A new numerical strategy with space-time adaptivity and error control for multi-scale streamer discharge simulations

This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma discharges, considering drift-diffusion equations and the computation of electric field. The proposed numerical method provides a time-space accuracy control of the solution, and thus, an effective accurate resolution independent of the fastest physical time scale. An important improvement of the computational efficiency is achieved whenever the required time steps go beyond standard stability constraints associated with mesh size or source time scales for the resolution of the drift-diffusion equations, whereas the stability constraint related to the dielectric relaxation time scale is respected but with a second order precision. Numerical illustrations show that the strategy can be efficiently applied to simulate the propagation of highly nonlinear ionizing waves as streamer discharges, as well as highly multi-scale nanosecond repetitively pulsed discharges, describing consistently a broad spectrum of space and time scales as well as different physical scenarios for consecutive discharge/post-discharge phases, out of reach of standard non-adaptive methods.Comment: Support of Ecole Centrale Paris is gratefully acknowledged for several month stay of Z. Bonaventura at Laboratory EM2C as visiting Professor. Authors express special thanks to Christian Tenaud (LIMSI-CNRS) for providing the basis of the multiresolution kernel of MR CHORUS, code developed for compressible Navier-Stokes equations (D\'eclaration d'Invention DI 03760-01). Accepted for publication; Journal of Computational Physics (2011) 1-2

The physics of streamer discharge phenomena

In this review we describe a transient type of gas discharge which is commonly called a streamer discharge, as well as a few related phenomena in pulsed discharges. Streamers are propagating ionization fronts with self-organized field enhancement at their tips that can appear in gases at (or close to) atmospheric pressure. They are the precursors of other discharges like sparks and lightning, but they also occur in for example corona reactors or plasma jets which are used for a variety of plasma chemical purposes. When enough space is available, streamers can also form at much lower pressures, like in the case of sprite discharges high up in the atmosphere. We explain the structure and basic underlying physics of streamer discharges, and how they scale with gas density. We discuss the chemistry and applications of streamers, and describe their two main stages in detail: inception and propagation. We also look at some other topics, like interaction with flow and heat, related pulsed discharges, and electron runaway and high energy radiation. Finally, we discuss streamer simulations and diagnostics in quite some detail. This review is written with two purposes in mind: First, we describe recent results on the physics of streamer discharges, with a focus on the work performed in our groups. We also describe recent developments in diagnostics and simulations of streamers. Second, we provide background information on the above-mentioned aspects of streamers. This review can therefore be used as a tutorial by researchers starting to work in the field of streamer physics.Comment: 89 pages, 29 figure

On the propagation and multiple reflections of a blast wave travelling through a dusty gas in a closed box

This paper concerns the propagation of shock waves in an enclosure filled with dusty gas. The main motivation for this problem is to probe the effect on such dynamics of solid particles dispersed in the fluid medium. This subject, which has attracted so much attention over recent years given its important implications in the study of the structural stability of systems exposed to high-energy internal detonations, is approached here in the framework of a hybrid numerical two-way coupled Eulerian-Lagrangian methodology. In particular, insights are sought by considering a relatively simple archetypal setting corresponding to a shock wave originating from a small spherical region initialized on the basis of available analytic solutions. The response of the system is explored numerically with respect to several parameters, including the blast intensity (via the related value of the initial shock Mach number), the solid mass fraction (mass load), and the particle size (Stokes number). Results are presented in terms of pressure-load diagrams. Beyond practical applications, it is shown that a kaleidoscope of fascinating patterns is produced by the “triadic” relationships among multiple shock reflections events and particle-fluid and particle-wall interaction dynamics. These would be of great interest to researchers and scientists interested in fundamental problems relating to the general theory of pattern formation in complex nonlinear multiphase systems

An acoustic view of ocean mixing

Knowledge of the parameter K (turbulent diffusivity/"mixing intensity") is a key to understand transport processes of matter and energy in the ocean. Especially the almost vertical component of K across the ocean stratification (diapycnal diffusivity) is vital for research on biogeochemical cycles or greenhouse gas budgets. Recent boost in precision of water velocity data that can be obtained from vessel-mounted acoustic instruments (vmADCP) allows identifying ocean regions of elevated diapycnal diffusivity during research cruises - in high horizontal resolution and without extra ship time needed. This contribution relates acoustic data from two cruises in the Tropical North East Atlantic Oxygen Minimum Zone to simultaneous field observations of diapycnal diffusivity: pointwise measurements by a microstructure profiler as well as one integrative value from a large scale Tracer Release Experiment

The physics of streamer discharge phenomena

In this review we describe a transient type of gas discharge which is commonly called a streamer discharge, as well as a few related phenomena in pulsed discharges. Streamers are propagating ionization fronts with self-organized field enhancement at their tips that can appear in gases at (or close to) atmospheric pressure. They are the precursors of other discharges like sparks and lightning, but they also occur in for example corona reactors or plasma jets which are used for a variety of plasma chemical purposes. When enough space is available, streamers can also form at much lower pressures, like in the case of sprite discharges high up in the atmosphere. We explain the structure and basic underlying physics of streamer discharges, and how they scale with gas density. We discuss the chemistry and applications of streamers, and describe their two main stages in detail: inception and propagation. We also look at some other topics, like interaction with flow and heat, related pulsed discharges, and electron runaway and high energy radiation. Finally, we discuss streamer simulations and diagnostics in quite some detail. This review is written with two purposes in mind: First, we describe recent results on the physics of streamer discharges, with a focus on the work performed in our groups. We also describe recent developments in diagnostics and simulations of streamers. Second, we provide background information on the above-mentioned aspects of streamers. This review can therefore be used as a tutorial by researchers starting to work in the field of streamer physics

Application of Uncertainty Quantification techniques to CFD simulation of twin entry radial turbines

L'argomento principale della tesi \ue8 l'applicazione delle tecniche di quantificazione dell'incertezza (UQ) alla simulazione numerica (CFD) di turbine radiali twin entry impiegate nella turbosovralimentazione automobilistica. Lo studio approfondito di questo tipo di turbomacchine \ue8 affrontato nel capitolo 3, finalizzato alla comprensione dei principali parametri che caratterizzano e influenzano le prestazioni fluidodinamiche delle turbine twin scroll. Il capitolo 4 tratta di una piattaforma per l'analisi UQ sviluppata internamente tramite il set di strumenti open source \u2018Dakota\u2019. La piattaforma \ue8 stata testata dapprima su un caso di interesse industriale, ovvero un ugello de Laval supersonico (capitolo 5); l'analisi ha evidenziato l'utilizzo pratico delle tecniche di quantificazione dell'incertezza nella previsione delle prestazioni di un ugello affetto da condizioni di fuori progetto con complessit\ue0 fluidodinamica dovuta alla forte non linearit\ue0. L'esperienza maturata con l'approccio UQ ha agevolato l'identificazione di metodi idonei per applicare la propagazione dell\u2019incertezza alla simulazione CFD di turbine radiali twin scroll (capitolo 6). In tal caso sono state studiate e messe in pratica diverse tecniche di quantificazione dell'incertezza al fine di acquisire un'esperienza approfondita sull\u2019attuale stato dell'arte. Il confronto dei risultati ottenuti dai diversi approcci e la discussione dei pro e dei contro relativi a ciascuna tecnica hanno portato a conclusioni interessanti, che vengono proposte come linee guida per future applicazioni di quantificazione dell\u2019incertezza alla simulazione CFD delle turbine radiali. L'integrazione di modelli e metodologie UQ, oggi utilizzati solo da alcuni centri di ricerca accademica, con solutori CFD commerciali consolidati ha permesso di raggiungere l'obiettivo finale della tesi di dottorato: dimostrare all'industria l'elevato potenziale delle tecniche UQ nel migliorare, attraverso distribuzioni di probabilit\ue0, la previsione delle prestazioni relative ad un componente soggetto a diverse fonti di incertezza. Lo scopo dell\u2019attivit\ue0 di ricerca consiste pertanto nel fornire ai progettisti dati prestazionali associati a margini di incertezza che consentano di correlare meglio simulazione e applicazione reale. Per accordi di riservatezza, i parametri geometrici relativi alla turbina twin entry in oggetto sono forniti adimensionali, i dati sensibili sugli assi dei grafici sono stati omessi e nelle figure si \ue8 reso necessario eliminare le legende dei contours ed ogni eventuale riferimento dimensionale.The main topic of the thesis is the application of uncertainty quantification (UQ) techniques to the numerical simulation (CFD) of twin entry radial turbines used in automotive turbocharging. The detailed study of this type of turbomachinery is addressed in chapter 3, aimed at understanding the main parameters which characterize and influence the fluid dynamic performance of twin scroll turbines. Chapter 4 deals with the development of an in-house platform for UQ analysis through \u2018Dakota\u2019 open source toolset. The platform was first tested on a test case of industrial interest, i.e. a supersonic de Laval nozzle (chapter 5); the analysis highlighted the practical use of uncertainty quantification techniques in predicting the performance of a nozzle affected by off-design conditions with fluid dynamic complexity due to strong non-linearity. The experience gained with the UQ approach facilitated the identification of suitable methods for applying the uncertainty propagation to the CFD simulation of twin entry radial turbines (chapter 6). In this case different uncertainty quantification techniques have been investigated and put into practice in order to acquire in-depth experience on the current state of the art. The comparison of the results coming from the different approaches and the discussion of the pros and cons related to each technique led to interesting conclusions, which are proposed as guidelines for future uncertainty quantification applications to the CFD simulation of radial turbines. The integration of UQ models and methodologies, today used only by some academic research centers, with well established commercial CFD solvers allowed to achieve the final goal of the doctoral thesis: to demonstrate to industry the high potential of UQ techniques in improving, through probability distributions, the prediction of the performance relating to a component subject to different sources of uncertainty. The purpose of the research activity is therefore to provide designers with performance data associated with margins of uncertainty that allow to better correlate simulation and real application. Due to confidentiality agreements, geometrical parameters concerning the studied twin entry radial turbine are provided dimensionless, confidential data on axes of graphs are omitted and legends of the contours as well as any dimensional reference have been shadowed

Small business innovation research. Abstracts of completed 1987 phase 1 projects

Non-proprietary summaries of Phase 1 Small Business Innovation Research (SBIR) projects supported by NASA in the 1987 program year are given. Work in the areas of aeronautical propulsion, aerodynamics, acoustics, aircraft systems, materials and structures, teleoperators and robotics, computer sciences, information systems, spacecraft systems, spacecraft power supplies, spacecraft propulsion, bioastronautics, satellite communication, and space processing are covered

Analysis and development of numerical methodologies for simulation of flow control with dielectric barrier discharge actuators

The aim of this thesis is to investigate and develop different numerical methodologies for modeling the Dielectric Barrier discharge (DBD) plasma actuators for flow control purposes. Two different modeling approaches were considered; one based on Plasma-fluid model and the other based on a phenomenological model. A three component Plasma fluid model based on the transport equations of charged particles was implemented in this thesis in OpenFOAM, using several techniques to reduce the numerical issues. The coupled plasma-fluid problem involves wide range of length and time scales which make the numerical simulation difficult. Therefore, to obtain stable and accurate results in a reasonable computational run time, several numerical procedures were implemented including: semi-implicit treatment of coupling of Poisson equation and charge density equation, super-time-stepping and operator splitting algorithm. We examined our code for a constant positive voltage, testing for the dependency of the behavior of the current density to the selected numerical scheme. In addition, although there is no clear numerical or experimental benchmark case for DBD plasma actuator problem, the developed plasma solver was compared quantitively and qualitively with several numerical works in the literature. Afterward, the developed numerical methodology was used to explore the possibility of influencing the flow, with higher speed, using nano-second (NS) pulsed DBD plasma actuator. Therefore, the interaction of the transonic flow and actuation effects of DBD plasma actuator with nano second pulsed voltage was simulated. The effect of gas heating and body force was calculated by the plasma solver and was supplied into the gas dynamic solver for simulating the flow field. Moreover, the results of the plasma fluid model were used to develop an energy deposition model. It was shown that the energy deposition model is able to capture the main features of the effect of NS DBD plasma actuators correctly, with less computational time. It was also shown that fast energy transfer, from plasma to fluid, leads to the formation of micro-shock waves that modify locally the features of the transonic flow. Although the numerical efficiency of the plasma fluid model was improved, the computational cost of simulating the effect of DBD plasma actuator on a real scale flow situation was still high. Therefore, a simple model for plasma discharge and its effect on the flow was developed based on scaling of the thrust generated by DBD plasma actuators. The scaled thrust model correctly predicts the nonlinear dependency of the thrust produced and the applied voltage. These scales were then introduced into a simple phenomenological model to estimate and simulate the body force distribution generated by the plasma actuator. Although the model includes some experimental correlations, it does not need any fitting parameter. The model was validated with experimental results and showed better accuracy compared to previous plasma models. Using a simple phenomenological model that was developed here, a numerical study was conducted to investigate and compare the effect of steady and unsteady actuation for controlling the flow at relatively high Reynolds number. Firstly it was shown that the size of the time-averaged separation bubble is greatly reduced and the flow structure is sensitive to the frequency of burst modulation of DBD plasma actuators. The results also confirmed that in the case of unsteady actuation, the burst frequency and burst ratio are crucial parameters for influencing the capability of the actuators to control the flow. It was found that burst frequencies near the natural frequencies of the system were able to excite the flow structure in a resonance mode. This observation also confirmed that with proper frequencies of excitation, the flow structure can be well rearranged and the flow losses can be reduced. In the end, Plasma actuators were used for controlling the flow over the Coanda surface of the ACHEON nozzle. When the plasma actuator was used, it was possible to postpone separation of the flow and increase the deflection angle of the exit jet of the nozzle. To find the optimum position of the actuators, seven DBD actuators in forward forcing mode were placed over the Coanda surface considering the numerically obtained separation points. Results show that when the actuator is placed slightly before the separation point, enhanced thrust vectorizing with the use of DBD actuator is achievable. Preliminary results of the experiments agree with planned/foreseen deflection angle obtained from numerical computation.O objetivo deste trabalho visa a investigação e desenvolvimento de diferentes métodos numéricos para modelação de actuadores a plasma de Descarga em Barreira Dieléctrica, (DBD), tendo em vista o controlo do escoamento na camada limite. Esta modelação numérica foi abordada de duas formas diferentes, uma baseada num modelo de “plasma-fluid” e outra fundamentada num modelo fenomenológico. Neste trabalho é usado um modelo “plasma-fluid” de três componentes que é baseado numa equação de transporte para as partículas electricamente carregadas. Este foi implementado no software OpenFOAM fazendo uso de diversas técnicas para minimização de problemas numéricos que ocorriam na resolução das equações. O cálculo de um problema com acoplamento entre plasma e fluido envolve uma gama diversa de escalas, tanto temporais como dimensionais, trata-se então de uma simulação numérica delicada. Como tal, e por forma a obter resultados estáveis e precisos num tempo de cálculo considerado razoável, foram implementados diversos procedimentos numéricos, tais como o tratamento semiimplícito do acoplamento da equação de Poisson com a equação da densidade de carga, o super-passo-tempo e ainda um algoritmo do tipo divisão de operador. Foi considerado o caso de uma diferença de potencial positiva, constante, e testada a dependência da densidade de corrente com os diferentes esquemas numéricos. Apesar de não existir atualmente uma base de dados, de tipo numérica ou experimental, com casos de teste para actuadores a plasma tipo DBD, o modelo computacional desenvolvido para calcular o plasma foi validado qualitativamente, bem como quantitativamente, usando os vários trabalhos numéricos disponíveis na literatura. Após esta validação inicial, a metodologia numérica desenvolvida foi utilizada para explorar a possibilidade de influenciar um escoamento de maior velocidade, através de actuadores a plasma tipo DBD com impulsos de tensão da ordem de nano-segundos (NS). Desta forma foi simulada a interacção entre um escoamento transónico e o efeito dos actuadores a plasma tipo DBD sobre o escoamento, usando pulsos de nano-segundos. O efeito térmico do gás, assim como a força resultante, foram calculados usando o modelo numérico para cálculo de plasmas desenvolvido neste trabalho. O resultado obtido é acoplado ao modelo de cálculo para a dinâmica de gases, o que torna possível simular as condições do escoamento resultante. Adicionalmente, os resultados do modelo de “plasma-fluid” foram reaproveitados para desenvolver um modelo de deposição de energia. Este demonstrou ter a capacidade de capturar correctamente as características principais do efeito de actuadores de plasma, de tipo NS-DBD, com um tempo de computação menor. Foi demonstrada que uma rápida transferência de energia, do plasma para o fluido, leva à formação de micro-ondas de choque que alteram localmente as características do escoamento transónico. Apesar da eficiência numérica do modelo de “plasma-fluid” ter sido melhorada, o seu custo computacional para a simulação de actuadores a plasma tipo DBD à escala real continua bastante elevado. Neste sentido, a partir de uma escala de propulsão gerada pelo actuador plasma DBD, foi desenvolvido um modelo mais simples para a descarga do plasma e para determinar os seus efeitos sobre o escoamento. O modelo inicial previa correctamente uma dependência não-linear entre a força propulsiva gerada e a diferença de potencial aplicada. Estas escalas foram então introduzidas num modelo fenomenológico mais simples para estimar, e simular, a distribuição de forças geradas pelo actuador a plasma. Apesar de o modelo incluir algumas correlações experimentais, este não requer qualquer parâmetro de afinação. O modelo foi validado com resultados experimentais, demonstrando melhores resultados quando comparado com outros modelos de plasma . Utilizando um modelo fenomenológico simplificado, que foi desenvolvido no presente trabalho, foi feito um estudo numérico com o objetivo de investigar, e comparar, os efeitos que uma actuação estacionária e não-estacionária exibe sobre o controlo do escoamento a números de Reynolds relativamente elevados. Foi demostrado que a dimensão da bolha de separação é reduzida em muito e que a estrutura do escoamento é sensível à frequência da modulação “burst” do actuador a plasma tipo DBD. Os resultados também confirmaram que, para o caso de actuação não-estacionária, a frequência de “burst” e o “burst ratio”, são parâmetros cruciais para influenciar a capacidade de controlo do escoamento por parte dos actuadores a plasma. Determinou-se que as frequências “burst”, semelhantes às frequências naturais do sistema, são capazes de excitar as estruturas do escoamento num modo de ressonância. Esta observação confirma igualmente que, com frequências de excitação apropriadas, a estrutura de um escoamento de camada limite consegue ser correctamente modificada, e que as perdas no escoamento são reduzidas. Por fim, os actuadores a plasma foram utilizados para o controlo do escoamento sobre uma superfície Coanda de uma tubeira. Quando nesta foi aplicado um plasma, tornou-se possível retardar a separação do escoamento e aumentar o ângulo de deflexão do jacto gerado pelo propulsor. Por forma a encontrar a posição óptima para os actuadores, sete actuadores de tipo DBD foram distribuídos ao longo da superfície Coanda, tendo em consideração os pontos de separação do escoamento na camada limite obtidos numericamente. Os resultados mostram que quando o actuador DBD é colocado ligeiramente antes do ponto de separação do escoamento, há um aumento da capacidade de controlo e vectorização do jacto gerado. Os resultados preliminares das experiências efectuadas estão de acordo com o ângulo de deflexão do jacto previsto pelo modelo computacional