Floquet and Force Analysis of Fluid Structures Generated by Oscillating Cylinders

This investigation focuses on the flow structures produced from a cylinder in transverse and rotational oscillatory motion using Floquet stability analysis developed by the investigators in combination with an efficient spectral element simulation code. The proposed techniques are computationally intensive and either involve large numbers of short runs to implement a parametric search (Floquet analysis) or utilize multiple CPU s (parallel Direct Numerical Simulation (DNS)). The facilities at the APAC National Facility are ideal for these types of simulations. A number of conference papers and a journal paper have arisen from this work and in addition the work performed at the National Facility is being utilised in the preparation of a further journal paper and a PhD thesis.

Principal Investigator John Sheridan Department of Mechanical Engineering Monash University	Project d92
Co-Investigators John Elston Department of Mechanical Engineering Monash University Hugh Blackburn Manufacturing & Infrastructure Technology CSIRO	RFCD Codes 291801

Significant Achievements, Anticipated Outcomes and Future Work

Investigations into the flow resulting from oscillating a circular cylinder in an initially quiescent flow have been conducted. A number of flows states have been identified and the transitions between these states have been studied using a combination of Direct-Numerical simulation (DNS) and Floquet analysis. The two-dimensional symmetry breaking transitions in the time-periodic flow generated by the rigid cylinder oscillating with simple harmonic rectilinear motion have received particular attention. The base flow possesses two symmetries: a spatio-temporal symmetry and a spatial reflection symmetry about the axis of oscillation. Two distinct branches have been identified by Floquet analysis to transition from this state. These correspond to (I) a pair of real Floquet multipliers simultaneously crossing the unit circle and (II) a pair of complex-conjugate crossing the unit circle (a Neimark-Sacker Bifurcation). In both transitions the spatial reflection symmetry of the base flow is broken but for branch (I) the spatio-temporal symmetry of the base flow is retained.

In previous studies the locations of three methods of transition (both two- and three-dimensional transitions) for a cylinder in pure translational oscillation in a quiescent fluid on a Keulegan--Carpenter, Stokes number control space have been mapped. The three transitions are: 1) a change from two-dimensional symmetric flow to three-dimensional symmetric flow; 2) a transition from this three-dimensional symmetric ordered state to a chaotic state; and 3) a connected two and three-dimensional change from the initial symmetric state to a three-dimensional ordered flow pattern. The mapping of these transitions utilized a large number of simulations to determine a solution's symmetry and instability characteristics.

In addition the APAC National Facility has been used to examine the thrust generated by a heaving and pitching bluff body. Three-dimensional DNS results have been obtained which show the influence of the ratio of peak heaving velocity to peak pitching velocity. Higher peak pitching velocities for a set heaving velocity tend to increase the thrust produced and produce a wake similar to a reversed von Kármán wake. Future work will focus on classifying the transitions as sub-critical, super-critical or other form of bifurcation. The investigation into the combined pitching and heaving of the circular cylinder will be extended to investigate the influence of other parameters and to determine the effect of these parameters on the spanwise flow structures produced..

Computational Techniques Used

We use a parallel DNS code to simulate time-dependent incompressible flows. Essentially this amounts to time-integration of Navier-Stokes problems; a time-splitting scheme is used to reduce the complexity of each integration sub-step combined with a spectral element/Fourier spatial discretisation. The spectral element method is a high-order finite element technique that combines the geometric flexibility of finite elements with the high accuracy of spectral methods. The method was pioneered in the mid 1980s by Anthony Patera and students at MIT.

Floquet analysis is achieved by developing two-dimensional time-periodic flows using the spectral element method described previously. This "base" flow is then perturbed with random noise and used in a specially modified version of the spectral element solver which permits us to monitor the growth rates for individual spanwise wavenumbers. The predictions for growth are then tested using the full version of the solver.

Publications, Awards and External Funding

External Funding and Awards

None.

Publications

J. R. Elston, J. Sheridan and H. M. Blackburn, Two-Dimensional Floquet Stability Analysis of the Flow Produced by an Oscillating Circular Cylinder in Quiescent Fluid. Bluff Body Vortex-Induced Vibrations (BBVIV3), Port Douglas, Queensland, Australia, 17-20 December 2002.(submitted)

J. R. Elston, J. Sheridan and H. M. Blackburn, Two-Dimensional Floquet Stability Analysis of the Flow Produced by an Oscillating Circular Cylinder in Quiescent Fluid. European Journal of Fluid Mechanics B.

J. Sheridam, J.R.Elston and H.M.Blackburn, Flow over an oscillating cylinder, International Union of Theoretical and Applied Mechanics Conference on Fluid-Structure Interaction (Keynote address) Rutgers University, USA, June, 2003.