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.
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.
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.
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.
Wide field of view stereoscopic PIV measurements in a Rayleigh-Bénard cell. - In: Experimentelle Strömungsmechanik - 29. Fachtagung, 6.-8. September 2022, Ilmenau, (2022), 44
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.
Predictions of Reynolds and Nusselt numbers in turbulent convection using machine-learning models. - In: Physics of fluids, ISSN 1089-7666, Bd. 34 (2022), 2, S. 025102-1-025102-10
In this paper, we develop a multivariate regression model and a neural network model to predict the Reynolds number (Re) and Nusselt number in turbulent thermal convection. We compare their predictions with those of earlier models of convection: Grossmann-Lohse [Phys. Rev. Lett. 86, 3316 (2001)], revised Grossmann-Lohse [Phys. Fluids 33, 015113 (2021)], and Pandey-Verma [Phys. Rev. E 94, 053106 (2016)] models. We observe that although the predictions of all the models are quite close to each other, the machine-learning models developed in this work provide the best match with the experimental and numerical results.
Supercritical and subcritical rotating convection in a horizontally periodic box with no-slip walls at the top and bottom. - In: Physics of fluids, ISSN 1089-7666, Bd. 34 (2022), 10, 104117, insges. 14 S.
The study of instabilities in the convection of rotating fluids is one of the classical topics of research. However, in spite of more than five decades of research, the instabilities and related transition scenarios near the onset of rotating convection of low Prandtl number fluids are not well understood. Here, we investigate the transition scenario in rotating Rayleigh–Bénard convection with no-slip boundary conditions by performing 3D direct numerical simulations (DNS) and low-dimensional modeling. The governing parameters, namely, the Taylor number (Ta), Rayleigh number (Ra), and Prandtl number (Pr), are varied in the ranges 0 < Ta ≤ 8 × 10^3, 0 < Ra < 1 × 10^4, and 0 < Pr ≤ 0.35, where convection appears as a stationary cellular pattern. In DNS, for Pr < 0.31, the supercritical or subcritical onset of convection appears, according as Ta > Tac(Pr) or Ta < Tac(Pr), where Tac(Pr) is a Pr dependent threshold of Ta. On the other hand, only supercritical onset of convection is observed for Pr ≥ 0.31. At the subcritical onset, both finite amplitude stationary and time dependent solutions are manifested. The origin of these solutions are explained using a low dimensional model. DNS show that as Ra is increased beyond the onset of convection, the system becomes time dependent and depending on Pr, standing and traveling wave solutions are observed. For very small Pr (≤ 0.045), interestingly, finite amplitude time dependent solutions are manifested at the onset for higher Ta.
On the benefits and limitations of Echo State Networks for turbulent flow prediction. - In: Measurement science and technology, ISSN 1361-6501, Bd. 34 (2022), 1, 014002, S. 1-18
The prediction of turbulent flow by the application of machine learning (ML) algorithms to big data is a concept currently in its infancy which requires further development. It is of special importance if the aim is a prediction that is good in a statistical sense or if the vector fields should be predicted as good as possible. For this purpose, the statistical and deterministic prediction of the unsteady but periodic flow of the von Kármán Vortex Street (KVS) was examined using an Echo State Network (ESN) which is well suited for learning from time series due to its recurrent connections. The experimental data of the velocity field of the KVS were collected by Particle Image Velocimetry (PIV). Then, the data were reduced by Proper Orthogonal Decomposition (POD) and the flow was reconstructed by the first hundred most energetic modes. An ESN with 3000 neurons was optimized with respect to its three main hyperparameters to predict the time coefficients of the POD modes. For the deterministic prediction, the aim was to maximize the correct direction of the vertical velocities. The results indicate that the ESN can mimic the periodicity and the unsteadiness of the flow. It is also able to predict the sequence of the upward and downward directed velocities for longer time spans. For the statistical prediction, the similarity of the probability density functions of the vertical velocity fields between the predicted and actual flow was achieved. The leaking rate of the ESN played a key role in the transition from deterministic to statistical predictions.
Inverse cascades of kinetic energy and thermal variance in three-dimensional horizontally extended turbulent convection. - In: Physical review research, ISSN 2643-1564, Bd. 4 (2022), 4, S. 043098-1-043098-14
Inverse cascades of kinetic energy and thermal variance in the subset of vertically homogeneous modes in spectral space are found to cause a slow aggregation to a pair of convective supergranules that eventually fill the whole horizontally extended, three-dimensional, turbulent Rayleigh-Bénard convection layer when a heat flux is prescribed at the top and bottom. An additional weak rotation of the layer around the vertical axis stops this aggregation at a scale that is smaller than the lateral domain extension and ceases the inverse cascade for the thermal variance. The inverse cascade for the kinetic energy remains intact, even for times at which the root-mean-square values of temperature and velocity have reached the statistically steady state. This kinetic energy inverse cascade sustains the horizontally extended convection patterns which are best visible in the temperature field. The resulting characteristic length of the aggregated convection patterns depends on the thermal driving and linearly on the strength of rotation. Our study demonstrates the importance of inverse energy cascades beyond the two-dimensional turbulence case in a three-dimensional convection flow that is subject to a multiscale energy injection by thermal plumes and driven by boundary heat fluxes as typically present in natural geo- and astrophysical systems, such as solar convection.