Dissertations / Theses on the topic 'K-epsilon turbulence model'

Le fonctionnement à l'équilibre du réacteur à fusion de prochaine génération, ITER, nécessitera le développement d'outils numériques fiables permettant d'estimer les paramètres d'ingénierie clés à un coût de calcul raisonnable. Les codes de transport répondent à cette exigence car ils reposent sur des équations fluides bidimensionnelles qui sont moyennées sur les fluctuations temporelles, de la même manière que les modèles « Reynolds Averaged Navier-Stokes » couramment utilisés dans la communauté des fluides neutres. De plus, les codes de transport peuvent rassembler la plupart des ingrédients physiques régissant le comportement du plasma de bord, ainsi que une topologie magnétique réaliste et la géométrie du mur. Cependant, leur prévisibilité est limitée par une description inadéquate des flux turbulents perpendiculaires aux lignes de champ magnétique, qui influent fortement e confinement du plasma sur de longues périodes. En effet les flux perpendiculaires, supposés diffusifs, sont grossièrement déterminés par des coefficients de diffusion homogènes ou "ad-hoc", ou par des procédures à boucle de rétroaction appliquées "a-posteriori" à des données expérimentales. Motivés par ces questions, nous présentons dans ce travail un nouveau modèle pour estimer de manière cohérente la distribution des flux perpendiculaires dans les codes de transport, lorsque les plasmas en régime permanent sont concernés. La stratégie consiste à introduire des outils numériques efficaces largement utilisés dans la communauté de la turbulence neutre en physique des plasmas. Deux concepts clés sont inspirants dans la communauté des fluides neutres. Le premier est "l'hypothèse de Boussinesq". Elle consiste à linéariser le tenseur de contraintes de Reynolds dansl'équation de Navier-Stokes moyennée dans le temps via une relation de diffusion dans laquelle le terme de proportionnalité est appelé « eddy viscosity ». Le deuxième concept est le modèle "k-epsilon", dans lequel les équations de transport pour l'énergie turbulente cinétique moyenne et le taux d'échange d'énergie entre les structures turbulentes sont conçues de manière semi-empirique. A l'équilibre, k et epsilon permettent une estimation auto-cohérente de l’« eddy viscosity », intégrant ainsi l'impact de la turbulence sur les flux moyennés à l'état d'équilibre. Ces concepts ne peuvent pas être appliqués directement pour enrichir la modélisation des flux perpendiculaires dans les plasmas en raison de différentes propriétés de turbulence. Par conséquent, nous suggérons une adaptation du modèle k-epsilon pour les flux neutres à des plasmas à confinement magnétique, où deux équations de transport pour l’énergie cinétique turbulente et son taux de dissipation sont dérivées algébriquement, y compris la physique de l’instabilité d’interchange linéaire, responsable de la distribution "ballonnée" du transport perpendiculaire dans le bord du plasma. Différentes approches sont décrites pour fermer les paramètres libres : premièrement, une procédure de boucle de rétroaction pour optimiser les résultats numériques comparés avec un test expérimental. Ensuite, on assume une loi d'échelle de référence pour la largeur du profil de flux de chaleur dans la SOL, déterminée empiriquement à partir des mesures expérimentales du flux de chaleur sur le divertor externe dans diverses machines. Le nouveau modèle est intégré au package de transport SolEdge2D-EIRENE, développé en collaboration entre le CEA et le laboratoire M2P2 de l'Université d'Aix-Marseille. Les résultats numériques à l’état d’équilibre sont discutés et on démontre qu’ils se comparent favorablement aux données expérimentales soit à l'outer midplane que au divertor externe. De plus, on montre que les distributions de diffusivité présentent des asymétries poloïdales cohérentes avec la distribution "ballonnée" du transport perpendiculaire observée dans les mêmes conditions dans les codes de premier principe et les expériences
Steady-state operations of the next-generation fusion device ITER will require the development of reliable numerical tools to estimate key engineering parameters suitable for technological constraints at reasonable computational cost.So-called transport codes fulfil this requirement since they rely on 2D fluid equations averaged over time fluctuations, similarly to Reynolds Averaged Navier-Stokes models commonly used for engineering applications in the neutral fluid community. Furthermore, transport codes can gather most of the physical ingredients ruling the edge plasma behaviour, as well as realistic magnetic topology and wall geometry. However, their predictability is limited by a crude description of turbulent fluxes perpendicular to the magnetic field lines. In the plasma community, a special concern is devoted to acquire a detailed understanding of these fluxes, since they strongly impact on the power extraction and the confinement of plasma over extended periods of time. In transport codes though, turbulent fluxes, which are assumed diffusive, are crudely determined by either homogeneous, or ad-hoc diffusive coefficients, or feedback-loop procedures applied a-posteriori on experimental data.Motivated by these issues, in this work we introduce step-by-step a new approach with the aim to self-consistently estimate the distribution of turbulent fluxes in transport codes, when steady-state plasmas are concerned. The underlying strategy is inspired by the work done from the 60’s in neutral turbulence and adapted here to plasma for fusion applications.The first key concept is the Boussinesq assumption. It consists in assuming a colinearity between the Reynolds stress tensor - which represents the contribution of turbulence to the mean flow - and the mean rate of strain tensor - expressed by the gradient of the mean velocity through a coefficient: the so-called eddy-viscosity. The second concept is to express this new eddy viscosity coefficient as a function of characteristic turbulence quantities. We have focused here on the most popular in Computational Fluid Dynamics, the κ-ε model, where transport equations for the averaged kinetic turbulent energy and the turbulence dissipation rate are designed semi-empirically. Steady-state κ and ε allow for a self-consistent estimation of the eddy-viscosity coefficient, thus including the impact of turbulence in steady-state mean flows. We propose a κ-ε -like model where two transport equations for turbulent kinetic energy and its dissipation rate are derived algebraically, including the physics of the linear interchange instability. For the numerical implementation, we exploit the flexibility of the transport package SolEdge2D-EIRENE, developed for many years through the collaboration of the IRFM at the CEA and the laboratory M2P2 at Aix-Marseille University.Since the new model is semi-empirical, it presents some free parameters to be closed. In this work, we have proposed different approaches. In particular, in order to increase the predictive capabilities of the model, a reference scaling law for the width of the heat-flux profile in the scrape-off layer has been assumed, empirically determined from the experimental measurements of the outer target heat load in various machines. The new model is integrated in SolEdge2D-EIRENE for simulations with diverted plasma in TCV and WEST-like geometries, for L-mode discharges. Steady-state results are discussed and shown to favourably compare with experimental data at both the outer mid-plane and the outer divertor. Moreover, self-consistent distributions of diffusivities are shown to exhibit poloidal asymmetries consistently with the ballooned distribution of cross-field transport due to the interchange instability and observed at the same conditions in both first-principle codes and experiments

La modélisation dite "bi-couche" est un concept relativement nouveau. Elle consiste à scinder l'écoulement turbulent en deux couches et à modéliser la zone près de la paroi à l'aide d'un modèle simplifié ; par ailleurs, on utilise un modèle d'ordre élevé pour la zone externe. Cette approche, déjà expérimentée en convection forcée, prédit une meilleure physique de l'écoulement pariétal, mais permet aussi une réduction considérable de l'effort de calcul. Nous nous efforçons dans ce travail à développer d'avantage ce concept. Notre contribution sur l'analyse de la couche limite en convection natuelle se base sur les résultats récents des DNS des écoulements dans un canal ainsi que sur l'expérience de la couche limite sur une paroi verticale. Un modèle simplifié de la turbulence en zone pariétale est ainsi mise au point. Par la suite, le modèle développé est combiné avec un modèle de type k-ε bas-Reynolds dans une approche "bi-couche" pour la simulation de diverses configurations simples
A two-layer modeling is a relatively new concept. It consists of divinding the turbulent flow into two regions so as to model the near wall zone using a simplified model whereas the bulk flow could be modelled using any high order modelling. This concept, already tested in forced convection, predicts better physics of near wall flow but allows also a substantial reduction in calculation effort. This work aims to develop this concept. The contribution in the analysis of boundary layer of natual convection flow is based on recent results of several DNS of flow in a channel along with measures performed for boundary layer developing on heated vertical wall. A simplified model is thus adjusted and combined with k-epsilon to simulate various and simple configurations

For turbulent flow calculations, some of the well-known turbulence models in the literature are applied on a previously developed Navier-Stokes solver designed to handle laminar flows. A finite volume formulation, which is cell-based for inviscid terms and cell-vertex for viscous terms, is used for numerical discretization of the Navier-Stokes equations in conservative form. This formulation is combined with one-step, explicit time marching Lax-Wendroff numerical scheme that is second order accurate in space. To minimize non-physical oscillations resulting from the numerical scheme, second and fourth order artificial smoothing terms are added. To increase the convergence rate of the solver, local time stepping technique is applied. Before applying turbulence models, Navier-Stokes solver is tested for a case of subsonic, laminar flow over a flat plate. The results are in close agreement with Blasius similarity solutions. To calculate turbulent flows, Boussinesq eddy-viscosity approach is utilized. The eddy viscosity (also called turbulent viscosity), which arises as a consequence of this approach, is calculated using Cebeci-Smith, Michel et. al., Baldwin-Lomax, Chien&rsquo
s k-epsilon and Wilcox&rsquo
s k-omega turbulence models. To evaluate the performances of these turbulence models and to compare them with each other, the solver has been tested for a case of subsonic, laminar - transition fixed - turbulent flow over a flat plate. The results are verified by analytical solutions and empirical correlations.

This dissertation focuses on aerosol transport modeling in occupational environments and mining sites in Arizona using computational fluid dynamics (CFD). The impacts of human exposure in both environments are explored with the emphasis on turbulence, wind speed, wind direction and particle sizes. Final emissions simulations involved the digitalization process of available elevation contour plots of one of the mining sites to account for realistic topographical features. The digital elevation map (DEM) of one of the sites was imported to COMSOL MULTIPHYSICS® for subsequent turbulence and particle simulations. Simulation results that include realistic topography show considerable deviations of wind direction. Inter-element correlation results using metal and metalloid size resolved concentration data using a Micro-Orifice Uniform Deposit Impactor (MOUDI) under given wind speeds and directions provided guidance on groups of metals that coexist throughout mining activities. Groups between Fe-Mg, Cr-Fe, Al-Sc, Sc-Fe, and Mg-Al are strongly correlated for unrestricted wind directions and speeds, suggesting that the source may be of soil origin (e.g. ore and tailings); also, groups of elements where Cu is present, in the coarse fraction range, may come from mechanical action mining activities and saltation phenomenon. Besides, MOUDI data under low wind speeds (<2 m/s) and at night showed a strong correlation for particles 1-micrometer in diameter between the groups: Sc-Be-Mg, Cr-Al, Cu-Mn, Cd-Pb-Be, Cd-Cr, Cu-Pb, Pb-Cd, As-Cd-Pb. The As-Cd-Pb group correlates strongly in almost all ranges of particle sizes. When restricted low wind speeds were imposed more groups of elements are evident and this may be justified with the fact that at lower speeds particles are more likely to settle. When linking these results with CFD simulations and Pb-isotope results it is concluded that the source of elements found in association with Pb in the fine fraction come from the ore that is subsequently processed in the smelter site, whereas the source of elements associated to Pb in the coarse fraction is of different origin. CFD simulation results will not only provide realistic and quantifiable information in terms of potential deleterious effects, but also that the application of CFD represents an important contribution to actual dispersion modeling studies; therefore, Computational Fluid Dynamics can be used as a source apportionment tool to identify areas that have an effect over specific sampling points and susceptible regions under certain meteorological conditions, and these conclusions can be supported with inter-element correlation matrices and lead isotope analysis, especially since there is limited access to the mining sites. Additional results concluded that grid adaption is a powerful tool that allows to refine specific regions that require lots of detail and therefore better resolve flow detail, provides higher number of locations with monotonic convergence than the manual grids, and requires the least computational effort. CFD simulations were approached using the k-epsilon model, with the aid of computer aided engineering software: ANSYS® and COMSOL MULTIPHYSICS®. The success of aerosol transport simulations depends on a good simulation of the turbulent flow. A lot of attention was placed on investigating and choosing the best models in terms of convergence, independence and computational effort. This dissertation also includes preliminary studies of transient discrete phase, eulerian and species transport modeling, importance of saltation of particles, information on CFD methods, and strategies for future directions that should be taken.

Uma parte significativa dos escoamentos encontrados em aplicações tecnológicas é caracterizada por envolver altos números de Reynolds, principalmente aqueles em regime turbulento e com superfície livre. Obter soluções numéricas representativas para essa classe de problemas é extremamente difícil, devido à natureza não-linear das equações diferenciais parciais envolvidas nos modelos. Conseqüentemente, o tema tem sido uma das principais preocupações da comunidade científica moderna em dinâmica de fluidos computacional. Aproximações de primeira ordem para os termos convectivos são as mais adequadas para amortecer oscilações que estão associadas às aproximações de alta ordem não-limitadas. Todavia, elas introduzem dissipação artificial nas representações discretas comprometendo os resultados numéricos. Para minimizar esse efeito não-físico e, ao mesmo tempo, conseguir aproximações incondicionalmente estáveis, é indispensável adotar uma estratégia que combine aproximações de primeira ordem com as de ordem mais alta e que leve em conta a propagação de informações físicas. Os resultados dessa composição são os esquemas "upwind" limitados de alta ordem. Em geral, espera-se que esses esquemas sejam apropriados para a representação das derivadas convectivas nos modelos de turbulência kappa-varepsilon. No contexto de diferenças finitas, a presente tese dedica-se à solução numérica das equações de Navier-Stokes no regime de números de Reynolds elevados. Em particular, ela contém uma análise de algoritmos monotônicos e antidifusivos e modelos de turbulência kappa-varepsilon para a simulação de escoamentos incompressíveis envolvendo superfícies livres. Esquemas de convecção são implementados nos códigos GENSMAC para proporcionar um tratamento robusto dos termos convectivos nas equações de transporte. Duas versões do modelo kappa-varepsilon de turbulência são implementadas nos códigos GENSMAC, para problems bidimensionais e com simetria radial, para descrever os efeitos da turbulência sobre o escoamento médio. Resultados numéricos de escoamentos com simetria radial são comparados com resultados experimentais e analíticos. Simulações numéricas de problemas tridimensionais complexos são apresentadas para avaliar o desempenho de esquemas "upwind". Finalmente, os modelos de turbulência kappa-varepsilon são utilizados para a simulação de escoamentos confinados e com superfícies livres.
A considerable part of fluid flows encountered in technological applications is characterised by involving high-Reynolds numbers, especially those in turbulent regime and with free-surface. It is extremely difficult to obtain representative numerical solutions for this class of problems, due to the non-linear nature of the partial differential equations involved in the models. Consequently, this subject has been one of main concerns in the modern computational fluid dynamics community. First-order approximation to the convective terms is one of the most appropriate to smooth out oscilations/instabilities which are associated with high-order unlimited approximation. However, it introduces numerical dissipation in the discrete representation jeopardizing the numerical results. In order to minimize this non-physical effect and, at the same time, to obtain unconditionally stable approximation, it is essential to adopt a strategy that combines first and high-order approximations and takes into account the propagation of physical information. The results of this composition are the high-order bounded upwind techniques. In general, it is expected that these algorithms are satisfactory for the representation of the convective derivatives in the kappa-varepsilon turbulence model. In the context of finite-difference, the present thesis deals with the numerical solution of the Navier-Stokes equations at high-Reynolds number regimes. In particular, it contains an analysis of monotonic and anti-difusive convection schemes and kappa-varepsilon turbulence models for the simulation of free-surface fluid flows. Upwinding methods are implemented into the GENSMAC codes to provide a robust treatment of the convective terms in the transport equations. Two versions of the K-Epsilon turbulence model are implemented into the two-dimensional and axisymmetric GENSMAC codes, in order to describe the turbulent effects on the average flow. Numerical results of axisymmetric flows are compared with experimental and analytical results. Numerical simulations of complex three-dimensional problems are presented to assess the performance of high-order bounded upwind schemes. Finally, the K-Epsilon turbulence models are employed in the simulation of confined and free-surface flows.

Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2009.
Committee Chair: Abdel-Khalik, Said; Committee Member: Ammar, Mostafa H.; Committee Member: Ghiaasiaan, S. Mostafa; Committee Member: Hertel, Nolan E.; Committee Member: Liu, Yingjie.

Cette etude est axee sur le developpement et la validation d'un code de calcul destine a la simulation numerique des ecoulements turbulents a l'echelle d'un quartier urbain. Le code de calcul 3d, baptise chensi, est destine a resoudre le systeme elliptique et instationnaire des equations dynamique et thermique dans une geometrie complexe. Un modele de turbulence de type k-e standard est utilise. Le code utilise une formulation discrete aux differences finies explicite pour le temps et implicite pour la pression sur un maillage spatial non homogene decale. La discretisation des termes de convection est effectuee avec un schema amont pondere; le couplage vitesse-pression est traite par la methode de compressibilite artificielle. La loi de paroi par launder et spalding est utilisee. La validation du code a porte sur l'epanouissement d'un jet non-portant, sur l'ecoulement isotherme au-dessus d'une marche descendante et sur le developpement d'une couche limite thermique au-dessus d'une plaque plane non-uniformement chauffee. Le code est utilise pour la simulation des ecoulements turbulents dans une rue canyon ou le vent au-dessus des toits est perpendiculaire a l'axe de la rue. Une equation d'evolution d'un contaminant passif est introduite afin d'etudier les phenomenes de diffusion dans la rue pour trois conditions de chauffage de parois ainsi que dans des canyons de rapports de forme differents. Une simulation 3d sur une situation choisie de chauffage est realisee

As bombas ejetoras são dispositivos apropriados para aspirar e bombear um fluido que pode ser líquido, gás ou vapor ou uma mistura bifásica. Tais dispositivos são caracterizados pela troca da energia cinética de uma corrente de fluido primária com a uma corrente de fluido secundária em uma câmara de mistura. Devido à simplicidade na estrutura, na ausência de partes móveis e na conveniência da manutenção, bombas ejetoras têm sido usadas extensivamente em muitos campos da Engenharia para várias finalidades. Bombas ejetoras são usadas principalmente em atividades como: bombeamento ou sucção de fluidos, dragas, bombeamento de produtos químicos, transporte de partículas sólidas grandes ou até mesmos produtos alimentícios. Uma bomba ejetora é geometricamente simples consistindo de 4 componentes principais: um bocal, câmara de sucção, garganta misturadora e difusor. Nesta dissertação, a ferramenta de Dinâmica dos Fluidos Computacional (DFC) foi utilizada para calcular o escoamento tridimensional no interior de uma bomba ejetora com dados geométricos e de desempenho disponíveis na literatura com o objetivo principal de avaliar a qualidade dos resultados obtidos. Para tanto as equações de conservação da massa, 2 Lei de Newton, conservação de energia e para o modelo de turbulência k- foram resolvidas utilizando o método de volumes finitos com um algoritmo segregado para o acoplamento dos campos de velocidade e pressão. Para obtenção da solução foi utilizado o código comercial Fluent versão 6.3.17. Os resultados numéricos obtidos para eficiência da bomba ejetora foram comparados com resultados experimentais e com os de uma formulação unidimensional onde os coeficientes de perda por atrito foram medidos experimentalmente nas seções da bomba ejetora ensaiada experimentalmente e simulada numericamente. Os resultados apresentaram boa concordância em toda a faixa disponível de resultados experimentais. A ferramenta de CFD também permitiu analisar os campos de velocidade e a distribuição de pressão nos componentes da bomba ejetora (bocal, garganta misturadora e difusor).

Vegetation is commonly modelled as emergent arrays of rigid, circular cylinders. However, the drag coefficient (CD) of real stems or trunks is closer to that of cylinders with a square cross-section. In this thesis, vegetation has been idealised as square cylinders in laboratory experiments with a turbulence intensity of the order of 10% which is similar to that of typical river flows. These cylinders may also represent other obstacles such as architectural structures. This research has determined CD of an isolated cylinder and cylinder pairs as a function of position as well as the average drag coefficient (CDv) of larger arrays. A strain gauge was used to measure CD whilst CDv was computed with a momentum balance which was validated by strain gauge measurements for a regularly spaced array. The velocity and turbulence intensity surrounding a pair of cylinders arranged one behind the other with respect to mean flow (in tandem) were also measured with an Acoustic Doppler Velocimeter. The isolated cylinder CD was found to be 2.11 in close agreement with other researchers. Under fixed flow conditions CD for a cylinder in a pair was found to be as low as -0.40 and as high as 3.46 depending on their relative positioning. For arrays, CDv was influenced more by the distribution of cylinders than the flow conditions over the range of conditions tested. Mean values of CDv for each array were found to be between 1.52 and 3.06. This new insight therefore suggests that CDv for vegetation in bulk may actually be much higher than the typical value of 1 which is often assumed to apply in practice. If little other information is available, a crude estimate of CDv = 2 would be reasonable for many practical applications. The validity of a 2D realizable k-epsilon turbulence model for predicting the flow around square cylinders was evaluated. The model was successful in predicting CD for an isolated cylinder. In this regard the model performed as well as Large Eddy Simulations by other authors with a significant increase in computational efficiency. However, the numerical model underestimates CD of downstream cylinders in tandem pairs and overestimates velocities in their wake. This suggests it may be necessary to expand the model to three-dimensions when attempting to simulate the flow around two or more bluff obstacles with sharp edges.

Simulações são realizadas utilizando a dinâmica de fluidos computacional (DFC) para prever o desempenho e características de escoamento em uma bomba ejetora anular. A simulação numérica do escoamento no interior da bomba ejetora anular é realizada utilizando o código FLUENT 6.3.26. No presente estudo, o método de volumes finitos é utilizado para resolver um escoamento tridimensional, em regime permanente e incompressível modelado pelas seguintes equações matemáticas: continuidade, momentum e modelo de turbulência . Uma boa concordância foi obtida na comparação entre os resultados numéricos e experimentais disponíveis. Então, os resultados numéricos são utilizados para analisar as seguintes dependências: razão de altura manométrica versus razão de vazão volumétrica e a eficiência global versus razão de vazão volumétrica. Os perfis de velocidade e pressão estática também são usados para estudar o processo de mistura entre as duas correntes na câmara de mistura da bomba ejetora. A boa concordância com os resultados experimentais e a compreensão do escoamento de água obtidos nesta análise numérica mostram que uma abordagem adequada do DFC pode ser utilizada para melhorar o desempenho da bomba ejetora.

Spark ignited engines are still important for conventional as well as for hybrid power trains and are thus objective to optimization. Today a lot of functionalities arise from software solutions, which have to be calibrated. Modern engine technologies provide an extensive variability considering their valve train, fuel injection and load control. Thus, calibration efforts are really high and shall be reduced by introduction of virtual methods. In this work a physical 0D combustion model is set up, which can cope with a new generation of spark ignition engines. Therefore, at first cylinder thermodynamics are modeled and validated in the whole engine map with the help of a real-time capable approach. Afterwards an up to date turbulence model is introduced, which is based on a quasi-dimensional k-epsilon-approach and can cope with turbulence production from large scale shearing. A simplified model for ignition delay is implemented which emphasizes the transfer from laminar to turbulent flame propagation after ignition. The modeling is completed with the calculation of overall heat release rates in a 0D entrainment approach with the help of turbulent flame velocities. After validation of all sub-models, the 0D combustion prediction is used in combination with a 1D gas exchange analysis to virtually calibrate the modern engine torque structure and the ECU function for exhaust gas temperature with extensive simulations
Moderne Ottomotoren spielen heute sowohl in konventionellen als auch hybriden Fahrzeugantrieben eine große Rolle. Aktuelle Konzepte sind hochvariabel bezüglich Ventilsteuerung, Kraftstoffeinspritzung und Laststeuerung und ihre Optimierungspotentiale erwachsen zumeist aus neuen Softwarefunktionen. Deren Applikation ist zeit- und kostenintensiv und soll durch virtuelle Methoden unterstützt werden. In der vorliegenden Arbeit wird ein physikalisches 0D Verbrennungsmodell für Ottomotoren aufgebaut und bis zur praktischen Anwendung geführt. Dafür wurde zuerst die Thermodynamik echtzeitfähig modelliert und im gesamten Motorenkennfeld abgeglichen. Der Aufbau eines neuen Turbulenzmodells auf Basis der quasidimensionalen k-epsilon-Gleichung ermöglicht anschließend, die veränderlichen Einflüsse globaler Ladungsbewegung auf die Turbulenz abzubilden. Für den Brennverzug wurde ein vereinfachtes Modell abgeleitet, welches den Übergang von laminarer zu turbulenter Flammenausbreitung nach der Zündung in den Vordergrund stellt. Der restliche Brennverlauf wird durch die physikalische Ermittlung der turbulenten Brenngeschwindigkeit in einem 0D Entrainment-Ansatz dargestellt. Nach Validierung aller Teilmodelle erfolgt die virtuelle Bedatung der Momentenstruktur und der Abgastemperaturfunktion für das Motorsteuergerät

碩士
國立成功大學
航空太空工程學系
86
As deduced by Chapman and Kuhn [3], the damping function f-mu must satisfy the near-wall limiting behavior . It is clear that f-mu value should tend to unity in the fully turbulent zone, while 01 as grid nodes being located very close to wall. Thus, the grid- independence of computation mesh, particularly in the near wall region of reattached flow, is usually difficult topursue, and it sometimes aggravates the instability in the computationaliteration process. The objective of this study is to remove the unrealistic condition of f-mu>1 from the low- Reynolds-number k-epsilon models when y<<1 . It is shown that the Kolmogorov time scale is the smallest time scale in turbulence. A criterion is thus set as f-mu=0 in the viscous sublayer When the turbulent time scale being smaller than the Kolmogorov time scale. Verification of the validity of the f-mu functions associated with the criterion is implemented through the test with a channel flow and a backward-facing step flow. It is showed that the skin friction coefficient prediction can be improved by introducing the criterion of f-mu function into the calculations.The energy equation governing the thermal field is re-derived. It reveals that the molecular Prandtl number, which is shown in the conventional, Reynolds-averaged energy equation, must be defined in terms of the constant-volume specific heat capacity. With this correction, it is shown that the usual overpredictions of the Nusselt number obtained with the energy equation based on Pr_cp(in terms of the constant-pressure specific heat capacity) can be significantly improved by the energy equation based on Pr_cv (in terms of the constant-volume specific heat capacity).