PUBLICATIONS

1. Hejranfar, K., and Rahmani, S. "An Assessment of Shock-Disturbances Interaction Considering Real Gas Effects. " Journal of Fluids Engineering 141.1 (2019): 011201.

2. Hejranfar, K., and Rahmani, S. "Numerical simulation of shock-disturbances interaction in high-speed compressible inviscid flow over a blunt nose using weighted essentially non-oscillatory scheme." Wave Motion 88 (2019): 167-195.

3. Rahmani, S., and Hejranfar, K., "Numerical study of shock-disturbances interaction in hypersonic inviscid flows with real gas effects using high-order WENO scheme.", Under review by Computers and Fluids.

4. Rahmani, S., and Hejranfar, K., "A compact-WENO scheme for shock-disturbances interaction in hypersonic viscous flows with real gas effects." Undergoing

RESEARCH INTERESTS

1. Computational Fluid Dynamics (CFD)

2. Mathematical/Analytical Solutions in Engineering

3. Research and Development in High-Order and High-Resolution Methods in CFD

4. High-Speed Flows

5. Reacting Flows and Real Gas Effects

6. Turbulent Flows

7. Wave/Disturbance Propagation in Fluid Mechanics

8. Shock-Turbulence Interaction

9. Acoustics

10. Aero-Acoustics

11. Thermo-Acoustics

12. Statistical Thermodynamics

13. Analytical and Numerical Methods in Perturbation Theory

14. Multiphase Flows

UNDERGRADUATE STUDIES

Based on my interests, I planned to study Aerospace Engineering after graduating from high-school. Fortunately, in the National University Entrance Exam, I ranked 290^th among 400,000+ candidates and was qualified to study Aerospace Engineering at Sharif University of Technology, considered to be the best Iranian university in engineering programs. When I entered university, I became familiar with lots of interesting scientific subjects which astonished me to expand my knowledge in them. Hence, during my B.Sc. years, I participated in many activities in addition to my university curriculum. I participated in the competition of designing glider at Sharif University of Technology and this teamwork experience is still a valuable practical experience for me. During my B.Sc. program, I became familiar with interesting subjects, like Acoustics, High-Speed Turbulent Flows, Reacting Flows, Real Gas Effects, Disturbance Propagation in Fluid Mechanics, and Mathematical/Analytical Solutions in Engineering and I did some research in these fields. Since I wanted to include most of these subjects in my B.Sc. thesis, I started cooperating with Prof. Hejranfar whose interests were similar to these fields. We defined my thesis entitled "An Assessment of Shock-Disturbances Interaction Considering Real Gas Effects". During my thesis, I realized that I should deepen my knowledge in Mathematics to do the thesis perfectly, and hence, I took a minor program in the Mathematical Science department. This program helped me not only to do my B.Sc. thesis, which was based on an analytical solution, but also to realize that Mathematics can be very useful in solving the problems in engineering. I did my B.Sc. thesis perfectly and these efforts eventually published in Journal of Fluids Engineering [1].

GRADUATE STUDIES

Then, I decided to deepen my knowledge in the fields related to my B.Sc. thesis. I realized that analytical solutions are not applicable enough to continue the fields and I should be knowledgeable in numerical simulations to investigate the fields thoroughly. Hence, I decided to continue my education in the M.Sc. program. Fortunately, in the Master's Degree Entrance Exam, I ranked 98^th among 50,000+ candidates and was qualified to study the M.Sc. program in Aerospace Engineering at Sharif University of Technology. In my M.Sc. program, I became familiar with more interesting subjects like Computational Fluid Dynamics, Perturbations Theory, Statistical Thermodynamics, and Multiphase Flows and I also had the chance to deepen my knowledge in High-Speed Aerodynamics, Turbulent Flows, Shock-Turbulence Interaction, Acoustics, and Aero-Acoustics. Research and development in Computational Fluid Dynamics made it possible for me to simulate complicated phenomena in High-Speed Aerodynamics, like Shock-Turbulence Interaction and Reacting Flows, using high-order/resolution computational methods. Hence, I continued cooperating with professor Hejranfar and did my M.Sc. thesis entitled "Numerical Simulation of Shock-Disturbances Interaction in 2-D Compressible Flows Considering Real Gas Effects by using WENO Method". These efforts led to a publication in Wave Motion Journal [2]. In addition, another article related to my M.Sc. thesis is under review by Computers and Fluids Journal [3]. I still work on this research field to add viscous effects to the simulation and publish another article in a new suitable journal [4]. Apart from my M.Sc. thesis, I had the chance to study Statistical Thermodynamics in a graduate course named Advanced Thermodynamics taught by Dr. Kebriaee and my efforts led to a solution manual for one of the sourcebooks in this course [5].

Utilizing CFD for my thesis made me familiar with different applications of this strong field and I realized that this field can be utilized for many problems in engineering. Hence, I did not limit myself to my thesis only and used Computational Fluid Dynamics to simulate other engineering problems, like Multiphase Flows.

Academic background related to Mathematics

I have had some interesting courses related to Mathematics during my undergraduate and graduate programs. During my undergraduate program, I had Differential Equations, Engineering Mathematics, and Numerical Computation with valuable sourcebooks some of which can be seen in Refs. [6-8]. Although these courses were interesting and applicable in my undergraduate program, I felt that more courses in Mathematics were needed to deepen my knowledge for utilizing in my B.Sc. thesis. Hence, I took a minor program in Mathematical Science department and this program gave me a chance to be familiar with lots of other interesting and applicable courses including Probability and Its Application, Linear Algebra I, Mathematical Analysis I, and Statistics and Its Application, with worthwhile sourcebooks some of which can be seen in Refs. [9-12]. Although some of these courses were difficult for one with an engineering viewpoint, they gave me a fundamental perception and I became able to use this perception in different types of engineering subjects like Statistical Thermodynamics, Linearization, Linear and Non-linear Partial Differential Equations (PDEs), Method of Characteristics and so on. During my M.Sc. program, Advanced Mathematics was the course that made me familiar with different mathematical topics with applications in engineering. This course was extremely useful in realizing the nature of Partial Differential Equations, which is very important in CFD applications [13, 14].

Academic background related to Computational Fluid Dynamics (CFD)

As mentioned, CFD has been my main focus in my academic program during the last 6 years. I have had some courses including CFD I, CFD II, and Grid Generation. In the first two courses, I got the knowledge about different categorizations of PDEs including parabolic, elliptic, and hyperbolic systems of equations and used this knowledge in solving Navier-Stokes and Euler equations numerically. In these numerical simulations, I used different approaches including finite difference, finite volume, and finite element. Another issue that I became familiar with in these courses was the implementation of different boundary condition methods. In the Grid Generation course, I became familiar with the generation of structured and unstructured grids around different geometries. These three courses had several projects some of which can be seen in Refs. [15-20]. Another course that was related to numerical simulation was Subsonic Aerodynamics taught by Prof. Soltani. This course had two numerical term projects [21, 22]. In these projects, I utilized software packages like MATLAB, Maple, and Mathematica to design different airfoils and compute the corresponding Aerodynamics Coefficients.

Academic background related to Acoustics and Aero-Acoustics

One of the main phenomena in my B.Sc. and M.Sc. theses is the disturbances field, including acoustic waves and also entropy wave, propagation in high-speed compressible flows. First, I became familiar with Acoustics course taught by Prof. Taeibi Rahni during my B.Sc. program and during the course, I wrote a solution manual for the sourcebook of the course [23]. Then, I deepened my knowledge in this field during my M.Sc. program in Perturbation Theory course and used this knowledge in my M.Sc. thesis to simulate the propagation of acoustic waves in fluid flows numerically. In addition, I simulated the interaction of the acoustic waves with the shock wave formed in high-speed flows considering real gas effects numerically in my thesis. Familiarity with the acoustic waves and the effects of their amplitude and frequency on the fluid in which they propagate, helped me to investigate the flow pattern in the presence of these waves in different air flows. In addition, using the high-order/resolution WENO scheme to capture the subsequent complicated phenomena helped the simulation to be accurate and reliable.

Academic background related to Thermodynamics and Heat Transfer

Thermodynamics is one of the most prominent scientific subjects utilized in my B.Sc. and M.Sc. theses. In particular, one of the novelties in my B.Sc. and M.Sc. theses is utilizing different equations of state. In high-speed air flows, the temperature and convective velocity behind the shock wave are extremely high, and hence, the perfect gas assumption is not valid anymore. In such environments, the oxygen dissociation, the nitrogen dissociation, and ionization occur. Hence, instead of using the perfect gas assumption, the equilibrium air equation of state is to be implemented. The equilibrium equation of state defines the relations between different thermodynamics variables in an environment with chemical reactions between the particles of the air flow (the oxygen dissociation, the nitrogen dissociation, and ionization). In addition, the governing equations of my M.Sc. thesis are Euler equations. Hence, the energy equation is solved in the numerical simulation to calculate the temperature in the behind-shock region and investigate the effects of the high values of temperature on the shock-disturbances interaction phenomenon. Hence, I am familiar with heat transfer in high-speed flows around blunt noses.

Academic background related to research and development in CFD

As a CFD man, I am familiar with CFD software packages and have used them in some projects during my academic programs. However, I believe that although utilizing the commercial CFD software packages in solving engineering problems is good, I prefer to write programs/codes myself. The reason is that writing programs/codes can make a chance for me to add different phenomena to the simulation and also change the resolution/order of the methods used. In other words, when I write the program/code myself, I can do research and development (R&D) in the simulation. There is no need to mention that the numerical simulations performed in my M.Sc. thesis and also my publications are based on the programs/codes written by me and no commercial software package has been used in them. The two significant novelties in my M.Sc. thesis, including incorporating the real gas effects and using high-order WENO scheme in the simulation, are completely based on my research and development in CFD. At the present, I work on an article related to combining the WENO scheme with the compact methods to decrease the CPU time required in the simulation of shock-disturbances interaction [4]. In addition, I also work on another research to investigate the WENO scheme analytically and numerically to enhance the performance of the scheme for different simulations.

Familiarity with different programming languages

Although my main programming languages are Fortran and C++ and I have performed my M.Sc. thesis and most of my academic projects with these languages, I am familiar with other programming languages like MATLAB, MAPLE, and Mathematica, and used them in some of my projects during my education. In particular, I am an expert in MAPLE and have been a teacher assistant of this software for several semesters for different courses taught by Doctor Kebriaee. I am also familiar with CFD software packages like ANSYS Fluent, ANSYS CFX, and OpenFoam. In particular, OpenFoam is an open-source software package that can be modified by the programmer. This feature is very important for me to do my research and development in CFD codes.

Academic background related to Turbulent Flows

Although I have vast experience in simulation of different types of fluid flows, the main focus of my M.Sc. thesis and also publications is the propagation of turbulence in high-speed air flows and the interaction of turbulence with the shock formed in the environment. This interaction produces some complicated phenomena, and hence, high-order methods in CFD should be implemented to capture and indicate all these phenomena. I utilized a high-order Weighted Essentially Non-Oscillatory (WENO) scheme, which is suitable for capturing discontinuous regions in the flow field without needing numerical artifacts, for capturing the interaction. In addition, since the WENO scheme does not need numerical artifacts, It does not change the frequency of the waves related to turbulence propagated in the environment, which is not the case in the conventional schemes. This feature makes the WENO scheme suitable for environments with turbulence. Based on my knowledge in Perturbations Theory, which was one of my graduate courses taught by Doctor Kebriaee, I also performed a mathematical analysis to validate the results of the numerical simulation in my M.Sc. thesis.

Numerical simulations of complicated phenomena

It is obvious that the shock-disturbances interaction is a complicated engineering problem. In the environment of the flow field in this problem, there are some discontinuous regions and these discontinuities can make the numerical simulation extremely stiff. Furthermore, incorporating the real gas effects causes even more complexity in the simulation. To make the story worse, in my M.Sc. thesis I utilized Euler equations. These equations do not have any dissipation terms. Hence, the simulation of these equations in such a stiff environment needs lots of carefulness in implementing the method and also the boundary conditions. Although it was extremely challenging for me, I utilized lots of different time and space discretizations in conjunction with different boundary condition treatments to make a simulation with the desired order/resolution.

Academic background related to Multiphase Flows

During my M.Sc. program, I became familiar with Multiphase Flows in the Advanced Thermodynamics course. In this course, I gathered some knowledge about concepts like phase transition, equilibrium state of a liquid-vapor system, and coalescence and break up of bubbles. Based on my knowledge in CFD, I performed a numerical simulation about the cavitation of a water-flow in a circular tube as the term project of Advanced Thermodynamics course [24]. Since I am familiar with the equilibrium state from my B.Sc. and M.Sc. theses, I have no challenge to realize the equilibrium state of the liquid-vapor system, which is one of the most challenging issues in Multiphase Flows.

REFERENCES

[1] Hejranfar, K., & Rahmani, S. (2019). "An Assessment of Shock-Disturbances Interaction Considering Real Gas Effects", Journal of Fluids Engineering, 141(1), 011201.

[2] Hejranfar, K., & Rahmani, S. (2019). "Numerical simulation of shock-disturbances interaction in high-speed compressible inviscid flow over a blunt nose using weighted essentially non-oscillatory scheme", Wave Motion, 88, 167-195.

[3] Rahmani, S., and Hejranfar, K. " Numerical study of shock-disturbances interaction in hypersonic inviscid flows with real gas effects using high-order weighted essentially non-oscillatory scheme ", Under review by Computers and Fluids.

[4] Rahmani, S., and Hejranfar, K., "A compact-WENO scheme to simulate shock-disturbances interaction in hypersonic viscous flows with real gas effects." Undergoing (to be submitted as soon as possible).

[5] Richard E. Sonntag, Gordon J. Van Wylen. Fundamentals of Statistical Thermodynamics.

[6] Boyce, W. E., & DiPrima, R. C. (2005). Elementary differential equations. Boyce. New York: John Wiley & Sons.

[7] Kreyszig, Erwin, Herbert Kreyszig, and E. J. Norminton. 2014. Advanced engineering mathematics. Hoboken: John Wiley Inc.

[8] Burden, Richard L., and J. Douglas Faires. 1997. Numerical analysis. Pacific Grove: Brooks/Cole Publishing Company.

[9] Ross, Sheldon. 2010. First Course in Probability. Pearson Education Canada.

[10] Hoffman, K., & Kunze, R. A. (1962). Linear Algebra, Englewood Cliffs, N.J., Prentice-Hall.

[11] Rudin, Walter. 1976. Principles of mathematical analysis. New York; Montréal: McGraw-Hill.

[12] Larsen, R. R., & Marx, M. L. (1981). An introduction to mathematical statistics and its applications. London: Prentice-Hall.

[13] Myint-U, Tyn, and Lokenath Debnath. 2009. Linear partial differential equations for scientists and engineers. Boston: Birkhäuser.

[14] Debnath, Lokenath. 2012. Nonlinear Partial Differential Equations for Scientists and Engineers.

[15] Numerical Simulation of the Incompressible Laminar Viscous Flow Past a Backward-Facing Step using the Stream Function Vorticity Formulation, the fourth project of CFD I, Instructor: Prof. Kazem Hejranfar, Fall, 2014.

[16] Numerical Simulation of the Quasi-One-Dimensional Compressible Flow Inside the "Shubin Nozzle", the first project of CFD II, Instructor: Prof. Kazem Hejranfar, Spring, 2015.

[17] Numerical Simulation of the Steady Compressible Euler Equations in the Two-Dimensional Channel with a Bump for Subsonic, Transonic, and Supersonic Inflows using Finite Volume Method (FVM), the third project of CFD II, Instructor: Prof. Kazem Hejranfar, Spring, 2015.

[18] Numerical Simulation of the Incompressible Laminar Viscous Flow Past a Backward-Facing Step using the Artificial Compressibility Method, the fourth project of CFD II, Instructor: Prof. Kazem Hejranfar, Spring, 2015.

[19] Generation of Unstructured Meshes using the Advancing-Front Method and the Structured Background Grids for Different Two-Dimensional Geometries, the first project of Grid Generation, Instructor: Prof. Kazem Hejranfar, Fall, 2015.

[20] Generation of Computational Grids using the Partial Differential Equations for the NACA0012 Airfoil Inside a Circle (O-Type), the second project of Grid Generation, Instructor: Prof. Kazem Hejranfar, Fall, 2015.

[21] Programming a MATLAB Code for Designing an Airfoil and Computing its Aerodynamics Coefficients using Karman-Trefftez, Van de Vooren, and Joukowski Methods, Instructor: Prof. Mohammad Reza Soltani, Spring, 2016.

[22] Using the Eppler Airfoil Code to Design an Airfoil and Computing its Aerodynamics Coefficients, Instructor: Prof. Mohammad Reza Soltani, Spring, 2016.

[23] Lawrence E. Kinsler and Austin R. Frey, Fundamentals of Acoustics, 4th Edition, published by Wiley.

[24] Numerical simulation of cavitation of a water flow in a circular tube using a central difference finite volume scheme for multiphase Euler equations, Term project of Advanced Thermodynamics, Instructor: Dr. Kebriaee, Spring, 2015.