40 research outputs found
Calculation of the mean velocity profile for strongly turbulent Taylor–Couette flow at arbitrary radius ratios
No full textTaylor–Couette (TC) flow is the shear-driven flow between two coaxial independently rotating cylinders. In recent years, high-fidelity simulations and experiments revealed the shape of the streamwise and angular velocity profiles up to very high Reynolds numbers. However, due to curvature effects, so far no theory has been able to correctly describe the turbulent streamwise velocity profile for a given radius ratio, as the classical Prandtl–von Kármán logarithmic law for turbulent boundary layers over a flat surface at most fits in a limited spatial region. Here, we address this deficiency by applying the idea of a Monin–Obukhov curvature length to turbulent TC flow. This length separates the flow regions where the production of turbulent kinetic energy is governed by pure shear from that where it acts in combination with the curvature of the streamlines. We demonstrate that for all Reynolds numbers and radius ratios, the mean streamwise and angular velocity profiles collapse according to this separation. We then develop the functional form of the velocity profile. Finally, using the newly developed angular velocity profiles, we show that these lead to an alternative constant in the model proposed by Cheng et al. (J. Fluid Mech., vol. 890, 2020, A17) for the dependence of the torque on the Reynolds number, or, in other words, of the generalized Nusselt number (i.e. the dimensionless angular velocity transport) on the Taylor number
Direct numerical simulations of Taylor-Couette turbulence: The effects of sand grain roughness
No full textProgress in roughness research, mapping any given roughness geometry to its fluid dynamic behaviour, has been hampered by the lack of accurate and direct measurements of skin-friction drag, especially in open systems. The Taylor-Couette (TC) system has the benefit of being a closed system, but its potential for characterizing irregular, realistic, three-dimensional (3-D) roughness has not been previously considered in depth. Here, we present direct numerical simulations (DNSs) of TC turbulence with sand grain roughness mounted on the inner cylinder. The model proposed by Scotti (Phys. Fluids, vol. 18, 031701, 2006) has been modified to simulate a random rough surface of monodisperse sand grains. Taylor numbers range from (corresponding to Re-{\unicode[STIX]{x1D70F}}=82) to (Re-{\unicode[STIX]{x1D70F}}=635). We focus on the influence of the roughness height in the transitionally rough regime, through simulations of TC with rough surfaces, ranging from up to . We analyse the global response of the system, expressed both by the dimensionless angular velocity transport Nu-{\unicode[STIX]{x1D714}} and by the friction factor . An increase in friction with increasing roughness height is accompanied with enhanced plume ejection from the inner cylinder. Subsequently, we investigate the local response of the fluid flow over the rough surface. The equivalent sand grain roughness is calculated to be , where is the size of the sand grains. We find that the downwards shift of the logarithmic layer, due to transitionally rough sand grains exhibits remarkably similar behaviour to that of the Nikuradse (VDI-Forsch., vol. 361, 1933) data of sand grain roughness in pipe flow, regardless of the Taylor number dependent constants of the logarithmic layer. Furthermore, we find that the dynamical effects of the sand grains are contained to the roughness sublayer with
Toward Understanding Polar Heat Transport Enhancement in Subglacial Oceans on Icy Moons
No full textThe interior oceans of several icy moons are considered as affected by rotation. Observations suggest a larger heat transport around the poles than at the equator. Rotating Rayleigh-Bénard convection (RRBC) in planar configuration can show an enhanced heat transport compared to the non-rotating case within this “rotation-affected” regime. We investigate the potential for such a (polar) heat transport enhancement in these subglacial oceans by direct numerical simulations of RRBC in spherical geometry for Ra = 106 and 0.7 ≤ Pr ≤ 4.38. We find an enhancement up to 28% in the “polar tangent cylinder,” which is globally compensated by a reduced heat transport at low latitudes. As a result, the polar heat transport can exceed the equatorial by up to 50%. The enhancement is mostly insensitive to different radial gravity profiles, but decreases for thinner shells. In general, polar heat transport and its enhancement in spherical RRBC follow the same principles as in planar RRBC.</p
Flow organisation in laterally unconfined Rayleigh–Bénard turbulence
No full textWe investigate the large-scale circulation (LSC) of turbulent Rayleigh–Bénard convection in a large box of aspect ratio Γ=32Γ=32 for Rayleigh numbers up to Ra=109Ra=109 and at a fixed Prandtl number Pr=1Pr=1 . A conditional averaging technique allows us to extract statistics of the LSC even though the number and the orientation of the structures vary throughout the domain. We find that various properties of the LSC obtained here, such as the wall-shear stress distribution, the boundary layer thicknesses and the wind Reynolds number, do not differ significantly from results in confined domains ( Γ≈1Γ≈1 ). This is remarkable given that the size of the structures (as measured by the width of a single convection roll) more than doubles at the highest RaRa as the confinement is removed. An extrapolation towards the critical shear Reynolds number of Recrits≈420Rescrit≈420 , at which the boundary layer (BL) typically becomes turbulent, predicts that the transition to the ultimate regime is expected at Racrit≈O(1015)Racrit≈O(1015) in unconfined geometries. This result is in line with the Göttingen experimental observations (He et al., Phys. Rev. Lett., vol. 108, 2012, 024502; New J. Phys., vol. 17, 2015, 063028). Furthermore, we confirm that the local heat transport close to the wall is highest in the plume impacting region, where the thermal BL is thinnest, and lowest in the plume emitting region, where the thermal BL is thickest. This trend, however, weakens with increasing RaRa
Flow organization and heat transfer in turbulent wall sheared thermal convection
No full textWe perform direct numerical simulations of wall sheared Rayleigh-Bénard convection for Rayleigh numbers up to, Prandtl number unity and wall shear Reynolds numbers up to. Using the Monin-Obukhov length we observe the presence of three different flow states, a buoyancy dominated regime (; with the thermal boundary layer thickness), a transitional regime (; with the height of the domain) and a shear dominated regime (). In the buoyancy dominated regime, the flow dynamics is similar to that of turbulent thermal convection. The transitional regime is characterized by rolls that are increasingly elongated with increasing shear. The flow in the shear dominated regime consists of very large-scale meandering rolls, similar to the ones found in conventional Couette flow. As a consequence of these different flow regimes, for fixed and with increasing shear, the heat transfer first decreases, due to the breakup of the thermal rolls, and then increases at the beginning of the shear dominated regime. In the shear dominated regime the Nusselt number effectively scales as with, while we find in the buoyancy dominated regime. In the transitional regime, the effective scaling exponent is 1/3$]]>, but the temperature and velocity profiles in this regime are not logarithmic yet, thus indicating transient dynamics and not the ultimate regime of thermal convection
Heat transport in bubbling turbulent convection
No full textBoiling is an extremely effective way to promote heat transfer from a hot surface to a liquid due to numerous mechanisms, many of which are not understood in quantitative detail. An important component of the overall process is that the buoyancy of the bubble compounds with that of the liquid to give rise to a much-enhanced natural convection. In this article, we focus specifically on this enhancement and present a numerical study of the resulting two-phase Rayleigh–Bénard convection process in a cylindrical cell with a diameter equal to its height. We make no attempt to model other aspects of the boiling process such as bubble nucleation and detachment. The cell base and top are held at temperatures above and below the boiling point of the liquid, respectively. By keeping this difference constant, we study the effect of the liquid superheat in a Rayleigh number range that, in the absence of boiling, would be between 2 × 106 and 5 × 109. We find a considerable enhancement of the heat transfer and study its dependence on the number of bubbles, the degree of superheat of the hot cell bottom, and the Rayleigh number. The increased buoyancy provided by the bubbles leads to more energetic hot plumes detaching from the cell bottom, and the strength of the circulation in the cell is significantly increased. Our results are in general agreement with recent experiments on boiling Rayleigh–Bénard convectio
Radial boundary layer structure and Nusselt number in Rayleigh–Benard convection
No full textResults from direct numerical simulation (DNS) for three-dimensional Rayleigh–Bénard convection in a cylindrical cell of aspect ratio 1/2 and Prandtl number Pr=0.7 are presented. They span five decades of Rayleigh number Ra from 2 × 10^6 to 2 × 10^11. The results are in good agreement with the experimental data of Niemela et al. (Nature, vol. 404, 2000, p. 837). Previous DNS results from Amati et al. (Phys. Fluids, vol. 17, 2005, paper no. 121701) showed a heat transfer that was up to 30% higher than the experimental values. The simulations presented in this paper are performed with a much higher resolution to properly resolve the plume dynamics. We find that in under-resolved simulations the hot (cold) plumes travel further from the bottom (top) plate than in the better-resolved ones, because of insufficient thermal dissipation mainly close to the sidewall (where the grid cells are largest), and therefore the Nusselt number in under-resolved simulations is overestimated. Furthermore, we compare the best resolved thermal boundary layer profile with the Prandtl–Blasius profile. We find that the boundary layer profile is closer to the Prandtl–Blasius profile at the cylinder axis than close to the sidewall, because of rising plumes close to the sidewall
Nu ∼ Ra1/2 scaling enabled by multiscale wall roughness in Rayleigh–Bénard turbulence
No full textIn turbulent Rayleigh–Bénard (RB) convection with regular, mono-scale, surfaceroughness, the scaling exponent β in the relationship between the Nusselt numberNu and the Rayleigh number Ra, Nu ∼ Raβcan be ≈1/2 locally, provided that Ra islarge enough to ensure that the thermal boundary layer thickness λθis comparable tothe roughness height. However, at even larger Ra, λθ becomes thin enough to followthe irregular surface and β saturates back to the value for smooth walls (Zhu et al.,Phys. Rev. Lett., vol. 119, 2017, 154501). In this paper, we prevent this saturationby employing multiscale roughness. We perform direct numerical simulations oftwo-dimensional RB convection using an immersed boundary method to capture therough plates. We find that, for rough boundaries that contain three distinct lengthscales, a scaling exponent of β = 0.49 ± 0.02 can be sustained for at least threedecades of Ra. The physical reason is that the threshold Ra at which the scalingexponent β saturates back to the smooth wall value is pushed to larger Ra, when thesmaller roughness elements fully protrude through the thermal boundary layer. Themultiscale roughness employed here may better resemble the irregular surfaces thatare encountered in geophysical flows and in some industrial applications.<br
Turbulent thermal superstructures in Rayleigh-Bénard convection
No full textWe report the observation of superstructures, i.e., very large-scale and long living coherent structures in highly turbulent Rayleigh-Bénard convection up to Rayleigh Ra=109. We perform direct numerical simulations in horizontally periodic domains with aspect ratios up to Γ=128. In the considered Ra number regime the thermal superstructures have a horizontal extend of six to seven times the height of the domain and their size is independent of Ra. Many laboratory experiments and numerical simulations have focused on small aspect ratio cells in order to achieve the highest possible Ra. However, here we show that for very high Ra integral quantities such as the Nusselt number and volume averaged Reynolds number only converge to the large aspect ratio limit around Γ≈4, while horizontally averaged statistics such as standard deviation and kurtosis converge around Γ≈8, the integral scale converges around Γ≈32, and the peak position of the temperature variance and turbulent kinetic energy spectra only converge around Γ≈64
The effect of Prandtl number on turbulent sheared thermal convection
No full textIn turbulent wall sheared thermal convection, there are three different flow regimes, depending on the relative relevance of thermal forcing and wall shear. In this paper, we report the results of direct numerical simulations of such sheared Rayleigh–Bénard convection, at fixed Rayleigh number Ra = 10^6, varying the wall Reynolds number in the range 0 <= Rew <= 4000 and Prandtl number 0.22 <= Pr <= 4.6, extending our prior work by Blass et al. (J. Fluid Mech., vol. 897, 2020, A22), where Pr was kept constant at unity and the thermal forcing (Ra) varied. We cover a wide span of bulk Richardson numbers 0.014 <= Ri <= 100 and show that the Prandtl number strongly influences the morphology and dynamics of the flow structures. In particular, at fixed Ra and Rew, a high Prandtl number causes stronger momentum transport from the walls and therefore yields a greater impact of the wall shear on the flow structures, resulting in an increased effect of Rew on the Nusselt number. Furthermore, we analyse the thermal and kinetic boundary layer thicknesses and relate their behaviour to the resulting flow regimes. For the largest shear rates and Pr numbers, we observe the emergence of a Prandtl–von Kármán log layer, signalling the onset of turbulent dynamics in the boundary layer
