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Dive into the research topics where Tobias Kempe is active.

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Featured researches published by Tobias Kempe.


Journal of Computational Physics | 2012

An improved immersed boundary method with direct forcing for the simulation of particle laden flows

Tobias Kempe; Jochen Fröhlich

An efficient approach for the simulation of finite-size particles with interface resolution was presented by Uhlmann [M. Uhlmann, An immersed boundary method with direct forcing for the simulation of particulate flows, J. Comput. Phys. 209 (2005) 448-476.]. The present paper proposes several enhancements of this method which considerably improve the results and extend the range of applicability. An important step is a simple low-cost iterative procedure for the Euler-Lagrange coupling yielding a substantially better imposition of boundary conditions at the interface, even for large time steps. Furthermore, it is known that the basic method is restricted to ratios of particle density and fluid density larger than some critical value above 1, hence excluding, for example, non-buoyant particles. This can be remedied by an efficient integration step for the artificial flow field inside the particles to extend the accessible density range down to 0.3. This paper also shows that the basic scheme is inconsistent when moving surfaces are allowed to approach closer than twice the step size. A remedy is developed based on excluding from the force computation all surface markers whose stencil overlaps with the stencil of a marker located on the surface of a collision partner. The resulting algorithm is throughly validated and is demonstrated to substantially improve upon the original method.


Journal of Computational Physics | 2015

Imposing the free-slip condition with a continuous forcing immersed boundary method

Tobias Kempe; Matthias Lennartz; Stephan Schwarz; Jochen Fröhlich

The numerical simulation of spherical and ellipsoidal bubbles in purified fluids requires the imposition of the free-slip boundary condition at the bubble surface. This paper describes a numerical method for the implementation of free-slip boundary conditions in the context of immersed boundary methods. In contrast to other numerical approaches for multiphase flows, the realization is not straightforward. The reason is that the immersed boundary method treats the liquid as well as the gas phase as a field of constant density and viscosity with a fictitious fluid inside the bubble. The motion of the disperse phase is computed explicitly by solving the momentum balance for each of its elements and is coupled to the continuous phase via additional source terms in the Navier-Stokes equations. The paper starts with illustrating that an ad hoc method is unsuccessful. On this basis, a new method is proposed employing appropriate direct forcing at the bubble surface. A central finding is that with common ratios between the step size of the grid and the bubble diameter, curvature terms need to be accounted for to obtain satisfactory results. The new method is first developed for spherical objects and then extended to generally curved interfaces. This is done by introducing a local coordinate system which approximates the surface in the vicinity of a Lagrangian marker with the help of the two principal curvatures of the surface at this point. The numerical scheme is then validated for spherical and ellipsoidal objects with or without prescribed constant angular velocity. It is shown that the proposed method achieves similar convergence behavior as the method for no-slip boundaries. The results are compared to analytical solutions for creeping flow around a sphere and to numerical reference data obtained on a body-fitted grid. The numerical tests confirm the excellent performance of the proposed method.


Journal of Hydraulic Research | 2016

Entrainment of single particles in a turbulent open-channel flow: a numerical study

Bernhard Vowinckel; Ramandeep Jain; Tobias Kempe; Jochen Fröhlich

ABSTRACT This paper investigates erosion events in a turbulent open channel flow laden with monodisperse spherical particles. The data were generated in a previous study using direct numerical simulations with a phase-resolving immersed boundary method. The particles have a mobility below their nominal threshold of incipient motion and settle onto the rough bed that consists of a hexagonally packed layer of spheres with the same size. Conditioned averaging is employed to extract the characteristic features of an erosion event, defining a suitable criterion for detection and accounting for possible asymmetry of flow structures. The highly resolved dataset provides detailed insight into the key-mechanisms of erosion. The results show that a particle collision, together with a subsequent sweep event on time scales of several bulk units, is responsible for the erosion.


Journal of Computational Physics | 2016

An immersed boundary method for the simulation of bubbles with varying shape

Stephan Schwarz; Tobias Kempe; Jochen Fröhlich

The paper presents a numerical method for the simulation of bubbles with variable shape in the framework of an immersed boundary method. The liquid-gas interface is described analytically by a series expansion in spherical harmonics. Such a representation of the interface is very accurate and robust and the error of the computed surface curvature is substantially smaller compared to a discrete representation of the surface by grid points. The shape of the bubble is computed by minimizing the local displacement energy of pressure and surface tension forces and is coupled to the continuous phase by adapting the Lagrangian surface mesh in each time step. This is done with the constraint of constant bubble volume exactly implemented. As a first step the bubbles are restricted to axisymmetric shapes. The resulting algorithm is thoroughly validated by several numerical tests and finally applied to freely rising bubbles with stationary and oscillatory shape as well. The computed bubble shapes are in very good agreement with experimental and numerical reference data.


International Journal of Multiphase Flow | 2015

Efficient modelling of particle collisions using a non-linear viscoelastic contact force

Shouryya Ray; Tobias Kempe; Jochen Fröhlich

Abstract In this paper the normal collision of spherical particles is investigated. The particle interaction is modelled in a macroscopic way using the Hertzian contact force with additional linear damping. The goal of the work is to develop an efficient approximate solution of sufficient accuracy for this problem which can be used in soft-sphere collision models for Discrete Element Methods and for particle transport in viscous fluids. First, by the choice of appropriate units, the number of governing parameters of the collision process is reduced to one, which is a simple combination of known material parameters as well as initial conditions. It provides a dimensionless parameter that characterizes all such collisions up to dynamic similitude. Next, a rigorous calculation of the collision time and restitution coefficient from the governing equations, in the form of a series expansion in this parameter is provided. Such a calculation based on first principles is particularly interesting from a theoretical perspective. Since the governing equations present some technical difficulties, the methods employed are also of interest from the point of view of the analytical technique. Using further approximations, compact expressions for the restitution coefficient and the collision time are then provided. These are used to implement an approximate algebraic rule for computing the desired stiffness and damping in the framework of the adaptive collision model (Kempe and Frohlich, J. Fluid Mech. 709: 445–489, 2012). Numerical tests with binary as well as multiple particle collisions are reported to illustrate the accuracy of the proposed method and its superiority in terms of numerical efficiency.


Journal of Computational Physics | 2017

A non-iterative immersed boundary method for spherical particles of arbitrary density ratio

Silvio Tschisgale; Tobias Kempe; Jochen Frhlich

In this paper an immersed boundary method with semi-implicit fluidsolid coupling for mobile particles of arbitrary density ratio is developed. The new scheme does not require any iterations to balance fluid forces and particle forces at the interface. A new formulation of the particle equations of motion is proposed which not only accounts for the particle itself but also for a Lagrangian layer surrounding the particle surface. Furthermore, it is shown by analytical considerations that the six equations for the linear and angular velocity of the spherical particle decouple which allows their sequential solution. On this basis a new time integration scheme is obtained which is unconditionally stable for all fluidsolid density ratios and enables large time steps, with Courant numbers around unity. The new scheme is extensively validated for various test cases and its convergence is assessed. An appealing issue is that compared to existing immersed boundary methods the new scheme only alters coefficients in the particle equations and the order of the steps, making it easy to implement in present codes with explicit coupling. This substantially extends the field of application of such methods. An extremely efficient semi-implicit IBM for mobile particles of arbitrary density ratio is developed.Unconditional stability is achieved without any iterative coupling to balance fluid and particle forces at the interface.The new scheme only alters coefficients in the particle equations and the sequence of the operations in each time step.Extensive validation for various test cases, including buoyant particles with zero mass.


Journal of Hydraulic Research | 2017

Momentum balance in flows over mobile granular beds: application of double-averaging methodology to DNS data

Bernhard Vowinckel; Vladimir Nikora; Tobias Kempe; Jochen Fröhlich

ABSTRACT This paper presents the application of the double-averaging methodology to actual data obtained for the mobile-bed conditions from direct numerical simulations using an immersed boundary method. The dimensions of the computational domain resemble those for open-channel flows with small relative submergence. The domain bottom is a plane covered with one layer of hexagonally packed, single-size spheres fixed to the bed. The fixed particles are covered by 2000 mobile particles of the same size that are free to move. Two simulation scenarios at distinctly different values of the Shields parameter are studied representing a fully mobilized and partially mobilized granular bed. The effects of the averaging time and the averaging domain size and shape on the double-averaged flow quantities are identified first. Then, the data analysis focuses on the detailed assessment of the key terms of the double-averaged momentum balance equation formulated for mobile-bed conditions. The paper demonstrates that the double-averaging methodology provides an efficient reduction of the massive datasets produced by the fully resolved simulations to a manageable number of physically meaningful double-averaged quantities, which should help devising closure strategies for modelling mobile-bed flows.


Journal of Hydraulic Research | 2017

Spatially-averaged momentum fluxes and stresses in flows over mobile granular beds: a DNS-based study

Bernhard Vowinckel; Vladimir Nikora; Tobias Kempe; Jochen Fröhlich

ABSTRACT Based on direct numerical simulations, the paper investigates momentum fluxes and hydrodynamic stresses within and above a mobile granular bed in a turbulent open-channel flow laden with monodisperse spherical particles. Two simulation scenarios are considered: one with partially mobilized particles (“heavy” particles) and another with all particles in motion (“light” particles). The momentum fluxes were computed as temporal and spatial averages following the double-averaging methodology for rough-bed flows. The analysis, hence, allows the DNS data to be convoluted in a rigorous way to provide detailed description and quantification of the physical mechanisms involved in momentum exchanges. In particular, it was found that heavy particles create streamwise bedforms causing heterogeneity in the spanwise direction. This yields significant form-induced momentum fluxes that cannot be neglected. For both scenarios, the mobile particles take up a substantial amount of the momentum supplied, which ultimately increases the hydraulic resistance of the channel. These effects enhance and stabilize secondary flows in the channel.


International Journal of Numerical Methods for Heat & Fluid Flow | 2016

Immersed boundary methods for heat transfer

Claudio Santarelli; Tobias Kempe; Jochen Fröhlich

Purpose – The purpose of this paper is to present two different methods for the imposition of thermal boundary conditions (BCs) in the framework of two-phase flows: an immersed boundary method (IBM) and a Ghost cell method. Both methods are able to handle Dirichlet as well as Neumann BCs. Design/methodology/approach – Direct numerical simulations of two-phase flows are performed where the thermal BCs at the phase boundary is accounted for with two different approaches. Findings – Both methods are validated with the results obtained on a body-fitted mesh. Simulations of the three-dimensional flow and temperature field around a sphere demonstrate versatility and accuracy of both methods. Originality/value – This is the first time Neumann BCs are imposed by means of an IBM with a direct heating approach employing regularized delta functions. The test cases considered may also serve as benchmarks for other studies.


36th AIAA Fluid Dynamics Conference and Exhibit | 2006

Large-Eddy-Simulation of Turbulent Flows Using Implicit Subgrid-Scale Modeling

Tobias Kempe; Winfried Heller

In this paper we present large-eddy simulations of the turbulentflow in a channel with streamwise periodic constrictionsusingimplicitsubgrid-scale (SGS)modeling. Theemployed implicitsubgrid-scale model is thesocalled adaptive local deconvolution method (ALDM) recently proposed by Hickel & Adams. 1 In implicit SGS modeling numerical discretization and subgrid-scale modeling are merged together. Therefore, the explicit computation of the SGS stress tensor becomes unnecessary. ALDM is the first approach of providing a systematically framework for implicit SGS modeling in turbulent flows. Our computations are intended to compare the performance of the implicit model ALDM and the well-established Smagorinsky model with dynamic procedure on identically numerical grids. Results of computations performed at three different Reynolds numbers Re=10595, 5600 and 2808 are presented in in comparison to data provided by highly-resolved large-eddy simulation of Fr¨ 2 and Direct Numerical Simulation of Peller & Manhardt. 3 In the comparative tests it is shown that the implicit model performs at least as well as the explicit-subgrid scale model. Additionally, the realizability of the Reynolds stresses predicted by ALDM is verified by means of invariants of the anisotropy tensor. In the investigations we found that ALDM satisfies the realizability conditions of Lumley 4 without exception.

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Jochen Fröhlich

Dresden University of Technology

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Bernhard Vowinckel

Dresden University of Technology

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Ramandeep Jain

Dresden University of Technology

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Stephan Schwarz

Dresden University of Technology

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Silvio Tschisgale

Dresden University of Technology

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Alvaro Aguilera

Dresden University of Technology

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Andreas Herwig

Dresden University of Technology

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Claudio Santarelli

Dresden University of Technology

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Matthias H. Buschmann

Dresden University of Technology

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