Hugh M Blackburn |
Publications |
Semtex DNS code |
Flow gallery |
Monash UAS |
A classic experiment by Ludwig Prandtl (circa 1930) provided convincing support for the circulation theory of lift generated by airfoils. Accelerating an airfoil from rest in an intially stationary fluid, circulation is generated in such a way that the net amount is zero; this leaves a starting vortex in the fluid and a net circulation of opposite sign bound to the airfoil. If the airfoil is then bought to rest, the bound circulation is shed from the airfoil in the form of a stopping vortex, leaving the overall circulation in the fluid zero, as it was in the beginning. This animation (Wang & Blackburn 2018) illustrates the process using a two-dimensional simulation of flow generated by a NACA-0012 airfoil at 4o angle of attack and a peak translational Reynolds number of 10,000. Vorticity in the starting vortex is coloured red, while that in the stopping vortex is coloured blue. Note the additional detail of a smaller pair of vortices generated during the stopping process near the leading edge on the airfoil's upper surface.
This animation of axial vorticity for azimuthal Fourier modes 1, 5 and 6 helps to illustrate a triadic resonance instability mechanism for flow in a precessing, rotating cylinder of fluid (Albrecht, Blackburn, Lopez, Manasseh & Meunier 2015). The animations are seen in the frame of reference of the cylinder, in which the forcing directly driven by precessional acceleration occurs in Fourier mode 1 and rotates with the precession frequency. Theory dictates that the other two modes which directly participate in the triad must differ by 1 in azimuth (6-5=1) and counter-rotate in the cylinder frame, exactly as seen here.
Animation of bypass transition in pulsatile stenotic pipe flow in which the pulse waveform represents typical flow in the human common carotid artery (Mao, Sherwin & Blackburn 2010). Linear transient energy growth is extremely large, of order 1×1025 within half a pulse period for suitable intial disturbances at Reynolds number Re=300. For even a tiny seeding with the optimal initial disturbance, a puff of turbulence is generated downstream of the stenosis. This washes slowly downstream and decays during subsequent pulse cycles. Mean flow is from left to right and the stenosis is to the left of the field of view.
Animation of transient two-dimensional convective instability in flow over a backward-facing step at Re=500 (Blackburn, Barkley & Sherwin 2008, Barkley, Blackburn & Sherwin 2008), visualised as contours of perturbation vorticity. The optimal disturbance initial condition is a wave packet that is very tightly clustered around the step edge, and grows into an array of counter-rotating rollers that fill the downstream channel, at a location past both (upper and lower) separation zones, before eventually decaying. The maximum two-dimensional energy growth at this Reynolds number is 63.1×103.
The flow generated by a circular cylinder moving from side to side in quiescent fluid has a number of different instability modes, depending on the amplitude and period of the motion. This image of massless particles advected by a quasi-periodic instability mode shows how small puffs form up into large-scale vortices that move away from the cylinder along the axis of oscillation (Elston, Blackburn & Sheridan, 2006).
Mode A, Re=195 | Mode B, Re=265 | Mode TW, Re=400 |
t=t0 | t=t0+T/2 |
Periodic axisymmetric state, Re=3000 | Rotating wave with 6-fold symmetry, Re=4000 |
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Instabilities of the flow produced by steady rotation of the lower lid of a cylindrical cavity with height/radius ratio H/R=2.5. At low Reynolds numbers the flow is axisymetric, steady, and has an axial vortex breakdown. The flow first becomes unstable to a periodic axisymmetric instability through a Hopf bifurcation at Re=2707, but at higher Reynolds numbers rotating waves also become unstable, and are modulated by the axisymmetric pulsation. Blackburn & Lopez (2000), Blackburn (2002), Blackburn & Lopez (2002).
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