Flow intensification in the solution of 3-dimensional euler equations

Deshpande, MD and Sharma, Gaurav (1999) Flow intensification in the solution of 3-dimensional euler equations. Technical Report. National Aerospace Laboratories, Bangalore, India.

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    Abstract

    Inviscid flow in a cubical cavity is computed by solving the Euler equations numerically starting from smooth initial conditions obtained for the case of viscous lid-driven cavity. The flow is seen to intensify at two symmetrical locations, symmetry decided by that of the initial conditions. These two spots of high local kinetic energy and vorticity move to two corners. Finally there is attrition of one of them and the accretion of the other, the choice between them being equally probable but for the hidden numerical bias. Thus an unstable two-ball situation leads to a stable single ball of high kinetic energy and vorticity. The global kinetic energy decreases slowly after integration due to numerical dissipation but a corrective algorithm is devised to conserve this quantity. The calculation of this intensification is limited by the choice of grid, the finer grid giving higher values. The flow elsewhere in the cube comes to rest by the action of normal stresses alone. This behaviour indicates a finite time singularity even though the numerical evidence is not conclusive. The calculations done with modifications for the 2-D case are able to calculate viscous results accurately, reproduce inviscid results for an exact solution and also indicate the possibility of multiplicity of solutions. The 3-D viscous results available in the literature where the flow is seen to divide itself into cells or compartments is probably a precursor to the intensification and formation of a singularity into a corner

    Item Type: Proj.Doc/Technical Report (Technical Report)
    Uncontrolled Keywords: Euler equations;Cavity flow;Finite time singularity; Vorticity;Flow intensification;Computation
    Subjects: AERONAUTICS > Aeronautics (General)
    Division/Department: Computational and Theoretical Fluid Dynamics Division, Other
    Depositing User: M/S ICAST NAL
    Date Deposited: 12 May 2009
    Last Modified: 17 Jun 2010 15:04
    URI: http://nal-ir.nal.res.in/id/eprint/5098

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