A non-linear quasi-3D model for air management modelling in engines

El modelado se ha convertido en los últimos años en una herramienta esencial en el diseño de motores de combustión interna alternativos, ya que permite reducir considerablemente el tiempo y los costes de desarrollo. Las metodologías de diseño clásicas se basan en la fabricación de prototipos y la realización de pruebas de ensayo y error. Actualmente, la mayoría de estas pruebas han sido sustituidas por cálculos numéricos, de modo que sólo las opciones de diseño más prometedoras se prueban en realidad en banco motor. Durante años, los códigos unidimensionales de dinámica de gases en el dominio del tiempo han sido suficientes para modelar tanto las prestaciones y el consumo del motor como el ruido de admisión y escape. Sin embargo, para un nivel más exigente de diseño, una representación 1D puede no ser suficiente para describir con precisión el flujo en ciertos elementos. Esto es especialmente importante en el caso de silenciadores, donde la hipótesis unidimensional sólo se puede aplicar a geometrías simples. En el caso de las uniones de conductos es la existencia de estructuras tridimensionales de flujo complejas lo que establece el límite de la aplicabilidad de una descripción simple cero-dimensional. En vista de estas limitaciones, la primera opción sería el uso de un modelo de dinámica de fluidos computacional (CFD); sin embargo, su aplicación conllevaría un tiempo de cálculo excesivo. Una posible solución de compromiso viene dada por los modelos cuasi-3D, basados en esquemas tridimensionales, pero con ciertas simplificaciones capaces de reducir significativamente el tiempo de cálculo sin afectar excesivamente a la precisión. Tales soluciones se han convertido en estándar en los códigos comerciales y se han aplicado con éxito a los silenciadores, tanto para excitaciones acústicas en el régimen lineal como en condiciones reales de motor, típicamente no lineales. Esta tesis tiene como objetivo el desarrollo de un nuevo método numérico cuasi-3D en una malla escalonada, basado en la simplificación de la ecuación de la cantidad de movimiento, para ser incluido en un código unidimensional existente. Tal método, sin embargo, no está libre de inconvenientes. En particular, se ve afectado por la aparición de oscilaciones no físicas, especialmente en gradientes de presión significativos. De la revisión bibliográfica se determina que este comportamiento es típico en esquemas de segundo orden y se puede ver acentuado por las simplificaciones adoptadas. Tras estudiar las posibles soluciones aplicables a este problema, se desarrollan tres limitadores de flujo diferentes, basados en las metodologías MDT, FCT y TVD. Una vez definido el método numérico y asegurada su estabilidad, es necesario desarrollar las condiciones de contorno adecuadas que permitan su utilización. Con este objetivo, se desarrollan las condiciones de pulso de presión de entrada y de extremo anecoico, los cuales permiten simular un banco de impulso. No hay que olvidar, sin embargo, que el objetivo final es la conexión con un código unidimensional, por lo que hay que comprobar que el método numérico cuasi-3D creado es compatible con los unidimensionales existentes, mostrando algunos resultados preliminares. Finalmente, con el método ya completamente operativo, se procede a su validación en las aplicaciones para las que ha sido diseñado principalmente, las cuales son, modelado de silenciadores y uniones de conductos. Para el caso de los silenciadores, se modelan dispositivos de complejidad creciente, pasando por geometrías de sección constante hasta sistemas con geometrías reales. Los resultados obtenidos se validan con otras herramientas tanto lineales como no lineales. En el caso de las uniones de conductos, el objetivo principal es el de establecer el potencial del nuevo método numérico frente a los tradicionales unidimensionales, por lo que los resultados de ambos se comparan con datos experimentEngine modelling has become an essential tool in the design of internal combustion engines, allowing considerable reductions in development time and cost. Classical design methodologies are based on prototype manufacturing and trial-and-error tests, but currently, most of those tests have been replaced by numerical computations, so that only the most promising design options are actually tested on engine bench. For years, one-dimensional gas dynamics codes in the time domain have offered sufficiently good solutions for modelling both engine performance and intake and exhaust noise. However, for a more demanding level of design, a 1D representation may not be sufficient to describe accurately the flow in certain elements. This is especially important in the case of silencers. In the case of duct junctions, the existence of complex 3D flow structures is what sets the applicability limit for a simple zero-dimensional description. In view of these limitations, the first option would typically be the use of a computational fluid dynamics (CFD) model; however, the application of such a model to a complete intake or exhaust system entails an excessive computational time. A possible compromise solution is given by quasi-3D models, based on three-dimensional schemes, but with certain simplifications able to significantly reduce the calculation time without excessively affecting the accuracy. Such solutions have become standard in commercial codes and have been successfully applied to silencers with perforated tubes and absorbing material, both in the linear acoustic regime and in real engine conditions, typically non-linear. The objective of this thesis is the development a new quasi-3D numerical method in a staggered-grid, based on the simplification of the momentum equation, to be included in an existing one-dimensional code. Such method however, is not hassle free. In particular, it is affected by the appearance of non-physical oscillations, specially near significant pressure gradients. From the literature review it is determined that this behaviour is typical among second-order schemes and it can be aggravated by the simplifications adopted. After researching the possible solutions to face this problem, three different flux limiters are developed, based on the MDT, FCT and TVD methodologies. In the case of the two latter methods, its effectiveness is well established for finite differences schemes, thus defining a clear improving line for quasi-3D models. Once the numerical method is defined and its stability assured, proper boundary conditions that allow its use must be developed. With this objective, a pressure pulse inlet and an anechoic termination boundary condition are developed, which allow the simulation of an impulse test rig. It should not be forgotten, however, that the ultimate objective is the connection with a one-dimensional code, therefore the compatibility of the quasi-3D numerical method created with the existing one-dimensional methods has to be tested, showing some preliminary results. Eventually, with a fully operative method, the validation process for the applications which it has been mainly developed for, takes place, namely, mufflers and duct junctions modelling. In the case of mufflers, increasingly complex devices are modelled, from constant section geometries to real geometry systems. The results obtained are validated with both linear and non-linear tools. In the case of duct junctions, the main objective is to establish the potential of the new numerical method against the traditional one-dimensional schemes, consequently, results from both approaches are compared to experimental measures, obtaining promising results.El modelatge s'ha convertit en els últims anys en una eina essencial en el disseny de motors de combustió interna alternatius, ja que permet reduir considerablement el temps i els costos de desenvolupament. Les metodologies de disseny clàssiques es basen en la fabricació de prototips i la realització de proves d'assaig i error. Actualment, la majoria d'aquestes proves han sigut substituïdes per càlculs numèrics, de manera que només les opcions de disseny més prometedores es proven en realitat en banc motor. Durant anys, els codis unidimensionals de dinàmica de gasos en el domini del temps han sigut suficients per a modelar tant les prestacions i el consum del motor com el soroll d'admissió i escapament. No obstant això, per a un nivell més exigent de disseny, una representació 1D pot no ser prou per a descriure amb precisió el flux en certs elements. Açò és especialment important en el cas de silenciadors, on la hipòtesi unidimensional només es pot aplicar a geometries simples. En el cas de les unions de conductes és l'existència d'estructures tridimensionals de flux complexes el que establix el límit de l'aplicabilitat d'una descripció simple zero-dimensional. En vista d'estes limitacions, la primera opció seria típicament l'ús d'un model de dinàmica de fluids computacional (CFD); no obstant això, l'aplicació comporta un temps de càlcul excessiu. Una possible solució de compromís ve donada pels models quasi-3D, basats en esquemes tridimensionals, però amb certes simplificacions capaços de reduir significativament el temps de càlcul sense afectar excessivament la precisió. Tals solucions s'han convertit en estàndard en codis comercials i s'han aplicat amb èxit als silenciadors, tant per a excitacions acústiques en el règim lineal com en condicions reals de motor, típicament no lineals. Aquesta tesi té com a objectiu el desenvolupament d'un nou mètode numèric quasi-3D en una malla escalonada, basat en la simplificació de l'equació de la quantitat de moviment, per a ser inclòs en un codi unidimensional existent. Tal mètode, però, no està lliure d'inconvenients. En particular, es veu afectat per l'aparició d'oscil·lacions no físiques, especialment en gradients de pressió significatius. De la revisió bibliogràfica es determina que aquest comportament és típic en esquemes de segon ordre i es pot veure accentuat per les simplificacions adoptades. Després d'estudiar les possibles solucions aplicables a aquest problema, es desenvolupen tres limitadors de flux diferents, basats en les metodologies MDT, FCT i TVD. En el cas dels dos últims mètodes, la seua efectivitat està ben establida per als esquemes de diferències finites, la qual cosa definix una clara via de millora per als models quasi-3D. Una vegada definit el mètode numèric i assegurada la seua estabilitat, és necessari desenvolupar les condicions de contorn adequades que permeten la seua utilització. Amb aquest objectiu, es desenvolupen les condicions de pols de pressió d'entrada i d'extrem anecoic, els quals permeten simular un banc d'impuls. No cal oblidar que l'objectiu final és la connexió amb un codi unidimensional, per la qual cosa cal comprovar que el mètode numèric cuasi-3D creat és compatible amb els unidimensionals existents, mostrant alguns resultats preliminars. Finalment, es procedix a la seua validació en les aplicacions per a les que ha sigut dissenyat principalment, les quals són, modelatge de silenciadors i unions de conductes. Per al cas dels silenciadors, es modelen dispositius de complexitat creixent, passant per geometries de secció constant fins a sistemes amb geometries reals. Els resultats obtinguts es validen amb altres eines tant lineals com no lineals. En el cas de les unions de conductes, l'objectiu principal és el d'establir el potencial del nou mètode numèric front als unidimensionals tradicionals, per la qual cosa els resultats d'ambdós es comparen amb dades experimHernández Marco, M. (2018). A non-linear quasi-3D model for air management modelling in engines [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/103683TESI

Thermoacoustic instability - a dynamical system and time domain analysis

This study focuses on the Rijke tube problem, which includes features relevant to the modeling of thermoacoustic coupling in reactive flows: a compact acoustic source, an empirical model for the heat source, and nonlinearities. This thermo-acoustic system features a complex dynamical behavior. In order to synthesize accurate time-series, we tackle this problem from a numerical point-of-view, and start by proposing a dedicated solver designed for dealing with the underlying stiffness, in particular, the retarded time and the discontinuity at the location of the heat source. Stability analysis is performed on the limit of low-amplitude disturbances by means of the projection method proposed by Jarlebring (2008), which alleviates the linearization with respect to the retarded time. The results are then compared to the analytical solution of the undamped system, and to Galerkin projection methods commonly used in this setting. This analysis provides insight into the consequences of the various assumptions and simplifications that justify the use of Galerkin expansions based on the eigenmodes of the unheated resonator. We illustrate that due to the presence of a discontinuity in the spatial domain, the eigenmodes in the heated case, predicted by using Galerkin expansion, show spurious oscillations resulting from the Gibbs phenomenon. By comparing the modes of the linear to that of the nonlinear regime, we are able to illustrate the mean-flow modulation and frequency switching. Finally, time-series in the fully nonlinear regime, where a limit cycle is established, are analyzed and dominant modes are extracted. The analysis of the saturated limit cycles shows the presence of higher frequency modes, which are linearly stable but become significant through nonlinear growth of the signal. This bimodal effect is not captured when the coupling between different frequencies is not accounted for.Comment: Submitted to Journal of Fluid Mechanic

Free and smooth boundaries in 2-D finite-difference schemes for transient elastic waves

A method is proposed for accurately describing arbitrary-shaped free boundaries in single-grid finite-difference schemes for elastodynamics, in a time-domain velocity-stress framework. The basic idea is as follows: fictitious values of the solution are built in vacuum, and injected into the numerical integration scheme near boundaries. The most original feature of this method is the way in which these fictitious values are calculated. They are based on boundary conditions and compatibility conditions satisfied by the successive spatial derivatives of the solution, up to a given order that depends on the spatial accuracy of the integration scheme adopted. Since the work is mostly done during the preprocessing step, the extra computational cost is negligible. Stress-free conditions can be designed at any arbitrary order without any numerical instability, as numerically checked. Using 10 grid nodes per minimal S-wavelength with a propagation distance of 50 wavelengths yields highly accurate results. With 5 grid nodes per minimal S-wavelength, the solution is less accurate but still acceptable. A subcell resolution of the boundary inside the Cartesian meshing is obtained, and the spurious diffractions induced by staircase descriptions of boundaries are avoided. Contrary to what occurs with the vacuum method, the quality of the numerical solution obtained with this method is almost independent of the angle between the free boundary and the Cartesian meshing.Comment: accepted and to be published in Geophys. J. In

Modeling seismic wave propagation and amplification in 1D/2D/3D linear and nonlinear unbounded media

To analyze seismic wave propagation in geological structures, it is possible to consider various numerical approaches: the finite difference method, the spectral element method, the boundary element method, the finite element method, the finite volume method, etc. All these methods have various advantages and drawbacks. The amplification of seismic waves in surface soil layers is mainly due to the velocity contrast between these layers and, possibly, to topographic effects around crests and hills. The influence of the geometry of alluvial basins on the amplification process is also know to be large. Nevertheless, strong heterogeneities and complex geometries are not easy to take into account with all numerical methods. 2D/3D models are needed in many situations and the efficiency/accuracy of the numerical methods in such cases is in question. Furthermore, the radiation conditions at infinity are not easy to handle with finite differences or finite/spectral elements whereas it is explicitely accounted in the Boundary Element Method. Various absorbing layer methods (e.g. F-PML, M-PML) were recently proposed to attenuate the spurious wave reflections especially in some difficult cases such as shallow numerical models or grazing incidences. Finally, strong earthquakes involve nonlinear effects in surficial soil layers. To model strong ground motion, it is thus necessary to consider the nonlinear dynamic behaviour of soils and simultaneously investigate seismic wave propagation in complex 2D/3D geological structures! Recent advances in numerical formulations and constitutive models in such complex situations are presented and discussed in this paper. A crucial issue is the availability of the field/laboratory data to feed and validate such models.Comment: of International Journal Geomechanics (2010) 1-1

Wavefield Analysis of Rayleigh Waves for Near-Surface Shear-Wave Velocity

Shear (S)-wave velocity is a key property of near-surface materials and is the fundamental parameter for many environmental and engineering geophysical studies. Directly acquiring accurate S-wave velocities from a seismic shot gather is usually difficult due to the poor signal-to-noise ratio. The relationship between Rayleigh-wave phase velocity and frequency has been widely utilized to estimate the S-wave velocities in shallow layers using the multichannel analysis of surface waves (MASW) technique. Hence, Rayleigh wave is a main focus of most near-surface seismic studies. Conventional dispersion analysis of Rayleigh waves assumes that the earth is laterally homogeneous and the free surface is horizontally flat, which limits the application of surface-wave methods to only 1D earth models or very smooth 2D models. In this study I extend the analysis of Rayleigh waves to a 2D domain by employing the 2D full elastic wave equation so as to address the lateral heterogeneity problem. I first discuss the accurate simulation of Rayleigh waves through finite-difference method and the boundary absorbing problems in the numerical modeling with a high Poisson's ratio ( 0.4), which is a unique near-surface problem. Then I develop an improved vacuum formulation to generate accurate synthetic seismograms focusing on Rayleigh waves in presence of surface topography and internal discontinuities. With these solutions to forward modeling of Rayleigh waves, I evaluate the influence of surface topography to conventional dispersion analysis in 2D and 3D domains by numerical investigations. At last I examine the feasibility of inverting waveforms of Rayleigh waves for shallow S-wave velocities using a genetic algorithm. Results of the study show that Rayleigh waves can be accurately simulated in near surface using the improved vacuum formulation. Spurious reflections during the numerical modeling can be efficiently suppressed by the simplified multiaxial perfectly matched layers. The conventional MASW method can tolerate gentle topography changes with insignificant errors. Finally, many near-surface features with strong lateral heterogeneity such as dipping interfaces, faults, and tunnels can be imaged by the waveform inversion of Rayleigh waves for shallow S-wave velocities. This thesis consists of four papers that are either published (chapter 1) or in review (chapter 2, 3, and 4) for consideration of publication to peer-refereed journals. Each chapter represents a paper, and therefore inadvertently there will be a certain degree of overlap between chapters (particularly for the introduction parts, where references to many common papers occur)

Modelling Seismic Wave Propagation for Geophysical Imaging

International audienceThe Earth is an heterogeneous complex media from the mineral composition scale (10−6m) to the global scale ( 106m). The reconstruction of its structure is a quite challenging problem because sampling methodologies are mainly indirect as potential methods (Günther et al., 2006; Rücker et al., 2006), diffusive methods (Cognon, 1971; Druskin & Knizhnerman, 1988; Goldman & Stover, 1983; Hohmann, 1988; Kuo & Cho, 1980; Oristaglio & Hohmann, 1984) or propagation methods (Alterman & Karal, 1968; Bolt & Smith, 1976; Dablain, 1986; Kelly et al., 1976; Levander, 1988; Marfurt, 1984; Virieux, 1986). Seismic waves belong to the last category. We shall concentrate in this chapter on the forward problem which will be at the heart of any inverse problem for imaging the Earth. The forward problem is dedicated to the estimation of seismic wavefields when one knows the medium properties while the inverse problem is devoted to the estimation of medium properties from recorded seismic wavefields