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The analogy between rotating shear flow and thermal convection suggests the existence of plumes, inertial waves and plume currents in plane Poiseuille flow under spanwise rotation. The existence of these flow structures is examined with the results of three-dimensional and two-dimensional three-component direct numerical simulations. The dynamics of plumes near the unstable side is embodied in a truncated exponential distribution of turbulent fluctuations. For large rotation numbers, inertial waves are identified near the stable side, and these can be used to explain the abnormal flow statistics, such as the large root-mean-square of the streamwise velocity fluctuation and the nearly negligible Reynolds shear stress. For small or medium rotation numbers, plumes generated from the unstable side form large-scale plume currents and the patterns of the plume currents show different capabilities in scalar transport.
In this paper, we propose a series expansion of the baroclinic torque in low-Mach-number flows, so that the accuracy and universality of any buoyancy term could be examined analytically, and new types of buoyancy terms could be constructed and validated. We first demonstrate that the purpose of introducing a buoyancy term is to approximate the baroclinic torque, and straightforwardly the error of any buoyancy term could be defined with the deviation of its curl from the corresponding baroclinic torque. Then a regular perturbation method is introduced for the elliptic equation of the hydrodynamic pressure in low-Mach-number flows, resulting in a sequence of Poisson equations, whose solutions lead to the series representation of the baroclinic torque and the new types of buoyancy terms. It is found that the frame invariance of the momentum equation is maintained with one of the new types of buoyancy terms. With the error definition of buoyancy terms and the series representation of the baroclinic torque, the validity and accuracy of previous and new buoyancy terms are examined. Finally, numerical simulations confirm that, with a decreasing density variation or an increasing order of our new buoyancy term, the simplified equations can converge to the original low-Mach-number equations.
In this paper, we designed two different configurations with locally isothermal sidewalls, where the temperature is set to be the bulk temperature, to control the large-scale circulation in turbulent Rayleigh–Bénard convection, namely two-point control and four-point control. At fixed Rayleigh number $Ra=10^8$ and Prandtl number $Pr=2$, a series of direct numerical simulations are performed on both two-dimensional (2-D) and quasi-two-dimensional (quasi-2-D) cavities with both types of control, where the width of the control area is fixed at $\delta _c=0.05$ and the vertical distance from the cavity centre $h_c$ varies from 0 to 0.45 with an interval of 0.05. Our results show that the control effect depends on $h_c$, the control configurations as well as the flow dimensions. For 2-D cavities, both two-point control and four-point control suppress the flow reversal when $h_c \geq 0.05$, accompanied by the enhancement of vertical heat transfer and the strength of the large-scale circulation. For quasi-2-D cavities, the suppression of the flow reversals is obvious with two-point control and $h_c\geq 0.05$, while the effect is rather limited with four-point control. Further experiments with $Pr=5.7$ and $Ra$ up to $7.36\times10^8$ show that two-point control with $h_c=0.15$ can effectively suppress the flow reversal, while two-point control with $h_c=0$ can suppress the reversals at low $Ra=1.93\times 10^8$ and activate them at higher $Ra=7.36\times 10^8$, which agrees well with our numerical simulations.
In this paper, we report that reversals of large-scale circulation in two-dimensional Rayleigh–Bénard convection could be suppressed or enhanced by imposing local constant-temperature control on sidewalls. When the control area is away from the centre of the sidewalls, the control can successfully eliminate the flow reversal if the size of the control region is large enough. With a proper location, the width can be as small as 1 % of the system size. When the control region is located around the centre, the control may enhance the flow reversal. It may also stimulate the occurrence of a double-roll mode when the control is located in the centre. Explanations are also discussed based on the twofold effects of the control region on the nearby plumes and the concept of symmetry. The present work provides a new way to control the flow reversals in Rayleigh–Bénard convection through modifying sidewall boundary conditions.
Spanwise rotating plane Poiseuille flow (RPPF) is one of the canonical flow problems to study the effect of system rotation on wall-bounded shear flows and has been studied a lot in the past. In the present work, a two-dimensional-three-component (2D/3C) model for RPPF is introduced and it is shown that the present model is equivalent to a thermal convection problem with unit Prandtl number. For low Reynolds number cases, the model can be used to study the stability behaviour of the roll cells. It is found that the neutral stability curves, critical eigensolutions and critical streamfunctions of RPPF at different rotation numbers ($Ro$) almost collapse with the help of a rescaling with a newly defined Rayleigh number $Ra$ and channel height $H$. Analytic expressions for the critical Reynolds number and critical wavenumber at different $Ro$ can be obtained. For a turbulent state with high Reynolds number, the 2D/3C model for RPPF is self-sustained even without extra excitations. Simulation results also show that the profiles of mean streamwise velocity and Reynolds shear stress from the 2D/3C model share the same linear laws as the fully three-dimensional cases, although differences on the intercepts can be observed. The contours of streamwise velocity fluctuations behave like plumes in the linear law region. We also provide an explanation to the linear mean velocity profiles observed at high rotation numbers.
Nanociystalline Z1O2 powders, prepared by plasma-chemical method, were sintered by microwave heating. The experimental results indicated that the thermal runaway and hot spot are two important obstacles to successful microwave sintering of nanocrystalline ZrO2. By controlling ratio of dielectric loss between sintered ZrO2 compact and adjacent thermal insulator, the ZrO2 compact with diameter larger than 30 mm could be microwave-heated rapidly and uniformly from room temperature to 1600 °C in 80 minutes, the mean grain size of ZrCh ( 96% T.D. sintered at 1500°C for 5 minutes) is lower than 20 nm determined by means of quantitative XRD and TEM. The change of ZrO2 grain size may be related to phase transformation (t→m).
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