Nandan

Hello, I am applying for Ph.D. programs in mechanical engineering in the U.S. Many people on this forum advise that you should contact a professor to inquire about Ph.D. openings before applying. I believe that I followed all the suggestions on other forums on writing a precisely targeted email to each PI. However, in response, I only got a brief response along the lines of "We don't have any openings right now, but we encourage you to apply for Fall 2020" from those that did reply. How do I read this response? Does it mean that its pointless to apply to that school, as there is no opening? Or does it mean that they are interested in my profile?

Hello everyone, I am applying to PhD prgrammes in mechanical engineering. Would anyone be open to reviewing my SOP and comment on some content that I can add/remove. Your help would be greatly appreciated- A rapid increase in energy demand and stricter environmental regulations have led to the necessity of highly efficient energy systems. Multiphase flows form the backbone of conventional energy systems like IC engines and thermal power plants, and their understanding is vital for better design decisions. The sharp interface in multiphase flows is computationally expensive to analyze, and so, the industry relies on interface-averaged models like the Two-Fluid Model (TFM) for analysis. However, such approaches are not predictive enough for the stringent design demands as they rely heavily on experimental fine-tuning. In the backdrop of these requirements, I intend to study multiphase flows related to energy applications at the micro-scale using interface-resolved methods. Furthermore, I wish to explore the development of reduced-order models for the macro-scale based on these results. My academic background has motivated my interest in this field and imparted me with the necessary skills. I enrolled at the Master of Science program at the University of Michigan to prepare for an advanced career in CFD. I took courses in fluid dynamics and heat transfer to build a solid technical foundation. The most notable experience that I carry forward through my coursework was the final project for my CFD course, where I developed a Navier-Stokes solver with Lagrangian Particle Tracking. This project provided me with experience in developing CFD solvers from scratch. I worked on a Multidisciplinary Design Project sponsored by Isuzu Motors to develop a simplified heat transfer model for their powertrain cooling system. I performed CFD simulations of the water jackets over a range of operating conditions to create a 1-D model using regression. I aim to leverage the experience gained in regression analysis and model development for research in my Ph.D. program. For my final project at UM, I explored improvements to the closure terms used by the TFM for bubbly flows. I utilized a wall-lubrication equation from the literature that utilized new experimental data. I also derived a modification to the wall-thermal treatment to account for the reduction of the wall-liquid contact area due to bubbles touching the wall. These modifications accurately predicted the results in the specific case of monodisperse bubbly flow in a thin tube. However, their efficacy did not extend to other conditions due to the limitation of the TFM to model the differential forces experienced by differently sized bubbles in polydisperse flow. It is this learning experience that has developed my stated interest in studying interface-resolved approaches to multiphase flow modeling for my Ph.D. After my MS, I joined Bloom Energy as a CFD engineer, where I work on performing CFD simulations of Bloom's Energy Servers. The projects have exposed me to various multiphysics problems involving radiation, laminar-turbulent transitions, and porosity. They have also given me experience with translating CFD results to new design recommendations. Thus, I have gained a practical skill-set through my job, which has complemented my coursework. I also have strived to learn new programming skills outside of my employment by taking various online certifications. These courses have improved my coding skills in C++ and Python, as well as given me some background with parallel programming. The V Mech. Engg program aligns with my goals due to its thrust on energy sciences. Prof. J's research on the DNS modeling of evaporating sprays particularly resonates with my interests. I am interested in his multiscale approach of using DNS for micro-scales to obtain data for LES modeling at the macro-scale. I would be thrilled to be a part of his group and study evaporating sprays. Ultimately, my final goal is to enter academia after my Ph.D. and apply CFD modeling techniques to solve engineering challenges. A Ph.D. from V University would provide me a platform to grow as a researcher and learn from some of the best minds in the field. I thank you for your courtesy in going through my application and look forward to being a part of the program in Fall 2020.

I am no expert in astrophysics. However, looking at your SOP, I liked how you have succintly expressed your skills and experience, as well as how you gained an interest in the field. I have just one feedback. I feel you should also include some information about - A] What you wish to achieve in your PhD program? It looks like you have just mentioned X-ray astronomy. Is there any specific problem that you wouold like to study? Futher, it would be good if you include just a few lines about what have been the recent advancements in the field, and how do your research interests match with those advancements. Also, do include some information about some labs/professers at that particular university whose work resonates with your interests. B] What are your plans after the PhD? How will a PhD degree help in achieving those plans