nanofluid Cavity with Mixed Partially Boundary Conditions ». Energies 14, no 20 (9 octobre 2021) : 6448. http://dx.doi.org/10.3390/en14206448.
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In recent decades, research utilizing numerical schemes dealing with fluid and nanoparticle interaction has been relatively intensive. It is known that CuO nanofluid with a volume fraction of 0.1 and a special thermal boundary condition with heat supplied to part of the wall increases the average Nusselt number for different aspect ratios ranges and for high Rayleigh numbers. Due to its simplicity, stability, accuracy, efficiency, and ease of parallelization, we use the thermal single relaxation time Bhatnagar-Gross-Krook (SRT BGK) mesoscopic approach D2Q9 scheme lattice Boltzmann method in order to solve the coupled Navier–Stokes equations. Convection of CuO nanofluid in a square enclosure with a moderate Rayleigh number of 105 and with new boundary conditions is highlighted. After a successful validation with a simple partial Dirichlet boundary condition, this paper extends the study to deal with linear and sinusoidal thermal boundary conditions applied to part of the wall.
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Balestra, Gioele, Nicolas Kofman, P. T. Brun, Benoit Scheid et François Gallaire. « Three-dimensional Rayleigh–Taylor instability under a unidirectional curved substrate ». Journal of Fluid Mechanics 837 (19 décembre 2017) : 19–47. http://dx.doi.org/10.1017/jfm.2017.817.
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We investigate the Rayleigh–Taylor instability of a thin liquid film coated on the inside of a cylinder whose axis is orthogonal to gravity. We are interested in the effects of geometry on the instability, and contrast our results with the classical case of a thin film coated under a flat substrate. In our problem, gravity is the destabilizing force at the origin of the instability, but also yields the progressive drainage and stretching of the coating along the cylinder’s wall. We find that this flow stabilizes the film, which is asymptotically stable to infinitesimal perturbations. However, the short-time algebraic growth that these perturbations can achieve promotes the formation of different patterns, whose nature depends on the Bond number that prescribes the relative magnitude of gravity and capillary forces. Our experiments indicate that a transverse instability arises and persists over time for moderate Bond numbers. The liquid accumulates in equally spaced rivulets whose dominant wavelength corresponds to the most amplified mode of the classical Rayleigh–Taylor instability. The formation of rivulets allows for a faster drainage of the liquid from top to bottom when compared to a uniform drainage. For higher Bond numbers, a two-dimensional stretched lattice of droplets is found to form on the top part of the cylinder. Rivulets and the lattice of droplets are inherently three-dimensional phenomena and therefore require a careful three-dimensional analysis. We found that the transition between the two types of pattern may be rationalized by a linear optimal transient growth analysis and nonlinear numerical simulations.
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Asmadi, M. S., R. Md. Kasmani, Z. Siri et H. Saleh. « Thermal performance analysis for moderate Rayleigh numbers of Newtonian hybrid nanofluid-filled U-shaped cavity with various thermal profiles ». Physics of Fluids 33, no 3 (1 mars 2021) : 032006. http://dx.doi.org/10.1063/5.0040903.
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Cloitre, M., et E. Guyon. « Forced Rayleigh scattering in turbulent plane Poiseuille flows. Part 1. Study of the transverse velocity-gradient component ». Journal of Fluid Mechanics 164 (mars 1986) : 217–36. http://dx.doi.org/10.1017/s0022112086002537.
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In this article, we describe an optical set-up designed to measure directly velocity gradients (strophometry). This strophometer is based on the analysis of the distortions of a fringe pattern ‘written’ instantaneously in a flow field. We apply it to study the transverse velocity-gradient component ∂u/∂y in a plane Poiseuille flow at moderate Reynolds numbers. Mean values and different moments of the fluctuating gradient distribution related to viscous dissipation, vorticity dynamics and intermittency are obtained. These results are interpreted in terms of the large-scale structures which are present in the flow.
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Shen, Bo-Wen. « Aggregated Negative Feedback in a Generalized Lorenz Model ». International Journal of Bifurcation and Chaos 29, no 03 (mars 2019) : 1950037. http://dx.doi.org/10.1142/s0218127419500378.
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In this study, we first present a generalized Lorenz model (LM) with [Formula: see text] modes, where [Formula: see text] is an odd number that is greater than three. The generalized LM (GLM) is derived based on a successive extension of the nonlinear feedback loop (NFL) with additional high wavenumber modes. By performing a linear stability analysis with [Formula: see text] and [Formula: see text], we illustrate that: (1) within the 3D, 5D, and 7D LMs, the appearance of unstable nontrivial critical points requires a larger Rayleigh parameter in a higher-dimensional LM and (2) within the 9DLM, nontrivial critical points are stable. By comparing the GLM with various numbers of modes, we discuss the aggregated negative feedback enabled by the extended NFL and its role in stabilizing solutions in high-dimensional LMs. Our analysis indicates that the 9DLM is the lowest order generalized LM with stable nontrivial critical points for all Rayleigh parameters greater than one. As shown by calculations of the ensemble Lyapunov exponent, the 9DLM still produces chaotic solutions. Within the 9DLM, a larger critical value for the Rayleigh parameter, [Formula: see text], is required for the onset of chaos as compared to a [Formula: see text] for the 3DLM, a [Formula: see text] for the 5DLM, and a [Formula: see text] for the 7DLM. In association with stable nontrivial critical points that may lead to steady-state solutions, the appearance of chaotic orbits indicates the important role of a saddle point at the origin in producing the sensitive dependence of solutions on initial conditions. The 9DLM displays the coexistence of chaotic and steady-state solutions at moderate Rayleigh parameters and the coexistence of limit cycle and steady-state solutions at large Rayleigh parameters. The first kind of coexistence appears within a smaller range of Rayleigh parameters in lower-dimensional LMs (i.e. [Formula: see text] within the 3DLM) but in a wider range of Rayleigh parameters within the 9DLM (i.e. [Formula: see text]). The second kind of coexistence has never been reported in high-dimensional Lorenz systems.
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Ruiz, Xavier, et Jordi Pallarés. « On the accuracy of the diffusion coefficient measurements using different initial shear cell configurations at low and moderate Rayleigh numbers ». International Journal of Heat and Mass Transfer 55, no 23-24 (novembre 2012) : 6966–78. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.07.010.
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SAMEEN, A., et RAMA GOVINDARAJAN. « The effect of wall heating on instability of channel flow ». Journal of Fluid Mechanics 577 (19 avril 2007) : 417–42. http://dx.doi.org/10.1017/s0022112007004636.
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A comprehensive study of the effect of wall heating or cooling on the linear, transient and secondary growth of instability in channel flow is conducted. The effect of viscosity stratification, heat diffusivity and of buoyancy are estimated separately, with some unexpected results. From linear stability results, it has been accepted that heat diffusivity does not affect stability. However, we show that realistic Prandtl numbers cause a transient growth of disturbances that is an order of magnitude higher than at zero Prandtl number. Buoyancy, even at fairly low levels, gives rise to high levels of subcritical energy growth. Unusually for transient growth, both of these are spanwise-independent and not in the form of streamwise vortices. At moderate Grashof numbers, exponential growth dominates, with distinct Poiseuille–Rayleigh–Bénard and Tollmien–Schlichting modes for Grashof numbers up to ∼ 25 000, which merge thereafter. Wall heating has a converse effect on the secondary instability compared to the primary instability, destabilizing significantly when viscosity decreases towards the wall. It is hoped that the work will motivate experimental and numerical efforts to understand the role of wall heating in the control of channel and pipe flows.
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Pigeonneau, Franck, Alexandre Cornet et Fredéric Lopépé. « Thermoconvective instabilities of a non-uniform Joule-heated liquid enclosed in a rectangular cavity ». Journal of Fluid Mechanics 843 (23 mars 2018) : 601–36. http://dx.doi.org/10.1017/jfm.2018.168.
Texte intégralRésumé :
Natural convection produced by a non-uniform internal heat source is studied numerically. Our investigation is limited to a two-dimensional enclosure with an aspect ratio equal to two. The energy source is Joule dissipation produced by an electric potential applied through two electrodes corresponding to a fraction of the vertical walls. The system of conservative equations of mass, momentum, energy and electric potential is solved assuming the Boussinesq approximation with a discontinuous Galerkin finite element method integrated over time. Three parameters are involved in the problem: the Rayleigh number $Ra$, the Prandtl number $Pr$ and the electrode length $L_{e}$ normalized by the enclosure height. The numerical method has been validated in a case where electrodes have the same length as the vertical walls, leading to a uniform source term. The threshold of convection is established above a critical Rayleigh number, $Ra_{cr}=1702$. Due to asymmetric boundary conditions on thermal field, the onset of convection is characterized by a transcritical bifurcation. Reduction of the size of the electrodes (from bottom up) leads to disappearance of the convection threshold. As soon as the electrode length is smaller than the cavity height, convection occurs even for small Rayleigh numbers below the critical value determined previously. At moderate Rayleigh number, the flow structure is mainly composed of a left clockwise rotation cell and a right anticlockwise rotation cell symmetrically spreading around the vertical middle axis of the enclosure. Numerical simulations have been performed for a specific $L_{e}=2/3$ with $Ra\in [1;10^{5}]$ and $Pr\in [1;10^{3}]$. Four kinds of flow solutions are established, characterized by a two-cell symmetric steady-state structure with down-flow in the middle of the cavity for the first one. A first instability occurs for which a critical Rayleigh number depends strongly on the Prandtl number when $Pr<3$. The flow structure becomes asymmetric with only one steady-state cell. A second instability occurs above a second critical Rayleigh number that is quasiconstant when $Pr>10$. The flow above the second critical Rayleigh number becomes periodic in time, showing that the onset of unsteadiness is similar to the Hopf bifurcation. When $Pr<3$, a fourth steady-state solution is established when the Rayleigh number is larger than the second critical value, characterized by a steady-state structure with up-flow in the middle of the cavity.
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Eilertsen, Justin, et Jerry Magnan. « On the Chaotic Dynamics Associated with the Center Manifold Equations of Double-Diffusive Convection Near a Codimension-Four Bifurcation Point at Moderate Thermal Rayleigh Number ». International Journal of Bifurcation and Chaos 28, no 08 (juillet 2018) : 1850094. http://dx.doi.org/10.1142/s0218127418500943.
Texte intégralRésumé :
We analyze the dynamics of the Poincaré map associated with the center manifold equations of double-diffusive thermosolutal convection near a codimension-four bifurcation point when the values of the thermal and solute Rayleigh numbers, [Formula: see text] and [Formula: see text], are comparable. We find that the bifurcation sequence of the Poincaré map is analogous to that of the (continuous) Lorenz equations. Chaotic solutions are found, and the emergence of strange attractors is shown to occur via three different routes: (1) a discrete Lorenz-like attractor of the three-dimensional Poincaré map of the four-dimensional center manifold equations that forms as the result of a quasi-periodic homoclinic explosion; (2) chaos that follows quasi-periodic intermittency occurring near saddle-node bifurcations of tori; and, (3) chaos that emerges from the destruction of a 2-torus, preceded by frequency locking.
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Kanchana, C., J. A. Vélez, L. M. Pérez, D. Laroze et P. G. Siddheshwar. « Influence of higher-order modes on ferroconvection ». Chaos : An Interdisciplinary Journal of Nonlinear Science 32, no 8 (août 2022) : 083129. http://dx.doi.org/10.1063/5.0097398.
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Using Fourier representations, an elaborate study of regular cellular-convective and chaotic motions in a ferrofluid is made. Investigation is made on the adequacy or otherwise of the minimal mode in studying such motions. Higher-order modes are also considered by adding modes (vertical/horizontal/combined extension). For higher modes, the extensions yield a dynamical system of order greater than three. The characteristic features of extended ferromagnetic-Lorenz models are analyzed using the largest Lyapunov exponent(LE), second largest LE, bifurcation diagram, and phase-space plots. The effect of additional modes on critical modal-Rayleigh (infinitesimal and finite-amplitude ones) numbers and the Rayleigh number at which transition to chaos occurs are examined to report features of ferroconvection hitherto unseen in previous studies. As both horizontal and vertical modes are increased, our findings infer that the dynamical system displays advanced onset of regular convection and delayed chaotic motion. Vigorous-chaotic motion is seen on adding vertical modes, whereas on adding horizontal modes, intense chaos appears with decreased intensity for large values of the scaled Rayleigh number. Most important finding from the study is that as modes are increased (vertical/horizontal), the transition from regular to chaotic motion is greatly modified and leads the system to a hyper-chaotic state. Conventionally, the chaotic or hyper-chaotic state is intermittent with a periodic/quasi-periodic state but it can be retained in the chaotic or hyper-chaotic state by considering moderate values of the Prandtl number and/or by bringing in the ferromagnetic effect.
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Razelos, P. « An interferometric investigation of the effect of separation distance and temperature imbalance on natural convection for two horizontal cylinders at moderate Rayleigh numbers ». Wärme- und Stoffübertragung 19, no 4 (décembre 1985) : 255–62. http://dx.doi.org/10.1007/bf01002279.
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Morgan, R. V., W. H. Cabot, J. A. Greenough et J. W. Jacobs. « Rarefaction-driven Rayleigh–Taylor instability. Part 2. Experiments and simulations in the nonlinear regime ». Journal of Fluid Mechanics 838 (12 janvier 2018) : 320–55. http://dx.doi.org/10.1017/jfm.2017.893.
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Experiments and large eddy simulation (LES) were performed to study the development of the Rayleigh–Taylor instability into the saturated, nonlinear regime, produced between two gases accelerated by a rarefaction wave. Single-mode two-dimensional, and single-mode three-dimensional initial perturbations were introduced on the diffuse interface between the two gases prior to acceleration. The rarefaction wave imparts a non-constant acceleration, and a time decreasing Atwood number, $A=(\unicode[STIX]{x1D70C}_{2}-\unicode[STIX]{x1D70C}_{1})/(\unicode[STIX]{x1D70C}_{2}+\unicode[STIX]{x1D70C}_{1})$, where $\unicode[STIX]{x1D70C}_{2}$ and $\unicode[STIX]{x1D70C}_{1}$ are the densities of the heavy and light gas, respectively. Experiments and simulations are presented for initial Atwood numbers of $A=0.49$, $A=0.63$, $A=0.82$ and $A=0.94$. Nominally two-dimensional (2-D) experiments (initiated with nearly 2-D perturbations) and 2-D simulations are observed to approach an intermediate-time velocity plateau that is in disagreement with the late-time velocity obtained from the incompressible model of Goncharov (Phys. Rev. Lett., vol. 88, 2002, 134502). Reacceleration from an intermediate velocity is observed for 2-D bubbles in large wavenumber, $k=2\unicode[STIX]{x03C0}/\unicode[STIX]{x1D706}=0.247~\text{mm}^{-1}$, experiments and simulations, where $\unicode[STIX]{x1D706}$ is the wavelength of the initial perturbation. At moderate Atwood numbers, the bubble and spike velocities approach larger values than those predicted by Goncharov’s model. These late-time velocity trends are predicted well by numerical simulations using the LLNL Miranda code, and by the 2009 model of Mikaelian (Phys. Fluids., vol. 21, 2009, 024103) that extends Layzer type models to variable acceleration and density. Large Atwood number experiments show a delayed roll up, and exhibit a free-fall like behaviour. Finally, experiments initiated with three-dimensional perturbations tend to agree better with models and a simulation using the LLNL Ares code initiated with an axisymmetric rather than Cartesian symmetry.
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Hu, Jun, Daniel Henry, Xie-Yuan Yin et Hamda BenHadid. « Linear biglobal analysis of Rayleigh–Bénard instabilities in binary fluids with and without throughflow ». Journal of Fluid Mechanics 713 (19 octobre 2012) : 216–42. http://dx.doi.org/10.1017/jfm.2012.455.
Texte intégralRésumé :
AbstractThree-dimensional Rayleigh–Bénard instabilities in binary fluids with Soret effect are studied by linear biglobal stability analysis. The fluid is confined transversally in a duct and a longitudinal throughflow may exist or not. A negative separation factor $\psi = \ensuremath{-} 0. 01$, giving rise to oscillatory transitions, has been considered. The numerical dispersion relation associated with this stability problem is obtained with a two-dimensional Chebyshev collocation method. Symmetry considerations are used in the analysis of the results, which allow the classification of the perturbation modes as ${S}_{l} $ modes (those which keep the left–right symmetry) or ${R}_{x} $ modes (those which keep the symmetry of rotation of $\lrm{\pi} $ about the longitudinal mid-axis). Without throughflow, four dominant pairs of travelling transverse modes with finite wavenumbers $k$ have been found. Each pair corresponds to two symmetry degenerate left and right travelling modes which have the same critical Rayleigh number ${\mathit{Ra}}_{c} $. With the increase of the duct aspect ratio $A$, the critical Rayleigh numbers for these four pairs of modes decrease and closely approach the critical value ${\mathit{Ra}}_{c} = 1743. 894$ obtained in a two-dimensional situation, one of the mode (a ${S}_{l} $ mode called mode A) always remaining the dominant mode. Oscillatory longitudinal instabilities ($k\approx 0$) corresponding to either ${S}_{l} $ or ${R}_{x} $ modes have also been found. Their critical curves, globally decreasing, present oscillatory variations when the duct aspect ratio $A$ is increased, associated with an increasing number of longitudinal rolls. When a throughflow is applied, the symmetry degeneracy of the pairs of travelling transverse modes is broken, giving distinct upstream and downstream modes. For small and moderate aspect ratios $A$, the overall critical Rayleigh number in the small Reynolds number range studied is only determined by the upstream transverse mode A. In contrast, for larger aspect ratios as $A= 7$, different modes are successively dominant as the Reynolds number is increased, involving both upstream and downstream transverse modes A and even the longitudinal mode.
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Hurlburt, N. E., M. R. E. Proctor, N. O. Weiss et D. P. Brownjohn. « Nonlinear compressible magnetoconvection Part 1. Travelling waves and oscillations ». Journal of Fluid Mechanics 207 (octobre 1989) : 587–628. http://dx.doi.org/10.1017/s0022112089002703.
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Two-dimensional compressible convection in a polytropic layer with an imposed vertical magnetic field is studied in a series of numerical experiments. We consider a shallow layer, spanning only a fraction of a scale height in density, and increase the ratio (β−1) of the magnetic to the thermal pressure in a regime where convection sets in at an oscillatory bifurcation. Initially there are stable periodic oscillations (standing wave solutions). For moderate values of β the only deviations from Boussinesq behaviour are where the field is locally intense but as β is decreased magnetic pressure fluctuations become increasingly important. When β is of order unity at the top of the layer standing waves become unstable at higher Rayleigh numbers and travelling waves are preferred. This is an essentially compressible effect in which magnetic pressure plays a crucial role. The associated bifurcation structure is investigated in some detail.
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Shishkina, Olga, et Claus Wagner. « Modelling the influence of wall roughness on heat transfer in thermal convection ». Journal of Fluid Mechanics 686 (27 septembre 2011) : 568–82. http://dx.doi.org/10.1017/jfm.2011.348.
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AbstractThe objective of this study is to approximate heat transport in thermal convection enhanced by the roughness of heated/cooled horizontal plates. The roughness is introduced by a set of rectangular heated/cooled obstacles located at the corresponding plates. An analytical model to estimate the Nusselt number deviations caused by the wall roughness is developed. It is based on the two-dimensional Prandtl–Blasius boundary layer equations and therefore is valid for moderate Rayleigh numbers and regular wall roughness, for which the height of the obstacles and the distances between them are significantly larger than the thickness of the thermal boundary layers. To validate this model, the transport of heat and momentum in rectangular convection cells is studied in two-dimensional Navier–Stokes simulations, for different aspect ratios of the obstacles. It is found that the model predicts the heat transport with errors ${\leq }6\hspace{0.167em} \% $ for all investigated cases.
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Hyun, Jae Min, et Jun Sang Park. « Spin-up from rest of a compressible fluid in a rapidly rotating cylinder ». Journal of Fluid Mechanics 237 (avril 1992) : 413–34. http://dx.doi.org/10.1017/s0022112092003471.
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Spin-up flows of a compressible gas in a finite, closed cylinder from an initial state of rest are studied, The flow is characterized by small reference Ekman numbers, and the peripheral Mach number is O(1). Comprehensive numerical solutions have been obtained for the full, time-dependent compressible Navier-Stokes equations. The details of the flow, temperature, and density evolution are described. In the early phase of spin-up, owing to the thermoacoustic disturbances caused by the compressible Rayleigh effect, the flows are oscillatory, and this oscillatory behaviour is pronounced at higher Mach numbers. The principal dynamical role of the Ekman layer is dominant over moderate times of orders of the homogeneous spin-up timescales. Owing to the density stratification in the radial direction, the Ekman layer is thicker in the central region of the interior. The interior azimuthal flows are mainly uniform in the axial direction. As the Mach number increases, the rate of spin-up in the interior becomes slower, and the propagating shear front is more diffusive. Explicit comparisons with the results for an infinite cylinder are made to ascertain the contributions of the endwall disks. In contrast to the usual incompressible spin-up from rest, the viscous effects are relatively more important for the case of a compressible fluid.
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GILLET, N., D. BRITO, D. JAULT et H. C. NATAF. « Experimental and numerical studies of convection in a rapidly rotating spherical shell ». Journal of Fluid Mechanics 580 (21 mai 2007) : 83–121. http://dx.doi.org/10.1017/s0022112007005265.
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Thermal convection in a rapidly rotating spherical shell is investigated experimentally and numerically. The experiments are performed in water (Prandtl number P=7) and in gallium (P=0.025), at Rayleigh numbers R up to 80 times the critical value in water (up to 6 times critical in gallium) and at Ekman numbers E∼10−6. The measurements of fluid velocities by ultrasonic Doppler velocimetry are quantitatively compared with quasi-geostrophic numerical simulations incorporating a varying β-effect and boundary friction (Ekman pumping). In water, unsteady multiple zonal jets, weaker in amplitude than the non-axisymmetric flow, are experimentally observed and numerically reproduced at moderate forcings (R/Rc<40). In this regime, zonal flows and vortices share the same length scale. Gallium experiments and strongly supercritical convection experiments in water correspond to another regime. In these turbulent flows, the zonal motion amplitude U dominates the non-axisymmetric motion amplitude Ũ. As a result of the reverse cascade of kinetic energy, the characteristic Rhines length scale $\ell_{\beta} \,{\sim}\, \sqrt{\overline{U}/\beta}$ of zonal jets emerges, and the boundary friction becomes the main brake on the growth of the zonal flow. A scaling law U ∼ Ũ4/3 is then derived and verified both numerically and experimentally.
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Tonegawa, Takashi, Yusuke Yamashita, Tsutomu Takahashi, Masanao Shinohara, Yasushi Ishihara, Shuichi Kodaira et Yoshiyuki Kaneda. « Spatial relationship between shallow very low frequency earthquakes and the subducted Kyushu-Palau Ridge in the Hyuga-nada region of the Nankai subduction zone ». Geophysical Journal International 222, no 3 (30 mai 2020) : 1542–54. http://dx.doi.org/10.1093/gji/ggaa264.
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SUMMARY Shallow very low frequency earthquakes (sVLFEs) have occurred recurrently at the shallow plate interface of the Hyuga-nada region of the western Nankai subduction zone, Japan. Although the locations of sVLFE epicentres have been determined using land-based seismic records with moderate accuracy, it is necessary to determine their locations more precisely to explore the relationship between sVLFEs and other shallow slow earthquakes and examine the structural factors that may control sVLFE activity. Here, we identified sVLFE epicentres using seismic records obtained from temporarily deployed ocean bottom seismometers (OBSs) in the Hyuga-nada region. Seismic observations involved the deployment of 5–13 OBSs for approximately 1 yr, with deployments conducted three times during 2014–2016 each time with changing OBS numbers and array distribution. As a result, one sVLFE episode, containing successive Rayleigh wave pulses with slow velocities due to marine sediments, could be detected at a frequency band of 0.1–0.15 Hz per observation, resulting in a total of three episodes. Rayleigh wave amplitudes of ordinary earthquakes in the continuous records were suppressed using earthquake catalogues. We estimated the dispersion curve for the Rayleigh wave group velocity for each array, which represented the averaged group velocity within the array, using coda interferometry, and applied an envelope correlation method (ECM) using the group velocities to continuous records. These processing provided sVLFE epicentres with horizontal distance errors of <5 km. Our results showed that sVLFEs depths, which were inferred from the contour line of the top of the Phillipine Sea Plate, had increased from <10 km to 10–15 km in the region of the subducted Kyusyu-Palau Ridge (KPR). It was also apparent that migration of sVLFE epicentres occurred in 2015 from a depth of 15 km to shallower depths along the northern margin of the subducted KPR. These results identified the subducted KPR as a structural factor controlling the excitation conditions of sVLFE activities.
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Clavin, P., P. Lallemand, Y. Pomeau et G. Searby. « Simulation of free boundaries in flow systems by lattice-gas models ». Journal of Fluid Mechanics 188 (mars 1988) : 437–64. http://dx.doi.org/10.1017/s0022112088000795.
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It has been recently proved that lattice-gas models with Boolean particles can provide a very powerful method to study viscous flows at moderate Reynolds and small Mach numbers (d'Humières, Pomeau & Lallemand 1985; Frisch, Hasslacher & Pomeau 1986; d'Humières & Lallemand 1986). We present here algorithms for an extension of these models to provide a simple and efficient way to simulate a large variety of flow problems with free boundaries. This is done by introducing two different types of particles that can react following a specific kinetic scheme based on autocatalytic reactions. In order to check the powerful character and the reliability of the method we also present preliminary results of two-dimensional computer simulations concerning problems ranging from the competition between molecular diffusion and turbulent mixing in flows presenting a Kelvin-Helmholtz instability to the spontaneous generation of turbulence in premixed flame fronts subject to the Darrieus-Landau instability. The dynamics of an interface developing a Rayleigh-Taylor instability is also considered as well as some typical problems of phase transition such as spinodal decomposition and the nucleation process.
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Ghernoug, Chahinez, Mahfoud Djezzar, Hassane Naji et Abdelkarim Bouras. « Towards numerical computation of double-diffusive natural convection within an eccentric horizontal cylindrical annulus ». International Journal of Numerical Methods for Heat & ; Fluid Flow 26, no 5 (6 juin 2016) : 1346–64. http://dx.doi.org/10.1108/hff-10-2014-0330.
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Purpose – The purpose of this paper is to numerically study the double-diffusive natural convection within an eccentric horizontal cylindrical annulus filled with a Newtonian fluid. The annulus walls are maintained at uniform temperatures and concentrations so as to induce aiding thermal and mass buoyancy forces within the fluid. For that, this simulation span a moderate range of thermal Rayleigh number (100RaT100,000), Lewis (0.1Le10), buoyancy ratio (0N5) and Prandtl number (Pr=0.71) to examine their effects on flow motion and heat and mass transfers. Design/methodology/approach – A finite volume method in conjunction with the successive under-relaxation algorithm has been developed to solve the bipolar equations. These are written in dimensionless form in terms of vorticity, stream function, temperature and concentration. Beforehand, the implemented computer code has been validated through already published findings in the literature. The isotherms, streamlines and iso-concentrations are exhibited for various values of Rayleigh and Lewis numbers, and buoyancy ratio. In addition, heat and mass transfer rates in the annulus are translated in terms of Nusslet and Sherwood numbers along the enclosure’s sides. Findings – It is observed that, for the range of parameters considered here, the results show that the average Sherwood number increases with, while the average Nusselt number slightly dips as the Lewis number increases. It is also found that, under the convective mode, the local Nusselt number (or Sherwood) increases with the buoyancy ratio. Likewise, according to Lewis number’s value, the flow pattern is either symmetric and stable or asymmetric and random. Besides that, the heat transfer is transiting from a conductive mode to a convective mode with increasing the thermal Rayleigh number, and the flow structure and the rates of heat and mass transfer are significantly influenced by this parameter. Research limitations/implications – The range of the Rayleigh number considered here covers only the laminar case, with some constant parameters, namely the Prandtl number (Pr = 0.71), and the tilt angle (α=90°). The analysis here is only valid for steady, two-dimensional, laminar and aiding flow within an eccentric horizontal cylindrical annulus. This motivates further investigations involving other relevant parameters as N (opposite flows), Ra, Pr, Le, the eccentricity, the tilt angle, etc. Practical implications – An original framework for handling the double-diffusive natural convection within annuli is available, based on the bipolar equations. In addition, the achievement of this work could help researchers design thermal systems supported by annulus passages. Applications of the results can be of value in various arrangements such as storage of liquefied gases, electronic cable cooling systems, nuclear reactors, underground disposal of nuclear wastes, manifolds of solar energy collectors, etc. Originality/value – Given the geometry concerned, the bipolar coordinates have been used to set the inner and outer walls boundary conditions properly without interpolation. In addition, since studies on double-diffusive natural convection in annuli are lacking, the obtained results may be of interest to handle other configurations (e.g., elliptical-shaped speakers) with other boundary conditions.
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NET, MARTA, FERRAN GARCIA et JUAN SÁNCHEZ. « On the onset of low-Prandtl-number convection in rotating spherical shells : non-slip boundary conditions ». Journal of Fluid Mechanics 601 (25 avril 2008) : 317–37. http://dx.doi.org/10.1017/s002211200800061x.
Texte intégralRésumé :
Accurate numerical computations of the onset of thermal convection in wide rotating spherical shells are presented. Low-Prandtl-number (σ) fluids, and non-slip boundary conditions are considered. It is shown that at small Ekman numbers (E), and very low σ values, the well-known equatorially trapped patterns of convection are superseded by multicellular outer-equatorially-attached modes. As a result, the convection spreads to higher latitudes affecting the body of the fluid, and increasing the internal viscous dissipation. Then, from E < 10−5, the critical Rayleigh number (Rc) fulfils a power-law dependence Rc ~ E−4/3, as happens for moderate and high Prandtl numbers. However, the critical precession frequency (|ωc|) and the critical azimuthal wavenumber (mc) increase discontinuously, jumping when there is a change of the radial and latitudinal structure of the preferred eigenfunction. In addition, the transition between spiralling columnar (SC), and outer-equatorially-attached (OEA) modes in the (σ, E)-space is studied. The evolution of the instability mechanisms with the parameters prevents multicellular modes being selected from σ≳0.023. As a result, and in agreement with other authors, the spiralling columnar patterns of convection are already preferred at the Prandtl number of the liquid metals. It is also found that, out of the rapidly rotating limit, the prograde antisymmetric (with respect to the equator) modes of small mc can be preferred at the onset of the primary instability.