8 results
Search Results
Now showing 1 - 8 of 8
- ItemPredicting the dominating factors during heat transfer in magnetocaloric composite wires(Amsterdam : Elsevier B.V., 2020) Krautz, M.; Beyer, L.; Funk, A.; Waske, A.; Weise, B.; Freudenberger, J.; Gottschall, T.Magnetocaloric composite wires have been studied by pulsed-field measurements up to μ0ΔH = 10 T with a typical rise time of 13 ms in order to evaluate the evolution of the adiabatic temperature change of the core, ΔTad, and to determine the effective temperature change at the surrounding steel jacket, ΔTeff, during the field pulse. An inverse thermal hysteresis is observed for ΔTad due to the delayed thermal transfer. By numerical simulations of application-relevant sinusoidal magnetic field profiles, it can be stated that for field-frequencies of up to two field cycles per second heat can be efficiently transferred from the core to the outside of the jacket. In addition, intense numerical simulations of the temperature change of the core and jacket were performed by varying different parameters, such as frequency, heat capacity, thermal conductivity and interface resistance in order to shed light on their impact on ΔTeff at the outside of the jacket in comparison to ΔTad provided by the core.
- ItemNonequilibrium phase transitions in finite arrays of globally coupled Stratonovich models: Strong coupling limit(College Park, MD : Institute of Physics Publishing, 2009) Senf, F.; Altrock, P.M.; Behn, U.A finite array of N globally coupled Stratonovich models exhibits a continuous nonequilibrium phase transition. In the limit of strong coupling, there is a clear separation of timescales of centre of mass and relative coordinates. The latter relax very fast to zero and the array behaves as a single entity described by the centre of mass coordinate. We compute analytically the stationary probability distribution and the moments of the centre of mass coordinate. The scaling behaviour of the moments near the critical value of the control parameter ac(N) is determined. We identify a crossover from linear to square root scaling with increasing distance from ac. The crossover point approaches ac in the limit N →∞ which reproduces previous results for infinite arrays. Our results are obtained in both the Fokker-Planck and the Langevin approach and are corroborated by numerical simulations. For a general class of models we show that the transition manifold in the parameter space depends on N and is determined by the scaling behaviour near a fixed point of the stochastic flow. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
- ItemA cascaded laser acceleration scheme for the generation of spectrally controlled proton beams(College Park, MD : Institute of Physics Publishing, 2010) Pfotenhauer, S.M.; Jäckel, O.; Polz, J.; Steinke, S.; Schlenvoigt, H.-P.; Heymann, J.; Robinson, A.P.L.; Kaluza, M.C.We present a novel, cascaded acceleration scheme for the generation of spectrally controlled ion beams using a laser-based accelerator in a 'double-stage' setup. An MeV proton beam produced during a relativistic laser-plasma interaction on a thin foil target is spectrally shaped by a secondary laser-plasma interaction on a separate foil, reliably creating well-separated quasi-monoenergetic features in the energy spectrum. The observed modulations are fully explained by a one-dimensional (1D) model supported by numerical simulations. These findings demonstrate that laser acceleration can, in principle, be applied in an additive manner. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
- ItemBehavior of a porous particle in a radiofrequency plasma under pulsed argon ion beam bombardment(College Park, MD : Institute of Physics Publishing, 2010) Wiese, R.; Sushkov, V.; Kersten, H.; Ikkurthi, V.R.; Schneider, R.; Hippler, R.The behavior of a single porous particle with a diameter of 250 μm levitating in a radiofrequency (RF) plasma under pulsed argon ion beam bombardment was investigated. The motion of the particle under the action of the ion beam was observed to be an oscillatory motion. The Fourier-analyzed motion is dominated by the excitation frequency of the pulsed ion beam and odd higher harmonics, which peak near the resonance frequency. The appearance of even harmonics is explained by a variation of the particles's charge depending on its position in the plasma sheath. The Fourier analysis also allows a discussion of neutral and ion forces. The particle's charge was derived and compared with theoretical estimates based on the orbital motion-limited (OML) model using also a numerical simulation of the RF discharge. The derived particle's charge is about 7-15 times larger than predicted by the theoretical models. This difference is attributed to the porous structure of the particle. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
- ItemTransient numerical simulation of sublimation growth of SiC bulk single crystals : modeling, finite volume method, results(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2003) Philip, PeterThis work treats transient numerical simulation of growth of silicon carbide (SiC) bulk single crystals by physical vapor transport (also called the modified Lely method). A transient mathematical model of the growth process is presented. Subsequently, the finite volume method for the discretization of evolution equations, which constitutes the basis for the numerical simulations presented in this work, is studied mathematically, proving the existence of discrete solutions. All material data used for numerical simulations in this work are collected in the appendix. Starting with a description of the physical growth procedure, problems arising during the growth process are discussed as well as techniques that are used for process control. It is explained why numerical simulation is an important tool for control, and the advantages of a transient approach are considered. Within the presented transient model, continuous mixture theory is used to obtain balance equations for energy, mass, and momentum inside the gas phase. In particular, reaction-diffusion equations are deduced. Heat conduction is treated inside solid materials. Heat transport by radiation is modeled via the net radiation method for diffuse-gray radiation to allow for radiative heat transfer between the surfaces of cavities. The model includes the semi-transparency of the single crystal via a band approximation. Induction heating is modeled by an axisymmetric complex-valued magnetic scalar potential that is determined as the solution of an elliptic problem. The resulting heat source distribution is calculated from the magnetic potential. The heat sources are updated continuously during the solution of the transient problem for the temperature evolution to allow for changes in the electrical conductivity depending on temperature and for changes due to a moving induction coil. The finite volume method is treated in a rigorous mathematical framework. It allows the discretization of parabolic, hyperbolic, and elliptic partial differential equations, as they arise from the mathematical model of the growth process, including nonlocal contributions due to radiative heat transfer. The general abstract setting consists of a system of nonlinear evolution equations in arbitrary finite space dimension, each evolution equation living on a different polytope domain. In general, each evolution equation has diffusive and convective contributions as well as source and sink terms. Each contribution is permitted to depend on the solution. Discontinuities of the solution are allowed at domain interfaces. Interface conditions in terms of the solution and its flux are considered. Moreover, nonlocal interface conditions are considered. Outer boundary conditions include Dirichlet conditions, flux conditions, emission conditions, and nonlocal conditions. Time discretization is performed by an implicit Euler scheme, where an explicit discretization is allowed in certain dependencies such that the temperature-dependent emissivities can be taken from the previous time step. As usual, the space discretization is performed by integrating the evolution equations over control volumes and then using quadrature formulas. As an axisymmetric setting and cylindrical coordinates are used in the simulations, a treatment of change of variables is included in the abstract considerations. For the case that the evolution equations constitute nonlinear heat equations, still allowing nonlinear diffusion, convection, and source and sink terms, as well as nonlocal interface and boundary conditions as they arise from modeling radiative heat transfer, discrete L∞ - L1 a priori estimates are established for the system resulting from the finite volume discretization. A fixed point argument is then used to prove the existence and uniqueness of discrete solutions. The presented numerical simulations are conducted in an axisymmetric setting. They constitute transient investigations of control parameters affecting the temperature evolution during the heating of the growth apparatus. A cylindrically symmetric finite volume scheme provides the discretization for both the transient nonlinear heat problem and the stationary magnetic potential problem. For different heating powers and different vertical coil positions, the temperature evolution is monitored at the surface of the crystal and at the surface of the source powder as well as at the top and at the bottom of the growth apparatus. It is studied how the temperature difference between source and seed, which is highly relevant to the growth process, is related to the measurable temperature difference between bottom and top. Results concerning the time lack between the heating of the surface of the source powder and the heating of its interior are considered. Finally, the global evolution of temperature and heat sources is investigated.
- ItemTransient numerical study of termperature gradients during sublimation growth of SiC: Dependence on apparatus design(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2005) Geiser, Jürgen; Klein, Olaf; Philip, PeterUsing a transient mathematical heat transfer model including heat conduction, radiation, and radio frequency (RF) induction heating, we numerically investigate the time evolution of temperature gradients in axisymmetric growth apparatus during sublimation growth of silicon carbide (SiC) bulk single crystals by physical vapor transport (PVT) (modified Lely method). Temperature gradients on the growing crystal's surface can cause defects. Here, the evolution of these gradients is studied numerically during the heating process, varying the apparatus design, namely the amount of the source powder charge as well as the size of the upper blind hole used for cooling of the seed. Our results show that a smaller upper blind hole can reduce the temperature gradients on the surface of the seed crystal without reducing the surface temperature itself.
- ItemFractional-splitting and domain-decomposition methods for parabolic problems and applications(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Daoud, Daoud; Geiser, JürgenIn this paper we consider the first order fractional splitting method to solve decomposed complex equations with multi-physical processes for applications in porous media and phase-transitions. The first order fractional splitting method is also considered as basic solution for the overlapping Schwarz-Waveform-Relaxation method for an overlapped subdomains. The accuracy and the efficiency of the methods are investigated through the solution of different model problems of scalar, coupling and decoupling systems of convection reaction diffusion equation.
- ItemDroplets on liquids and their long way into equilibrium(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Bommer, Stefan; Jachalski, Sebastian; Peschka, Dirk; Seemann, Ralf; Wagner, BarbaraThe morphological paths towards equilibrium droplets during the late stages of the dewetting process of a liquid film from a liquid substrate is investigated experimentally and theoretically. As liquids, short chained polystyrene (PS) and polymethyl-methacrylate (PMMA) are used, which can be considered as Newontian liquids well above their glass transition temperatures. Careful imaging of the PS/air interface of the droplets during equilibration by in situ scanning force microscopy and the PS/PMMA interface after removal of the PS droplets reveal a surprisingly deep penetration of the PS droplets into the PMMA layer. Droplets of sufficiently small volumes develop the typical lens shape and were used to extract the ratio of the PS/air and PS/PMMA surface tensions and the contact angles by comparison to theoretical exact equilibrium solutions of the liquid/liquid system. Using these results in our dynamical thin-film model we find that before the droplets reach their equilibrium they undergo several intermediate stages each with a well-defined signature in shape. Moreover, the intermediate droplet shapes are independent of the details of the initial configuration, while the time scale they are reached depend strongly on the droplet volume. This is shown by the numerical solutions of the thin-film model and demonstrated by quantitative comparison to experimental results