### Operator splitting and Adaptive Mesh Refinement: *Scientific Computing/CFD*

These schemes are currently being used to investigate the impact of thermal interactions between the heat-conducting burner plates (flame-holders) and premixed flames. Their role in static and dynamic stability is being investigated. These are direct simulations with all the time and length scales resolved. Adaptive Mesh Refinement procedures are being incorporated in the codes to be able to increase the size of the simulation domain.

Temperature contours are shown in the above video and the image for a flame stabilizing on a bluff body. Adaptive meshes can be seen along the flame front.

### Dynamic Response of Premixed Flames: *Combustion Dynamics*

Since the 90's, there have been increasingly stringent regulations on pollutants emitted out of gas turbines. These have led engine manufacturers to operate combustors with premixed fuel and air. This allows for temperature control of the combustion process and hence the concentration of emissions. One significant drawback of operation in the premixed mode though, is the dynamic behavior of these combustors.
Combustion dynamics includes the phenomenon of pressure oscillations in both, aircraft and land-based power generation engines. These lead to cracks and thermal hot-spots in different parts of the engine. Understanding and control of these oscillations are key to the reliable and robust operation of power-plants and propulsion systems.

Perforated-plate stabilized premixed flames are used extensively in industrial and compact household burners. In these systems, the coupling between the acoustics and the unsteady heat release rate often leads to self-excited oscillations, which in extreme cases may result in fatal structural damage. The dynamic response of the flame to the velocity perturbations in the system determines the nature of the combustion instability, and has thus received significant attention in the recent years. This response is typically characterized by the flame transfer function (FTF). From experimental investigtations by many researchers, it has been well established that at certain low frequencies, the heat release amplitude (non-dimensionalized by the mean) is greater than the non-dimensional amplitude of the imposed velocity oscillations. We are investigating the physical mechanisms behind such resonance like behavior of the system.

In our recent work, we have shown that the dynamic response of a premixed flame stabilized on a heat-conducting perforated plate depends critically on their coupled thermal interaction. We are investigating this problem using detailed numerical simulations with thermal coupling between the heat-conducting solid burner and the fluid domain. We are also developing simplified analytical models to predict the dynamic response of the flames.

### Non-normality in Thermo-acoustic Instabilities: *Combustion Dynamics*

A system is said to be non-normal if its eigenvectors are not orthogonal.

A linearly stable system is such that all its eigenvalues are negative or all the eigenvectors decay with time. However, if its eigenvectors are not orthogonal (i.e. if the system is non-normal), there may be a transient or short-term growth of the resultant vector before its eventual decay. This transient growth may trigger nonlinearities in the system and a linearly stable system may exhibit combustion instability.

An investigation of this was carried out in detail in my dual degree thesis at IIT Madras.

### Relevant Course work

__Teaching Assistant Experience__- Fundamentals and Applications of Combustion (MIT)
- Combustion Instabilities (IIT Madras)

List of courses undertakenList of courses undertaken

**Applied Math and Computational Engineering**

- Numerical Methods for Partial Differential Equations (MIT)
- Numerical Linear Algebra (MIT)
- Optimization Methods (MIT)
- Parallel Computing (MIT)
- Numerical Methods for Stochastic Modeling (MIT)
- Computational Fluid Dynamics (IIT Madras)

**Fluid and Thermal Sciences**

- Advanced Heat & Mass Transfer (MIT)
- Advanced Fluid Mechanics (MIT)
- Fluid Dynamics (MIT)
- Fundamentals and Applications of Combustion (MIT)
- Thermodynamics (MIT)
- Combustion Instabilities (IIT Madras)
- High Temperature Gas Dynamics (IIT Madras)
- Combustion and Flow Diagnostics (IIT Madras)

**Aerospace Engineering**

- Dynamics (MIT)
- Aerodynamics (IIT Madras)
- Gas Dynamics (IIT Madras)
- Helicopter Aerodynamics (IIT Madras)
- Aero-acoustics (IIT Madras)
- Air Breathing and Non Air Breathing Propulsion Systems (IIT Madras)
- Aerospace Design (IIT Madras)
- Aerospace Structures (IIT Madras)