The labyrinth seal is a non-contact annular type sealing device used to reduce the internal leakage of the working fluid which is caused by the pressure difference between each stage in a turbomachine. Reducing the leakage mass flow rate of the working fluid through the labyrinth seal is desirable because it improves the efficiency of the turbomachine. The carry-over coefficient, based on the divergence angle of the jet, changed with flow parameters with fixed seal geometry while earlier models expressed the carry-over coefficient solely as a function of seal geometry. For both compressible and incompressible flows, the Reynolds number based on clearance was the only flow parameter which could influence the carry-over coefficient. In the case of incompressible flow based on the simulations for various seal geometries and operating conditions, for a given Reynolds number, the carry-over coefficient strongly depended on radial clearance to tooth width ratio. Moreover, in general, the lower the Reynolds number, the larger is the divergence angle of the jet and this results in a smaller carry-over coefficient at lower Reynolds numbers. However, during transition from laminar to turbulent, the carry-over coefficient reduced initially and once the Reynolds number attained a critical value, the carry-over coefficient increased again. In the case of compressible flow, the carry-over coefficient had been slightly increased if radial clearance to tooth width ratio and radial clearance to tooth pitch ratio were increased. Further, the carry-over coefficient did not considerably change if only radial clearance to tooth width ratio was decreased. The discharge coefficient for compressible and incompressible flows depended only on the Reynolds number based on clearance. The discharge coefficient of the tooth in a single cavity labyrinth seal was equivalent to that in a multiple tooth labyrinth seal indicating that flow downstream had negligible effect on the discharge coefficient. In particular, for compressible fluid under certain flow and seal geometric conditions, the discharge coefficient did not increase with an increase in the Reynolds number. It was correlated to the pressure ratio, Pr. Moreover, it was also related to the fact that the flow of the fluid through the constriction became compressible and the flow eventually became choked. At low pressure ratios (less than 0.7), Saikishan’s incompressible model deviated from CFD simulation results. Hence, the effects of compressibility became significant and both the carry-over coefficient compressibility factor and the discharge coefficient compressibility factor needed to be considered and included into the leakage model. The carry-over coefficient compressibility factor, phi, had two linear relationships with positive and negative slopes regarding the pressure ratios. This result was not associated with the seal geometry because the seal geometry ratios for each instance were located within the nearly same ranges. Further, the phi-Pr relationship was independent of the number of teeth regardless of single and multiple cavity labyrinth seals. The discharge coefficient compressibility factor, psi, was a linear relationship with pressure ratios across the tooth as Saikishan predicted. However, in certain flow and seal geometric conditions, Saikishan’s model needed to be modified for the deviation appearing when the pressure ratios were decreased. Hence, a modified psi-Pr relationship including Saikishan’s model was presented in order to compensate for the deviation between the simulations and his model.

Le golfe de Gascogne (GdG), un milieu riche en processus physiques a été étudié à partir de simulations numériques. L’étude est construite autour d'échelles allant du GdG à la sous méso-échelle. Dans la première partie, nous avons examiné la variabilité interannuelle de la température et de la salinité de surface sur une période de 53 ans : nous avons pu décrire deux tendances en lien avec I'Atlantique Nord-Est. Le refroidissement et la dessalure jusqu'en 1976 seraient liés à la grande anomalie de salinité, le réchauffement et la salinification actuels liés à I'augmentation de CO2 atmosphérique. Le GdG se caractérise par un courant de pente, lberian Poleward Current (lPC) : sa variabilité serait liée au vent du Sud-Ouest qui renforce l'lPC par un courant géostrophique dans le Bassin lbérique. L’un des résultats intéressant trouvé dans les simulations et confìrmé par les observations est l'apparition des anomalies froides liées à des upwellings en alternance avec des anomalies chaudes "La Navidad". Ces upwellings seraient liés au vent de Nord dans le Bassin lbérique mais au courant d'Ouest le long des côtes Nord espagnoles. Dans une deuxième partie, nous nous sommes attachés à la méso et sous méso-échelle à travers la détection des tourbillons et la variabilité des spectres d'énergie. Un indice basé sur le rapport entre I'anomalie de densité de surface et I'anomalie de niveau de la mer permet de détecter les tourbillons de subsurface et de les distinguer des tourbillons de surface. Une application de cet indice à partir des données satellites confirme le potentiel de détection des Slope Water Oceanic eDDIES (tourbillons de subsurface caractéristiques du GdG). La description de l'énergie cinétique turbulente (EKE) dans le GdG montre une variabilité spatiale avec un maximum le long de la côte Nord espagnole liée à I'lPC. Les pentes des spectres (k-4.2 pour la SSH, en k-2.4 pour la SST et en k-2.4 pour l'énergie cinétique) sont différents des observations satellites, mais comparables avec les précédentes études. Ces pentes de spectres ont également une variabilité saisonnière avec un maximum en hiver et un minimum en été, liée au cycle saisonnier de I'EKE. / The Bay of Biscay (BoB), an environment rich in physical processes has been studied from numerical simulations. Thestudy is built around scales from the size of BoB until sub mesoscale.ln the first part, we examined the interannual variability of the sea surface temperature and saliniÇ over a period of 53years: we were able to describe two trends related to the North-East Atlantic. Cooling and freshening until 1976 thatcould be related to the Great Salinity Anomaly and current salinification related to the atmospheric increase of CO2.The Bay of Biscay is characterized by a slope current, the lberian Poleward Current (lPC): its variability is linked to theSouth West wind strengthens the IPC by a geostrophic current in the lberian Basin. One of the interesting results foundin simulations and confirmed by observations is the appearance of cold anomalies related to upwellings and alternatingwith warm anomalies 'La Navidad'. These upwellings could be linked to the north wind in the lberian Basin but to the West current along the northern Spanish coast.ln the second part, we are committed to the meso and sub mesoscale eddies through a method of detection and throughthe variability of energy spectra. An index based on the ratio of surface density anomaly and sea level anomaly allowsdetecting subsurface vortices and distinguishing them from the surface ones. The application of this index from thesatellite data confirms the detection potential of Slope Water Oceanic Eddies (subsurface vortices of BoB).The description of the Eddy Kinetic Energy (EKE) in the BoB. shows a spatial variability with maximum along the Spanishnorth coast linked to the lPC. The slopes of the spectra (k-4.2 for SSH, k-2.4 for SST and k-2.4 for the kinetic energy) are different from satellite observations, but comparable with previous studies. These spectral slopes have a seasonalvariability with a maximum in winter and minimum in summe¡ related to the seasonal cycle of EKE.

Ultra low power wireless sensors and sensor systems are of increasing interest in a variety of applications ranging from structural health monitoring to industrial process control. Electrochemical batteries have thus far remained the primary energy sources for such systems despite the finite associated lifetimes imposed due to limitations associated with energy density. However, certain applications (such as implantable biomedical electronic devices and tire pressure sensors) require the operation of sensors and sensor systems over significant periods of time, where battery usage may be impractical and add cost due to the requirement for periodic re-charging and/or replacement. In order to address this challenge and extend the operational lifetime of wireless sensors, there has been an emerging research interest on harvesting ambient vibration energy. Vibration energy harvesting is a technology that generates electrical energy from ambient kinetic energy. Despite numerous research publications in this field over the past decade, low power density and variable ambient conditions remain as the key limitations of vibration energy harvesting. In terms of the piezoelectric transducers, the open-circuit voltage is usually low, which limits its power while extracted by a full-bridge rectifier. In terms of the interface circuits, most reported circuits are limited by the power efficiency, suitability to real-world vibration conditions and system volume due to large off-chip components required. The research reported in this thesis is focused on increasing power output of piezoelectric transducers and power extraction efficiency of interface circuits. There are five main chapters describing two new design topologies of piezoelectric transducers and three novel active interface circuits implemented with CMOS technology. In order to improve the power output of a piezoelectric transducer, a series connection configuration scheme is proposed, which splits the electrode of a harvester into multiple equal regions connected in series to inherently increase the open-circuit voltage generated by the harvester. This topology passively increases the rectified power while using a full-bridge rectifier. While most of piezoelectric transducers are designed with piezoelectric layers fully covered by electrodes, this thesis proposes a new electrode design topology, which maximizes the raw AC output power of a piezoelectric harvester by finding an optimal electrode coverage. In order to extract power from a piezoelectric harvester, three active interface circuits are proposed in this thesis. The first one improves the conventional SSHI (synchronized switch harvesting on inductor) by employing a startup circuitry to enable the system to start operating under much lower vibration excitation levels. The second one dynamically configures the connection of the two regions of a piezoelectric transducer to increase the operational range and output power under a variety of excitation levels. The third one is a novel SSH architecture which employs capacitors instead of inductors to perform synchronous voltage flip. This new architecture is named as SSHC (synchronized switch harvesting on capacitors) to distinguish from SSHI rectifiers and indicate its inductorless architecture.

In this thesis, a miniaturized energy harvester system is developed. The energy harvester converts fluid kinetic energy into electrical energy without using any rotating components. The working principle of the energy harvester is based on the so called vortex-induced vibration. Such systems have the potential to provide energy for wireless sensor networks in the field of inline measurements for gas, oil or water transportation systems. The theoretical background of the vortex-induced vibration (VIV) is studied. Based on the studies, a fluid-structure interaction simulation is carried out to optimize the structure of the energy harvester. As result, the conversion efficiency is significantly improved, which is experimentally confirmed. A series of demonstrators are manufactured according to the simulation and optimization results. It is tested on a self-constructed test bench. To further improve the performance, an electromagnetic generator is proposed, and therefore, a multimethod demonstrator realized. The demonstrators are working in air flow already at a velocity of 2 m/s, and reach the maximum efficiency at 3.6 m/s. This performance ranks among the best published results and is discussed in detail. / In der vorliegenden Arbeit wird ein miniaturisiertes Energiegewinnungssystem entwickelt, das unter Verzicht auf rotierende Komponenten kinetische Strömungsenergie in elektrische Energie umwandelt. Die Funktion dieses Wandlers basiert auf der sogenannten wirbelinduzierten Vibration. Derartige Systeme besitzen unter anderem das Potenzial, drahtlose Sensornetzwerke zur Erfassung von Messdaten in Gas-, Öl- oder Wassertransportsystemen mit Energie zu versorgen zu können. In der Arbeit wird der theoretische Hintergrund der wirbelinduzierten Vibration untersucht und darauf basierend werden Fluid-Struktur-Wechselwirkungssimulationen zur Strukturoptimierung durchgeführt in deren Ergebnis eine theoretische Verbesserung der Effizienz des Wandlers um ein Mehrfaches erreicht wird, die auch praktisch bestätigt wird. Unter Berücksichtigung der Simulations- und Optimierungsergebnisse wurden eine Reihe von Demonstratoren gefertigt, die auf einem selbst konstruierten Prüfstand getestet wurden. Zur weiteren Erhöhung der Leistungsfähigkeit des Wandlers wird ein zusätzlicher elektromagnetischer Generator vorgeschlagen und damit ein Multi-Methoden-Demonstrator technisch realisiert. Die Demonstratoren arbeiten in strömender Luft bereits bei Geschwindigkeiten von 2 m/s und erreichen bei 3,6 m/s ihre maximale Effizienz. Die erreichten Ergebnisse ordnen sich im Vergleich mit denen aus entsprechenden Publikationen vorn ein und werden ausführlich diskutiert.

[EN] In the current work, the characterization of the combustion process inside a stratified pre-chamber spark ignition (PCSI) system is performed. An extensive bibliographical review about the pre-chamber systems developed from the second half of the 20th century until modern times is presented. The review shows that the latest generation systems have the potential to accomplish the emissions limits while providing high performance and low fuel consumption. Nevertheless, many efforts of the scientific community are still needed to allow the large-scale application of the technology. Indeed, based on the outstanding challenges observed, the investigation plan is developed including both experimental and numerical parts. All experiments were performed by means of the rapid compressionexpansion machine (RCEM) in the CMT-Motores Térmicos laboratory. The original cylinder head layout was modified to allow the housing of the prechamber itself, fuel injectors, spark plug, pressure transducers in both chamber, and a thermocouple. The test methodology involved the acquisition of the pressure evolution in both main chamber and pre-chamber, the piston position (used to compute the instantaneous cylinder volume), the duration of the auxiliary injection, and the spark ignition point. These are used as input for the zero-dimensional thermodynamic model which simulates the fundamental parameters aims to characterize the PCSI system working cycle. Therefore, a deeper knowledge of the mass interchanged process, induced turbulence field, heat release rate, combustion speed, and flame regime is generated. Subsequently, to calibrate the zero-dimensional model coefficients under motoring conditions, several 3D CFD simulations were carried out by means of Converge software. Hence, the results of the simulations in terms of interchanged mass and pre-chamber turbulent kinetic energy have been used to calibrate the nozzle discharge coefficient and the turbulence sub-model coefficients for all the pre-chamber geometries. Furthermore, the 3D CFD simulations outputs are analysed to fully understand the flow field structure and the local effect induced by the different nozzles at the spark activation time. The turbulent kinetic energy in terms of intensity and orientation is investigated over several relevant pre-chamber sections. The results reveal a clear relationship between the turbulence developed within the pre-chamber and the orifices structure. Straight orifices or perpendicular jets impact, promote more intense local turbulence due to direct collision while tilted orifices guarantee more homogeneity due to the swirling motion. Additionally, increase the orifice numbers shows benefits on the fluid dynamic homogeneity. Thus, preceding the experimental campaign several fundamental aspects of the system are evaluated. The cycle-to-cycle dispersion is explored by means of the statistical assessment showing low pressure peak deviation. The auxiliary injection pressure and timing are optimized for avoiding wall wetting phenomena while ensuring proper air/fuel mixing. Finally, the spark activation point is chosen as a function of the theoretically maximum turbulent flame speed. Thereby, the experimental campaign is carried out according to tests matrix, in order to evaluate the effect of the equivalence ratio of both chambers, and how the orifices diameter, number, and distribution affect the combustion process. Moreover, chemiluminescence visualization tests, performed by means of the available optical access of the RCEM, are combined with zerodimensional and 3D CFD results to shed light on the work cycle. Conclusions suggest a slightly rich mixture inside the pre-chamber combined with the highest number of tilted orifices as the better configuration for improving combustion efficiency under lean and ultra-lean main chamber mixture conditions. Nevertheless, axial orifices should be considered for further investigations. Finally, the author proposes a series of developments considered interesting in both the experimental and numerical fields. / [ES] En el presente trabajo se realiza la caracterización del proceso de combustión dentro de un sistema de encendido por pre-cámara bajo carga estratificada. Por lo tanto, se presenta una extensa revisión bibliográfica sobre los sistemas de pre-cámara desarrollados desde la segunda mitad del siglo XX hasta los tiempos modernos. El resumen muestra que los sistemas de última generación tienen el potencial de cumplir con los límites de las emisiones, al tiempo que proporcionan un alto rendimiento y un bajo consumo de combustible. No obstante, todavía se necesitan muchos esfuerzos de la comunidad científica para permitir la difusión a gran escala de la tecnología. De hecho, sobre la base de los desafíos abiertos observados, se desarrolla el plan de investigación incluyendo tanto una parte experimental como numérica. Todos los experimentos se realizan mediante la máquina de compresión-expansión rápida (RCEM) de que dispone el laboratorio CMT-Motores Térmicos . La disposición original de la culata se modificó para permitir el alojamiento de la propia pre-cámara, los inyectores , la bujía, los sensores de presión y un termopar. La metodología de ensayo implica la adquisición de la evolución de la presión tanto en cámara principal como en pre-cámara, el volumen del cilindro, la duración de la inyección auxiliar y el punto de ignición de la bujía. Estos se utilizan como parámetros de entrada para el modelo termodinámico cero-dimensional que devuelve los parámetros fundamentales que caracterizan ciclo de trabajo del sistema PCSI. Por lo tanto, se genera un conocimiento más profundo del proceso de intercambio de masas, del campo de turbulencias inducidas, de la tasa de liberación de calor, de la velocidad de combustión y del régimen de la llama. Posteriormente, para calibrar los coeficientes del modelo cero-dimensional bajo condiciones de arrastre, se llevaron a cabo varias simulaciones CFD en 3D mediante el software Converge. Por lo tanto, los resultados de las simulaciones en términos de masa intercambiada y energía cinética turbulenta de la precámara se han utilizado para calibrar el coeficiente de descarga de la tobera y los coeficientes del sub-modelo de turbulencia para todas las geometrías de la pre-cámara. Además, se analizan los resultados de las simulaciones CFD para comprender plenamente la estructura del campo de flujo y el efecto local inducido por las diferentes geometriás en el tiempo de activación de la chispa. La energía cinética turbulenta en términos de intensidad y orientación se investiga en varias secciones relevantes de la pre-cámara. Los resultados revelan una clara relación entre la turbulencia desarrollada dentro de la pre-cámara y la estructura de los orificios. Los orificios rectos o los chorros perpendiculares, promueven una turbulencia local más intensa debido a la colisión directa mientras que los orificios inclinados del campo fluido y del dosado. Precedentemente al desarrollo de la campaña experimental se evalúan varios aspectos fundamentales del sistema. La dispersión ciclo a ciclo se explora por medio de la evaluación estadística que muestra una baja desviación de los picos de presión. La presión y el punto de inyección auxiliar se optimizan para evitar los fenómenos de mojado de las paredes, asegurando al mismo tiempo una mezcla adecuada de aire/combustible. Finalmente, el punto de activación de la chispa se elige en función de la velocidad máxima teórica de la llama turbulenta. De este modo, la campaña experimental se lleva a cabo de acuerdo con la matriz de pruebas, con el fin de evaluar el efecto del dosado equivalente de ambas cámaras, y cómo el diámetro, el número y la distribución de los orificios afectan al proceso de combustión. Además, las pruebas de visualización de quimioluminiscencia, realizadas mediante el acceso óptico disponible de la RCEM, se combinan con resultados de CFD y resultados del modelo cerodimen para arrojar luz sobre el ciclo de trabajo. Las conclusiones sugieren que una mezcla ligeramente rica dentro de la pre-cámaracombinadaconelmayornúmerodeorificiosdesfasadoseslamejor configuración para garantizar un elevada eficiencia de la combustión en condiciones de mezcla pobre y ultra-pobre de la cámara principal. No obstante, los orificios axiales deben ser considerados para investigaciones futuras. Por último, el autor propone una serie de desarrollos considerados interesantes tanto en el campo experimental como en el numérico. / [CA] En el present treball es realitza la caracterització del procés de combustió dins d'un sistema d'encesa de pre-cambra soto càrrega estratifi-cada. Per tant, es presenta una extensa revisió bibliogràfica sobre els sistemes de precambra desenvolupats des de la segona meitat del segle XX fins als temps moderns. El resum mostra que els sistemes d'última generació tenen el potencial de complir amb els límits de les emissions, al mateix temps que proporcionen un alt rendiment i un baix consum de combustible. No obstant això, encara es necessiten molts esforços de la comunitat científica per a permetre la difusió a gran escala de la tecnologia. De fet, sobre la base dels desafiaments oberts observats, es desenvolupa el pla d'investigació incloent tant una part experimental com numèrica. Tots els experiments es realitzen mitjançant la màquina de compressió-expansió ràpida (RCEM) de què disposa el laboratori CMT-Motors Tèrmics. La disposició original de la culata es va modificar per a permetre l'allotjament de la pròpia pre-cambra, els injectors , la bugia, els sensors de pressió i un termoparell. La metodologia d'assaig implica l'adquisició de l'evolució de la pressió tant en cambra principal com en pre-cambra, el volum del cilindre, la duració de la injecció auxiliar i el punt d'ignició de l'espurna. Aquests s'utilitzen com a paràmetres d'entrada per al model termodinàic zero-dimensional que retorna els paràmetres fonamen-tals que caracteritzen cicle de treball del sistema PCSI. Per tant, es genera un coneixement més profund del procés d'intercanvi de masses, del camp de turbulències induïdes, de la taxa d'alliberament de calor, de la velocitat de combustió i del règim de la flama. Posteriorment, per a calibrar els coefi-cients del model zerodimensional sota condicions d'arrossegament, es van dur a terme diverses simulacions CFD en 3D mitjançant el programari Converge. Per tant, els resultats de les simulacions en termes de massa intercanviada i energia cinètica turbulenta de la pre-cambra s'han utilitzat per a calibrar el coeficient de descàrrega de la tovera i els coeficients del sub-model de turbulència per a totes les geometries de la pre-cambra. A més, s'analitzen els resultats de les simulacions CFD per a comprendre plenament l'estructura del camp de flux i l'efecte local induït per les diferents geometries en el temps d'activació de l'espurna. L'energia cinètica turbulenta en termes d'intensitat i orientació s'investiga en diverses seccions rellevants de la pre-cambra. Els resultats revelen una clara relació entre la turbulència desenvolupada dins de la pre-cambra i l'estructura dels orificis. Els orificis rectes o els dolls perpendiculars, promouen una turbulència local més intensa a causa de la col·lisió directa mentre que els orificis inclinats garanteixen una major homogeneïtat a causa de la generació d'un macro-remolì. A més, l'augment del nombre d'orificis mostra beneficis en l'homogeneïtat fluid-dinàmica. Llavors, abans de la campanya experimental s'avaluen diversos aspectes fonamentals del sistema. La dispersió cicle a cicle s'explora per mitjà de l'avaluació estadística que mostra una baixa desviació dels pics de pressió. La pressió i el punt d'injecció auxiliar s'optimitzen per a evitar els fenòmens de mullat de les parets, assegurant al mateix temps una mescla adequada d'aire/combustible. Finalment, el punt d'activació de l'espurna es tria en funció de la velocitat màxima teòrica de la flama turbulenta. D'aquesta manera, la campanya experimental es duu a terme d'acord amb la matriu de proves, amb la finalitat d'avaluar l'efecte del dosatge equivalent de totes dues cambres, i com el diàmetre, el numero i la distribució dels orificis afecten el procés de combustió. A més, les proves de visualització de quimioluminescència, realitzades mitjançant l’accés òptic disponible de la RCEM, es combinen amb resultats de CFD i resultats del model zero-dimensional per a llançar llum sobre el cicle de treball. Les conclusions suggereixen que una mescla lleugerament rica dins de la pre-cambra combinada amb el major nombre d’orificis desfasats és la millor configuració per a garantir un elevada eficiència de la combustió en condicions de mescla pobra i ultra-pobre de la cambra principal. No obstant això, els orificis axials han de ser considerats per a investigacions futures. Finalment, l’autor proposa una sèrie de desenvolupaments considerats interessants tant en el camp experimental com en el numèric. / Pagano, V. (2020). Analysis of a stratified pre-chamber spark ignition system under lean mixture conditions [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/152486

<div>A growing global population and improved standard of living in developing countries have resulted in an unprecedented increase in energy demand over the past several decades. While renewable energy sources are increasing, a huge portion of energy is still converted into useful work using heat engines. The combustion process in diesel and petrol engines releases carbon dioxide and other greenhouse gases as an unwanted side-effect of the energy conversion process. By improving the efficiency of internal combustion engines, more chemical energy stored in petroleum resources can be realized as useful work and, therefore, reduce global emissions of greenhouse gases. This research focused on improving the thermal efficiency of opposed-piston engines, which, unlike traditional reciprocating engines, do not use a cylinder head. The cylinder head is a major source of heat loss in reciprocating engines. Therefore, the opposed-piston engine has the potential to improve overall engine efficiency relative to inline or V-configuration engines.</div><div><br></div>The objective of this research project was to further improve the design of opposed-piston engines by using computational fluid dynamics (CFD) modeling to optimize the engine geometry. The CFD method investigated the effect of intake port geometry and exhaust piston lead angle on the scavenging process and in-cylinder turbulence. After the CFD data was analyzed, scavenging efficiency was found insensitive to transfer port geometry and exhaust piston lead angle with a maximum change of 0.61%. Trapping efficiency was altered exclusively by exhaust piston lead angle and changed from 18% to 26% as the lead angle was increased. The in-cylinder turbulence parameters of the engine (normalized swirl circulation, normalized tumble circulation, and normalized TKE) experienced more complex relationships. All turbulence parameters were sensitive to changing transfer port geometry and exhaust piston lead angle. Some examples of trends seen during the analysis include: an increase in normalized swirl circulation from 0.01 to 4.45 due to changes in swirl angle, a change in normalized tumble circulation from -28.52 to 21.11 as swirl angle increased, and an increase in normalized tumble circulation from 14.20 to 33.68 as exhaust piston lead angle was increased. Based on the present work, an optimum configuration was identified for a swirl angle of 15°, a tilt angle of 10°, and an exhaust piston lead angle of 20°. Future work includes expanding the numerical model’s domain to support a complete cylinder-port configuration, adding combustion products to the diffusivity equation in the UDF, and running additional test cases to describe the entire input space for the sensitivity analysis.<br>

No description available.