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Käufer, Theo; Vieweg, Philipp; Schumacher, Jörg; Cierpka, Christian
Thermal boundary condition studies in large aspect ratio Rayleigh-Bénard convection. - In: European journal of mechanics, ISSN 1873-7390, Bd. 101 (2023), S. 283-293

We study the influence of thermal boundary conditions on large aspect ratio Rayleigh-Bénard convection by a joint analysis of experimental and numerical data sets for a Prandtl number Pr=7 and Rayleigh numbers Ra=105−106. The spatio-temporal experimental data are obtained by combined Particle Image Velocimetry and Particle Image Thermometry measurements in a cuboid cell filled with water at an aspect ratio Γ=25. In addition, numerical data are generated by Direct Numerical Simulations (DNS) in domains with Γ=25 and Γ=60 subject to different idealized thermal boundary conditions. Our experimental data show an increased characteristic horizontal extension scale ÜÞλ of the flow structures for increasing Ra , which due to an increase of the convective heat transfer also leads to an increase of the Biot number (Bi) at the cooling plate. However, we find the experimental flow structure size to range in any case in between the ones observed for the idealized thermal boundary conditions captured by the simulations: On the one hand, they are larger than in the numerical case with applied uniform temperatures at the plates. On the other hand, they are smaller than in the case of an applied constant heat flux, the latter of which leads to a structure that grows gradually up to the horizontal domain size. We are able to link this observation qualitatively to theoretical predictions for the onset of convection. Furthermore, we study the effect of the asymmetric boundary conditions on the heat transfer. Contrasting experimental and numerical data reveals an increased probability of far-tail events of reversed heat transfer. The successive decomposition of the local Nusselt number Nuloc traces this effect back to the sign of the temperature deviation ÜÞΘ, eventually revealing asymmetries of the heating and cooling plate on the thermal variance of the generated thermal plumes.
Maity, Priyanka; Bittracher, Andreas; Koltai, Péter; Schumacher, Jörg
Collective variables between large-scale states in turbulent convection. - In: Physical review research, ISSN 2643-1564, Bd. 5 (2023), 3, S. 033061-1-033061-19

The dynamics in a confined turbulent convection flow is dominated by multiple long-lived macroscopic circulation states that are visited subsequently by the system in a Markov-type hopping process. In the present work, we analyze the short transition paths between these subsequent macroscopic system states by a data-driven learning algorithm that extracts the low-dimensional transition manifold and the related new coordinates, which we term collective variables, in the state space of the complex turbulent flow. We therefore transfer and extend concepts for conformation transitions in stochastic microscopic systems, such as in the dynamics of macromolecules, to a deterministic macroscopic flow. Our analysis is based on long-term direct numerical simulation trajectories of turbulent convection in a closed cubic cell at a Prandtl number Pr=0.7 and Rayleigh numbers Ra=10^6 and 10^7 for a time lag of 10^5 convective free-fall time units. The simulations resolve vortices and plumes of all physically relevant scales, resulting in a state space spanned by more than 3.5 million degrees of freedom. The transition dynamics between the large-scale circulation states can be captured by the transition manifold analysis with only two collective variables, which implies a reduction of the data dimension by a factor of more than a million. Our method demonstrates that cessations and subsequent reversals of the large-scale flow are unlikely in the present setup, and thus it paves the way for the development of efficient reduced-order models of the macroscopic complex nonlinear dynamical system.
Maity, Priyanka;
Heavy inertial particles in rotating turbulence: distribution of particles in flow and evolution of Lagrangian trajectories. - In: Physical review, ISSN 2470-0053, Bd. 107 (2023), 6, S. 065107-1-065107-9

We revisit the problem of heavy particles suspended in homogeneous box turbulence flow subjected to rotation along the vertical axis, which introduces anisotropy along the vertical and horizontal planes. We investigate the effects of the emergent structures due to rotation, on the spatial distribution and temporal statistics of the particles. The distribution of particles in the flow are studied using the joint probability distribution function (JPDFs) of the second and third principle invariants of the velocity gradient tensor, Q and R. At high rotation rates, the JPDFs of Lagrangian Q-R plots show remarkable deviations from the well-known teardrop shape. The cumulative probability distribution functions for times during which a particle remains in vortical or straining regions show exponentially decaying tails except for the deviations at the highest rotation rate. The average residence times of the particles in vortical and straining regions are also affected considerably due to the addition of rotation. Furthermore, we compute the temporal velocity autocorrelation and connect it to the Lagrangian anisotropy in presence of rotation. The spatial and temporal statistics of the particles are determined by a complex competition between the rotation rate and inertia of the particle.
Bhattacharya, Shashwat; Boeck, Thomas; Krasnov, Dmitry; Schumacher, Jörg
Effects of strong fringing magnetic fields on turbulent thermal convection. - In: Journal of fluid mechanics, ISSN 1469-7645, Bd. 964 (2023), S. A31-1-A31-29

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.
Krasnov, Dmitry; Listratov, Yaroslav; Belyaev, Ivan; Kolesnikov, Yuri; Sviridov, Evgeny; Zikanov, Oleg
MHD flow of submerged jets behind the inlet disturbance. - In: Proceedings in applied mathematics and mechanics, ISSN 1617-7061, Bd. 22 (2023), 1, e202200200, S. 1-6

In a broad variety of configurations in technology and industrial applications, the properties of liquid metal flows subjected to strong magnetic fields, are largely governed by the dynamics of coherent structures, known to settle several basic types, such as thin shear layers, forming near the walls or within the fluid domain, vortices extended along the field, or planar and round jets. In some cases, these structures are created by the design, like a submerged jet formed by a sudden expansion from the nozzle into a blanket channel, or jets formed behind some flow obstruction. In the other cases this may be due to instability and evolution of secondary structures, for example, descending and ascending jets appearing as a result of convective instability in blanket channels. In this study, we undertake an attempt to affect liquid metal flow via inlet disturbance formed by a simple rod placed along the magnetic induction lines. The disturbance can generate flat jets behind the rod and, furthermore, a sustainable flow of anisotropic vortical perturbations further downstream the flow. We seek to analyze the most important mechanisms of the flow dynamics and effects of magnetic field on the integral system properties of enhancing mixing, mass and heat transport for such flow. The most optimal regimes of vortex generation are found to be governed by the magnetic interaction parameter (Stuart number). The exact ratio of the optimal Stuart number is found to be in a range between 20 and 40, based on the channel double width as a characteristic size. The observed vortices attain quasi-2D shape and exist at a length of dozens of duct calibers, being the strongest at higher flow rates. The obtained flow regimes and their turbulent properties are also found to resemble significant similarity to the results on quasi-2D turbulence found in prior studies of channel and duct flows under spanwise magnetic field.
Sharifi Ghazijahani, Mohammad; Kästner, Christian; Valori, Valentina; Thieme, Alexander; Täschner, Kerstin; Schumacher, Jörg; Cierpka, Christian
The SCALEX facility - an apparatus for scaled fluid dynamical experiments. - In: Technisches Messen, ISSN 2196-7113, Bd. 90 (2023), 5, S. 296-309

The working conditions of the Scaled Convective Airflow Laboratory Experiment (SCALEX) at Technische Universität Ilmenau and sample experiments are reported. The SCALEX facility is a pressure vessel which allows for downscaling of laboratory experiments up to a factor of 20 by compression of gaseous working fluids, air or sulfur hexafluoride, to change the material properties of the fluid. The requirements and conditions for downscaling of fluid dynamical problems are discussed in detail. Long-term high and low pressure tests are conducted to screen the stability of the experimental environment inside the vessel against pressure and temperature fluctuations. Finally, a Rayleigh-Bénard convection experiment at an aspect ratio 10 is performed inside the SCALEX facility as a proof of concept. The reference experiment was conducted under 4.5 bar pressure for Ra = 1.9 × 10^5. However, the Rayleigh number could be varied in a wide range of Ra = 10^4  … 10^8. The flow investigation was pursued with stereoscopic particle image velocimetry in horizontal mid-plane through the convection cell. To improve the image quality the cameras were placed inside the pressure cell and tested up to 6 bar. Thus the feasibility of optical flow measurements at elevated pressures is shown.
Krasnov, Dmitry; Akhtari, Ali; Zikanov, Oleg; Schumacher, Jörg
Tensor-product-Thomas elliptic solver for liquid-metal magnetohydrodynamics. - In: Journal of computational physics, ISSN 1090-2716, Bd. 474 (2023), 111784, S. 1-23

A new approach to numerical simulation of magnetohydrodynamic flows of liquid metals is presented. It combines the conservative finite-difference discretization with a tensor-product-Thomas solution of the elliptic problems for pressure, electric potential, velocity, and temperature. The method is realizable on an arbitrarily clustered structured grid. The main novelty of the approach is the efficient solution of the practically important and computationally challenging elliptic problems for electric potential in flow domains with thin electrically conducting walls. The method is verified via solution of benchmark problems for streamwise-uniform and nonuniform, steady and unsteady magnetohydrodynamic flows in ducts, and for thermal convection in boxes of various aspect ratios. Computational efficiency of the method in comparison to the existing ones is demonstrated.
Belyaev, Ivan A.; Mironov, Ivan S.; Luchinkin, Nikita A.; Listratov, Yaroslav I.; Kolesnikov, Yuri; Kransov, Dmitry; Zikanov, Oleg; Molokov, Sergei
Experimental study of submerged liquid metal jet in a rectangular duct in a transverse magnetic field. - In: Journal of fluid mechanics, ISSN 1469-7645, Bd. 953 (2022), A10

A liquid metal flow in the form of a submerged round jet entering a square duct in the presence of a transverse magnetic field is studied experimentally. A range of high Reynolds and Hartmann numbers is considered. Flow velocity is measured using electric potential difference probes. A detailed study of the flow in the duct's cross-section about seven jet's diameters downstream of the inlet reveals the dynamics, which is unsteady and dominated by high-amplitude fluctuations resulting from the instability of the jet. The flow structure and fluctuation properties are largely determined by the value of the Stuart number N. At moderate N, the mean velocity profile retains a central jet with three-dimensional perturbations increasingly suppressed by the magnetic field as N grows. At higher values of N, the flow becomes quasi-two-dimensional and acquires the form of an asymmetric macrovortex, with high-amplitude velocity fluctuations reemerging.
Sharifi Ghazijahani, Mohammad; Valori, Valentina; Schumacher, Jörg; Cierpka, Christian
Wide field of view stereoscopic PIV measurements in a Rayleigh-Bénard cell. - In: Experimentelle Strömungsmechanik - 29. Fachtagung, 6.-8. September 2022, Ilmenau, (2022), 44

Heyder, Florian; Mellado, Juan Pedro; Schumacher, Jörg
Generalizability of reservoir computing for flux-driven two-dimensional convection. - In: Physical review, ISSN 2470-0053, Bd. 106 (2022), 5, S. 055303-1-055303-21

We explore the generalization properties of an echo state network applied as a reduced-order model to predict flux-driven two-dimensional turbulent convection. To this end, we consider a convection domain with constant height with a variable ratio of buoyancy fluxes at the top and bottom boundaries, which break the top-down symmetry in comparison to the standard Rayleigh-Bénard case, thus leading to highly asymmetric mean and fluctuation profiles across the layer. Our direct numerical simulation model describes a convective boundary layer in a simple way. The data are used to train and test a recurrent neural network in the form of an echo state network. The input of the echo state network is obtained in two different ways, either by a proper orthogonal decomposition or by a convolutional autoencoder. In both cases, the echo state network reproduces the turbulence dynamics and the statistical properties of the buoyancy flux, and is able to model unseen data records with different flux ratios.