1) Some fundamental fluid dynamics phenomena are studied in my thesis
based on the asymptotic analysis of the Navier-Stokes equations at
large values of Reynolds number. In the first part
of the thesis, a numerical method comprising of finite difference
representation measured along the body surface and Chebychev collocation along the
normal direction is discussed; this method has been used earlier
in the paper by Korolev et al. We extend this technique to study,
a) Jet like boundary-layer encountering corners, humps and indents.
b) Liquid layers encountering convex corner, humps and indents.
c) Supersonic flow past humps, indents.
The second problem deals with understanding the phenomena of
shock/wave boundary-layer interaction over moving walls. The problem
has been investigated numerically. The
separation is provoked by shock wave impinging on the
boundary-layer. The interaction process may be
described by the equations of the triple-deck theory. We have
obtained the numerical results for the wall moving
either in the downstream or in upstream direction. According to the
numerical results, we have found that the Moore, Rott & Sears
criterion for separation for the viscous-inviscid interaction
problem is satisfied for the downstream moving wall but is not applicable
for the upstream moving wall in supersonic flow. We have also found
that the pressure calculated analytically,
agrees with the numerical calculation.
The third problem is concerned with control of
shock/wave boundary-layer interaction by means of grooves. The
dimensions of the cross-section of the grooves are considered to be small
as compared to the characteristic thickness of the lower tier of the
three-tiered interaction structure. A groove region is introduced
where the Stokes approximation is applicable, and
the method of matched
asymptotic expansion is used to match the solution from the viscous
lower tier of the interaction structure to the groove region. Analysis has also been done with the
Blasius boundary-layer in presence of periodic grooves. It is suggested that the presence of the grooves has the similar effect as
that of moving walls i.e, delay in the separation.

2) Prediction of Unsteady Flow Fields and Trajectories of Tumbling Plates Using Reduced Order Modelling : Prediction of unsteady flow fields and trajectories at different instants of time and for varying values of the ratio of the density of a tumbling plate to that of the ambient fluid is carried out using Proper Orthogonal Decomposition with interpolation (PODI) which is an extension of Proper Orthogonal Decomposition (POD) on snapshots of flowfields simulated by computational fluid dynamics (CFD) softwares. Similar predictions have also been obtained using the method of Singular Value Decomposition (SVD). Pressure distributions, aerodynamic loads and trajectories of the centre of mass of tumbling plates obtained from reduced order modeling are then validated with the CFD simulations. It is shown that the results obtained by means of Singular Value Decomposition (SVD) are accurate compared to the results obtained from Proper Orthogonal Decomposition Interpolation (PODI). For more details reference is made to R.Yapalparvi, Dominic, D. J. Chandar and M. Damodaran," Prediction of Unsteady Flow Fields and Trajectories of Tumbling Plates Using Reduced Order Modelling", AIAA-2009-329, 47th AIAA Aerospace Sciences meeting and Exhibit, Orlando, FL, Jan 5-8 2009

3)Reduced Order Modelling Using Marching Proper Orthogonal Decomposition Extrapolation (MPODE): This work is concerned with the coupling of Proper Orthogonal Decomposition (POD) approach with interpolation and marching extrapolation procedures to predict the temporal evolution of unsteady flow fields by ensembling the data obtained from computational fluid dynamics (CFD) simulations. The problem of a free falling rectangular plate has been chosen to demonstrate the efficiency and accuracy of the proposed method. The ratio of the density of a tumbling plate to that of the ambient fluid (density ratio) and time are used as the two parameters for which the POD snapshots are ensembled by varying these parameters in a specified interval. POD with interpolation provides accurate prediction of solutions when the parameter lies within the snapshot span. In order to predict the flow field outside the snapshot span, marching POD extrapolation is used. Pressure distributions of tumbling plates obtained from these methods are then validated against CFD simulations and errors assessed. Reference: R. Yapalparvi and M. Damodaran," Reduced Order Modelling Using Marching Proper Orthogonal Decomposition Extrapolation (MPODE)" Under review for publication in Physics of Fluids

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