non-Oberbeck Boussinesq Research Articles

Experimental evidence of the correlation between the flow rolling structures and momentum transfer in Rayleigh–Bénard convection

The formation of large-scale circulating structures (LSC) is one of the critical characteristics of turbulent Rayleigh–Bénard convection (RBC). Although the effect of LSC in turbulent RBC was disputed due to conflicting results, recently, the results of three-dimensional direct numerical simulation [Zwirner et al., “Elliptical instability and multiple-roll flow modes of the large-scale circulation in confined turbulent Rayleigh-Bénard convection,” Phys. Rev. Lett. 125, 54502 (2020)] confirmed that in RBC flows with a low Prandtl number, Pr=0.1 within Oberbeck–Boussinesq assumption, the formation of higher number of LSC leads to a decrease in heat and momentum transfer. However, it was shown that for higher Prandtl numbers, heat/momentum transfer is not correlated with the number of LSC. Experimental evidence is investigated of an inverse correlation between the momentum transfer and small-scale rolling structures for high Prandtl non-Oberbeck–Boussinesq condition. Experiments were undertaken at a Prandtl number of Pr=7 and Rayleigh number of Ra=5.3×107 in a cubical convection cell with an unit aspect ratio. Particle image velocimetry along with a robust combinatorial vortex detection algorithm was used to capture the flow field, detect the rolling structures, and estimate their size. It was found that although the flow structures were dominated by the LSC, the number of smaller rolling structures was significant. The results also showed that after the initiation of convection while the flow was still undeveloped, the majority of rolling structures were small scale. For this state, an inverse correlation between the number of rolling structures and momentum transfer was observed highlighting the influence of flow rolling structures regardless of the formation of the LSC.

Influence of thermal buoyancy on the wake dynamics of a heated square cylinder

Direct numerical simulation of the three-dimensional (3-D) wake transition of a heated square cylinder subjected to horizontal cross-flow is performed in the presence of buoyancy. In order to capture the effects of large-scale heating, a non-Oberbeck–Boussinesq model is utilized, which includes the governing equations for compressible gas flow. All computations are performed at low free stream Mach number $M=0.1$ using air (free stream Prandtl number, $Pr=0.71$ ) as the working fluid. The 3-D instability modes A and B, which correspond to free stream Reynolds numbers of 180 and 250, are observed with longer and shorter spanwise wavelengths, respectively, and the onset of three-dimensionality is triggered at a Reynolds number of 173. In the presence of buoyancy, baroclinic vorticity production in the near-wake plays an important role for streamwise vorticity generation. The chaotic wake of the Mode-A instability bifurcates into periodic and quasiperiodic wakes at various heating levels, expressed by the overheat ratio, $\varepsilon =(T_w-T_\infty )/T_\infty$ , where $T_w$ and $T_\infty$ are the temperature of the cylinder surface and the ambient air, respectively. At low heating ( $\varepsilon =0.2$ ), the 3-D Mode-A instability is suppressed leading to a two-dimensional wake flow. Further increase in heating, again brings back the three-dimensionality in the wake through Mode-E instability. The variation of thermophysical properties and the effective Reynolds number with increase in heating level around the cylinder is examined. It is shown that the effect of thermophysical properties competes with the baroclinic streamwise vorticity generation at higher levels of heating ( $\varepsilon \geqslant 0.4$ ) to control the 3-D modes and wake dynamics.

Symmetry breaking of rotating convection due to non-Oberbeck–Boussinesq effects

The non-Oberbeck–Boussinesq (NOB) effects arising from variations in thermal expansivity are theoretically and numerically studied in the context of rotating Rayleigh–Bénard convection in forms of two-dimensional rolls. The thermal expansivity increases with pressure (depth), and its variation is measured by a dimensionless factor ε. Utilizing an asymptotic expansion with weak nonlinearity, we derive an amplitude equation, revealing that NOB effects amplify the magnitude of convection. An ε2-order NOB correction leads to a symmetry breaking about the horizontal mid-plane, manifested in the strengthening of convection near the bottom and its weakening near the top, forming bottom-heavy profiles. At ε3-order, the conjunction of NOB effects and nonlinear advection leads to a horizontal symmetry breaking. The values of Taylor number and Prandtl number determine whether upward or downward plumes are stronger. Numerical calculations validate the theoretical analyses in weakly nonlinear regime. This work advances our understanding of hydrothermal plumes in some winter lakes on Earth and in the subglacial oceans on icy moons as well as tracer transport from the seafloor to the ice shell.

Non-Oberbeck–Boussinesq effects on a differentially heated vertical cavity with high-Prandtl number fluid

This study explores the non-Oberbeck–Boussinesq (NOB) effects on hydrodynamics and heat transport in two-dimensional glycerol-filled differentially heated vertical cavity (DHVC). The simulations span Rayleigh numbers (Ra) from 2×103 to 5×109 and temperature difference (Δθ̃) up to 50 K at a Prandtl number (Pr) of 2547. We showed the emergence of stratified flow structures, delineated the NOB effects on temperature distribution symmetry, and analyzed the scaling behaviors of the Nusselt number (Nu), Reynolds number (Re), and thermal boundary layer (BL) thicknesses (λ¯hθ and λ¯cθ) against Ra. For Ra≥3×105, the stratification number (S) shows reduced sensitivity to changes in Ra, stabilizing around 0.5. Additionally, the center temperature (θcen) appears to be unaffected by Ra and increases linearly with Δθ̃ for Ra>106, satisfying θcen≈2.99×10−3K−1Δθ̃. Our results also revealed that Nu∼Raγ Nu and Re∼RaγRe with 0.2649≤γ Nu≤0.2654 and 0.3633≤γ Re≤0.3643, respectively, where γ Nu and γ Re exhibit a monotonic decrease as NOB effects intensify. For all investigated Ra values, NuNOB/NuOB<1 and ReNOB/ReOB>1 hold consistently, with deviations from OB predictions capped at 6.38% and 2.63% for Ra≥108, respectively. The analysis of thermal BL thickness reveals distinct scaling behaviors, characterized by λ¯h,cθ∼Raγ λ¯ h, c, with scaling exponents ranging from −0.2690 to −0.2669 for both OB and NOB scenarios. Notably, it reveals a divergence from water-based DHVC trends, showing linear decreases in the hot wall's scaling exponent and increases for the cold wall.

Non-Oberbeck–Boussinesq effects on the linear stability of a vertical natural convection boundary layer

The non-Oberbeck–Boussinesq effects on the stability of a vertical natural convection boundary layer are investigated using the linearised disturbance equations for air flows up to a temperature difference of $\Delta T=100\,{\rm K}$ . Based on the linear stability results, the neutral curve is shown to be sensitive to the choice of reference temperature. When evaluated using the film temperature $T_f$ , a lower film Grashof number is required to trigger the linear instability for larger $\Delta T$ . The relative contributions of shear and buoyant production to the perturbation kinetic energy budget reveals that the marginally unstable modes are amplified based on different mechanisms: for lower wavenumbers at relatively small Grashof number, the instability is driven by buoyancy; whereas for higher wavenumbers and larger Grashof number, the flow becomes unstable due to a shear instability. The use of reference temperature is found to scale the shear- and buoyant-driven instabilities differently so that no single reference temperature definition would collapse the neutral curves. The linear stability result further demonstrates that at a given Grashof number a higher temperature difference would give a larger amplification rate of the perturbation, which then leads to an earlier onset of the nonlinearities when evaluated at $T_f$ . Finally, by comparing the amplification rates obtained from direct numerical simulation and the linear stability results, the extent of the linear regime is determined for $\Delta T = 100\,{\rm K}$ .

Temperature field of non-Oberbeck–Boussinesq Rayleigh–Bénard convection in a low aspect ratio cell

A time-resolved experimental investigation was undertaken on the temperature evolution of Rayleigh–Bénard convection (RBC) in a slender convection cell with aspect ratio of Γ=0.1. Experiments were conducted for Rayleigh numbers of Ra=5.3×107, 7.6×107, and 9.5×107 and Prandtl number of Pr≈6 within the non-Oberbeck–Boussinesq (NOB) condition with a temperature difference variation in the range of 30 °C≤ΔT≤40 °C. Measurement of the temperature was by applying time-resolved two-color planar laser-induced fluorescence over the initial 2400 s. Experimental observations showed that the lateral confinement of the convection cell leads to the development of a single large-scale thermal plume instead of multiple plumes. Results showed that contrary to expectations, lateral confinement was found to be ineffective in suppressing temperature oscillations near thermal boundaries. Results also indicated that for Ra=5.3×107, 7.6×107, the temperature oscillations had a frequency of f≈0.028 Hz similar to the frequency of the oscillations in Oberbeck–Boussinesq (OB) RBC. For Ra=9.5×107, however, it was found that the frequency of the oscillations was much lower than the OB RBC with a relatively wide range of the oscillations in the vicinity of f≈0.006 Hz. It is also found that the lateral confinement and formation of singular high-energy thermal plumes leads to an increase in the nonsymmetrical temperature distribution of NOB RBC with a bimodal distribution of the temperature field, deviating significantly from the Gaussian distribution temperature field found in OB RBC.

Effects of inclination angle on Rayleigh–Bénard convection under non-Oberbeck–Boussinesq approximation in air

This study employs direct numerical simulations to explore the combined effects of inclination angles (ϕ) and non-Oberbeck–Boussinesq (NOB) conditions on heat transfer and flow patterns in inclined Rayleigh–Bénard convection (RBC). The simulations, conducted in air, classify flow behavior into seven regimes based on roll number and flow state. Heat-transport efficiency is found to be higher in the single-roll state. The study investigates the influence of NOB and inclination on top-bottom symmetry in a fluid-filled cavity, with systematic analysis revealing complex non-monotonic behaviors of the Nusselt number (Nu) and Reynolds number (Re) under different conditions. The effects of ϕ on heat transfer are significant in the modest to moderate range of Rayleigh numbers, becoming less pronounced as these values increase. The study finds that power-law scalings of Nu and Re are sensitive to the inclination angle and robust against NOB effects for ϕ≥40∘. Moreover, in NOB scenarios, the distributions of the local thermal boundary layers (BLs) along the hot and cold walls exhibit a lack of antisymmetry. As a result, there is an obvious deviation between the hot and cold global thermal BLs, which is further influenced by the inclination angle.

Modulation of Rayleigh–Bénard convection with a large temperature difference by inertial nonisothermal particles

This study investigates the modulation by inertial nonisothermal particles in two-dimensional Rayleigh–Bénard (RB) convection with non-Oberbeck–Boussinesq effects due to a large temperature difference. Direct numerical simulations combined with a Lagrangian point-particle method are performed for 1×106≤Ra≤1×108 and 6.1×10−3≤Stf≤1.2, where the Rayleigh number Ra and Stokes number Stf measure the vigor of convection and particle response time, respectively. The typical aspect ratio Γ = 1 is of primary concern. We find that a horizontally arranged double-roll flow pattern prevails at intermediate Stokes numbers with optimal heat transfer efficiency, which has never been reported before. Compared to the single-phase cases, the heat transfer efficiency is enhanced by a factor of two or three. For micro Stokes numbers, unlike cases in the Oberbeck–Boussinesq limit where the addition of particles causes a small amount of flow structure changes, in this study, it is observed that a tiny volume load of particles could actually induce significant flow oscillations or trigger fluid instability for Ra=106; conversely, for medium Rayleigh numbers (Ra=107), it is found that flow reversal is slightly suppressed by small particles. For intermediate Stokes numbers, where particle–fluid couplings are strongest and a wealth of new phenomena emerge, special attention is paid. Considering different aspect ratios, after the addition of particles, it is found that closed RB systems tend to contain an even number of convection rolls rather than odd ones. Quantitatively, heat transfer also improves significantly for various aspect ratios for intermediate Stokes numbers. Subsequent investigations reveal that the narrowing of the horizontal size of convection rolls cannot fully explain the significant enhancement; instead, it should also be attributed to strong couplings between particles and fluid dynamics. Moreover, it is found that both momentum and thermal couplings play crucial roles in enhancing heat transfer efficiency.

Effects of aspect ratio on Rayleigh–Bénard convection under non-Oberbeck–Boussinesq effects in glycerol

Effects of aspect ratio on Rayleigh–Bénard convection under non-Oberbeck–Boussinesq effects in glycerol

Enhancing heat transfer from a circular cylinder undergoing vortex induced vibration based on reinforcement learning

Machine learning approaches have been proven to be effective and efficient in mediating flow dynamics so as to realize drag reduction, vibration suppression, etc. In this article, an intelligent active flow control approach is proposed to enhance heat transfer of a heated circular cylinder at Re=100 undergoing vortex induced vibration in the lock-in condition. A high-fidelity solver based on the generalized interpolation-supplemented lattice Boltzmann method (GILBM) with moving reference frame (MRF) is used to establish the real-time numerical environment with structural motion, momentum transport, and heat transport. A reinforcement learning (RL) agent realized by proximal policy optimization (PPO) is adopted to establish the model-free controller, which receives sensorymotor cues as feedback signals and determines the real-time velocity issued from the jet as actuation. Through a group of trainings, each of whom involves 200 independent cases, the RL agent eventually learns an effective and efficient control strategy that improves the average heat transfer rate by 76.7%, quantified by the dimensionless Nusselt number. Through analyzing the spatiotemporal variations of vorticity and temperature fields, local Nusselt number and pressure coefficient along the cylinder surface, as well as the statistical flow quantities, it is proved that that the enhanced heat transfer is contributed by both the mediated vortex formation and shedding in vicinity of the blowing jet, as well as the augmented vibration. Extra tests also confirm that the synthetic jets play a much more significant role than the augmented vibration. Furthermore, the success of the control strategy is attributed mainly by the phase lag between the maximum vibration displacement and the moment when the synthetic jets oppose their directions. Moreover, the more realistic but more complicated case with the non-Oberbeck-Boussinesq (NOB) approximation is also tested, confirming good self-adaptivity of the learnt strategy. Through this study, it is verified that the RL to be a powerful tool for mediating flows involving complicated momentum and heat transport.

Non-Oberbeck–Boussinesq effects on a water-filled differentially heated vertical cavity

In this study, we examined non-Oberbeck–Boussinesq (NOB) effects on a water-filled differentially heated vertical cavity through two-dimensional direct numerical simulations. The simulations encompassed a Rayleigh number (Ra) span of 107–1010, temperature difference (Δθ̃) up to 60 K, and a Prandtl number (Pr) fixed at 4.4. The center temperature (θcen) was found to be independent of Ra and to increase linearly with Δθ̃, as presented by θcen≈1.18×10−3 K−1Δθ̃. The thermal boundary layer (BL) thicknesses near the hot and cold walls (λ¯hθ and λ¯cθ, respectively) are found to scale as λ¯h,cθ∼Raγ λ¯h,c, where the scaling exponent γ λ¯h,c ranges from −0.264 to −0.262. For more detail, the scaling exponent γ λ¯h displays an increasing trend, while γ λ¯c demonstrates a decreasing trend. However, the sum of the hot and cold thermal BL thicknesses was found to be constant at a fixed Ra in the presence of NOB effects. Our detailed investigation of the Nusselt number (Nu) and Reynolds number (Re) revealed that Nu∼Ra0.258 and Re∼Ra0.364, showing insensitivity to NOB effects. These exponents were smaller than those for Rayleigh–Bénard convection. The NOB modifications on Nu and Re were less than 1.2% and 2.5%, respectively, even at Δθ̃=60 K. Our results also revealed that key parameters such as θcen and normalized ratios [(λ¯NOBθ/λ¯OBθ)h,c, NuNOB/NuOB, and ReNOB/ReOB] exhibit universal correlations with Δθ̃. Remarkably, these relationships are consistent across varying Ra values. This observation underscored the influence of NOB effects on these parameters could be confidently forecasted using just the temperature difference (Δθ̃) for Ra∈[107,1010].

Three-dimensional wake transition of a heated square cylinder in the presence of cross-buoyancy

The three-dimensional flow transition is examined in the wake of a heated square cylinder subjected to horizontal cross-flow perpendicular to gravity utilizing a direct numerical simulation approach. The surface of the square cylinder is heated uniformly to an elevated temperature Tw, and the amount of excess temperature is represented as the over-heat ratio ε=(Tw−T∞)/T∞, where T∞ represents the surrounding temperature. The effects of large-scale heating on the transport properties and thermal straining of the fluid particles are captured using an in-house non-Oberbeck–Boussinesq compressible model. The compressible flow governing equations (in a body-fitted coordinate system) are solved using a variant of flux-based particle velocity upwind-modified+ (PVU-M+) technique [Ahmad et al., “On the formation and sustenance of the compressible vortex rings in starting axisymmetric jets: A phenomenological approach,” Phys. Fluids 32, 126114 (2020)]. In this investigation, all computations are conducted at a low Mach number (Ma = 0.1) and air (Prandtl number, Pr = 0.71) is used as the working fluid. As the heating level rises, the shape and wavelength of the vortical structure undergo significant alterations. At Re = 250, the mode-B transition with a shorter spanwise wavelength and the mode-D transition with a longer wavelength are observed, respectively, for heating levels ε=0.0−0.2 and ε=0.8−1.0. Furthermore, for heating levels in the range 0.4≤ε≤0.6, an intermediate wavelength of the mode-E transition is detected. The temporal variation of fluid properties such as the force coefficient (CL, CD) and the Nusselt number (Nu) are shown at various heating levels. In addition, surface vorticity is examined in order to comprehend the flow dynamics near the surface of a heated square cylinder.

Non-Oberbeck–Boussinesq effects in two-dimensional Rayleigh–Bénard convection of different fluids

Non-Oberbeck–Boussinesq (NOB) effects in three representative fluids are quantitatively investigated in two-dimensional Rayleigh–Bénard convection. Numerical simulations are conducted in air, water, and glycerol with Prandtl numbers of Pr=0.71,4.4, and 2547, respectively. We consider Rayleigh number Ra∈[106,109] involving temperature difference (Δθ̃) of up to 60 K. The velocity and temperature profiles are found to be top-bottom antisymmetric under NOB conditions. As Pr increases, the time-averaged temperature of the cavity center ⟨θc⟩t increases under NOB conditions and the value of ⟨θc⟩t is only weakly influenced by Ra for all fluids. For Pr = 4.4 and 2547, with the enhancement of NOB effects, ⟨θc⟩t linearly increases and the maximum θ rms decreases/increases, and its location shifts toward/away from the wall near the bottom/top wall. Dispersed ⟨θc⟩t points and opposite phenomenon are observed in Pr = 0.71. The Nusselt number (Nu) and thermal boundary layer thickness at hot and cold walls (λ¯h,cθ) of the three fluids are comparable, and the Reynolds number (Re) significantly decreases as Pr increases. Under the NOB conditions with Pr = 4.4 and 2547, Nu decreases, Re increases, and λ¯hθ (λ¯cθ) thins (thickens) in an approximately linear fashion. Furthermore, the NOB effects on Nu, Re, and λ¯h,cθ are relatively small for Pr = 0.71 and 4.4, whereas the modifications caused by NOB effects at Pr = 2547 are more significant. The power-law scaling factors of Nu, Re, and λ¯h,cθ are demonstrated to be robust to Pr, as well as NOB effects.

A numerical framework for low-speed flows with large thermal variations

In the numerical simulation of fluid dynamic problems there are situations in which low-speed flows exhibit a non-negligible density variation driven by thermal or compositional distributions. A new method for solving the Low Mach Number equations governing such flows is developed. The basis of the formulation is the semi-implicit scheme build on the Non-oscillatory Forward-in-Time integrator encompassing Multidimensional Positive Definite Advection Transport Algorithm and a robust Krylov solver. The spatial discretisation is constructed using the median dual finite volumes and the method is second-order-accurate in space and time. A collocated arrangement of all flow variables is implemented. The validity of the presented method is evaluated using the Differentially Heated Cavity flows. Three-dimensional simulations demonstrate its efficacy and ability to capture the Non-Oberbeck–Boussinesq effects. Ideally, a numerical method should be able to treat different flow regimes without strong limitations. When implemented, it is shown that in the limit of small density variations the new formulation correctly reproduces simulations of incompressible flows subject to the Oberbeck–Boussinesq approximation. Furthermore, the three-dimensional computations set to the quasi-two-dimensional cases are in excellent agreement with the established two-dimensional Differentially Heated Cavity benchmarks.

PaScaL_TCS: A versatile solver for large-scale turbulent convective heat transfer problems with temperature-dependent fluid properties

PaScaL_TCS is an efficient and scalable solver for large-scale direct numerical simulations of natural convective flow that considers temperature-dependent fluid properties. For increased scalability on a massive-scale distributed memory system, the solver decomposes the computational domain into a cubic sub-domain. The numerical procedure is based on the monolithic projection method with staggered time discretization [1], which is an implicit and non-iterative solver for wall-bounded domains. The PaScaL_TDMA library is used to solve batched tridiagonal systems, which are partitioned according to domain decomposition. For parallel fast Fourier transform in a Fourier Poisson solver for pressure, two transpose schemes with different communicator sizes are proposed and compared according to the number of cores. An explicit intermediate aggregation scheme for MPI-IO is suggested to reduce the number of processes that simultaneously take part in parallel IO. The overall implementation was evaluated using the Nurion cluster system of the Korea Institute of Science and Technology Information with detailed performance profiling. With the efficient communication, the results showed good strong and weak scalability up to 131,072 cores. The file IO performance improved with the suggested MPI-IO scheme using explicit aggregation, especially when many processes are involved in parallel IO. The solver was verified by conducting large-scale differentially heated vertical convection flow simulations under the Oberbeck–Boussinesq (OB) approximation. The capability of the solver to capture and quantitatively describe the non-OB effect was demonstrated via glycerol Rayleigh–Bénard convection flow simulations. Program summaryProgram Title: PaScaL_TCSCPC Library link to program files:https://doi.org/10.17632/3b2bysrcxm.1Developer's repository link:https://github.com/MPMC-LabLicensing provisions: MITProgramming language: Fortran90Nature of problem: Solving the incompressible Navier-Stokes equations for natural convective flow considering the non-Oberbeck–Boussinesq effect, which considers the temperature dependence of fluids properties, in three-dimensional channel domain.Solution method: PaScaL_TCS uses the monolithic projection-based method with staggered time discretization (MPM-STD) [1]. It employs the Crank-Nicolson scheme along with staggered time which evaluates scalar and vector variables at the (n+1/2) and (n+1) time level, respectively. PaScaL_TDMA [2] is used to solve multiple tridiagonal matrix systems for decoupled energy and momentum equations in a distributed memory system. The Poisson equation solver for the pressure-correction scheme is based on Fourier diagonalization. MPI_Alltoallw is used for parallel FFT. PaScaL_TCS supports a single-file-based parallel IO for efficient data generation in large-scale computing.

Beyond the Oberbeck–Boussinesq and long wavelength approximation

We present the first simulations of a reduced magnetized plasma model that incorporates both arbitrary wavelength polarization and non-Oberbeck–Boussinesq effects. Significant influence of these two effects on the density, electric potential and vorticity and non-linear dynamics of interchange blobs are reported. Arbitrary wavelength polarization implicates so-called gyro-amplification that compared to a long wavelength approximation leads to highly amplified small-scale vorticity fluctuations. These strongly increase the coherence and lifetime of blobs and alter the motion of the blobs through a slower blob-disintegration. Non-Oberbeck–Boussinesq effects incorporate plasma inertia, which substantially decreases the growth rate and linear acceleration of high amplitude blobs, while the maximum blob velocity is not affected. Finally, we generalize and numerically verify unified scaling laws for blob velocity, acceleration and growth rate that include both ion temperature and arbitrary blob amplitude dependence.

Study of Rayleigh–Bénard Convection in Jet-A fuel with non-Oberbeck–Boussinesq effect

Two-dimensional Direct Numerical Simulation (DNS) of Rayleigh–Bénard Convection of Jet-A fluid (Pr=19.17) is performed in a square cavity. The Rayleigh number of this study is Ra=107 with a temperature difference ΔT=40 K between hot and cold plates to account for non-Oberbeck–Boussinesq (NOB) effect. The Jet-A fluid has higher viscosity and lower thermal conductivity compared to water and the Prandtl number is approximately 4.4 times higher than water at mean temperature of 40 °C. The fluid properties of the working fluid are defined as a polynomial function of temperature. The Boundary layer thicknesses, the Centre line temperature, Flow reversals and the Proper Orthogonal Decomposition (POD) modes are investigated. We report the standard and cessation type flow reversals for the Jet-A fluid with Prandtl number of around 19. The power spectral density (PSD) of velocity follows the Bolgiano–Obukhov (BO) scaling.

Turbulent Rotating Rayleigh–Bénard Convection

Rotation with thermally induced buoyancy governs many astrophysical and geophysical processes in the atmosphere, ocean, sun, and Earth's liquid-metal outer core. Rotating Rayleigh–Bénard convection (RRBC) is an experimental system that has features of rotation and buoyancy, where a container of height H and temperature difference Δ between its bottom and top is rotated about its vertical axis with angular velocity Ω. The strength of buoyancy is reflected in the Rayleigh number (∼ H3Δ) and that of the Coriolis force in the Ekman and Rossby numbers (∼Ω−1). Rotation suppresses the convective onset, introduces instabilities, changes the velocity boundary layers, modifies the shape of thermal structures from plumes to vortical columns, affects the large-scale circulation, and can decrease or enhance global heat transport depending on buoyant and Coriolis forcing. RRBC is an extremely rich system, with features directly comparable to geophysical and astrophysical phenomena. Here we review RRBC studies, suggest a unifying heat transport scaling approach for the transition between rotation-dominated and buoyancy-dominated regimes in RRBC, and discuss non-Oberbeck–Boussinesq and centrifugal effects.

Monolithic projection-based method with staggered time discretization for solving non-Oberbeck–Boussinesq natural convection flows

This paper presents an efficient monolithic projection-based method with staggered time discretization (MPM-STD) to examine the non-Oberbeck–Boussinesq (NOB) effects in several natural convection problems involving dramatic temperature-dependent changes in fluid properties. The proposed approach employs the Crank–Nicolson scheme along with staggered time discretization to discretize the momentum and energy equations. The momentum and energy equations are decoupled by evaluating the velocity vector at integral time levels (n+1), and the scalar variables (pressure and temperature) at half-integral time levels (n+12). The observed density variations in all terms result in a variable-coefficient Poisson equation, which is difficult to solve efficiently. The convergence is accelerated via adoption of an appropriate pressure-correction scheme that transforms the aforementioned Poisson equation to a constant-coefficient form. The numerical simulations concerning two-dimensional (2D) periodic NOB Rayleigh–Bénard convection (RBC) in glycerol and 2D differentially heated cavity (DHC) problem in air confirmed the second-order temporal and spatial accuracies of the proposed method. By simulating the 2D DHC problem in air and the RBC problem in liquid (water or glycerol) considering NOB effects, it is concluded that the proposed MPM-STD significantly mitigates the time-step restriction, thereby increasing the computational efficiency, which exceeds that of existing semi-implicit and explicit schemes. Moreover, the potential of the proposed approach with regard to solving challenging three-dimensional (3D) turbulent problems is demonstrated by performing direct simulations of turbulent RBCs under NOB effects involving temperature differences up to 60 K with a corresponding Rayleigh number (Ra=106).

Vortex Flow on the Surface Generated by the Onset of a Buoyancy-Induced Non-Boussinesq Convection in the Bulk of a Normal Liquid Helium.

The onset of the Rayleigh–Benard convection (RBC) in a heated from above normal He-I layer in a cylindrical vessel in the temperature range Tλ < T ≤ Tm (RBC in non-Oberbeck–Boussinesq approximation) is attended by the emergence of a number of vortices on the free liquid surface. Here, Tλ = 2.1768 K is the temperature of the superfluid He-II–normal He-I phase transition, and the liquid density passes through a well-pronounced maximum at Tm ≈ Tλ + 6 mK. The inner vessel diameter was D = 12.4 cm, and the helium layer thickness was h ≈ 2.5 cm. The mutual interaction of the vortices between each other and their interaction with turbulent structures appeared in the layer volume during the RBC development gave rise to the formation of a vortex dipole (two large-scale vortices) on the surface. Characteristic sizes of the vortices were limited by the vessel diameter. The formation of large-scale vortices with characteristic sizes twice larger than the layer thickness can be attributed to the arising an inverse vortex cascade on the two-dimensional layer surface. Moreover, when the layer temperature exceeds Tm, convective flows in the volume decay. In the absence of the energy pumping from the bulk, the total energy of the vortex system on the surface decreases with time according to a power law.