Implicit High-Order Flux Reconstruction Solver for High-Speed Compressible Flows

The present paper addresses the development and implementation of the first high-order Flux Reconstruction (FR) solver for high-speed flows within the open-source COOLFluiD (Computational Object-Oriented Libraries for Fluid Dynamics) platform. The resulting solver is fully implicit and able to simulate compressible flow problems governed by either the Euler or the Navier-Stokes equations in two and three dimensions. Furthermore, it can run in parallel on multiple CPU-cores and is designed to handle unstructured grids consisting of both straight and curved edged quadrilateral or hexahedral elements. While most of the implementation relies on state-of-the-art FR algorithms, an improved and more case-independent shock capturing scheme has been developed in order to tackle the first viscous hypersonic simulations using the FR method. Extensive verification of the FR solver has been performed through the use of reproducible benchmark test cases with flow speeds ranging from subsonic to hypersonic, up to Mach 17.6. The obtained results have been favorably compared to those available in literature. Furthermore, so-called super-accuracy is retrieved for certain cases when solving the Euler equations. The strengths of the FR solver in terms of computational accuracy per degree of freedom are also illustrated. Finally, the influence of the characterizing parameters of the FR method as well as the the influence of the novel shock capturing scheme on the accuracy of the developed solver is discussed

Arbitrary-Lagrangian-Eulerian One-Step WENO Finite Volume Schemes on Unstructured Triangular Meshes

In this article we present a new class of high order accurate Arbitrary-Eulerian-Lagrangian (ALE) one-step WENO finite volume schemes for solving nonlinear hyperbolic systems of conservation laws on moving two dimensional unstructured triangular meshes. A WENO reconstruction algorithm is used to achieve high order accuracy in space and a high order one-step time discretization is achieved by using the local space-time Galerkin predictor. For that purpose, a new element--local weak formulation of the governing PDE is adopted on moving space--time elements. The space-time basis and test functions are obtained considering Lagrange interpolation polynomials passing through a predefined set of nodes. Moreover, a polynomial mapping defined by the same local space-time basis functions as the weak solution of the PDE is used to map the moving physical space-time element onto a space-time reference element. To maintain algorithmic simplicity, the final ALE one-step finite volume scheme uses moving triangular meshes with straight edges. This is possible in the ALE framework, which allows a local mesh velocity that is different from the local fluid velocity. We present numerical convergence rates for the schemes presented in this paper up to sixth order of accuracy in space and time and show some classical numerical test problems for the two-dimensional Euler equations of compressible gas dynamics.Comment: Accepted by "Communications in Computational Physics

On the numerical simulation of compressible flows

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.Postprint (published version

Computational resolution of the Navier-Stokes equations for laminar and turbulents flows. Implementation of the Sparlart-Allmaras turbulence model

The present project consists on the computational study and resolution of the Navier-Stokes equations and the physical phenomena involved. The main objective is the development of C++ programming codes to solve flow’s governing equations using numerical methods. The project comprises the fluid dynamic and thermal study and analysis of both laminar and turbulent regimes. In addition to that, in case of turbulent flow, there has been selected to implement a RANS turbulence model called Spalart-Allmaras. The computational codes developed will be used to simulate the study cases LID Driven Cavity, LID Differentially Heated and Square Cylinder for the laminar regime and a supersonic pipe in case of the turbulent part. Additionally, the results obtained will be extensively analysed and verified using scientific publications

A STUDY OF THE EFFECTS AND SIGNIFICANCE OF TRANSITION MODELING FOR ROTORCRAFT APPLICATIONS

A four-blade helicopter rotor is modeled using computational fluid dynamics (CFD), and the impact on the flow-field with and without a floating fuselage geometry is assessed. The numerical predictions were made with CFD simulations using the NASA OVERFLOW 2.2n solver. For numerical simulations, the flow-field was discretized in a structured, overset topology with grids intended to solve the scope of the problem. Results based on a tip Mach number of 0.58 were acquired for various collective pitch angles. The simulations were completed with the Spalart-Allmaras (SA) one equation eddy-viscosity turbulence model along with the Spalart-Shur rotation/curvature correction coupled with the amplification factor transport (AFT) transition model. Additionally, Delayed, Detached Eddy Simulation (DDES) was used to induce hybrid RANS/LES behavior. Overall predicted figure of merit and laminar-to-turbulent transition patterns on the blade surfaces with and without the fuselage exhibited reasonable agreement with experimental data. Specifically, laminar-turbulent transition patterns on the blade surfaces at 10° collective pitch showed better agreement with experimental data than at 8° collective pitch. It was observed from the simulations that the blade root and tip vortex systems become increasingly unstable as the collective pitch is increased for both configurations

Cut Cell Methods in Global Atmospheric Dynamics

In this thesis, we study next generation techniques for the numerical simulation of global atmospheric dynamics, which range from modeling and grid generation to discretization schemes. Based on a detailed dimensional analysis of the compressible three-dimensional Navier-Stokes equations for small- and large-scale motions in the atmosphere, we derive the compressible Euler equations, the dynamical core of meteorological models. We also provide an insight into multiscale modeling and present a new numerical way of deriving reduced atmospheric models and gaining consistency of the modeling and discretization errors. The main focus of this thesis is the grid generation of the atmosphere. With regard to newly available surveys of the Earth's surface and the ever increasing computing capacities, the atmospheric triangulation techniques have to be reconsidered. In particular, the widely-used terrain-following coordinates prove to be disadvantaguous for highly resolved grids, since both the pressure gradient force error and the hydrostatic inconsistency of this vertical ansatz seriously increase with finer resolution. After a detailed analysis of the standard methods for vertical atmospheric triangulations, we present the cut cell approach as capable alternative. We construct a special cut cell method with two stabilizing constraints and provide a comprehensive guideline for an implementation of cut cells into existing atmospheric codes. For the spatial discretization of the dynamical core, we choose the Finite Volume method because of its favorable characteristics concerning conservation properties and handling of hyperbolicity. We accompany the Finite Volume discretization by a new non-linear interpolation scheme of the velocity field, which is adapted to the geometry and rotation of the Earth. To fathom the capabilities of cut cell grids together with our discretization and new interpolation scheme, we finally present several three-dimensional simulation runs. We apply standard benchmarks like an advection test and the simulation of a Rossby-Haurwitz wave and construct a new test case of counterbalancing flow between high- and low-pressure areas, with which we expose the potential of cut cell methods and the influences of different effects of the Euler equations as well as the topography of the Earth