Over the last two decades, we have witnessed spectacular improvements in the field of scientific computing. At the High Performance Computing Laboratory of Aerospace Engineering department, we played an active role in developing newer classes of high-accuracy high-performance computing methodologies that in turn helped in our goal of understanding insect/bird's motion to space flights better. Our methods have brought down the resolution requirements by an order of magnitude in each spatial direction. For the Direct Numerical Simulation (DNS) of Navier- Stokes equation, the holy-grail of fluid mechanics, this allows solving many problems on desk-top, instead of looking for super-computers. In the following, some canonical problems are discussed from aerospace engineering and fundamental fluid mechanics where these methods have been used.
Flapping and Hovering Flights of MAVs and Insects:
Although human quest for flight began by imitating bird-flight, it was given up due to a lack of understanding of unsteady flows and engineering difficulties of creating fail-safe articulated motion of wings. Simulation of such unsteady flows are currently feasible as we are able to resolve high frequencies and small scales by using our high accuracy compact schemes developed for DNS. In the following figures, calculated results are compared with experimental PIV results (courtesy, Prof. T.T. Lim of NUS Singapore ) for an airfoil (the quintessential element of a wing) exposed to accelerated low-speed flow.
Hypersonic Flow Transition:
This is an area where lab experiments are not possible, while flight experiments are prohibitively expensive (wherever possible- it costs about tens of millions of USD for each flight). In the following we show computed results for flow, at a Mach number of 4.0, over a rocket-like body as affected by stationary acoustic or vortical pulses. Indicated temperature variations, in the following figures, show heating by sound and cooling by vortices- an effect not known before. These calculations are performed in a cluster using twenty processors at a time, using the high accuracy methods developed here.
DNS of Jet Flows:
Like other results presented before, this is undertaken to check our theoretical results related to flow instabilities and transition. In the following figures, we show the evolution of a computed low-speed Bickley jet to verify the eigenvalue spectrum obtained theoretically.
Unstable Wave-Front Propagation:
This work was initiated as we do not understand how sharp fronts are created in shear layers by localized pulse(s) and their speed of propagation. This seems to be the case one notices when Tsunami is created by localized volcanic/ seismic excitation at sea-bed. In the following figures, we show the evolution of disturbance front with its associated wave-front created by a localized delta function in a shear layer, as calculated by spectral method requiring about twenty million points for a two-dimensional problem! One can clearly see in the figure below that although the main wave system (the trailing part) is damped, there is a growing wave-packet. This is a novel technique developed by us that departs from the conventional methods in the field.
This is a problem of fundamental fluid mechanics and has useful applications in understanding the advection of vortices associated with tropical storms and cyclones. It is often noted in weather reports, that the trajectories of the cyclonic vortices are wrongly predicted with totally erroneous time-lines! We are currently studying a problem where the effect of background shear in destabilizing a monopole vortex is looked at. In the figure below, we show the instability of a monopole vortex, where it transforms into a tripolar structure.
Also, the advection speed of such vortices during instability is found to be different from the local speed. These results are in conformity with our proposed theory of flow instability that was advanced a few years ago.
The above are just a few glimpses of a few topics of our current interest. For more details see our web-site: http://home.iitk.ac.in/~tksen and/ or contact:
Prof. Tapan Sengupta
High Performance Computing Laboratory
Department of Aerospace Engineering
Indian Institute of Technology Kanpur