Mode decomposition methods for the analysis of cavitating flows in turbomachinery

Abstract The present work is aimed at the characterization of the cavitating flow regimes by applying the coupled POD/DMD technique to the vapor volume fraction field. The proposed approach provided an improved spatio-temporal-frequency description of the flow, based on the detection of the most energetic flow structures with information about their shape and size, and their decomposition into wave patterns oscillating with specific frequency and decay rate. The novel technique was applied to numerical results concerning the bubble cavitation and the supercavitation regimes of 2D water flows around a NACA hydrofoil at ambient temperature. Numerical simulations were performed by using a homogenous mixture model equipped with an extended Schnerr-Sauer cavitation model, in combination with a Volume of Fluid (VOF) interface tracking method. The proposed approached provided a better characterization of the unsteady cavitating flow, and allowed for a deeper insight about the dynamics of the vapor cavity, especially in cases involving the more chaotic regime of supercavitation. In particular, POD results figured out the most energetic coherent vapor structures associated to each cavitation regime: the first mode highlighted the main sheet cavity which grew on the hydrofoil up to detached, the second mode pointed out the cavitating/condensating doublet structures and the third mode figured out the smaller structures owning less energy but a higher frequency content. DMD modes performed a decomposition of the coherent structures detected by means of the POD analysis, into a subset of vapor pattern periodically evolving with a single frequency and a characteristic decay rate. Furthermore, results showed that the supercavitating flow structures owned characteristic frequencies which ranged from 5 to 26 Hz, while the less intensive bubble cavitation regime was characterized by frequencies ranging from 15 to 42 Hz

Empirical eigenfunctions: application in unsteady aerodynamics

Mención Internacional en el título de doctorThe main aim of modal decompositions is to obtain a set of functions which can describe in a compact way the variability contained in a set of observables/data. While this can be easily obtained by means of the eigenfunctions of the operator from which the observables depends, the empirical eigenfunctions allow to obtain a similar result from a set of data, without the knowledge of the problem operator. In Fluid Mechanics and related sciences one of the most prominent techniques to obtain empirical eigenfunctions is referred to as Proper Orthogonal Decomposition (POD). This thesis contains applications of the empirical eigenfunctions to (Experimental) Aerodynamics data. The mathematical framework of the POD is introduced following the bi-orthogonal approach by Aubry (1991). The mathematical derivation of the POD is given, wherever possible, in its most general formulation, without bounding it to the decomposition of a specific quantity. This choice of the author depends on the variety of POD applications which are included in this dissertation, ranging from signal processing problems to applications more strictly related with flow physics. The mathematical framework includes also one of the POD extensions, the Extended POD (EPOD), which allows to extract modes linearly correlated to the empirical eigenfunctions of a second quantity. The first two applications of the empirical eigenfunctions are strictly connected with the signal treatment in experimental techniques for Fluid Mechanics. In Chapter 3, the empirical eigenfunctions are identified as an optimal basis in which perform a "low-pass" spectral filter of experimental fluid data, such as velocity fields measured with Particle Image Velocimetry (PIV). This filtering is extremely beneficial to reduce the random errors contained in the PIV fields and obtain a more accurate estimate of derivative quantities (such as, for instance, vorticity), which are more affected by random errors. In Chapter 4 the POD is exploited for the pre-treatment of a sequence of PIV images. The aim is to remove background and reflections, which are sources of uncertainty in PIV measurements. In this case a "high-pass" spectral filtering is applied to the PIV image ensemble in order to remove the highly-coherent part of the signal corresponding to the background. In the third and fourth applications, the POD is applied to recover the underlying dynamics of a flow. More specifically, in Chapter 5 the POD is applied to the complex wake of a pair of cylinders in tandem arrangement with the additional perturbation of the wall proximity. Through this technique it is possible to track the changes in the oscillatory behaviour of the wake instabilities ascribed to different geometrical configurations of the cylinders. In Chapter 6 the POD and the EPOD are applied respectively to the flow fields around an airfoil in plunging and pitching motion and to the unsteady aerodynamic forces acting on the airfoil. The decomposition allows to extract a reduced set of modes of the flow field which are related to the force generation mechanism. These modes correspond to well-recognizable phenomena of the flow which can be identified for diverse airfoil kinematics. This flow-field driven force decomposition is analysed on the light of existing force models, enabling their reinterpretation and driving towards possible corrections. The final application is devoted to overcome the low temporal resolution of typical flow field measurements, such as PIV, by proposing a robust estimation of turbulent flows dynamics. The method employs a modified version of the EPOD to identify the correlation between a non-time-resolved field measurement and a time-resolved point measurement. The estimation of the time-resolved flow fields is obtained exploiting the correlation of the flow fields with the temporal information contained in the point measurements.El objetivo principal de las descomposiciones modales es obtener un conjunto de funciones que sean capaces de describir de una manera compacta la variabilidad contenida en un conjunto de observables/datos. Si bien este objetivo puede ser fácilmente realizado mediante el uso de las autofunciones del operador del cual los observables dependen, las autofunciones empíricas permiten obtener un resultado similar partiendo de un conjunto de datos sin la necesidad de conocer el operador del problema. En Mecánica de Fluidos y en ciencias relacionadas con esta disciplina, una de las técnicas más relevantes para obtener autofunciones empíricas es la conocida como Descomposición Modal Ortogonal (Proper Orthogonal Decomposition, POD). Esta tesis contiene diversas aplicaciones de las autofunciones empíricas en datos de Aerodinámica (Experimental). La base matemática de la POD es introducida siguiendo la aproximación biortogonal realizada por Aubry (1991). La formulación matemática de la POD es expresada siempre que es posible en el marco más general posible, sin condicionarla a la descomposición de una variable en concreto. La elección del autor dependerá de las diferentes aplicaciones de la POD, todas ellas descritas en la presente tesis, las cuales abarcan desde problemas de procesado de señales hasta aplicaciones más estrictamente relacionadas con el análisis de la física del flujo. La formulación matemática incluye también uno de las extensiones de la POD, la POD Extendida (EPOD), la cual permite extraer modos linealmente correlacionados con las autofunciones empíricas de una segunda variable. Las dos primeras aplicaciones de las autofunciones empíricas están estrictamente relacionadas con el tratamiento de señales en técnicas experimentales de Mecánica de Fluidos. En el Capítulo 3, las autofunciones empíricas son identificadas como una base optima, la cual se puede utilizar para realizar un filtro pasa bajos espectral para datos experimentales de flujos, tales como campos de velocidad obtenidos mediante la técnica de Velocimetría por Imágenes de Partículas, (Particle Image Velocimetry, PIV). Este tipo de filtro es muy beneficioso para reducir los errores de carácter aleatorio contenidos en los campos de PIV y por tanto obtener una estimación más precisa en las cantidades que precisan del uso de derivadas (por ejemplo, la vorticidad), ya que están más afectadas por este tipo de errores. En el Capítulo 4, la POD es utilizada para el pretratamiento de una secuencia de imágenes de PIV. El objetivo es reducir el fondo de la imagen y las reflexiones, ambas fuentes de incertidumbre en las medidas de PIV. En este caso, un filtro pasa altos espectral es aplicado al conjunto de imágenes de PIV para poder quitar la parte mayormente correlacionada de la señal, la cual corresponde con el fondo de la imagen. En la tercera y cuarta aplicación de la POD, está técnica es utilizada para reconstruir las dinámicas fundamentales de un flujo. Concretamente, en el Capítulo 5 la POD es utilizada para analizar la estela compleja que se produce en una pareja de cilindros en tándem con la perturbación adicional de una pared próxima a ellos. A través de esta técnica, es posible poder estudiar los cambios en el comportamiento oscilatorio de las inestabilidades de la estela, las cuales están relacionadas con las diferentes configuraciones geométricas de los cilindros. En el capítulo 6, la POD y la EPOD son aplicadas respectivamente a campos fluidos y fuerzas aerodinámicas producidos por un perfil aerodinámico en movimiento (de rotación y desplazamiento vertical) no estacionario. La técnica de descomposición permite extraer un conjunto reducido de modos del campo fluido que están relacionados con el mecanismo que genera las fuerzas aerodinámicas. Estos modos corresponden con fenómenos característicos del flujo que pueden ser identificados para diferentes cinemáticas de perfiles aerodinámicos. Estas dinámicas del flujo que están conectadas con las fuerzas aerodinámicas son analizadas teniendo en cuenta los modelos ya existentes en la literatura que describen las fuerzas aerodinámicas, permitiendo su reinterpretación e incluso pudiendo añadir posibles correcciones. La última aplicación propuesta está destinada a subsanar la baja resolución temporal típica de las medidas de campo fluido, como en aquellas realizadas utilizando PIV, mediante una estimación robusta de las dinámicas del flujo turbulento. El método propuesto emplea una versión modificada de la EPOD para identificar para correlación entre un campo fluido medido que no está resuelto en el tiempo y una medida puntual que sí que está resulta en el tiempo. La estimación del campo fluido resuelto en el tiempo es obtenida mediante la correlación de los campos de flujo con la información temporal contenida en la medida puntual.This work has been partially supported by the Grant TRA2013-41103-P of the Spanish Ministry of Economy and Competitiveness, which includes FEDER funding, and by the Grant DPI2016-79401-R, funded by the Spanish State Research Agency (SRA) and European Regional Development Fund (ERDF).Programa Oficial de Doctorado en Mecánica de FluidosPresidente: Bharathram Ganapathisubramani.- Secretario: Francisco Javier Rodríguez Rodríguez.- Vocal: Francisco J. Huera-Huart

Thermo-fluid-dynamics of impinging swirling jets

The superimposition of a tangential motion on a conventional round jet has been demonstrated to significantly affect the large-scale topology of the flow. Swirling flows are widely employed, in the impinging configuration, in several industrial processes which involve both non-reacting and reacting applications. In the present dissertation, the simultaneously acquired thermal and three-dimensional velocity fields of an impinging hot jet emerging from a custom swirl generator in a cold ambient are presented. The velocity and temperature fields are experimentally measured using time-resolved Tomographic PIV and high-speed Infrared thermography in a combined system. A detailed description of a custom swirl generator is provided, and the time-averaged velocity profiles of a free swirling flow are discussed in order to estimate the swirl number. The instantaneous three-dimensional dynamics in proximity of the nozzle is discussed and the main features of a free swirling jet are investigated through the application of Proper Orthogonal Decomposition technique. The time-dependent features of velocity and temperature fields of an impinging swirling jet are investigated through the description of the time sequences of the temperature fluctuations and the synchronised instantaneous vortical structures. Taking advantage of the simultaneous acquisition and of the knowledge of the relative positioning of thermal and velocity frames, two different correlation techniques are applied, and their outcomes discussed

Time-Resolved PIV Measurements of Ship Airwakes with Quartering Winds

The unsteady, three-dimensional, turbulent airwake over the Simple Frigate Ship No. 2 (SFS2) with quartering wind flow directions was studied in a low-speed wind tunnel facility. Surface oil flow visualization and time-resolved stereoscopic and planar particle image velocimetry (PIV) measurements were made for three crosswise planes and a single centerline streamwise plane. Measurements included various configurations with the bow of the ship model at two different quartering wind conditions of 10 and 20 degrees, as well as cases with and without the effects of a simulated atmospheric boundary layer (ABL). A comparative analysis of the time-averaged flow structures between the quartering wind cases and the pure headwind measurements showed significant differences in the development of the airwake. For both quartering wind cases, the funnel wake had a trailing vortex on the windward side and large cross-sectional velocity magnitudes. The flight deck recirculation region decreased in size and became asymmetric for both quartering wind cases. Different flight deck vortical structures were found, indicating a difference within the flow field based on the yaw angle. A spectral analysis showed the streamwise fluctuations contained more energy for the quartering wind cases in the funnel wake region, which was also seen in the turbulent fluctuations. Two-point velocity correlations revealed large-scale coherent motion in the streamwise direction. The coherent behavior was further related to the observed time-averaged flow field structures through proper orthogonal decomposition (POD). The POD analysis highlighted the nontrivial behavior that was inherent to the airwake. These findings further emphasize the complexity of the airwake and necessity of understanding the development of the airwake under a broad range of conditions

An Experimental Investigation of Self-Excited Combustion Dynamics in a Single Element Lean Direct Injection (LDI) Combustor

The management of combustion dynamics in gas turbine combustors has become more challenging as strict NOx/CO emission standards have led to engine operation in a narrow, lean regime. While premixed or partially premixed combustor configurations such as the Lean Premixed Pre-vaporized (LPP), Rich Quench Lean burn (RQL), and Lean Direct Injection (LDI) have shown a potential for reduced NOx emissions, they promote a coupling between acoustics, hydrodynamics and combustion that can lead to combustion instabilities. These couplings can be quite complex, and their detailed understanding is a pre-requisite to any engine development program and for the development of predictive capability for combustion instabilities through high-fidelity models. The overarching goal of this project is to assess the capability of high-fidelity simulation to predict combustion dynamics in low-emissions gas turbine combustors. A prototypical lean-direct-inject combustor was designed in a modular configuration so that a suitable geometry could be found by test. The combustor comprised a variable length air plenum and combustion chamber, air swirler, and fuel nozzle located inside a subsonic venturi. The venturi cross section and the fuel nozzle were consistent with previous studies. Test pressure was 1 MPa and variables included geometry and acoustic resonance, inlet temperatures, equivalence ratio, and type of liquid fuel. High-frequency pressure measurements in a well-instrumented metal chamber yielded frequencies and mode shapes as a function of inlet air temperature, equivalence ratio, fuel nozzle placement, and combustor acoustic resonances. The parametric survey was a significant effort, with over 105 tests on eight geometric configurations. A good dataset was obtained that could be used for both operating-point-dependent quantitative comparisons, and testing the ability of the simulation to predict more global trends. Results showed a very strong dependence of instability amplitude on the geometric configuration of the combustor, i.e., its acoustic resonance characteristics, with measured pressure fluctuation amplitudes ranged from 5 kPa (0.5% of mean pressure) to 200 kPa (~20% of mean pressure) depending on combustor geometry. The stability behavior also showed a consistent and pronounced dependence on equivalence ratio and inlet air temperature. Instability amplitude increased with higher equivalence ratio and with lower inlet air temperature. A pronounced effect of fuel nozzle location on the combustion dynamics was also observed. Combustion instabilities with the fuel nozzle at the throat of the venturi throat were stronger than in the configuration with fuel nozzle 2.6 mm upstream of the nozzle. A second set of dynamics data was based on high-response-rate laser-based combustion diagnostics using an optically accessible combustor section. High-frequency measurements of OH*-chemiluminescence and OH-PLIF and velocity fields using PIV were obtained at a relatively stable, low equivalence ratio case and a less stable case at higher equivalence ratio. PIV measurements were performed at 5 kHz for non-reacting flow but glare from the cylindrical quartz chamber limited the field of view to a small region in the combustor. Quantitative and qualitative comparisons were made for five different combinations of geometry and operating condition that yielded discriminating stability behavior in the experiment with simulations that were carried out concurrently. Comparisons were made on the basis of trends and pressure mode data as well as with OH-PLIF measurements for the baseline geometry at equivalence ratios of 0.44 and 0.6. Overall, the ability of the simulation to match experimental data and trends was encouraging. Dynamic Mode Decomposition (DMD) analysis was performed on two sets of computations - a global 2-step chemistry mechanism and an 18-step chemistry mechanism - and the OH-PLIF images to allow comparison of dynamic patterns of heat release and OH distribution in the combustion zone. The DMD analysis was able to identify similar dominant unstable modes in the combustor. Recommendations for future work are based on the continued requirement for quantitative and spatio-temporally resolved data for direct comparison with computational efforts to develop predictive capabilities for combustion instabilities at relevant operating conditions. Discriminating instability behavior for the prototypical combustor demonstrated in this study is critical for any robust validation effort Unit physics based scaling of the current effort to multi-element combustors along with improvement in diagnostic techniques and analysis efforts are recommended for advancement in understanding of the complex physics in the multi-phase, three dimensional and turbulent combustion processes in the LDI combustor

Proper orthogonal decomposition, dynamic mode decomposition, wavelet and cross wavelet analysis of a sloshing flow

Internal hydrodynamics and its coupling with structural dynamics are non-negligible processes in the design phase of aerospace systems. An improved understanding of the nature of this coupling would allow for greater flexibility in modeling and design of such systems, and could lead eventually to the development of suitable active and/or passive control strategies for enhanced performances. In this manuscript we apply a number of data analysis techniques: proper orthogonal decomposition, dynamic mode decomposition and wavelet transform and their combination to time-resolved images of a liquid sloshing within an enclosure. We use these techniques to identify fluid-dynamic modes in space and time and to verify their coupling with the structural dynamics of vibrating structures. In particular we consider the transient case of a water tank mounted on a free oscillating cantilever. As the acceleration amplitude decays, we observe and quantify the transition from incoherent flow to standing waves. Our results show that the content of the images is very informative and can be used for quantitative analysis. As the main outcome, the hydrodynamic modes are identified using POD and DMD, and related to known features of sloshing flow, such as the frequency of the first symmetric free surface mode. Additionally we perform a comparison of wavelet transforms of POD time coefficients and measured acceleration signals at the tank base. Viewing the latter as the input and the former as the output of the fluid-dynamic system, we are able to correlate the enhanced damping of the cantilever oscillation to the different regimes of the hydrodynamic field

High Frame Rate Ultrasound Velocimetry of Fast Blood Flow Dynamics

In this thesis we develop and validate high frame rate ultrasound sequences for use with echo-particle image velocimetry (in 2D and 3D), with the aim of measuring the high velocity blood flow patterns in the left ventricle and abdominal aorta

Optical Techniques for Experimental Tests in Microfluidics

This PhD dissertation deals with the use of optical, non-invasive measurement techniques for the investigation of single and two-phase flows in microchannels. Different experimental techniques are presented and the achieved results are critically discussed. Firstly, the inverse use of the micro Particle Image Velocimetry technique for the detection of the real shape of the inner cross-section of an optical accessible microchannel is shown by putting in evidence the capability of this technique to individuate the presence of singularities along the wetted perimeter of the microchannel. Then, the experimental measurement of the local fluid temperature using non-encapsulated Thermochromic Liquid Crystal particles is discussed. A deep analysis of the stability of the color of these particles when exposed to different levels of shear stress has been conducted by demonstrating that these particles can be used for simultaneous measurements of velocity and temperature in water laminar flows characterized by low Reynolds numbers (Re < 10). A preliminary experiment where the TLC thermography is coupled to the APTV method for the simultaneous measurement of the three-dimensional velocity and temperature distribution in a microchannel is shown. Finally, an experimental analysis of the different flow patterns observed for an adiabatic air-water mixture generated by means of a micro T-junction is discussed. The main air-water mixture features have been deeply observed in 195 different experimental conditions in which values of superficial velocity ranging between 0.01 m/s and 0.15 m/s for both the inlet flows (air and water) are imposed. The flow patterns of the air-water mixture are strongly influenced by the value of the water superficial velocity; on the contrary, the air superficial velocity plays a secondary role for the determination of the characteristics of the bubbles (i.e. length)

Vortex shedding from elongated bluff bodies

As the spans of suspension bridges increase, the structures become inherently flexible. The flexibility of these structures, combined with the wind and particular aerodynamics, can lead to significant motions. From the collapse due to flutter of the Tacoma Narrows Bridge to the case of vortex-induced vibrations (VIV) of the Storebælt Bridge, it is evident that a better understanding of the aerodynamics of these geometries is necessary. The work herein is motivated by these two problems and is presented in two parts. In the first part, the focus is on the physical mechanisms of vortex shedding. It is shown that the wake formation for elongated bluff bodies is distinct from shorter bluff bodies due to the leading edge separating-reattaching flow. Pressure data are then used to propose a mechanism of competition between the flow at the leading and trailing edges rather than synchronization which occurs at low Reynolds numbers. Within the context of this framework, the wakes are orthogonally decomposed and it was discovered that new modes appear not previously observed for shorter bluff bodies. In Part II, a time-resolved Particle Image Velocimetry (PIV) system is developed. This system is used to capture both the high and low frequency dynamics of flutter due its uniquely long recording length. It is shown that, contrary to conventional understanding, the vortex shedding does not significantly change during flutter. Thus, the fact that these bodies shed vortices is only a secondary effect in relation to the flutter instability. There is a distinct contrast between flutter and VIV: the latter is known to be governed by the vortex shedding wake and it has been shown herein that the former is not. Regarding the problem of VIV, it is shown that the wakes of these bodies are formed due to interaction with the leading edge separating-reattaching flow. As the leading edge separation angle grows, it is shown to disturb the trailing edge vortex shedding altering many of the key parameters including fluctuating lift force and shedding frequency