147 research outputs found
Development and validation of a pressure based CFD methodology for acoustic wave propagation and damping
Combustion instabilities (thermo-acoustic pressure oscillations) have been recognised for some time as a problem limiting the development of low emissions (e.g., lean burn) gas turbine combustion systems, particularly for aviation propulsion applications. Recently, significant research efforts have been focused on acoustic damping for suppression of combustion instability. Most of this work has either been experimental or based on linear acoustic theory. The last 3-5 years has seen application of density based CFD methods to this problem, but no attempts to use pressure-based CFD methods which are much more commonly used in combustion predictions. The goal of the present work is therefore to develop a pressure-based CFD algorithm in order to predict accurately acoustic propagation and acoustic damping processes, as relevant to gas turbine combustors.
The developed computational algorithm described in this thesis is based on the classical pressure-correction approach, which was modified to allow fluid density variation as a function of pressure in order to simulate acoustic phenomena, which are fundamentally compressible in nature. The fact that the overall flow Mach number of relevance was likely to be low ( mildly compressible flow) also influenced the chosen methodology. For accurate capture of acoustic wave propagation at minimum grid resolution and avoiding excessive numerical smearing/dispersion, a fifth order accurate Weighted Essentially Non-Oscillatory scheme (WENO) was introduced. Characteristic-based boundary conditions were incorporated to enable accurate representation of acoustic excitation (e.g. via a loudspeaker or siren) as well as enable precise evaluation of acoustic reflection and transmission coefficients. The new methodology was first validated against simple (1D and 2D) but well proven test cases for wave propagation and demonstrated low numerical diffusion/dispersion. The proper incorporation of Characteristic-based boundary conditions was validated by comparison against classical linear acoustic analysis of acoustic and entropy waves in quasi-1D variable area duct flows.
The developed method was then applied to the prediction of experimental measurements of the acoustic absorption coefficient for a single round orifice flow. Excellent agreement with experimental data was obtained in both linear and non-linear regimes. Analysis of predicted flow fields both with and without bias flow showed that non-linear acoustic behavior occurred when flow reversal begins inside the orifice. Finally, the method was applied to study acoustic excitation of combustor external aerodynamics using a pre-diffuser/dump diffuser geometry previously studied experimentally at Loughborough University and showed the significance of boundary conditions and shear layer instability to produce a sustained pressure fluctuation in the external aerodynamic
HIGH ORDER SHOCK CAPTURING SCHEMES FOR HYPERBOLIC CONSERVATION LAWS AND THE APPLICATION IN OPEN CHANNEL FLOWS
Many applications in engineering practice can be described by thehyperbolic partial differential equations (PDEs). Numerical modeling of this typeof equations often involves large gradients or shocks, which makes it achallenging task for conventional numerical methods to accurately simulate suchsystems. Thus developing accurate and efficient shock capturing numericalschemes becomes important for the study of hyperbolic equations.In this dissertation, a detailed study of the numerical methods for linearand nonlinear unsteady hyperbolic equations was carried out. A new finitedifference shock capturing scheme of finite volume style was developed. Thisscheme is based on the high order Pad?? type compact central finite differencemethod with the weighted essentially non-oscillatory (WENO) reconstruction toeliminate non-physical oscillations near the discontinuities while maintain stablesolution in the smooth areas. The unconditionally stable semi-implicit Crank-Nicolson (CN) scheme is used for time integration.The theoretical development was conducted based on one-dimensionalhomogeneous scalar equation and system equations. Discussions were alsoextended to include source terms and to deal with problems of higher dimension.For the treatment of source terms, Strang splitting was used. For multidimensionalequations, the ?? -form Douglas-Gunn alternating direction implicit(ADI) method was employed. To compare the performance of the scheme withENO type interpolation, the current numerical framework was also applied usingENO reconstruction.The numerical schemes were tested on 1-D and 2-D benchmark problems,as well as published experimental results. The simulated results show thecapability of the proposed scheme to resolve discontinuities while maintainingaccuracy in smooth regions. Comparisons with the experimental results validatethe method for dam break problems. It is concluded that the proposed scheme isa useful tool for solving hyperbolic equations in general, and from engineeringapplication perspective it provides a new way of modeling open channel flows
Very high-order methods for 3D arbitrary unstructured grids
Understanding the motion of fluids is crucial for the development and analysis of new designs and processes in science and engineering. Unstructured meshes are used in this context since they allow the analysis of the behaviour of complicated geometries and configurations that characterise the designs of engineering structures today. The existing numerical methods developed for unstructured meshes suffer from poor computational efficiency, and their applicability is not universal for any type of unstructured meshes. High-resolution high-order accurate numerical methods are required for obtaining a reasonable guarantee of physically meaningful results and to be able to accurately resolve complicated flow phenomena that occur in a number of processes, such as resolving turbulent flows, for direct numerical simulation of Navier-Stokes equations, acoustics etc. The aim of this research project is to establish and implement universal, high-resolution, very high-order, non-oscillatory finite-volume methods for 3D unstructured meshes. A new class of linear and WENO schemes of very high-order of accuracy (5 th ) has been developed. The key element of this approach is a high-order reconstruction process that can be applied to any type of meshes. The linear schemes which are suited for problems with smooth solutions, employ a single reconstruction polynomial obtained from a close spatial proximity. In the WENO schemes the reconstruction polynomials, arising from different topological regions, are non-linearly combined to provide high-order of accuracy and shock capturing features. The performance of the developed schemes in terms of accuracy, non-oscillatory behaviour and flexibility to handle any type of 3D unstructured meshes has been assessed in a series of test problems. The linear and WENO schemes presented achieve very high-order of accuracy (5 th ). This is the first class of WENO schemes in the finite volume context that possess highorder of accuracy and robust non-oscillatory behaviour for any type of unstructured meshes. The schemes have been employed in a newly developed 3D unstructured solver (UCNS3D). UCNS3D utilises unstructured grids consisted of tetrahedrals, pyramids, prisms and hexahedral elements and has been parallelised using the MPI framework. The high parallel efficiency achieved enables the large scale computations required for the analysis of new designs and processes in science and engineering.EThOS - Electronic Theses Online ServiceGBUnited Kingdo
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 cientÃfica de la simulació numèrica de fluids compressibles, amb especial èmfasi en fluxos turbulents amb interaccions entre ones de xoc, capa lÃmit y vòrtex. Algunes de les aplicacions que es poden beneficiar d’aquesta investigació són: enginyeria marÃtima, combustió en motors, predicció meteorològica, aerodinà mica en la industria automotriu y aeronà utica, aplicacions biomèdiques y moltes altres. Tot i aixÃ, aquest treball s’emmarca en el camp de l’aerodinà mica 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 aerodinà mica, soroll y reducció d’emissions mitjançant el disseny geomètric i tècniques de control de flux en elements aerodinà mics 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
Hypersonic Boundary Layer Receptivity to Acoustic Disturbances Over Cones
The receptivity mechanisms of hypersonic boundary layers to free stream acoustic disturbances are studied using both linear stability theory (LST) and direct numerical simulations (DNS). A computational code is developed for numerical simulation of steady and unsteady hypersonic flow over cones by combining a fifth-order weighted essentially non-oscillatory (WENO) scheme with third-order total-variation-diminishing (TVD) Runge-Kutta method. Hypersonic boundary layer receptivity to free-stream acoustic disturbances in slow and fast modes over 5-degree, half-angle blunt cones and wedges are numerically investigated. The free-stream Mach number is 6.0, and the unit Reynolds number is 7.8×106/ft. Both the steady and unsteady solutions are obtained by solving the full Navier-Stokes equations in two-dimensional and axisymmetric coordinates.
Computations are performed in three steps. After the steady mean flow field is computed, linear stability analysis is performed to find the most amplified frequency and the unstable disturbance modes in different flow regions. Then time accurate computations are performed using slow and fast mode acoustic disturbances, and the initial generation, interaction and evolution of instability waves inside the boundary layers are studied.
Receptivity computations showed that the acoustic disturbance waves propagated uniformly to downstream, interact with the bow shock, enter the boundary layer, and then generate the initial amplitude of the instability waves in the leading edge region. Effects of the entropy layer due to nose bluntness to the receptivity process are studied. It is found that transition location moves downstream and is delayed by increasing bluntness, and the role of the entropy layer in this process is revealed. Also, the effects of wall cooling to the receptivity process using slow and fast mode acoustic disturbances are studied. The effects of cooling on the first and second mode regions are investigated. It is found that the first mode is stabilized and the second mode is destabilized by wall cooling when the flow is forced by acoustic waves in the slow mode
Compact-Reconstruction Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws
A new class of non-linear compact interpolation schemes is introduced in this dissertation that have a high spectral resolution and are non-oscillatory across discontinuities. The Compact-Reconstruction Weighted Essentially Non-Oscillatory (CRWENO) schemes use a solution-dependent combination of lower-order compact schemes to yield a high-order accurate, non-oscillatory scheme. Fifth-order accurate CRWENO schemes are constructed and their numerical properties are analyzed. These schemes have lower absolute errors and higher spectral resolution than the WENO scheme of the same order.
The schemes are applied to scalar conservation laws and the Euler equations of fluid dynamics. The order of convergence and the higher accuracy of the CRWENO schemes are verified for smooth solutions. Significant improvements are observed in the resolution of discontinuities and extrema as well as the preservation of flow features over large convection distances. The computational cost of the CRWENO schemes is assessed and the reduced error in the solution outweighs the additional expense of the implicit scheme, thus resulting in higher numerical efficiency. This conclusion extends to the reconstruction of conserved and primitive variables for the Euler equations, but not to the characteristic-based reconstruction. Further improvements are observed in the accuracy and resolution of the schemes with alternative formulations for the non-linear weights.
The CRWENO schemes are integrated into a structured, finite-volume Navier-Stokes solver and applied to problems of practical relevance. Steady and unsteady flows around airfoils are solved to validate the scheme for curvi-linear grids, as well as overset grids with relative motion. The steady flow around a three-dimensional wing and the unsteady flow around a full-scale rotor are solved. It is observed that though lower-order schemes suffice for the accurate prediction of aerodynamic forces, the CRWENO scheme yields improved resolution of near-blade and wake flow features, including boundary and shear layers, and shed vortices. The high spectral resolution, coupled with the non-oscillatory behavior, indicate their suitability for the direct numerical simulation of compressible turbulent flows. Canonical flow problems -- the decay of isotropic turbulence and the shock-turbulence interaction -- are solved. The CRWENO schemes show an improved resolution of the higher wavenumbers and the small-length-scale flow features that are characteristic of turbulent flows.
Overall, the CRWENO schemes show significant improvements in resolving and preserving flow features over a large range of length scales due to the higher spectral resolution and lower dissipation and dispersion errors, compared to the WENO schemes. Thus, these schemes are a viable alternative for the numerical simulation of compressible, turbulent flows
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