On the numerical simulation of compressible flows
Authors:   , Pedro Costa Juan Bautista 
Published: October 2023

In this thesis, numerical tools to simulate compressible flows in a wide range of situations are presented. It is intended to represent a step forward in the scientific research of the numerical simulation of compressible flows, with special emphasis on turbulent flows with shock wave-boundary-layer and vortex interactions. From an academic point of view, this thesis represents years of study and research by the author.
It is intended to reflect the knowledge and skills acquired throughout the years
that at the end demonstrate the author’s capability of conducting a scientific research, from the beginning to the end, present valuable genuine results, and potentially explore the possibility of real world applications with tangible social and economic benefits. Some of the applications that can take advantage of this thesis are: marine and offshore engineering, combustion in engines or weather forecast, aerodynamics (automotive and aerospace industry), biomedical applications and many others.
Nevertheless, the present work is framed in the field of compressible aerodynamics and gas combustion with a clear target: aerial transportation and engine technology.
The presented tools allow for studies on sonic boom, drag, noise and emissions
reduction by means of geometrical design and flow control techniques on subsonic, transonic and supersonic aerodynamic elements such as wings, airframes or engines.
Results of such studies can derive in new and ecologically more respectful, quieter vehicles with less fuel consumption and structural weight reduction.
We start discussing the motivation for this thesis in chapter one, which is placed
into the upcoming second generation of supersonic aircraft that surely will be flying the skies in no more than 20 years. Then, compressible flows are defined and the equations of motion and their mathematical properties are presented. Navier Stokes equations arise from conservation laws, and the hyperbolic properties of the Euler equations will be used to develop numerical schemes.
Chapter two is focused on the numerical simulation with Finite Volumes techniques of the compressible Navier-Stokes equations. Numerical schemes commonly found in the literature are presented, and a unique hybrid-scheme is developed that is able to accurately predict turbulent flows in all the compressible regimens (subsonic, transonic and supersonic). The scheme is applied on the flow around a NACA0012 airfoil at several Mach numbers, showing its ability to be used as a design tool in order to reduce drag or sonic boom, for example. At subsonic regimens, results show excellent agreement with reference data, which allowed the study of the same case at transonic conditions. We were able to observe the buffet phenomenon on the airfoil, which consists of shock-waves forming and disappearing, causing a dramatic loss of aerodynamic performance in a highly unsteady process.
To perform a numerical simulation, however, boundary conditions are also required in addition to numerical schemes. A new set of boundary conditions is introduced in chapter three. They are developed for three-dimensional turbulent flows with or without shocks. They are tested in order to assess its suitability. Results show good performance for three-dimensional turbulent flows with additional advantages with respect traditional boundary conditions formulations.
Unfortunately, compressible flows usually require high amounts of computational power to its simulation. High speeds and low viscosity result in very thin boundary layers and small turbulent structures. The grid required in order to capture this flow structures accurately often results in unfeasible simulations. This fact motivates the use of turbulent models and wall models in order to overcome this restriction. Turbulent models are discussed in chapter four. The Reynolds-Averaged Navier Stokes (RANS) approach is compared with Large-Eddy Simulation (LES) with and without wall modeling (WMLES). A transonic diffuser is simulated in order to evaluate its performance. Results showed the ability of RANS methods to capture shock-wave positions accurately, but failing in the detached part of the flow. LES, on the other hand, was not able to reproduce shock-waves positions accurately due to the lack of precision on the shock wave-boundary-layer interaction (SBLI). The use of a wall model, nevertheless, allowed to overcome this issue, resulting in an accurate method to capture shock-waves and also flow separation. More research on WMLES is encouraged for future studies on SBLIs, since they allow three-dimensional unsteady studies with feasible levels of computational requirements.
With all these tools, we are able to solve at this point any problem concerned with the aerodynamic design of high-speed vehicles which were identified in previous paragraphs.
Finally, multi-component flows are discussed in chapter five. Our hybrid scheme
is upgraded to deal with multi-component gases and tested in several cases. We demonstrate that with a redefinition of the discontinuity sensor multi-components flows can be solved with low levels of diffusion while being stable in the presence of high scalar gradients.
Because of the work of this thesis, a complete numerical approach to the numerical simulation of compressible turbulent multi-component flows with or without discontinuities in a wide range of Reynolds and Mach numbers is proposed and validated. Direct applications can be found in civil aviation (subsonic and supersonic) and engine operation.

En aquesta tesis es presenten tècniques numèriques per a la simulació de compressibles en una gran varietat de situacions. L’objectiu és el de donar un pas endavant en la investigació científica de la simulació numèrica de fluids compressibles, amb especial èmfasi en fluxos turbulents amb interaccions entre ones de xoc, capa límit y vòrtex. Algunes de les aplicacions que es poden beneficiar d’aquesta investigació són: enginyeria marítima, combustió en motors, predicció meteorològica, aerodinàmica en la industria automotriu y aeronàutica, aplicacions biomèdiques y moltes altres. Tot i així, aquest treball s’emmarca en el camp de l’aerodinàmica compressible y la combustió de gasos amb un clar objectiu: el transport aeri i la tecnologia de motors. Les ferramentes presentades permeten l’estudi del sònic boom, resistència aerodinàmica, soroll y reducció d’emissions mitjançant el disseny geomètric i tècniques de control de flux en elements aerodinàmics tals com ales o motors en règims subsònics, transsònics i supersònics. Els resultats de tals estudis poden donar lloc a nous vehicles més ecològics, respectuosos amb el medi ambient, més silenciosos, amb menor peso estructural i menys consum de combustible.