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1986 | Buch

Secondary Instabilities, Coherent Structures and Turbulence Kapitel lesen Erstes Kapitel lesen

Supercomputers and Fluid Dynamics

Proceedings of the First Nobeyama Workshop September 3–6, 1985

herausgegeben von: Kunio Kuwahara, Raul Mendez, Steven A. Orszag

Verlag: Springer Berlin Heidelberg

Buchreihe : Lecture Notes in Engineering

Enthalten in: Professional Book Archive

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Über dieses Buch

In the past several years, it has become apparent that computing will soon achieve a status within science and engineering to the classical scientific methods of laboratory experiment and theoretical analysis. The foremost tools of state-of-the-art computing applications are supercomputers, which are simply the fastest and biggest computers available at any given time. Supercomputers and supercomputing go hand-in-hand in pacing the development of scientific and engineering applications of computing. Experience has shown that supercomputers improve in speed and capability by roughly a factor 1000 every 20 years. Supercomputers today include the Cray XMP and Cray-2, manufactured by Cray Research, Inc., the Cyber 205, manufactured by Control Data Corporation, the Fujitsu VP, manufactured by Fujitsu, Ltd., the Hitachi SA-810/20, manufactured by Hitachi, Ltd., and the NEC SX, manufactured by NEC, Inc. The fastest of these computers are nearly three orders-of-magnitude faster than the fastest computers available in the mid-1960s, like the Control Data CDC 6600. While the world-wide market for supercomputers today is only about 50 units per year, it is expected to grow rapidly over the next several years to about 200 units per year.

Inhaltsverzeichnis

Frontmatter
Secondary Instabilities, Coherent Structures and Turbulence
Abstract
In this paper, we review recent progress on several problems of transition and turbulence. First, we explore the role of secondary instabilities in transition to turbulence in both wall bounded and free shear flows. It is shown how the competition between secondary instabilities and classical inviscid inflectional instabilities is important in determining the evolution of free shear flows. An outline of a general theory of inviscid instability is given. Then, we explore recent ideas on the force-free nature of coherent flow structures in turbulence. The role of viscosity in generating small-scale features of turbulence is discussed for both the Taylor-Green vortex and for two-dimensional turbulence. Finally, we survey recent ideas on the application of renormalization group methods to turbulence transport models. These methods yield fundamental relationships between various types of turbulent flow quantities and should be useful for the development of transport models in complex geometries with complicated physics, like chemical reactions and buoyant heat transfer.
Steven A. Orszag, Richard B. Pelz, Bruce J. Bayly
Bootstrapping in Turbulence Computation
Abstract
Classification schemes for methods for predicting turbulent flows were presented by Kline etal. (1978) and Ferziger etal. (1981); this scheme is given in Table 1. At each level in the scheme, a single method or model is more broadly applicable than a method at the preceding levels. This allows data for one flow to be used to predict other flows, an advantage of obvious importance. The primary disadvantage of the higher levels is that they cost more than the preceding levels; the data required to fix a model or correlation is also more difficult to acquire.
Joel H. Ferziger
Development of High-Reynolds-Number-Flow Computaion
Abstract
Finite-difference computaion of the Navier-Stokes equations has a long history. One of the earliest work was done by M. Kawaguti1) by using mechanical hand calculator in the early fifties. He computed a steady flow around a circular cylinder at Reynolds number 40 (Fig.1). He says in his paper “the nummerical integration in this study took about one year and a half with twenty working hours every week, with a considerable amount of labor and endurance”. With the appearance and development of electronic computers, this type of computation became easier and easier. However, the high-Reynolds-number-f1ow computation had remained difficult. The Reynolds numbers of the computed flows were less than 1000 in most cases.
Kunio Kuwahara
Spectral Element Simulation of Flow in Grooved Channels: Cooling Chips with Tollmien-Schlichting Waves
Abstract
The spectral element method is a high-order (p-type) finite element technique for the Navier-Stokes equations that combines the geometric flexibility of the finite element method with the rapid convergence and efficiency of spectral schemes. The method is applied here to steady and unsteady moderate Reynolds number flow and heat transfer in grooved channels. It is shown by direct numerical simulation that the least stable linear modes of the steady grooved- channel flow closely resemble Tollmien-Schlichting channel waves, forced by Kelvin-Helmholtz shear layer instability at the groove edge. For Reynolds numbers greater than a critical value, these modes become unstable and the flow takes the form of self-sustained oscillations. For Reynolds numbers less than this critical value, it is shown that oscillatory perturbation of the flow at the frequency of the least stable mode of the linearized system results in subcritical resonant excitation as the critical Reynolds number is approached. Application of this subcritical flow excitation to heat transfer enhancement and the cooling of chips (electronic components) is described.
A. T. Patera
A Vortex Ring Interacting with a Vortex Filament and its Deformation Near the Two-Dimensional Stagnation Point
Abstract
In this paper the interaction between vortex filaments and vortex rings and the deformation of vortex rings near the two-dimensional stagnation point are simulated by a three-dimensional vortex method (Shirayama etal. 1985, Leonard 1985). The two problems are respectively concerned with the effect of free-stream turbulence on turbulent plane mixing layers (Pui & Gartshore 1979) and the production of turbulence by the vortex stretching near saddles associated with large-scale coherent structures(Cantwell & Coles 1983, Kiya & Matsumura 1985). We assume that the first step to understand the free-stream turbulence effects is to study the interaction between a vortex ring and a vortex filament and that the process of deformation of a vortex ring gives us a clue to understand physical processes occurring near the saddles.
M. Kiya, T. Sato
A New Three-Dimensional Vortex Method
Abstract
A new vortex method based on the vorticitv equation is introduced to simulate incompressible vorticity-dominated flows. This method is based on Lagrangian way of tracking vortices a three-dimensional flow where the vortices are replaced by a number of disconnected vortex sticks. The interaction of vortex rings and three-dimensional flow past a parachute are simulated by this method. In the problems of flow past a parachute, a simplified vortex-lattice method is combined with this method and a potential theory is applied to introduce, an effect of porosity. The cross-linking of vortex rings and spiral structure of the wake behind the parachute were well simulated. Also the effect of the porosity and shape of the parachute can be estimated.
S. Shirayama, K. Kuwahara
Multi-Cell Vortices Observed in Fine-Mesh Solutions to the Incompressible Euler Equations
Abstract
Results are presented for a three dimensional flow, containing a vortex sheet shed from a delta wing. The numerical solution indicates that the shearing caused by the trailing edge of the wing sets up a torsional wave on the vortex core and produces a structure with multiple cells of vorticity. Although observed in coarse grid solutions too, this effect becomes better resolved with mesh refinement to 614 000 grid volumes. In comparison with a potential solution in which the vortex sheet is fitted as a discontinuity, the results are analyzed for the position of the vortex features captured in the Euler flow field, the accuracy of the pressure field, and for the diffusion of the vortex sheets.
Arthur Rizzi
Implicit Boundary Treatment for Joined and Disjoint Patched Mesh Systems
Abstract
The CSCM flux difference eigenvector split upwind scheme for the compressible Euler or Navier-Stokes equation is adapted to solve the problem of capturing embedded flow structures with high resolution on systems of aligned overset meshes.
Characteristics based upwind operationally explicit implicit difference relations with diagonally dominant approximate factorization are argued to be appropriate for compatibly and stably exchanging data in the vicinity of interior patch boundaries through simple interpolation of conservative variable data. Particular interpolation procedures are advocated that involve only positive weights and interpolant data with consistent upwind domain of dependence with respect to the receiving grid. A linearly equilvalent procedure involving interpolation of needed flux components is given and argued to be somewhat more accurate in the vicinity of discontinuities. With minimal overlap, sections on the coarse mesh that underly overset refinements are removed from the computation. The resulting segmented mesh data structure leads to interesting opportunities including nonaligned mesh-boundary intersections which we exploit for high resolution capture of shock reflections.
Factors in accuracy of the flow structure adaptive patching technique are demonstrated in an inviscid supersonic inlet problem involving weak shocks and an expansion fan. In the context of that two dimensional problem with shock aligned patched meshing, it is found that similar accuracy can be achieved with a savings of an order of magnitude in computed points relative to uniformly refined mesh.
C. K. Lombard, Ethiraj Venkatapathy
Computational Study of Three-Dimensional Wake Structure
Abstract
Three-dimensional wake structure is studied by numerically solving the incompressible Navier-Stokes equations. Results are visualized by a three-dimensional color graphic system. It was found that a pair of vortex tubes separated from a body plays the most important role in the wake. Near the body vortex tubes are rather stable, however, they gradually become unsteady as they flow down.
Ryutaro Himeno, Susumu Shirayama, Keisuke Kamo, Kunio Kuwahara
A Semi-Elliptic Analysis of Internal Viscous Flows
Abstract
The increased demands placed presently on the performance of compressors and turbines of gas-turbine engines have, for some time, pointed the need for accurate analysis of viscous flows in turbomachinery. With the recent developments of advanced computational facilities, much effort has been made to respond to ’this need. Various mathematical formulations, grid systems and numerical techniques have been developed for the numerical solution of the viscous flow equations (Refs. 1–4). The full Navier-Stokes equations as well as their corresponding thin-layer approximate form have been employed in H- as well as C-grids, using explicit or implicit methods, including convergence enhancement techniques based on multi-grid methodology. Nevertheless, obtaining converged solutions for general geometries on acceptably refined grids remains a computationally demanding task.
U. Ghia, R. Ramamurti, K. N. Ghia
Simulation of Self-Induced Unsteady Motion in the Near Wake of a Joukowski Airfoil
Abstract
Recent impetus for research in unsteady separated flows stems from a wide range of applications from low- to high- Reynolds number, Re. The physics of high-Re flows, in general, is quite complex and often involves multiple nonuniqueness and chaos, beyond simple unsteady separation. For the low-Re case, e.g. in the manuevering of fighter aircraft at high angle-of-attack in near- and post-stall regime, the vortex interaction dominates the flow field. The passage of vortices over the suction surface and their subsequent shedding leads to self-excited persistently unsteady flows. This flow field is extremely complicated due to the global effect of unsteady separated flow, coupled with the presence of hydrodynamic instabilities which may trigger transition and eventually lead to chaos. Besides supermaneuverability, interest also lies in this low-Re case because of the need for design of efficient airfoil sections for Re in the range of 105–106, for improving the performance of mini-RPV’s (remotely piloted vehicles) operating at low altitudes, jet engine compressor and turbine blades, helicopter rotor blades, etc.
K. N. Ghia, G. A. Osswald, U. Ghia
Viscous Compressible Flow Simulations Using Supercomputers
Abstract
The appearance of supercomputers accelerated the development of the sophisticated Computational Fluid Dynamics for the practical use. Even the “Reynolds-averaged” Navier-Stokes computations are in the matured stage with the help of supercomputers. For instance, two-dimensional Navier-Stokes code called ‘ARC2D’ developed by T.H.Pulliam and J.L.Steger at NASA Ames Research Center requires only 5 minutes to obtain the converged solution with 27000 grid points on CRAY XM-P[1]. The two-dimensional code called ‘LANS2D’ developed by Obayashi and the present author currently requires less than 1 minute with 6400 grid points and is becoming faster using Japanese supercomputer, Fujitsu VP-400[2]. Now, it seems that two-dimensional Navier-stokes codes such as these can be used as one of the design tools. Actually, Mitsubishi Heavy Industry is using the code ‘NSFOIL’ developed by the National Aerospace Laboratory,Japan for the design of a transonic airfoil, the detail of which was presented at the AIAA 3rd Applied Aerodynamics Conference with the experimental data[3].
Kozo Fujii
The Scalar Performance of Three Supercomputers Cray’s X-MP/2, Fujitsu’s VP-200 and NEC’s SX-2
Abstract
Since the first delivery, late in 1983, of the Cray X-MP/2, Fujitsu VP-200 and Hitachi S-810/20 supercomputers, the race in the scientific computing area has considerably accelerated its pace. In 1984, both the Fujitsu VP-400 and the Cray X-MP/4 were first introduced and in the Fall of 1985 the Cray2 and the NEC SX-2 supercomputers were first brought into the market. The total number of systems delivered up to now include more than 120 Cray systems, about 30 CDC systems, about 30 VP systems, 4 Hitachi systems. So far, 3 NEC SX systems have been shipped in Japan and one SX-2 system will be delivered to the Houston Area Research Center this year, it will be the first delivery of a Japanese system to an Academic Institution in the US. In this article we shall give an introduction to the SX-2 system, compare some of its features with those of the Fujitsu VP-200 and CRAY X- MP/2 supercomputers (although not discussing in detail the latter systems) and survey the scalar performance of these three systems on five fluid dynamics codes used as benchmarks. A vector performance study of these three systems will be postponed to a later article.
Raul H. Mendez
NEC Supercomputer SX System
Abstract
NEC Supercomputer SX System was developed to meet the demands for high-speed and large-scale computations in the fields such as aerodynamics, meteorology, molecular science and structural analysis.
Tadashi Watanabe
FX: A CMOS-Implemented Digital Spectro-Correlator System for Radio Astronomy
Abstract
A special purpose digital spectro-correlator system, FX, has been developed to perform the real time digital signal processing for the five-element synthesis telescope at the Nobeyama Radio Observatory of Tokyo Astronomical Observatory[Chikada etal.,1983]. This paper outlines the algorithms, architecture and implementation of the FX system. The test and maintenance of the system is also described. This paper is a revised version of an invited paper to the 4th Australian Microelectronics Conference, “Migrating Systems to Silicon”, held in Sidney, 13–15 May, 1985, sponsored by the Institution of Radio and Electronics Engineeres Australia.
Kenichi Miura, Toshiro Nakazuru, Yoshihiro Chikada
The Cray-2: The New Standard in Supercomputing
Abstract
An overview of the Cray-2 system, including its capability and performance, is provided. The Cray-2 consists of 4 background processors and a foreground processor for I/O. An extremely large multibank memory is a key feature, as is the cooling technology. The operating system is based on Unix System. V*. The Cray-2 may be considered as the new standard in supercomputing because of its unprecedentedly large main memory and its Unix operating system.
S. C. Perrenod
An Introduction to the ETA10
Abstract
The ETA10 supercomputer is ETA Systems, Incorporated’s initial product offering in the supercomputer marketplace. The ETA10 will have both general purpose features and high-speed calculation facilities. ETA Systems will add more features to the ETA10 as it is enhanced to meet growing customer needs.
C. J. Purcell
Metadaten
Titel
Supercomputers and Fluid Dynamics
herausgegeben von
Kunio Kuwahara
Raul Mendez
Steven A. Orszag
Copyright-Jahr
1986
Verlag
Springer Berlin Heidelberg
Electronic ISBN
978-3-642-82908-6
Print ISBN
978-3-540-17051-8
DOI
https://doi.org/10.1007/978-3-642-82908-6