Turbulent Convection Research Articles

Computational Analysis of Turbulent Natural Convection in Water Filled Tall Enclosure

In this study, the turbulent buoyancy driven fluid flow and heat transfer in a differentially heated rectangular enclosure filled with water is quantified numerically. The two dimensional governing differential equations are discretized using the finite volume method. SIMPLE algorithm is employed to obtain stabilized solution for high Rayleigh numbers by a computational code written in FORTRAN language. A parametric study is undertaken and the effect of Rayleigh numbers (1010 to 1014), the aspect ratio (30, 40 and 50), and the tilt angle (10o to 170o ) on fluid flow and heat transfer are investigated. The results of the adopted model in the present work is compared with previously published results and a qualitative agreement and a good validation is obtained. Results show that the fluid circulation and temperature fields are strongly affected by the enclosure tilt angle and Rayleigh Number.

Turbulent convection as a significant hidden provider of magnetic helicity in solar eruptions

Solar flares and coronal mass ejections, the primary space weather disturbances affecting the entire heliosphere and near-Earth environment, mainly emanate from sunspot regions harbouring high degrees of magnetic twist. However, it is not clear how magnetic helicity, the quantity for measuring the magnetic twist, is supplied to the upper solar atmosphere via the emergence of magnetic flux from the turbulent convection zone. Here, we report state-of-the-art numerical simulations of magnetic flux emergence from the deep convection zone. By controlling the twist of emerging flux, we find that with the support of convective upflow, the untwisted emerging flux can reach the solar surface without collapsing, in contrast to previous theoretical predictions, and eventually create sunspots. Because of the turbulent twisting of magnetic flux, the produced sunspots exhibit rotation and inject magnetic helicity into the upper atmosphere, amounting to a substantial fraction of injected helicity in the twisted cases that is sufficient to produce flare eruptions. This result indicates that the turbulent convection is responsible for supplying a non-negligible amount of magnetic helicity and potentially contributes to solar flares.

Propagation and interference of thermal waves in turbulent thermal convection

We observe propagation and interference of two coherent thermal waves in the highly turbulent core of convective Rayleigh-B\'enard flow of cryogenic helium gas generated by top and bottom boundaries with harmonically oscillating temperatures. When the same amplitude of modulation is applied to both plates at slightly different frequencies, the resulting temperature interference pattern in the turbulent core shows a periodic increase and decrease in amplitude. If the observed time record of thermal wave interference were converted to corresponding pressure oscillations and shifted to higher frequencies, one would hear the acoustic beats often used, e.g., in tuning stringed musical instruments.

Measurement of the turbulent heat fluxes in mixed convection using combined stereoscopic PIV and PIT

The results of simultaneous measurements of velocity and temperature fields in a turbulent mixed convection airflow are analyzed and discussed. To access local temperature and velocity fields in airflows, we present a combination of stereoscopic particle image velocimetry and particle image thermometry. The obtained flow fields make it possible to determine the local convective heat fluxes, thus giving insight into the dynamics of plumes and Taylor–Görtler-like vortices. The evaluated mean local heat fluxes further reveal that the main convection roll transports a substantial amount of heat along the cooling plate and back to the heated bottom plate. Yet, the associated mean turbulent heat fluxes remain positive as they are dominated by the correlation of the temperature and the vertical velocity component. More specifically, a statistical analysis of the local heat flux distribution reveals that Taylor–Görtler-like vortices lead to more skewed distributions of the turbulent convective heat fluxes than plumes.Graphical abstract

Effects of strong fringing magnetic fields on turbulent thermal convection

We study the influence of fringing magnetic fields on turbulent thermal convection in a horizontally extended rectangular domain. The magnetic field is created in the gap between two semi-infinite planar magnetic poles, with the convection layer located near the edge of the gap. We employ direct numerical simulations in this set-up for fixed Rayleigh and small Prandtl numbers, but vary the fringe width by controlling the gap between the magnetic poles and the convection cell. The magnetic field generated by the magnets is strong enough to cease the flow in the high magnetic flux region of the convection cell. We observe that as the local vertical magnetic field strength increases, the large-scale structures become thinner and align themselves perpendicular to the longitudinal sidewalls. We determine the local Nusselt and Reynolds numbers as functions of the local Hartmann number (based on the vertical component of the magnetic field), and estimate the global heat and momentum transport. We show that the global heat transport decreases with increasing fringe width for strong magnetic fields but increases with increasing fringe width for weak magnetic fields. In the regions of large vertical magnetic fields, the convective motion becomes confined to the vicinity of the sidewalls. The amplitudes of these wall modes show a non-monotonic dependence on the fringe width.

Boundary-Layer Disruption and Heat-Transfer Enhancement in Convection Turbulence by Oscillating Deformations of Boundary.

In this Letter, we propose a novel strategy for significantly enhancing the heat transfer in convection turbulence. By introducing a boundary deformation of the standing-wave type, flow modulation can be realized when the amplitude is comparable or larger than the boundary-layer thickness. For a fixed moderate frequency, the entire fluid layer follows the boundary motion at small wave numbers, while only the near-wall regions are affected by the boundary deformation at large wave numbers. The heat-flux enhancement happens for the latter. For a fixed wave number and gradually increasing frequency, the vortical flows inside the wave valleys exhibit nonlinear transition and alter the distribution of boundary heat flux, and the global heat flux increases significantly at large enough frequencies. The current findings suggest that oscillating deformations of boundary can efficiently break the boundary layers, which serves as the bottleneck of global heat transfer, and open a new venue for modulating the convection turbulence.

Effect of shear on local boundary layers in turbulent convection

In Rayleigh Bénard convection, for a range of Prandtl numbers $4.69 \leqslant Pr \leqslant 5.88$ and Rayleigh numbers $5.52\times 10^5 \leqslant Ra \leqslant 1.21\times 10^9$ , we study the effect of shear by the inherent large-scale flow (LSF) on the local boundary layers on the hot plate. The velocity distribution in a horizontal plane within the boundary layers at each $Ra$ , at any instant, is (A) unimodal with a peak at approximately the natural convection boundary layer velocities $V_{bl}$ ; (B) bimodal with the first peak between $V_{bl}$ and $V_{L}$ , the shear velocities created by the LSF close to the plate; or (C) unimodal with the peak at approximately $V_{L}$ . Type A distributions occur more at lower $Ra$ , while type C occur more at higher $Ra$ , with type B occurring more at intermediate $Ra$ . We show that the second peak of the bimodal type B distributions, and the peak of the unimodal type C distributions, scale as $V_{L}$ scales with $Ra$ . We then show that the areas of such regions that have velocities of the order of $V_{L}$ increase exponentially with increase in $Ra$ and then saturate. The velocities in the remaining regions, which contribute to the first peak of the bimodal type B distributions and the single peak of type A distributions, are also affected by the shear. We show that the Reynolds number based on these velocities scale as $Re_{bs}$ , the Reynolds number based on the boundary layer velocities forced externally by the shear due to the LSF, which we obtained as a perturbation solution of the scaling relations derived from integral boundary layer equations. For $Pr=1$ and aspect ratio $\varGamma =1$ , $Re_{bs} \sim Ra^{0.375}$ for small shear, similar to the observed flux scaling in a possible ultimate regime. The velocity at the edge of the natural convection boundary layers was found to increase with $Ra$ as $Ra^{0.35}$ ; since $V_{bl}\sim Ra^{1/3}$ , this suggests a possible shear domination of the boundary layers at high $Ra$ . The effect of shear, however, decreases with increase in $Pr$ and with increase in $\varGamma$ , and becomes negligible for $Pr\geqslant 100$ at $\varGamma =1$ or for $\varGamma \geqslant 20$ at $Pr=1$ , causing $Re_{bs}\sim Ra_w^{1/3}$ .

On the propagation of gravity waves in the lower solar atmosphere in different magnetic configurations

Gravity waves are generated by turbulent subsurface convection overshooting or penetrating locally into a stably stratified medium. While propagating energy upwards, their characteristic negative phase shift over height is a well-recognized observational signature. Since their first detailed observational detection and estimates of energy content, a number of studies have explored their propagation characteristics and interaction with magnetic fields and other waves modes in the solar atmosphere. Here, we present a study of the atmospheric gravity wave dispersion diagrams utilizing intensity observations that cover photospheric to chromospheric heights over different magnetic configurations of quiet-Sun (magnetic network regions), a plage, and a sunspot as well as velocity observations within the photospheric layer over a quiet and a sunspot region. In order to investigate the propagation characteristics, we construct two–height intensity - intensity and velocity- velocity cross-spectra and study phase and coherence signals in the wavenumber - frequency dispersion diagrams and their association with background magnetic fields. We find signatures of association between magnetic fields and much reduced coherence and phase shifts over height from intensity-intensity and velocity-velocity phase and coherence diagrams, both indicating suppression/scattering of gravity waves by the magnetic fields. Our results are consistent with the earlier numerical simulations, which indicate that gravity waves are suppressed or scattered and reflected back into the lower solar atmosphere in the presence of magnetic fields.

Turbulent Convection at Very High Rayleigh Numbers and the Weakly Nonlinear Theory

To provide insights into the challenging problem of turbulent convection, Jack Herring used a greatly truncated version of the complete Boussinesq equations containing only one horizontal wavenumber. In light of later observations of a robust large-scale circulation sweeping through convecting enclosures at high Rayleigh numbers, it is perhaps not an implausible point of view from which to reexamine high-Rayleigh-number data. Here we compare past experimental data on convective heat transport at high Rayleigh numbers with predictions from Herring’s model and, in fact, find excellent agreement. The model has only one unknown parameter compared to the two free parameters present in the lowest-order least-squares power-law fit. We discuss why the underlying simplistic physical picture, meant to work at Rayleigh numbers slightly past the critical value of a few thousand, is consistent with the data when the single free parameter in it is revised, over some eleven decades of the Rayleigh number—stretching from about a million to about 1017.

Numerical simulation of turbulent natural convection heat transfer in an MW-class offshore wind turbine nacelle based on a multi-feature acquisition meshing technique

In order to improve the computational accuracy of numerical simulations of complex thermal environments in MW-class offshore wind turbine nacelles, this paper improves the numerical simulation method for 10 MW offshore wind turbine nacelles. Firstly, the model of the wind turbine generator system (WTGS) inside the nacelle is designed and the model is simplified. Secondly, a multi-featured acquisition meshing is performed for the turbulent thermal behavior in the nacelle, using a combination of mesh geometry parameters, mesh accuracy parameters, mesh irrelevance parameters and detection verification parameters to construct a structural mesh topology. The modified SST k-ω turbulence model is used to solve the momentum and energy equations of the nacelle model. The complex physical phenomena of air recirculation, boundary layer separation and thermal stratification in the nacelle are verified based on the calculated results and compared with the experimental data, which are in good agreement with the experimental results. This paper has certain application value and guidance significance in the field of engineering such as the design of offshore wind turbine nacelle structure and cooling system design.

Vertical Structure and Ice Production Processes of Shallow Convective Postfrontal Clouds over the Southern Ocean in MARCUS. Part I: Observational Study

Abstract A study of the vertical structure of postfrontal shallow clouds in the marine boundary layer over the Southern Ocean is presented. The central question of this two-part study regards cloud phase (liquid/ice) of precipitation, and the associated growth mechanisms. In this first part, data from the Measurements of Aerosols, Radiation, and Clouds over the Southern Ocean (MARCUS) field campaign are analyzed, starting with a 75-h case with continuous sea surface-based thermal instability, modest surface heat fluxes, an open-cellular mesoscale organization, and very few ice nucleating particles (INPs). The clouds are mostly precipitating and shallow (tops mostly around 2 km above sea level), with weak up- and downdrafts, and with cloud-top temperatures generally around −18° to −10°C. The case study is extended to three other periods of postfrontal shallow clouds in MARCUS. While abundant supercooled liquid water is commonly present, an experimental cloud-phase algorithm classifies nearly two-thirds of clouds in the 0° to −5°C layer as containing ice (cloud ice, snow, or mixed phase), implying that much of the precipitation grows through cold-cloud processes. The best predictors of ice presence are cloud-top temperature, cloud depth, and INP concentration. Measures of convective activity and turbulence are found to be poor indicators of ice presence in the studied environment. The water-phase distribution in this cloud regime is explored through numerical simulations in Part II. Significance Statement Climate models generally predict a lower albedo than observed over the Southern Ocean, and this is largely attributed to a lack of cloudiness, especially in the postfrontal cold sector of midlatitude cyclones. This in turn may be due to an excess of ice in these simulated clouds, resulting in rapid precipitation fallout and an overly brief cloud lifespan. The objective of this study is to examine whether shallow postfrontal clouds over the Southern Ocean are dominated by supercooled drops, or by snow and ice, using data collected by a U.S. Department of Energy Atmospheric Radiation Measurement Mobile Facility deployed aboard an Australian Antarctic supply vessel. We find that these clouds contain much supercooled liquid, even though cloud-top temperatures generally are around −18° to −8°C, and that about two-thirds of the clouds just above the freezing level contain ice. Much of the precipitation appears to grow through cold-cloud processes above the freezing level, rather than drizzle/rain. Updrafts and/or turbulence in convection or in cloud-top generating cells do not initiate much ice, compared to observations elsewhere in a similar temperature range. This may be attributable to the extremely low concentration of ice nucleating particles in this environment. Ultimately, the deepest clouds with the coldest cloud tops are most likely to be ice dominated.

Interaction of solar inertial modes with turbulent convection

Context. Inertial modes have been observed on the Sun at low longitudinal wavenumbers. These modes probe the dynamics and structure of the solar convective zone down to the tachocline. While linear analysis allows the complex eigenfrequencies and eigenfunctions of these modes to be computed, it gives no information about their excitation nor about their amplitudes. Aims. We tested the hypothesis that solar inertial modes are stochastically excited by the turbulent motions entailed by convection. Unlike the acoustic modes, which are excited by vertical turbulent motions, the inertial modes are excited by the radial vorticity of the turbulent field. Methods. We have developed a theoretical formalism where the turbulent velocity fluctuations provide the mechanical work necessary to excite the modes. The modes are described by means of a 2D linear wave equation with a source term, under the β plane approximation. This wave equation restrained to a spherical surface is relevant for the quasi-toroidal inertial modes that are observed on the Sun. Latitudinal differential rotation is included in the form of a parabolic profile that approximates the solar differential rotation at low and mid latitudes. The turbulent vorticity field underlying the source term is treated as an input to the model and is constrained by observations of the solar surface. The solution to the linear inhomogeneous wave equation is written in terms of a Green function, which is computed numerically. Results. We obtain synthetic power spectra for the wave’s latitudinal velocity, longitudinal velocity, and radial vorticity, with azimuthal orders between 1 and 20. The synthetic power spectra contain the classical equatorial Rossby modes, as well as a rich spectrum of additional modes. The mode amplitudes are found to be of the same order of magnitude as observed on the Sun (∼1 m s−1). There is a qualitative transition between low and high azimuthal orders: the power spectra for m ≲ 5 show modes that are clearly resolved in frequency space, while the power spectra for m ≳ 5 display regions of excess power that consist of many overlapping modes. Conclusions. The general agreement between the predicted and observed inertial mode amplitudes supports the assumption of stochastic excitation by turbulent convection. Our work shows that the power spectra are not easily separable into individual modes, thus complicating the interpretation of the observations.

Turbulent natural convection heat transfer enhancement of nanofluids

This study investigates the enhancement of heat transfer for the fluid with the addition of nano-particles in a two-dimensional rectangular cavity. Thermo-physical properties of such fluids and volume fraction of nano-particles in those fluids and its heat transfer characteristics are studied. ANSYS Fluent code is utilized for this purpose. Validation of the computational model has been carried out against the benchmark data available from the literature. A heat transfer correlation in terms of the Nusselt number (Nu) average as a function of Grashoff number and volume fraction of the nano-particles in the base fluid for the turbulent flow is developed and formulated in this study.

Turbulent thermal convection in mixed porous–pure fluid domains

In this paper, we report on a direct numerical simulation (DNS) study of turbulent thermal convection in mixed porous–pure fluid domains. The computational domain consists of a cavity that contains a porous medium placed right above the bottom wall. The solid matrix is internally heated which, in turn, induces the convective motions of the fluid. The Rayleigh number of the flow in the pure fluid region above the porous medium is of the order of $10^7$ . In our study, we consider cases of different sizes of the porous medium, as well as cases with both uniform and non-uniform heat loading of the solid matrix. For each case, we analyse the convective structures in both the porous and the pure fluid domains and investigate the effect of the porous medium on the emerging flow patterns above it. Results for the flow statistics, as well as for the Nusselt number and each of its components, are also presented herein. Further, we make comparisons of the flow properties in this pure fluid region with those in Rayleigh–Bénard convection. Our simulations predict that, depending on the area coverage, the large-scale circulation above the porous medium can be in a single-roll, dual-roll or intermediate state. Also, when the area coverage increases, the temperatures inside it increase due to reduced fluid circulation. Accordingly, when the area coverage increases, then the Nusselt number becomes smaller whereas the Rayleigh number is increased.

Analysis of the remote microphone probe technique for the determination of turbulence quantities

Measuring the statistics of the wall-pressure fluctuations (WPFs) is essential for understanding and evaluating laminar/turbulent boundary layers and flow-induced noise. The remote microphone probe (RMP) technique is one of the most successful experimental approaches to measuring WPFs. Despite its extensive use in academic and industrial research, the scientific literature currently lacks an evaluation of the RMP influence on the determination of turbulence quantities, such as the WPF spectrum, the convection velocity, and the turbulence coherence length. To fulfill this necessity, this paper analyses the effects of the RMP on the determination of turbulence quantities, including comparisons between the results obtained using RMPs and flush-mounted microphones (FMMs). The RMPs and the FMMs measure the WPFs under a turbulent boundary layer developed on a zero-pressure-gradient flat wall. This study shows that the turbulence quantities determined from RMP measurements are influenced by the RMP setup, i.e., tube length and inner diameter. The tube length affects the phase between RMPs, which impacts the turbulent structure convection velocity estimation, which can be determined correctly by considering the calibrated phase. Furthermore, the tube inner diameter influences the coherence between a pair of RMPs, affecting the calculation of the turbulence correlation length. This research also shows that the turbulence quantities determined from the RMP and the FMM measurements differ, mainly in the coherence between pairs of microphones.

Direct numerical simulation of the fully developed turbulent free convection flow in an asymmetrically heated vertical channel

We report direct numerical simulations of the fully developed turbulent natural convection flow of a Boussinesq fluid (Pr = 0.71) in a vertical channel. One wall is heated with a constant heat flux and the other is assumed to be perfectly insulated. Simulations were performed at three different Rayleigh numbers (Ra = 5 × 105, 106 and 5 × 106). Predictions of the time averaged velocities, temperatures and intensities of the fluctuations agree with experiments reported in the literature. Under the fully developed flow conditions considered in this study the shear stress is greater on thermally active wall than that on the adiabatic wall, but the turbulent intensities and the turbulent shear stress are greater near the insulated wall. Conversely, the intensities of the temperature fluctuations and turbulent heat fluxes are higher near the thermally active wall than those near the adiabatic wall. Contrary to the vertical channel with constant but different wall temperatures, where buoyancy and turbulent shear dominate the generation of turbulent kinetic energy, in the asymmetrically heated channel the turbulent shear stress is the principal mechanism of turbulent kinetic energy production as in a forced convection channel flow.

Analysis of the Thermo-Aeraulic Behavior of a Heated Supply Air Window in Forced Convection: Numerical and Experimental Approaches

This paper presents work intended to characterize air flow and convective heat transfers within a ventilated window. This window is a device that allows for the entry of fresh air into a building while simultaneously preheating it in order to satisfy requirements in terms of air quality and thermal comfort in inhabited spaces. Therefore, this essential component of the building envelope functions herein as a heat exchanger with its own geometric characteristics and exchange conditions. In this research, a dual numerical and experimental approach has been implemented in order to highlight the temperatures, velocities and heat flux fields both at the glazing surfaces and in the ventilated air gaps. Several turbulence models were tested using CFD software (ANSYS-FLUENT®); their results were compared with each other as well as with the experimental results. This study shows that the air gap geometry in the window induces flow disturbances, recirculation phenomena and non-uniform heat exchanges, all of which prove to be important in terms of overall component performance. With regard to modeling and, in particular, at the level of turbulence models, the results obtained indicate that the model GEKO is best suited to the configuration under study when the phenomena of turbulent forced convection dominate the dynamics of the transfers. The k-ε models reveal a tremendous weakness in precisely estimating the problem’s characteristic quantities. From an experimental point of view, local measurements of thermal fluxes and temperatures demonstrate high efficiency with regard to experimental technique, which in turn could be extended to many different configurations for the local evaluation of convection heat transfer.

The Relationship between Horizontal and Vertical Velocity Wavenumber Spectra in Global Storm-Resolving Simulations

Abstract Several studies have reported vertical kinetic energy spectra almost white in horizontal wavenumber space with evidence of two maxima at synoptic scales and mesoscales, leaving the explanation of these maxima open. Processes known to influence the shape of the horizontal kinetic energy spectra include the superposition of quasi-linear inertia–gravity waves (IGWs), quasigeostrophic turbulence, and moist convection. In contrast, vertical kinetic energy has been discussed much less, as measuring vertical velocity remains challenging. This study compares the horizontal and vertical kinetic energy spectra and their relationships in global storm-resolving simulations from the DYAMOND experiment. The consistency of these relationships with linear IGW theory is tested by diagnosing horizontal wind fluctuations associated with IGW modes. Furthermore, it is shown that hydrostatic IGW polarization relations provide a quantitative prediction of the spectral slopes of vertical kinetic energy at large scales and mesoscales, where the intrinsic frequencies are inferred from the linearized vorticity equation. Our results suggest that IGW modes dominate the vertical kinetic energy spectra at most horizontal scales, whereas an incompressible, isotropic scaling of the continuity equation captures the relationship between horizontal and vertical kinetic energy spectra at small scales.

Nature of Intense Magnetism and Differential Rotation in Convective Dynamos of M-dwarf Stars with Tachoclines

Many of the M-dwarf stars, though they are tiny and dim, are observed to possess strong surface magnetic fields and exhibit remarkably intense flaring. Such magnetism may severely impact habitability on the exoplanets now discovered nearby. The origin of the magnetism must rest with dynamo action achieved by turbulent convection coupled to rotation within the M-dwarfs. To further explore the nature and diversity of the magnetism that can result, we turn here to an extensive set of 45 global MHD simulations to explore dynamos operating within deep convective envelopes of rapidly rotating M2 (0.4 M ⊙) stars. We observe a wide range of cycle periods present in the convection zones, whose durations we find to scale with the Rossby number as Ro−1.66±0.07 in concurrence with scalings identified in simulations of more massive stars. We find a unifying relationship between the ratio of magnetic to convective kinetic energy (ME/CKE) and the degree to which the differential rotation is quenched by magnetic fields. We show that the presence of a tachocline in these model stars enhances their axisymmetric magnetic field components, leading to a surface dipole fraction on average 78% greater than an equivalent star with only a CZ, potentially shedding light on the nature of the tachocline divide through resultant effects on the spin-down rate.

An efficient tracking method of evaporative and flat free surfaces for turbulent convection

In this paper, we present a tracking algorithm of evaporative and flat free surfaces on collocated grids. This algorithm combines the ghost-fluid method with a flux-interpolation technique and is well suited for the numerical treatment of gas–liquid flows involving turbulent convection, mixing, and phase change via evaporation across a free surface. Further, it can accurately take into account the jumps in the values of the various flow quantities across the free surface and the time-dependent interaction between the two phases. The efficiency of the proposed algorithm is illustrated via numerical tests. The first test involves Couette flow above a liquid at rest; our numerical predictions for the evaporative mass flux compares very favorably with the analytical solution. The second test involves 2D simulations and grid-convergence study of free convection with evaporation in a system comprising a column of water and a layer of air above it. Cases at different Rayleigh numbers are considered and our numerical predictions are compared with experimental data and with earlier single-phase simulations based on approximate evaporation models. Further, we present and discuss results from 3D numerical simulations involving evaporation across the free surface, turbulent convection below it (liquid side) and free convection with mixing above it (gas side). Our numerical results are in good agreement with experiments and show that the algorithm provides accurate predictions of the evaporative mass flux and is robust enough to handle the descent of the free surface and simultaneously resolve the emerging turbulent structures.