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

Development of Lattice Boltzmann Method for Compressible Flows

Ph.DDOCTOR OF PHILOSOPH

Arbitrary Lagrangian-Eulerian form of flowfield dependent variation (ALE-FDV) method for moving boundary problems

Flowfield Dependent Variation (FDV) method is a mixed explicit-implicit numerical scheme that was originally developed to solve complex flow problems through the use of so-called implicitness parameters. These parameters determine the implicitness of FDV method by evaluating local gradients of physical flow parameters, hence vary across the computational domain. The method has been used successfully in solving wide range of flow problems. However it has only been applied to problems where the objects or obstacles are static relative to the flow. Since FDV method has been proved to be able to solve many complex flow problems, there is a need to extend FDV method into the application of moving boundary problems where an object experiences motion and deformation in the flow. With the main objective to develop a robust numerical scheme that is applicable for wide range of flow problems involving moving boundaries, in this study, FDV method was combined with a body interpolation technique called Arbitrary Lagrangian-Eulerian (ALE) method. The ALE method is a technique that combines Lagrangian and Eulerian descriptions of a continuum in one numerical scheme, which then enables a computational mesh to follow the moving structures in an arbitrary movement while the fluid is still seen in a Eulerian manner. The new scheme, which is named as ALE-FDV method, is formulated using finite volume method in order to give flexibility in dealing with complicated geometries and freedom of choice of either structured or unstructured mesh. The method is found to be conditionally stable because its stability is dependent on the FDV parameters. The formulation yields a sparse matrix that can be solved by using any iterative algorithm. Several benchmark stationary and moving body problems in one, two and three-dimensional inviscid and viscous flows have been selected to validate the method. Good agreement with available experimental and numerical results from the published literature has been obtained. This shows that the ALE-FDV has great potential for solving a wide range of complex flow problems involving moving bodies

Simulation of all-scale atmospheric dynamics on unstructured meshes

The advance of massively parallel computing in the nineteen nineties and beyond encouraged finer grid intervals in numerical weather-prediction models. This has improved resolution of weather systems and enhanced the accuracy of forecasts, while setting the trend for development of unified all-scale atmospheric models. This paper first outlines the historical background to a wide range of numerical methods advanced in the process. Next, the trend is illustrated with a technical review of a versatile nonoscillatory forward-in-time finite-volume (NFTFV) approach, proven effective in simulations of atmospheric flows from small-scale dynamics to global circulations and climate. The outlined approach exploits the synergy of two specific ingredients: the MPDATA methods for the simulation of fluid flows based on the sign-preserving properties of upstream differencing; and the flexible finite-volume median-dual unstructured-mesh discretisation of the spatial differential operators comprising PDEs of atmospheric dynamics. The paper consolidates the concepts leading to a family of generalised nonhydrostatic NFTFV flow solvers that include soundproof PDEs of incompressible Boussinesq, anelastic and pseudo-incompressible systems, common in large-eddy simulation of small- and meso-scale dynamics, as well as all-scale compressible Euler equations. Such a framework naturally extends predictive skills of large-eddy simulation to the global atmosphere, providing a bottom-up alternative to the reverse approach pursued in the weather-prediction models. Theoretical considerations are substantiated by calculations attesting to the versatility and efficacy of the NFTFV approach. Some prospective developments are also discussed

Direct numerical simulation of bubble-bubble and droplet-droplet interaction using a Surface Thin Film model

This dissertation deals with the simulation of dispersed multiphase flow. The particle-particle and particle-fluid interactions in this class of flows play an important role on the hydrodynamics and fluid transport phenomena that govern the overall flow behaviour. Accurate computational modelling of the particle-particle and particle- fluid interactions is thus required to correctly model the flow. The aim of this study is to use a Direct Numerical Simulation approach based on a smoothed Volume Of Fluid method to model particle-particle interactions in a dispersed multiphase flow at a fundamental level, and employing a surface thin film model, to drastically reduce the computational effort required. A multiscale modelling approach is followed with the smoothed Volume Of Fluid simulation on the particle scale and the surface thin film model simulation on the thin- film scale. The resulting governing equations are the Navier-Stokes equations for an incompressible viscous multiphase Newtonian fluid undergoing laminar and isothermal three-dimensional flow, the interface advection equation and the reduced order surface thin film equation. The model equations are discretized using the Finite Volume Method and implemented into the open source software OpenFOAM®. The numerical solution is obtained by solving the resulting non-linear system of equations implicitly on a structured computational grid on parallel processors using a pressure correction algorithm to converge the pressure at each time step. The study is restricted to gas-liquid systems where particles could either be bubbles or droplets; rigid particles are not considered. The model is tested against experimental results from binary collision of hydrocarbon droplets. Good qualitative numerical results are obtained at a practical computational cost

Evaluation of a near-wall-modeled large eddy lattice boltzmann method for the analysis of complex flows relevant to IC engines

In this paper, we compare the capabilities of two open source near-wall-modeled large eddy simulation (NWM-LES) approaches regarding prediction accuracy, computational costs and ease of use to predict complex turbulent flows relevant to internal combustion (IC) engines. The applied open source tools are the commonly used OpenFOAM, based on the finite volume method (FVM), and OpenLB, an implementation of the lattice Boltzmann method (LBM). The near-wall region is modeled by the Musker equation coupled to a van Driest damped Smagorinsky-Lilly sub-grid scale model to decrease the required mesh resolution. The results of both frameworks are compared to a stationary engine flow bench experiment by means of particle image velocimetry (PIV). The validation covers a detailed error analysis using time-averaged and root mean square (RMS) velocity fields. Grid studies are performed to examine the performance of the two solvers. In addition, the differences in the processes of grid generation are highlighted. The performance results show that the OpenLB approach is on average 32 times faster than the OpenFOAM implementation for the tested configurations. This indicates the potential of LBM for the simulation of IC engine-relevant complex turbulent flows using NWM-LES with computationally economic costs

Verification of Statistical Turbulence Models in Aerodynamic Flows

Computational fluid dynamics (CFD) is a tool that is commonly used in industry and academia. Engineers and scientists are sometimes apprehensive about the use of CFD due to inconsistencies and/or errors in results obtained with different software packages for the same flow cases. As a result, efforts are being made to ensure that there is uniformity among results of flow simulations produced by the computer programs. The current research makes a contribution to the verification of an open-source CFD toolbox known as OpenFOAM. In doing so, flow results for two benchmark flow cases obtained with OpenFOAM are compared with the results obtained with high-accuracy NASA CFD codes CFL3D and FUN3D. The benchmark cases are the zero pressure gradient boundary layer of flow over a flat plate and a two-dimensional bump in a channel. A number of flow profiles obtained with NASAs definitions of \u27standard\u27 versions of the Spalart-Allmaras, Shear Stress Transport, and k-\u03c9 turbulence models are compared with their CFL3D and FUN3D counterparts. A grid convergence study is performed to measure the change in the results as a function of element size, specifically for the finest meshes. The flows\u27 mean velocity, skin friction coefficient, and turbulent variable profiles obtained with OpenFOAM are in agreement with NASA\u27s profiles for both cases. The grid convergence studies show that the differences between OpenFOAM and NASA results are found to be of less than 5% for all variables on the finest meshes in both benchmark cases. OpenFOAM\u27s capability to produce accurate results for the benchmark cases is confirmed.\u2

Unsteady wake modelling for tidal current turbines

The authors present a numerical model for three-dimensional unsteady wake calculations for tidal turbines. Since wakes are characterised by the shedding of a vortex sheet from the rotor blades, the model is based on the vorticity transport equations. A vortex sheet may be considered a jump contact discontinuity in tangential velocity with, in inviscid hydrodynamic terms, certain kinematic and dynamic conditions across the sheet. The kinematic condition is that the sheet is a stream surface with zero normal fluid velocity; the dynamic condition is that the pressure is equal on either side of the sheet. The dynamic condition is explicitly satisfied at the trailing edge only, via an approximation of the Kutta condition. The shed vorticity is the span-wise derivative of bound circulation, and the trailed vorticity is the time derivative of bound circulation, and is convected downstream from the rotors using a finite-volume solution of vorticity transport equations thus satisfying the kinematic conditions. Owing to an absence in the literature of pressure data for marine turbines, results from the code are presented for the NREL-UAE Phase IV turbine. Axial flow cases show a close match in pressure coefficients at various spanwise stations; however, yawed flow cases demonstrate the shortcomings of a modelling strategy lacking viscosity