06 Fakultät Luft- und Raumfahrttechnik und Geodäsie
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/7
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Item Open Access High-order methods for computational astrophysics(2015) Núñez-de la Rosa, Jonatan; Munz, Claus-Dieter (Prof. Dr.)In computational fluid dynamics, high-order numerical methods have gained quite popularity in the last years due to the need of high fidelity predictions in the simulations. High-order methods are suitable for unsteady flow problems and long-term simulations because they are more efficient when obtaining higher accuracy than low-order methods, and because of their outstanding dissipation and dispersion properties. In the present work, the development and application of three high-order numerical methods, namely, the conservative finite difference (FD) method, the finite volume (FV) method, and the discontinuous Galerkin spectral element method (DGSEM), is presented. These methods are used here for solving three equations systems arising in computational astrophysics on flat spacetimes, specifically, the ideal magnetohydrodynamics (MHD), relativistic hydrodynamics (SRHD) and relativistic magnetohydrodynamics (SRMHD). Our computational framework has been subject to the standard testbench in computational astrophysics. Numerical results of problems having smooth flows, and problems with shock-dominated flows, are also reported. Finite volume methods are numerical methods based on the weak solution of conservation laws in integral form. Unlike finite volume methods, where cell averages of the solution are evolved in time, in the conservative finite difference schemes only the solution at specific nodal points are considered. This difference offers a high efficiency of finite difference over finite volume methods in two and three dimensional high-order calculations because of the form of the utilized stencils in the reconstruction step. Recently, a lot of effort has been put into the development of efficient high-order accurate reconstruction procedures on structured and unstructured meshes. The most widely used procedure to achieve high-order spatial accuracy in finite volume and conservative finite difference methods is the WENO reconstruction. The basic idea of the WENO schemes is based on an adaptive reconstruction procedure to obtain a higher-order approximation on smooth regions while the scheme remains non-oscillatory near discontinuities. For this reason, the WENO formulation is particularly effective when solving conservation laws containing discontinuities. In this work, the FD and FV methods are extended to very high-order accuracy on regular Cartesian meshes by making use of the arbitrary high-order reconstruction WENO operator. The time discretization is carried out with a strong stability-preserving Runge-Kutta (SSPRK) method. The MHD, SRHD and SRMHD equations are then solved with these two methods for problems having strong shock configurations. The discontinuous Galerkin (DG) methods combine the ideas of the finite element (FE) and the finite volume methods. From the FE methods, the solution and test functions in the variational formulation of the conservation law are locally represented by polynomials, allowing to be discontinuous at element faces. In order to stabilize the scheme, from the FV methods are borrowed the ideas of using Riemann solvers, which permit to connect a given element with its direct neighboring ones. One special case in the family of DG methods is the DGSEM. In these methods, the domain is decomposed into quadrilateral/hexahedral elements, and the solution and the fluxes are represented by tensor-product basis functions (high-order Lagrangian interpolants). The integrals are approximated by quadrature, and the nodal points, where the solution is computed, are the Gauss-Legendre quadrature points. With these choices, the DG operator has a dimension-by-dimension splitting form, which yields more efficiency due to less operations and less memory consumption. In this work, the DGSEM has been also extended to the equations of computational astrophysics on flat spacetimes, but restricted only to the MHD and SRHD equations. Because discontinuous solutions form part of the nature of the hyperbolic conservation laws, shock capturing strategies have to be devised, especially for the discontinuous Galerkin method. For the DGSEM, a hybrid DG/FV shock capturing approach is used as the main building block for stabilization of the solution when shocks take place. The hybrid DGSEM/FV is constructed in such a way that, in regions of smooth flows, the DGSEM method is employed, and those parts of the flow having shocks, the DGSEM elements are interpreted as quadrilateral/hexahedral subdomains. In each of these subdomains, the nodal DG solution values are used to build a new local domain composed now of finite volume subcells, which are evolved with a robust finite volume method with third order WENO reconstruction. This new numerical framework for computational astrophysics based on the hybridization of high-order methods brings very promising results.Item Open Access The effects of airfoil thickness on dynamic stall characteristics of high‐solidity vertical axis wind turbines(2021) Bangga, Galih; Hutani, Surya; Heramarwan, HenidyaThe flow physics of high solidity vertical axis wind turbines (VAWTs) is influenced by the dynamic stall effects. The present study is aimed at investigating the effects of airfoil thickness on the unsteady characteristics of high solidity VAWTs. Seven different national advisory committee for aeronautics (NACA) airfoils (0008, 0012, 0018, 0021, 0025, 0030, 0040) are investigated. A high fidelity computational fluid dynamics (CFD) approach is used to examine the load and flow characteristics in detail. Before the study is undertaken, the CFD simulation is validated with experimental data as well as large eddy simulation results with sound agreement. The investigation demonstrates that increasing the airfoil thickness is actually beneficial not only for suppressing the dynamic stall effects but also to improve the performance of high solidity turbines. Interestingly this is accompanied by a slight reduction in thrust component. The strength and radius of the dynamic stall vortex decrease with increasing airfoil thickness. The airfoil thickness strongly influences the pressure distributions during dynamic stall process, which is driven by the suction peak near the leading edge. The knowledge gained might be used by blade engineers for designing future turbines and for improving the accuracy of engineering models.Item Open Access Experiments on the laminar to turbulent transition under unsteady inflow conditions(2023) Romblad, Jonas; Krämer, Ewald (Prof. Dr.-Ing.)Natural laminar flow (NLF) airfoils are key to the performance of sailplanes and wind turbines. They provide a significant reduction of friction drag by delaying the transition from laminar to turbulent boundary layer. However, the most common method for transition prediction in NLF airfoil design, the e^n method (Mack 1977), has limited capabilities for taking inflow turbulence into account. The current work employs wind tunnel experiments to study how the transition on an NLF airfoil is affected by free-stream turbulence. The effect of small- and large-scale turbulence is studied separately, as well as in combination. In the wind tunnel, turbulence grids generate small-scale turbulence, and a gust generator induces inflow angle oscillations corresponding to large-scale turbulence. The study includes a detailed characterization of the turbulence generated by grids placed in the settling chamber of the wind tunnel. The Reynolds number Re = 3400000 and the airfoil pressure distribution is matched to cruise or dash flight of general aviation aircraft. The results are compared with direct numerical simulation, linear stability theory (LST) and flight measurements. The results show that small-scale turbulence does have an influence on the transition location in the investigated range of turbulence level, 0.01% < Tu < 0.11%. The modified e^n method (Mack 1977) captures the general trend, but the sensitivity to Tu is airfoil dependent. The effects of 2D, single-mode inflow angle oscillations are investigated in the range of reduced frequency 0.06 < kappa < 1.7. In this range, the transition process changes from quasi-steady to clearly unsteady, but a fully convective transition mode is not formed. This is an intermediate range of unsteady flow in which trajectory-following LST is able to capture the main features of the unsteady transition process. No significant interaction between the effects of small- and large-scale turbulence are observed in the investigated range of Tu and kappa, indicating that the effects can be superposed.Item Open Access Computational studies of massively separated wake flows of transport aircraft(2021) Waldmann, Andreas; Krämer, Ewald (Prof. Dr.)This work focuses on the investigation of flow phenomena associated with low speed stall using a representative commercial transport aircraft configuration. Subsonic stall at high Reynolds number involves a highly complex turbulent flow field, which is difficult to analyze in ist entirety via experimental methods. Various computational approaches based on URANS and hybrid RANS/LES were evaluated, utilizing validation data from the European Transonic Windtunnel. Scale-resolving computational approaches were leveraged to gain deeper insight into the processes occurring in such a wake. DDES-based methods were found to be able to resolve the flow features occurring at the separation location and in the wake. An extensive study on the impact of solver settings, computational grids, model geometry and inflow Reynolds number was carried out in order to permit a validation of the chosen approach. Using these findings, the massively separated wake flow was studied at three angles of attack in post stall conditions. Three different regimes of formation of the separated wake were identified via the main locations where turbulence kinetic energy is produced. Analysis of anisotropy, turbulence length scales and signal characteristics provided insight into the propagation of the wake and the mixing processes. Modal analysis of the wake dynamics enabled the detection of a near-wing recirculation area and a von Kármán vortex street in the wake. Flow structures associated with both phenomena result in tailplane load fluctuations at their respective characteristic frequencies.Item Open Access Investigation of Lagrangian Areas of Minimal Stretching (LAMS) in a turbulent boundary layer(2023) Rist, Ulrich; Weinschenk, Matthias; Wenzel, Christoph