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Author: John, Volker × End date: 2022 ×

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Now showing 1 - 10 of 49
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    Vibrations of a laboratory-scale gas-stirred ladle with two eccentric nozzles and multiple sensors
    ([Singapore] : Springer Singapore, 2019) Alia, Najib; Pylvänäinen, Mika; Visuri, Ville-Valtteri; John, Volker; Ollila, Seppo
    During ladle stirring, a gas is injected into the steel bath to generate a mixing of the liquid steel. The optimal process control requires a reliable measurement of the stirring intensity, for which the induced ladle wall vibrations have proved to be a potential indicator. An experimental cold water ladle with two eccentric nozzles and eight mono-axial accelerometers was thus investigated to measure the vibrations. The effect of the sensors’ positions with respect to the gas plugs on the vibration intensity was analyzed, and experimental data on several points of the ladle were collected for future numerical simulations. It is shown that the vibration root-mean-square values depend not only on process parameters, such as gas flow rate, water, and oil heights, but also on the radial and axial positions of the sensors. The vibration intensity is clearly higher, close to the gas plumes, than in the opposite side. If one of the nozzles is clogged, the vibration intensity close to the clogged nozzle drops drastically (−36 to −59%), while the vibrations close to the normal operating nozzle are hardly affected. Based on these results, guidelines are provided for an optimized vibration-based stirring.
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    Optimal control of buoyancy-driven liquid steel stirring modeled with single-phase Navier–Stokes equations
    (Berlin ; Heidelberg : Springer, 2021) Wilbrandt, Ulrich; Alia, Najib; John, Volker
    Gas stirring is an important process used in secondary metallurgy. It allows to homogenize the temperature and the chemical composition of the liquid steel and to remove inclusions which can be detrimental for the end-product quality. In this process, argon gas is injected from two nozzles at the bottom of the vessel and rises by buoyancy through the liquid steel thereby causing stirring, i.e., a mixing of the bath. The gas flow rates and the positions of the nozzles are two important control parameters in practice. A continuous optimization approach is pursued to find optimal values for these control variables. The effect of the gas appears as a volume force in the single-phase incompressible Navier–Stokes equations. Turbulence is modeled with the Smagorinsky Large Eddy Simulation (LES) model. An objective functional based on the vorticity is used to describe the mixing in the liquid bath. Optimized configurations are compared with a default one whose design is based on a setup from industrial practice.
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    On the convergence order of the finite element error in the kinetic energy for high Reynolds number incompressible flows
    (Amsterdam [u.a.] : Elsevier Science, 2021) García-Archilla, Bosco; John, Volker; Novo, Julia
    The kinetic energy of a flow is proportional to the square of the norm of the velocity. Given a sufficient regular velocity field and a velocity finite element space with polynomials of degree , then the best approximation error in is of order . In this survey, the available finite element error analysis for the velocity error in is reviewed, where is a final time. Since in practice the case of small viscosity coefficients or dominant convection is of particular interest, which may result in turbulent flows, robust error estimates are considered, i.e., estimates where the constant in the error bound does not depend on inverse powers of the viscosity coefficient. Methods for which robust estimates can be derived enable stable flow simulations for small viscosity coefficients on comparatively coarse grids, which is often the situation encountered in practice. To introduce stabilization techniques for the convection-dominated regime and tools used in the error analysis, evolutionary linear convection–diffusion equations are studied at the beginning. The main part of this survey considers robust finite element methods for the incompressible Navier–Stokes equations of order , , and for the velocity error in . All these methods are discussed in detail. In particular, a sketch of the proof for the error bound is given that explains the estimate of important terms which determine finally the order of convergence. Among them, there are methods for inf–sup stable pairs of finite element spaces as well as for pressure-stabilized discretizations. Numerical studies support the analytic results for several of these methods. In addition, methods are surveyed that behave in a robust way but for which only a non-robust error analysis is available. The conclusion of this survey is that the problem of whether or not there is a robust method with optimal convergence order for the kinetic energy is still open.
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    On the feasibility of using open source solvers for the simulation of a turbulent air flow in a dairy barn
    (Amsterdam [u.a.] : Elsevier, 2020) Janke, David; Caiazzo, Alfonso; Ahmed, Naveed; Alia, Najib; Knoth, Oswald; Moreau, Baptiste; Wilbrandt, Ulrich; Willink, Dilya; Amon, Thomas; John, Volker
    Two transient open source solvers, OpenFOAM and ParMooN, and the commercial solver Ansys Fluent are assessed with respect to the simulation of the turbulent air flow inside and around a dairy barn. For this purpose, data were obtained in an experimental campaign at a 1:100 scaled wind tunnel model. All solvers used different meshes, discretization schemes, and turbulence models. The experimental data and numerical results agree well for time-averaged stream-wise and vertical-wise velocities. In particular, the air exchange was predicted with high accuracy by both open source solvers with relative differences less than 4% and by the commercial solver with a relative difference of 9% compared to the experimental results. With respect to the turbulent quantities, good agreements at the second (downwind) half of the barn inside and especially outside the barn could be achieved, where all codes accurately predicted the flow separation and, in many cases, the root-mean-square velocities. Deviations between simulations and experimental results regarding turbulent quantities could be observed in the first part of the barn. These deviations can be attributed to the utilization of roughness elements between inlet and barn in the experiment that were not modeled in the numerical simulations. Both open source solvers proved to be promising tools for the accurate prediction of time-dependent phenomena in an agricultural context, e.g., like the transport of particulate matter or pathogen-laden aerosols in and around agricultural buildings. © 2020 The Authors
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    Existence of solutions of a finite element flux-corrected-transport scheme
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) John, Volker; Knobloch, Petr
    The existence of a solution is proved for a nonlinear finite element flux-corrected-transport (FEM-FCT) scheme with arbitrary time steps for evolutionary convection-diffusion-reaction equations and transport equations.
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    An adaptive SUPG method for evolutionary convection-diffusion equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) de Frutos, Javier; García-Archilla, Bosco; John, Volker; Novo, Julia
    An adaptive algorithm for the numerical simulation of time-dependent convectiondiffusion-reaction equations will be proposed and studied. The algorithm allows the use of the natural extension of any error estimator for the steady-state problem for controlling local refinement and coarsening. The main idea consists in considering the SUPG solution of the evolutionary problem as the SUPG solution of a particular steady-state convectiondiffusion problem with data depending on the computed solution. The application of the error estimator is based on a heuristic argument by considering a certain term to be of higher order. This argument is supported in the one-dimensional case by numerical analysis. In the numerical studies, particularly the residual-based error estimator from [18] will be applied, which has proved to be robust in the SUPG norm. The effectivity of this error estimator will be studied and the numerical results (accuracy of the solution, fineness of the meshes) will be compared with results obtained by utilizing the adaptive algorithm proposed in [6]
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    Analysis of a full space-time discretization of the Navier-Stokes equations by a local projection stabilization
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Ahmed, Naveed; Rebollo, Tomás Chacón; John, Volker; Rubino, Samuele
    A finite element error analysis of a local projection stabilization (LPS) method for the time-dependent Navier-Stokes equations is presented. The focus is on the highorder term-by-term stabilization method that has one level, in the sense that it is defined on a single mesh, and in which the projection-stabilized structure of standard LPS methods is replaced by an interpolation-stabilized structure. The main contribution is on proving, theoretically and numerically, the optimal convergence order of the arising fully discrete scheme. In addition, the asymptotic energy balance is obtained for slightly smooth flows. Numerical studies support the analytical results and illustrate the potential of the method for the simulation of turbulent ows. Smooth unsteady flows are simulated with optimal order of accuracy.
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    An assessment of discretizations for convection-dominated convection-diffusion equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Augustin, Matthias; Caiazzo, Alfonso; Fiebach, André; Fuhrmann, Jürgen; John, Volker; Linke, Alexander; Umla, Rudolf
    The performance of several numerical schemes for discretizing convection-dominated convection-diffusion equations will be investigated with respect to accuracy and efficiency. Accuracy is considered in measures which are of interest in applications. The study includes an exponentially fitted finite volume scheme, the Streamline-Upwind Petrov--Galerkin (SUPG) finite element method, a spurious oscillations at layers diminishing (SOLD) finite element method, a finite element method with continuous interior penalty (CIP) stabilization, a discontinuous Galerkin (DG) finite element method, and a total variation diminishing finite element method (FEMTVD). A detailed assessment of the schemes based on the Hemker example will be presented.
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    Optimal control of a buoyancy-driven liquid steel stirring modeled with single-phase Navier--Stokes equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Wilbrandt, Ulrich; Alia, Najib; John, Volker
    Gas stirring is an important process used in secondary metallurgy. It allows to homogenize the temperature and the chemical composition of the liquid steel and to remove inclusions which can be detrimental for the end-product quality. In this process, argon gas is injected from two nozzles at the bottom of the vessel and rises by buoyancy through the liquid steel thereby causing stirring, i.e., a mixing of the bath. The gas flow rates and the positions of the nozzles are two important control parameters in practice. A continuous optimization approach is pursued to find optimal values for these control variables. The effect of the gas appears as a volume force in the single-phase incompressible NavierStokes equations. Turbulence is modeled with the Smagorinsky Large Eddy Simulation (LES) model. An objective functional based on the vorticity is used to describe the mixing in the liquid bath. Optimized configurations are compared with a default one whose design is based on a setup from industrial practice.
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    A study of isogeometric analysis for scalar convection-diffusion equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) John, Volker; Schumacher, Liesel
    Isogeometric Analysis (IGA), in combination with the Streamline Upwind PetrovGalerkin (SUPG) stabilization, is studied for the discretization of steady-state convection-diffusion equations. Numerical results obtained for the Hemker problem are compared with results computed with the SUPG finite element method of the same order. Using an appropriate parameterization for IGA, the computed solutions are much more accurate than those obtained with the finite element method, both in terms of the size of spurious oscillations and of the sharpness of layers.