DOCSLIB.ORG

Large Eddy Simulations of Compressible Magnetohydrodynamic Turbulence

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Large Eddy Simulations of Compressible Magnetohydrodynamic Turbulence Large eddy simulations of compressible magnetohydrodynamic turbulence Dissertation zur Erlangung des mathematisch-naturwissenschaftlichen Doktorgrades “Doctor rerum naturalium” der Georg-August-Universität Göttingen im Promotionsprogramm PROPHYS der Georg-August University School of Science (GAUSS) vorgelegt von Philipp Grete Göttingen, 2016 Betreuungsausschuss Prof. Dr. Dominik Schleicher Departamento de Astronomía, Universidad de Concepción, Chile PD Dr. Wolfram Schmidt Hamburger Sternwarte, Universität Hamburg, Germany Prof. Dr. Laurent Gizon Max-Planck-Institut für Sonnensystemforschung, Göttingen, Germany Institut für Astrophysik, Georg-August-Universität Göttingen, Germany Mitglieder der Prüfungskommision Referent: PD Dr. Wolfram Schmidt Hamburger Sternwarte, Universität Hamburg, Germany Korreferent: Prof. Dr. Dr.h.c. Eberhard Bodenschatz Max-Planck-Institut für Dynamik und Selbstorganisation, Göttingen, Germany Institut für Nicht-Lineare Dynamik, Georg-August-Universität Göttingen, Germany 2. Korreferent: Prof. Dr. Marcus Brüggen Hamburger Sternwarte, Universität Hamburg, Germany Weitere Mitglieder der Prüfungskommission: Prof. Dr. Dominik Schleicher Departamento de Astronomía, Universidad de Concepción, Chile Prof. Dr. Jens Niemeyer Institut für Astrophysik, Georg-August-Universität Göttingen, Germany Prof. Dr. Jörg Büchner Max-Planck-Institut für Sonnensystemforschung, Göttingen, Germany Prof. Dr. Andreas Dillmann Institut für Aerodynamik und Strömungstechnik, DLR, Göttingen, Germany Tag der mündlichen Prüfung: 9. September 2016 2 Contents Contents Abstract 5 1 Introduction 7 1.1 Motivation . 7 1.2 Turbulence . 9 1.2.1 Incompressible hydrodynamic turbulence . 9 1.2.2 Compressibility and presence of magnetic fields . 11 1.2.3 Turbulence in astrophysics . 13 1.3 Numerical methods . 15 1.3.1 Overview . 15 1.3.2 High-resolution methods . 17 1.4 Large eddy simulations . 19 1.4.1 Implicit LES . 21 1.4.2 Explicit LES . 22 1.4.3 Explicit discrete filters . 25 1.4.4 Verification and validation . 30 2 Paper I: Nonlinear closures for scale separation in supersonic MHD turbu- lence 33 3 Paper II: A nonlinear structural subgrid-scale closure for compressible MHD. I. Derivation and energy dissipation properties 45 4 Paper III: A nonlinear structural subgrid-scale closure for compressible MHD. II. A priori comparison on turbulence simulation data 55 5 Paper IV: Comparative statistics of selected subgrid-scale models in large eddy simulations of decaying, supersonic MHD turbulence 71 6 Summary and conclusions 85 Bibliography 91 A Discrete filter approximations 101 Scientific contributions 103 Acknowledgements 105 3 Abstract Supersonic, magnetohydrodynamic (MHD) turbulence is thought to play an important role in many processes — especially in astrophysics, where detailed three-dimensional observations are scarce. Simulations can partially fill this gap and help to understand these processes. However, direct simulations with realistic parameters are often not feasible. Consequently, large eddy simulations (LES) have emerged as a viable alternative. In LES the overall complexity is reduced by simulating only large and intermediate scales directly. The smallest scales, usually referred to as subgrid-scales (SGS), are introduced to the simulation by means of an SGS model. Thus, the overall quality of an LES with respect to properly accounting for small-scale physics crucially depends on the quality of the SGS model. While there has been a lot of successful research on SGS models in the hydrodynamic regime for decades, SGS modeling in MHD is a rather recent topic, in particular, in the compressible regime. In this thesis, we derive and validate a new nonlinear MHD SGS model that explic- itly takes compressibility effects into account. A filter is used to separate the large and intermediate scales, and it is thought to mimic finite resolution effects. In the derivation, we use a deconvolution approach on the filter kernel. With this approach, we are able to derive nonlinear closures for all SGS terms in MHD: the turbulent Reynolds and Maxwell stresses, and the turbulent electromotive force (EMF). We validate the new closures both a priori and a posteriori. In the a priori tests, we use high-resolution reference data of stationary, homogeneous, isotropic MHD turbulence to compare exact SGS quantities against predictions by the closures. The comparison includes, for example, correlations of turbulent fluxes, the average dissipative behavior, and alignment of SGS vectors such as the EMF. In order to quantify the performance of the new nonlinear closure, this comparison is conducted from the subsonic (sonic Mach number Ms ≈ 0:2) to the highly supersonic (Ms ≈ 20) regime, and against other SGS closures. The latter include established closures of eddy-viscosity and scale-similarity type. In all tests and over the entire parameter space, we find that the proposed closures are (significantly) closer to the reference data than the other closures. In the a posteriori tests, we perform large eddy simulations of decaying, supersonic MHD turbulence with initial Ms ≈ 3. We implemented closures of all types, i.e. of eddy-viscosity, scale-similarity and nonlinear type, as an SGS model and evaluated their performance in comparison to simulations without a model (and at higher resolution). We find that the models need to be calculated on a scale larger than the grid scale, e.g. by an explicit filter, to have an influence on the dynamics at all. Furthermore, we show that only the proposed nonlinear closure improves higher-order statistics. 5 1 Introduction 1.1 Motivation Turbulence accompanies everyone — for some people more unconscious, for example, if they rely on turbulent mixing by stirring their cup of coffee with sugar and milk, than for others, who consciously study turbulence. In general, a turbulent flow may be understood as a qualitative description of a system that is dominated by virtually random, chaotic motions with a huge number of excited modes and intermittent features. This behavior makes exact predictions on the evolution of the flow extremely challenging (if not impos- sible). The difficulty stems from the nonlinearity of the fundamental equations, e.g. the (u · r)u term in the incompressible (r · u = 0) Navier-Stokes equations @u 1 + (u · r) u = − rP + νr2u (1.1) @t ρ with velocity u, density ρ, pressure P and dynamic viscosity ν. While exact solutions only exists for a few specific cases, flows can often be described statistically or in an even more simplified qualitative manner. One important qualitative description is the (hydrodynamic) Reynolds number LV Re = ; (1.2) ν which combines a characteristic lengthscale L and velocity V with ν to give a dimen- sionless number, see e.g. textbooks of Frisch (1995), Pope (2000) and Davidson (2004). This Reynolds number is often used to characterize flows given that flows with similar Reynolds number have similar properties. Illustratively, this is the reason why e.g. the real air flow over an airplane wing can be imitated with a model of reduced size that is subject to a flow of higher velocity. Typically, a flow is considered turbulent at Reynolds number of O(103), which is already reached for the initially mentioned cup of coffee under stirring of one revolution per second. While an exact dynamical description of a cup of coffee is barely possible, the situ- ation is astrophysics is even worse. Not only is the dynamical range naturally larger by many orders of magnitudes, but also compressibility and the presence of magnetic fields introduce further complexity. Here, the dynamics for an electrically conducting fluid can be described by the magnetohydrodynamic (MHD) equations, which can be derived by combining Maxwell’s equations with the Navier-Stokes equations. The basic equations 7 1 Introduction of compressible ideal MHD are given by ∂ρ + r · (ρu) = 0; (1.3a) @t ! ∂ρu B2 + r · (ρu ⊗ u − B ⊗ B) + r P + = 0; (1.3b) @t 2 @B − r × (u × B) = 0: (1.3c) @t p with the magnetic field B incorporating units of 1= 4π. Even though they look rather simple, they provide the key to a plethora of phenomena and processes on vastly varying scales. These include, for example, the geo-dynamo, which is responsible for maintain- ing the Earth’s protective magnetic field, the strong collimation of astrophysical jets by magnetic fields, and the magnetorotational instability, which regulates angular momen- tum transport in accretion disks. A more detailed description of selected turbulent astro- physical systems including their characteristic quantities is given in in subsection 1.2.3. All these processes have in common large Reynolds numbers and the exact impact and importance of turbulence is still subject to active research in most processes. The lack of final answers to many questions is partially due to the lack of detailed ob- servations. Naturally, most astrophysical observations provide 2-dimensional information only and at a limited resolution. Here, numerical simulations can complement observa- tions as they provide not only a detailed control over the environment, but also allow for the analysis for full (instantaneous) 3-dimensional data. Unfortunately, direct numerical simulations covering realistic regimes, i.e. the Re > O(109), are not going to be possi- ble for quite some time. Even the largest purely hydrodynamic turbulence simulations reaches only Re ∼ O(104) (Federrath et al. 2016). Thus, alternative approaches that re- duce the complexity while still maintaining the fundamental physics are required. One approach is the so-called
Load more

Recommended publications
  • P-Odd Effects in Heavy Ion Collisions at NICA
    Nuclear Physics B Proceedings Supplement Nuclear Physics B Proceedings Supplement 00 (2014) 1–3 P-odd effects in heavy ion collisions at NICA SORIN, Alexander and TERYAEV, Oleg Joint Institute for Nuclear Research, 141980, Dubna, Russia and National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoe Shosse 31, 115409 Moscow, Russia Abstract Experimental manifestation of P-odd effects related to the vorticity and hydrodynamic helicity in non-central heavy ion collisions at MPD@NICA and BM@N detectors is discussed. For the NICA and FAIR energy range charac- terized by the large baryonic charge of the forming medium the effect should manifest itself in the specific neutron asymmetries. The polarization of strange particles probing the vorticity and helicity is also discussed. Keywords: vorticity, helicity, handedness 1. Introduction low energy scan mode) may result in the separation of the baryonic charge. A special interest is manifestation A search for local violations of discrete (C and P) of this separation in neutron asymmetries with respect symmetries from the discovery of the famous Chiral to the production plane, as soon as neutrons, from the Magnetic Effects (CME) [1] is a subject of intense the- theoretical side, are not affected by CME and, from the oretical and experimental studies. Here we concentrate experimental side, there is a unique opportunity to study on the effects related to the P-odd ”mechanical” effects, neutron production and asymmetries at MPD@NICA. like the orbital angular momentum, vorticity and helic- ity. In particular, we address to the neutron angular asym- metries [2], effects of the helicity separation [3, 4] and baryon polarization [2, 3] as well as the emergence of 3.
    [Show full text]
  • Helicity Separation in Heavy-Ion Collisions When It Has the Different Signs Below and Above of the Reaction Plane
    Helicity separation in Heavy-Ion Collisions Mircea Baznat,1,2, ∗ Konstantin Gudima,1,2, † Alexander Sorin,1,3, ‡ and Oleg Teryaev1,3, § 1 Joint Institute for Nuclear Research, 141980 Dubna (Moscow region), Russia 2 Institute of Applied Physics, Academy of Sciences of Moldova, MD-2028 Kishinev, Moldova 3 Dubna International University, Dubna (Moscow region) 141980, Russia (Dated: July 30, 2018) We study the P-odd effects related to the vorticity of the medium formed in noncentral heavy ion collisions. Using the kinetic Quark-Gluon Strings Model we perform the numerical simulations of the vorticity and hydrodynamical helicity for the various atomic numbers, energies and centralities. We observed the vortical structures typically occupying the relatively small fraction of the fireball volume. In the course of numerical simulations the noticeable hydrodanamical helicity was observed manifesting the specific mirror behaviour with respect to the reaction plane. The effect is maximal at the NICA and FAIR energy range. PACS numbers: 25.75.-q I. INTRODUCTION The local violation [1] of discrete symmetries in strongly interacting QCD matter is now under intensive theoret- ical and experimental investigations. The renowned Chiral Magnetic Effect (CME) uses the (C)P-violating (elec- tro)magnetic field emerging in heavy ion collisions in order to probe the (C)P-odd effects in QCD matter. There is an interesting counterpart of this effect, Chiral Vortical Effect (CVE)[2] due to coupling to P-odd medium vorticity. In its original form [2] this effect leads to the appearance of the same electromagnetic current as CME. Its straightforward generalization was proposed later resulting in generation of all conserved-charge currents [3], in particular baryonic ones (especially important when there is CME cancellation between three massless flavors [4]), and polarization of hyperons [3, 5].
    [Show full text]
  • Chaotic Vortical Flows and Their Manifestations
    Chaotic vortical flows and their manifestations M. Baznat^(a) , K. Gudima^(a), P. Fre^(b), A. Sorin^(c), O. Teryaev^(c) (a) Institute of Applied Physics, Moldova (b) Dipartimento di Fisica, Universita di Torino & INFN Sezione di Torino (c) Joint Institute for Nucler Research, Dubna 4th International Conference on New Frontiers in Physics Conference Center of the Orthodox Academy of Crete Kolymbari, Greece, August 25, 2015 OUTLINE Chaotic Arnold-Beltrami flows Vorticity and hydrodynamical helicity modelling Ʌ baryon polarization due to vorticity Conclusions Arnold-Beltrami flows • Nonrelativistic incompressible fluids with vorticity parallel to velocity • Compatible with Euler equation for steady flows • Bernoulli condition is valid in the whole volume of the fluid Chaotic streamlines Arnold's theorem: For flows taking place on compact three manifolds, the only velocity fields able to produce chaotic streamlines are those satisfying Beltrami equation. & Topological conception of contact structures, each of which admits a representative contact vector field also satisfying Beltrami equation. 4 Chaotic thermalization? • Arnold-Beltrami flows – Lagrangian turbulence • Simple explanation: Bernoulli in the volume – the streamlines come close to each other • Chaotic advection: laminar flows result in the chaotic motion of passive admixture • Fast Dynamo problem, the spontaneous generation of a exponential growing magnetic field in a flow of conducting fluid with vorticity • Possible role in the fast thermalization (complementary description)?!
    [Show full text]
  • Chaotic Vortical Flows and Their Manifestations
    126 EPJ Web of Conferences , 02030 (2016) DOI: 10.1051/epjconf/201612602030 ICNFP 2015 Chaotic vortical flows and their manifestations M. Baznat1,a, K. Gudima1,b, A. Sorin1,c,d, and O. Teryaev1,e 1Joint Institute for Nuclear Research, 141980 Dubna, Russia Abstract. We study vorticity and hydrodynamic helicity in semi-peripheral heavy-ion collisions using the kinetic model of Quark-Gluon Strings. The angular momentum, which is a source of P-odd observables, is preserved with a good accuracy. We observe formation of the specific toroidal structures of the vorticity field. Their existence, accom- panied by the strange chemical potential, is mirrored in the polarization of hyperons of the percent order. 1 Introduction The local violation [1] of discrete symmetries in strongly interacting QCD matter is now under inten- sive theoretical and experimental investigations. The Chiral Magnetic Effect (CME) uses the (C)P- violating (electro)magnetic field emerging in heavy ion collisions in order to probe the (C)P-odd effects in QCD matter. There is an even more interesting counterpart of this effect, Chiral Vortical Effect (CVE)[2] due to coupling to P-odd medium vorticity leading to the induced electromagnetic and [3] all conserved- charge currents, in particular the baryonic ones. The zeroth component of axial current and correspondent axial charge are related to hydrodynam- ical helicity H ≡ dV(u · w), being the projection of velocity u to vorticity w = curlu. This quantity is manifesting the recently discovered [4] and confirmed [5] phenomenon of separation, i.e. mirror behavior (same magnitude but different sign) in the half-spaces separated by the reaction plane Another important P-odd observable is the baryon polarizatiion.
    [Show full text]
  • Convective Storm Structure and Evolution Presented by the Warning Decision Training Branch
    Distance Learning Operations Course IC 5.7: Convective Storm Structure and Evolution Presented by the Warning Decision Training Branch Version: 0308.2 Distance Learning Operations Course Table of Contents Introduction ..................................................................................................... 1 Objectives ................................................................................................................................................ 3 Lesson 1....................................................................................................................................3 Lesson 2....................................................................................................................................3 Lesson 3....................................................................................................................................3 Lesson 1: Fundamental Relationships Between Shear and Instability on Convective Storm Structure and Type. ......................................................... 6 Objective 1 ............................................................................................................................................... 6 Effects of Shear .........................................................................................................................6 Objective 2 ............................................................................................................................................... 7 Objective 3 ............................................................................................................................................
    [Show full text]
  • Hydrodynamic Helicity and Strange Hyperon Polarization in Heavy-Ion Collisions
    Home Search Collections Journals About Contact us My IOPscience Hydrodynamic helicity and strange hyperon polarization in heavy-ion collisions This content has been downloaded from IOPscience. Please scroll down to see the full text. 2016 J. Phys.: Conf. Ser. 668 012084 (http://iopscience.iop.org/1742-6596/668/1/012084) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 131.169.4.70 This content was downloaded on 01/02/2016 at 20:48 Please note that terms and conditions apply. 15th International Conference on Strangeness in Quark Matter (SQM2015) IOP Publishing Journal of Physics: Conference Series 668 (2016) 012084 doi:10.1088/1742-6596/668/1/012084 Hydrodynamic helicity and strange hyperon polarization in heavy-ion collisions M. Baznat1;2, K. Gudima1;2, A. Sorin1;3, O. Teryaev1;3 1Joint Institute for Nuclear Research, 141980 Dubna, Russia 2Institute of Applied Physics, Academy of Sciences of Moldova, MD-2028 Kishinev, Moldova 3National Research Nuclear University (MEPhI), 115409 Moscow, Russia E-mail: [email protected] Abstract. We study the P-odd effects related to the vorticity of the medium formed in noncentral heavy ion collisions. Using the kinetic Quark-Gluon String Model, we perform numerical simulations of the vorticity and hydrodynamical helicity for various atomic numbers, energies and centralities. We observe vortical structures typically occupying a relatively small fraction of the fireball volume. In the course of numerical simulations a noticeable hydrodynamic helicity was observed manifesting a specific mirror behaviour with respect to the reaction plane. The effect is maximal at the NICA and FAIR energy range.
    [Show full text]
  • Arxiv:1307.3844V2
    Solar Physics DOI: 10.1007/•••••-•••-•••-••••-• Magnetic Field Extrapolations into the Corona: Success and Future Improvements S. R´egnier1 c Springer •••• Abstract The solar atmosphere being magnetic in nature, the understanding of the structure and evolution of the magnetic field in different regions of the solar atmosphere has been an important task over the past decades. This task has been made complicated by the difficulties to measure the magnetic field in the corona, while it is currently known with a good accuracy in the photosphere and/or chromosphere. Thus, to determine the coronal magnetic field, a mathematical method has been developed based on the observed magnetic field. This is the so-called magnetic field extrapolation technique. This technique relies on two crucial points: (i) the physical assumption leading to the system of differential equations to be solved, (ii) the choice and quality of the associated boundary conditions. In this review, I summarise the physical assumptions currently in use and the findings at different scales in the solar atmosphere. I concentrate the discussion on the extrapolation techniques applied to solar magnetic data and the comparison with observations in a broad range of wavelengths (from hard X-rays to radio emission). Keywords: Corona, Models - Corona, Structures - Magnetic Fields, Models - Active Regions 1. Introduction With the advent of photospheric magnetographs/magnetometers in the sixties, it has soon been realised that the coronal magnetic field can be derived by assuming an equilibrium state. The main forces excerted on the coronal plasma are the plasma pressure, the gravitational force, and the magnetic or Lorentz forces. This gives the magnetohydrostatic equilibrium: − ∇p + ρg + j × B = 0 (1) where p and ρ are the plasma pressure and density, g is the gravity, j is the arXiv:1307.3844v2 [astro-ph.SR] 16 Jul 2013 electric current density, and B is the magnetic field.
    [Show full text]
  • Topical Review on Skyrmions and Hall Transport
    Article Topical Review on Skyrmions and Hall Transport Bom Soo Kim 1,† * 1 [email protected] † Department of Physics, Loyola University Maryland, 4501 N. Charles Street, Baltimore, MD 21210, USA J. Phys.: Condens. Matter 31 (2019) 383001 https://doi.org/10.1088/1361-648X/ab273f Abstract: We review recent progresses towards an understanding of the Skyrmion Hall transport in insulating as well as conducting materials. First, we consider a theoretical breakthrough based on the quantum field theory Ward identity, a first principle analysis, relying on symmetries and conservation laws. Broken parity (inversion) symmetry plays a crucial role in Skyrmion Hall transport. In addition to the well known thermal and electric Hall conductivities, our analysis has led us to the discovery of a new and unforeseen physical quantity, Hall viscosity - an anti-symmetric part of the viscosity tensor. We propose a simple way to confirm the existence of Hall viscosity in the measurements of Hall conductivity as a function of momentum. We provide various background materials to assist the readers to understand the quantum field theory Ward identity. In the second part, we review recent theoretical and experimental advancements of the Skyrmion Hall effects and the topological (Magnon) Hall effects for conducting (insulting) magnets. For this purpose, we consider two enveloping themes: spin torque and thermo-electromagnetic effect. First, we overview various spin torques, such as spin transfer torque, spin-orbit torque, and spin Hall torque, and generalized Landau-Lifshitz-Gilbert equations and Thiele equations using a phenomenological approach. Second, we consider irreversible thermodynamics to survey possible thermo-electromagnetic effects, such as Seebeck, Peltier and Thompson effects in the presence of the electric currents, along with the Hall effects in the presence of a background magnetic field.
    [Show full text]
  • HYDRODYNAMIC WAKES and MINIMAL SURFACES with FRACTAL BOUNDARIES
    HYDRODYNAMIC WAKES and MINIMAL SURFACES with FRACTAL BOUNDARIES Robert M. Kiehn, Physics Department, University of Houston Houston TX 77004 Abstract: The observable features of hydrodynamic wakes can be put into correspondence with those characteristic surfaces of tangential discontinuities upon which the solutions to the evolutionary equations of hydrodynamics are not unique. Only the robust minimal surface subset, associated with a harmonic vector field, will be persistent and of minimal dissipation. Surprisingly, those minimal surfaces generated by iterates of complex holomorphic curves in four dimensions are related to fractal sets. Introduction Note that the Kelvin-Helmholtz instability A remarkable feature of hydrodynamic pattern is characterized by a replication of the wakes and coherent structures in stratified flows is primitive pattern of a Cornu spiral. The Rayleigh- that their associated "instability" patterns seem to Taylor instability pattern is characterized by a belong to two broad equivalence classes of spiral replication of the primitive pattern of a Mushroom shapes. These two patterns are epitomized by the spiral. Although an analytic description of the Kelvin-Helmholtz instability pattern (Figure 1a) Cornu spiral has been known for more than 100 and the Rayleigh-Taylor instability pattern years, only recently has the present author become (Figures 1b). aware of a closed form analytic description for the mushroom spiral. This work was presented at the August 1992, IUTAM meeting at Poitier, and is summarized in section 4. The essential questions are: Why do Figure 1a. The pattern of the Kelvin- these spiral patterns appear almost universally in Helmholtz instability. wakes? Why do they persist for such substantial periods of time? Why are they so sharply defined? What are the details of their creation? As H.K.Browand said [Browand, 1986] "There does not exist a satisfactory theoretical explanation for these wake patterns." Although the theory and ideas presented Figure 1b.
    [Show full text]
  • Distribution Function Approach to Redshift Space Distortions
    Prepared for submission to JCAP Distribution function approach to redshift space distortions. Part IV: perturbation theory applied to dark matter Zvonimir Vlah,a UroˇsSeljak,a;b;c;d Patrick McDonald,c;e Teppei Okumura,d and Tobias Baldaufa aInstitute for Theoretical Physics, University of Z¨urich, Winterthurerstrasse 190, Z¨urich, Switzerland bPhysics, Astronomy Department, University of California, Berkeley, California, USA. cLawrence Berkeley National Laboratory, Berkeley, CA, USA dInstitute for Early Universe, Ewha University, Seoul, S. Korea ePhysics Dept., Brookhaven National Laboratory, Upton, NY, USA E-mail: [email protected], [email protected] Abstract. We develop a perturbative approach to redshift space distortions (RSD) using the phase space distribution function approach and apply it to the dark matter redshift space power spectrum and its moments. RSD can be written as a sum over density weighted velocity moments correlators, with the lowest order being density, momentum density and stress energy density. We use standard and extended perturbation theory (PT) to determine their auto and cross correlators, comparing them to N-body simulations. We show which of the terms can be modeled well with the standard PT and which need additional terms that include higher order corrections which cannot be modeled in PT. Most of these additional terms are related to the small scale velocity dispersion effects, the so called finger of god (FoG) effects, which affect some, but not all, of the terms in this expansion, and which can be approximately modeled using a simple physically motivated ansatz such as the halo model. We point out that there are several velocity dispersions that enter into the detailed RSD analysis with very different amplitudes, which can be approximately predicted by the halo model.
    [Show full text]
  • Fluid-Structure Interaction Analysis of a Centrifugal Fan a Numerical Study to Investigate the Necessity of Including Aerodynamic Loads in Fatigue Estimation
    Fluid-Structure Interaction Analysis of a Centrifugal Fan A Numerical Study to Investigate the Necessity of Including Aerodynamic Loads in Fatigue Estimation Master’s thesis in Applied Mechanics DAVID KALLIN KNUT NORDENSKJÖLD Department of Applied Mechanics CHALMERS UNIVERSITY OF TECHNOLOGY Gothenburg, Sweden 2017 Master’s thesis in applied mechanics Fluid-Structure Interaction Analysis of a Centrifugal Fan A Numerical Study to Investigate the Necessity of Including Aerodynamic Loads in Fatigue Estimation DAVID KALLIN KNUT NORDENSKJÖLD Department of Applied Mechanics Division of Fluid Mechanics Chalmers University of Technology Gothenburg, Sweden 2017 Fluid-Structure Interaction Analysis of a Centrifugal Fan A Numerical Study to Investigate the Necessity of Including Aerodynamic Loads in Fatigue Estimation DAVID KALLIN KNUT NORDENSKJÖLD © DAVID KALLIN & KNUT NORDENSKJÖLD, 2017. Supervisors: Andreas Gustafsson, Federico Ghirelli, Johan Olsson, SEMCON Examiner: Professor Lars Davidson, Applied Mechanics Master’s Thesis 2017:54 ISSN 1652-8557 Department of Applied Mechanics Division of Fluid Mechanics Chalmers University of Technology SE-412 96 Gothenburg Sweden Telephone +46 31 772 1000 Cover: Wire-frame model of the centrifugal fan with pressure contours on the sur- faces of one fan sector as well as streamlines around one of the fan blades. Typeset in LATEX Printed by: Department of Applied Mechanics Gothenburg, Sweden 2017 iv Fluid-Structure Interaction Analysis of a Centrifugal Fan A Numerical Study to Investigate the Necessity of Including Aerodynamic Loads in Fatigue Estimation DAVID KALLIN KNUT NORDENSKJÖLD Department of Applied Mechanics Division of Fluid Mechanics Chalmers University of Technology Abstract Centrifugal fans are used within many applications where great ability to create pressure increase is of importance.
    [Show full text]
  • Analysis of the Radar Reflectivity of Aircraft Vortex Wakes
    Under consideration for publication in .I. Fluid Mech. Analysis of the radar reflectivity of aircraft vortex wakes By KARIM SHARIFFtAND ALAN WRAY t 1NASA Ames Research Center, Moffett Field, CA 94035, USA (Received ?? and in revised form ??) Radar has been proposed as a way to track wake vortices to reduce aircraft spacing and tests have revealed radar echoes from aircraft wakes in clear air. The results are always interpreted qualitatively using Tatarski's theory of weak scattering by isotropic atmo- spt,eric turbulence. The goal of the present work was to predict the value of the radar cross-section (RCS) using simpler models. This is accomplished in two steps. (l) First, the refractive index is obtained. Since the structure of aircraft wakes is different from at- mospheric turbulence, three simple mechanisms specific to vortex wakes are considered: (A) Radial density gradient in a 2D vortex (B) 3D fluctuations in the vortex cores'(C) Adiabatic transport of atmospheric fluid in a 2D oval surrounding the pair of vortices. The index of refraction is obtained more precisely for the 2D mechanisms than for the 3D ones. (2) [n the second step, knowing the index of refraction, a scattering analysis is performed. Tatarski's weak scattering approximation is kept but the usual assumpGons of a far-field and a uniform incident wave are dropped. Neither assumption is generally valid for a wake that is coherent across the radar beam. For analytical insight, a simpler approximation that invokes, in addition to weak scattering, the far-field and wide cylin- drical beam assumptions, is also developed and compared with the more general analysis.
    [Show full text]