Research Projects

During my undergraduate course work, I worked on multiple analytical and computational projects which involved studying relevant research publications and using computational tools like MATLAB and FORTRAN for numerical modelling. More details on each project can be found in the following section.

Brief Description

• Numerically solved 2-D incompressible Euler equation in MATLAB using explicit finite volume discretization.
• Used artificial compressibility method with isentropic flow assumption for solving the incompressible Euler equation.

Brief Description

• Numerically solved 2-D compressible Euler equation in MATLAB using explicit finite volume discretization.
• Employed Van-Leer flux splitting scheme at the cell interfaces with both first order and higher order MUSCL interpolation method.

Brief Description

• Employed Lump Vortex numerical method to a wing flapping vertically up and down with different speeds to estimate the load distribution on the airfoil and wake structure behind it.
• Compared the numerical solutions with the analytical solutions obtained by Wagner’s function.

Brief Description

• Numerically solved transverse deflection of a cantilever beam under a continuous triangular load distribution with two different end conditions (Pin joint – Pin joint or Fixed support – Free end).
• Coded in MATLAB considering C¹ cubic elements using Galerikin approach and compared the numerical results with results derived analytically using Euler-Bernoulli beam theory.

Brief Description

• Obtained acoustic wave propagation in 1-D constant area ducts with various axial temperature profiles using 4^th order Runge-Kutta numerical method in MATLAB.
• Linearized momentum, energy conservation and state equation in 1-D constant area duct assuming the properties like pressure, temperature, density, and velocity to be a combination of an average quantity and a fluctuating quantity.
• Developed wave equation from the linearized equations and solved it numerically assuming the pressure and velocity fluctuations to be a time dependent periodic function.
• Computed resonance frequencies for different axial temperature distributions with the applied boundary condition at the ends of the duct (closed/open).

Brief Description

• Derived governing equation for 1-dimensional acoustic field using momentum and energy conservation equations neglecting the effect of flow and temperature gradient.
• Adopted a modified form of King’s law suggested by Prof. Maria Heckl of Keele University known as Heckl’s correlation to model the heat release term.
• Non-dimensionalized the governing equations and converted the partial differential equations to ordinary differential equations using Galerikin technique by expressing velocity and pressure fluctuations as a superposition of basis functions.
• Incorporated a damping model and solved the pressure and velocity amplitudes using 4^th order Runge-Kutta numerical technique in MATLAB.
• Observed subcritical bifurcation with regions of global stability, global instability and bi-stability regions of pressure and velocity fluctuations by changing the non-dimensional parameters like heater power, heater location, damping coefficient, and time delay.