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Here're abstracts of my research...

Spectral and Hypersphere Decomposition of Stressed Correlation Matrix to Enforce Positive Semi-Definiteness - Pyxis 2008
Risk Management and option pricing often requires calculation of correlation matrix from the history of economic data. Monte Carlo simulation would require this correlation to reflect in the random numbers, requiring Cholesky decomposition of the correlation matrix. This however fails if the correlation matrix is not positive semi-definite (all eigenvalues positive). Common reasons include noise in the historical data and external stressing applied by the risk manager. The following Matlab codes utilise two candidate (1) spectral decomposition (2) hypersphere decomposition, first suggested by Jackel & Rebonato in this context, to systematically modify the correlation matrix for it to become positive semi-definite. The first technique is faster while the second more refined. The second technique involves solution of an optimization problem. Results from both the techniques show that the extent of modification to the original matrix is usually minimal and within acceptable limits. For detailed theory, refer the original paper.
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Flow Investigations in "S-Shaped" Compressor Transition Ducts - Cambridge 2005
Transition ducts joining the low speed compressor with the high speed compressor take a complicated S-shape. With the two compressors at the ends, the flow inside is very complex - it is transient, 3-dimensional, turbulent flow with strong curvature. The flow is further corrupted with a presence of thick struts airfoil running radially through the duct. The aim of the duct design is to have a shortest possible duct with minimum total pressure loss without any flow separation. CFD investigations have been done to study the major pressure velocity exchanges inside these ducts. An inviscid aerodynamic loading parameter is defined in terms of non-dimensional geometrical parameters. It is found that the inner wall of the annulus geometry is critical and close to separation. Further, the extent of interaction of the duct with upstream and downstream compressor is seen. The interaction of the duct pressure field with strut airfoil surface pressure distribution is seen. It is found that the diffusive portion of the strut surface makes the bulk flow unstable and close to separation, the minimum pressure region shifts downstream of the maximum thickness location on the airfoil. A new concept involving the integrated design of upstream compressor OGV, transition duct and downstream compressor IGV as a part of the duct system is proposed.
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Finite Element Modeling of Piezoelectric coupling in 1D Timoshenko Beam Element - NAL 1999
Distributed piezoelectric layers embedded into an elastic continuum can serve to develop sensors and actuators for smart structure applications. In the present study, general procedures of finite element method are extended to piezoelectric material, where the potential, phi is taken as field variable. A two-node Timoshenko beam element is developed using first order shear deformation theory to predict the mechanical and electric response of the coupled system. A constitutive relation for 1-D case is derived using static condensation of the general, 3-D stress-strain relation. Element load vector formulation is done for the mechanical and electrical loads. A numerical study based on above model is done and results are compared with existing theory and other approximate models.
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Solution of One Dimensional Flow in Non-Constant Area Duct with Heat Addition, Friction and Mass Injection - ISRO 2000
In the present work, numerical scheme has been devised and implemented for the solution of problems of complex one-dimensional flows involving simultaneous action of driving potentials, namely area variation, heat addition, friction and mass injection. Two separate solvers have been made; one based on the direct numerical solution of set of differential equations and the other on the method of influence coefficients. A comparison of results from the two solvers with standard results is done using different level of discretization of potentials. In general, both solvers give very good match throughout the flow regime. A deviation from the ideal results near the sonic point has been found. For that, a general derivation based on L'Hospital's rule is done for dealing with singularity at the sonic point. Finally, further improvements that can be done in the program are suggested.
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Shape Memory Alloys - An Introduction - IITB 1999
Shape memory alloys are functional materials which offer attractive potentials such as reversible strains of several percentages, generation of high recovery stresses, high power-to-weight ratio, high damping and high fatigue life. This seminar gives an introduction to the origin, mechanism and characteristics of the unique phenomena of shape memory effect and superelastic effects. Different properties and characterization techniques are also discussed. Various applications in the fields of engineering and bio-medicine are briefly discussed.
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Aero-thermal flow path analysis and design of a hypersonic propulsion unit - IITB 2002
Application of air breathing hypersonic power plants for propulsion poses a challenge to the world scientific community, even though the gas dynamics and aerodynamics of hypersonic flow have been investigated for several years now. In the present work, preliminary level work has been done to cover the ground for the design of a dual-mode ramjet scramjet power plant for hypersonic vehicles. Various issues in the design of such power plants have been presented. Brayton cycle suited to the mission requirements have been constructed and analyzed. An analytical approach to aid the initial design of the dual-mode ramjet-scramjet power plant for a hypersonic vehicle has been laid down. "Method of influence coefficients" have been suggested and numerically implemented for developing one-dimensional analysis capability. A detailed user manual for this software is separately made available. "Method of characteristics" has been suggested for detailed flow mapping in the nozzle. Simplistic estimate of the boundary layer and the fore body shock reflections in the inlet is made. The empirical laws available from earlier literature have been implemented to obtain the required length of the isolator, without going to the details of the shockwave-boundary layer interaction. A preliminary geometry of the propulsion unit has been proposed, which makes use of the detail combustor design studies done separately by others. The parametric performance study for the engine has been done using an available in-house developed code.
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Effect of inlet distortions, co-swirl and counter-swirl on single axial fan and contra-rotating axial fans - ISABE 2001
Inlet distortions are flow non-uniformities that result in a decrease in performance and lessening of the operating flow range of a compressor. This paper presents an inlet flow distortion study on a single axial fan and a contra-Rotating Twin rotor axial fan. Experiments were carried out for the following configurations: (a) Clean inlet condition, (b) 90 degree Circumferential Extent Steady Total Pressure Distortion and (c) A combination of 90 degree Total Pressure Distortion and localized 90 degree swirl (both co-swirl and counter swirl). Total pressure measurements were done at the inlet and exit of the axial fan/contra-stage, both in the distorted and clean regions. The experimental results were analyzed to obtain distortion parameters like Distortion Index and Axial/Contra-Fan performance parameters like the Pressure Rise coefficient, Mean flow coefficient etc. It is observed that the Distortion Index is highest for the case of combination of 90 degree Total Pressure Distortion and 90 degree localized Counter-Swirl. The severity of the combined distortion is more for a contra-rotating stage as compared to the single axial fan. A significant outcome of the study is the fact that in spite of a higher distortion, counter-swirl produces a lower degradation in performance compared to the co-swirl, which has lower distortion intensity. Also, the performance penalty in the case of the contra-rotating unit is less as compared to the single axial fan.
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An approach to preliminary component-wise design of dual-mode air breathing engine for hypersonic vehicles - ISABE 2003
A preliminary level work has been done to cover the ground for design of a dual-mode ramjet scramjet power plant for hypersonic vehicles. Various issues in the design of such power plants have been presented. Brayton cycle suited to the mission requirements have been constructed and analyzed. An analytical approach to aid the initial design of the dual-mode ramjet-scramjet power plant for a hypersonic vehicle has been laid down. A preliminary geometry of a typical propulsion unit has been proposed, which includes a combustor design study in some detail.
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Low speed studies of sweep and dihedral effects on compressor cascades - ASME TurboExpo 2002
The use of three dimensional blade designs incorporating end bend, sweep and dihedral to reduce secondary flow related losses, improve efficiency and stable operating range has gained ground in the recent years. In the present study a straight cascade, a swept cascade, and a dihedral cascade have been considered. Effects of sweep and dihedral along the span are studied at 0 degree and +20 degree stagger. The study shows that both the sweep and the dihedral have lower end-wall losses compared to the straight cascade. However, lower losses are accompanied with lower diffusion factors. At mid-span also the lowering of losses is achieved along with some lowering of diffusion factor. While the dihedral seems to contribute for stable operation more near the end-wall, the swept blade contributes more near the mid-span. The swept blade is able to sustain the flow at higher angles of attack. While the end-wall loss benefits are welcome with lower loading, at mid-span lower loading obtained may need to be corrected by increasing the design angle of incidence.
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From conception to realization: A case study of aircraft design laboratory course - IITB 2001
Conceptual design contributes strongly towards development of engineering judgment, and hence is considered to be an essential part of engineering education worldwide. This paper brings out the importance of student design projects in teaching aircraft conceptual design to university undergraduate students. The course contents of an existing aircraft design laboratory course were revamped from theoretical/computational work to a more practical, hands-on experience for the students. The students were divided into teams and were asked to design remotely controlled model aircrafts to meet specific performance requirements, which were evaluated against a figure of merit. The paper describes the various designs of the aircraft that were considered, and brings out the lessons learnt and experience gained, both from students' and instructor's point of view.
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Brass Tacks / Reflections / Vineyard / Potpourri / Scribbles / Winks / Movielist / GMAT-GRE wordlist / Art / भारत एक खोज (Bharat Ek Khoj; TV; Shyam Benegal) / Pleasures (Aldous Huxley) / The Fog Horn (Ray Bradbury) / A World Split Apart (Alexandr Solzhenitsyn at Harvard) / Integral of Secant Cubed / Calvin and Hobbes (Bill Waterson) / Stay Hungry, Stay Foolish (Steve Jobs at Stanford) / Jack Vettriano / Wormhole / नासदीय सूक्त (ॠग वेद) Naasadiiya Sookta (Rig Ved) / Francisco's Money Speech (Atlas Shrugged by Ayn Rand)