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  • 1
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 19 (1994), S. 905-938 
    ISSN: 0271-2091
    Keywords: Dynamic vorticity condition ; Theoretical analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The dynamic boundary conditions for vorticity, derived from the incompressible Navier-Stokes equations, are examined from both theoretical and computational points of view. It is found that these conditions can be either local (Neumann type) or global (Dirichlet type), both containing coupling with the boundary pressure, which is the main difficulty in applying vorticity-based methods. An integral formulation is presented to analyse the structure of vorticity and pressure solutions, especially the strength of the coupling. We find that for high-Reynolds-number flows the coupling is weak and, if necessary, can be effectively bypassed by simple iteration. In fact, even a fully decoupled approximation is well applicable for most Reynolds numbers of practical interest. The fractional step method turns out to be especially appropriate for implementing the decoupled approximation. Both integral and finite difference methods are tested for some simple cases with known exact solutions. In the integral approach smoothed heat kernels are used to increase the accuracy of numerical quadrature. For the more complicated problem of impulsively started flow over a circular cylinder at Re = 9500 the finite difference method is used. The results are compared against numerical solutions and fine experiments with good agreement. These numerical experiments confirm our thoeretical analysis and show the advantages of the dynamic condition in computing high-Reynolds-number flows.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
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  • 2
    Publication Date: 1993-09-01
    Description: This paper presents a general theory and physical interpretation of the interaction between a solid body and a Newtonian fluid flow in terms of the vorticity ω and the compression/expansion variable Π instead of primitive variables, i.e. velocity and pressure. Previous results are included as special simplified cases of the theory. The first part of this paper shows that the action of a solid wall on a fluid can be exclusively attributed to the creation of a vorticity-compressing ω-Π field directly from the wall, a process represented by respective boundary fluxes. The general formulae for these fluxes, applicable to any Newtonian flow over an arbitrarily curved surface, are derived from the force balance on the wall. This part of the study reconfirms and extends Lighthil's (1963) assertion on vorticity-creation physics, clarifies some currently controversial issues, and provides a sound basis for the formulation of initial boundary conditions for the ω-Π variables. The second part of this paper shows that the reaction of a Newtonian flow to a solid body can also be exclusively attributed to that of the ω-Π field created. In particular, the integrated force and moment formulae can be expressed solely in terms of the boundary vorticity flux. This implies an inherent unity of the action and reaction between a solid body and a ω-Π field. In both action and reaction phases the ω-Π coupling on the wall plays an essential role. Thus, once a solid wall is introduced into a flow, any theory that treats ω and Π separately will be physically incomplete. © 1993, Cambridge University Press. All rights reserved.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 3
    Publication Date: 1998-09-25
    Description: By using a Reynolds-averaged two-dimensional computation of a turbulent flow over an airfoil at post-stall angles of attack, we show that the massively separated and disordered unsteady flow can be effectively controlled by periodic blowing-suction near the leading edge with low-level power input. This unsteady forcing can modulate the evolution of the separated shear layer to promote the formation of concentrated lifting vortices, which in turn interact with trailing-edge vortices in a favourable manner and thereby alter the global deep-stall flow field. In a certain range of post-stall angles of attack and forcing frequencies, the unforced random separated flow can become periodic or quasi-periodic, associated with a significant lift enhancement. This opens a promising possibility for flight beyond the static stall to a much higher angle of attack. The same local control also leads, in some situations, to a reduction of drag. On a part of the airfoil the pressure fluctuation is suppressed as well, which would be beneficial for high-α buffet control. The computations are in qualitative agreement with several recent post-stall flow control experiments. The physical mechanisms responsible for post-stall flow control, as observed from the numerical data, are explored in terms of nonlinear mode competition and resonance, as well as vortex dynamics. The leading-edge shear layer and vortex shedding from the trailing edge are two basic constituents of unsteady post-stall flow and its control. Since the former has a rich spectrum of response to various disturbances, in a quite wide range the natural frequency of both constituents can shift and lock-in to the forcing frequency or its harmonics. Thus, most of the separated flow becomes resonant, associated with much more organized flow patterns. During this nonlinear process the coalescence of small vortices from the disturbed leading-edge shear layer is enhanced, causing a stronger entrainment and hence a stronger lifting vortex. Meanwhile, the unfavourable trailing-edge vortex is pushed downstream. The wake pattern also has a corresponding change: the shed vortices of alternate signs tend to be aligned, forming a train of close vortex couples with stronger downwash, rather than a Kármán street.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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