ISSN: 2041-6792

Clinical Investigation

Vortex Breakdown

 The scope of the present study is to demonstrate the use of spectral/hp element methods in understanding global instability mechanisms of vortical flows. In particular, BiGlobal stability analysis is used to form a two-dimensional eigenvalue problem, on a plane in which a non-axisymmetric vorticity distribution can be defined; with the axial direction taken to be homogeneous, resolved through a Fourier expansion. One motivation for applying linear instability theory is that, compared with direct numerical simulations, parametric studies can be performed over wider ranges and with greater efficiency. The numerical method applied consists of solving the eigenvalues of a matrix system corresponding to the linearised incompressible Navier-Stokes equations. Specifically, the Arnoldi algorithm is used to calculate the leading eigenvalues of the system, which is reduced to a Krylov subspace spanning the number of eigenvalues sought. Validation of the method was achieved by comparing the results for an isolated Batchelor trailing vortex (BTV) with the classical one-dimensional stability analysis of Mayer and Powell [1], which assumes both a streamwise and an azimuthal wavenumber. For a given streamwise wavenumber, BiGlobal stability analysis successfully captures the most unstable azimuthal wavenumber, whilst simultaneously capturing the remaining eigenspace. Figure 1 illustrates a typical inviscid and viscous core mode for an isolated BTV, with a swirl value of 0.475, and a Reynolds number based on the core radius of 100.  

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