Large-eddy simulations of fully developed turbulent channel and pipe flows with smooth and rough walls

Studies in turbulence often focus on two flow conditions, both of which occur frequently in real-world flows and are sought-after for their value in advancing turbulence theory. These are the high Reynolds number regime and the effect of wall surface roughness. In this dissertation, a Large-Eddy Simulation (LES) recreates both conditions over a wide range of Reynolds numbers Re_τ = O(10²)-O(10⁸) and accounts for roughness by locally modeling the statistical effects of near-wall anisotropic fine scales in a thin layer immediately above the rough surface. A subgrid, roughness-corrected wall model is introduced to dynamically transmit this modeled information from the wall to the outer LES, which uses a stretched-vortex subgrid-scale model operating in the bulk of the flow. Of primary interest is the Reynolds number and roughness dependence of these flows in terms of first and second order statistics. The LES is first applied to a fully turbulent uniformly-smooth/rough channel flow to capture the flow dynamics over smooth, transitionally rough and fully rough regimes. Results include a Moody-like diagram for the wall averaged friction factor, believed to be the first of its kind obtained from LES. Confirmation is found for experimentally observed logarithmic behavior in the normalized stream-wise turbulent intensities. Tight logarithmic collapse, scaled on the wall friction velocity, is found for smooth-wall flows when Re_τ ≥ O(10⁶) and in fully rough cases. Since the wall model operates locally and dynamically, the framework is used to investigate non-uniform roughness distribution cases in a channel, where the flow adjustments to sudden surface changes are investigated. Recovery of mean quantities and turbulent statistics after transitions are discussed qualitatively and quantitatively at various roughness and Reynolds number levels. The internal boundary layer, which is defined as the border between the flow affected by the new surface condition and the unaffected part, is computed, and a collapse of the profiles on a length scale containing the logarithm of friction Reynolds number is presented. Finally, we turn to the possibility of expanding the present framework to accommodate more general geometries. As a first step, the whole LES framework is modified for use in the curvilinear geometry of a fully-developed turbulent pipe flow, with implementation carried out in a spectral element solver capable of handling complex wall profiles. The friction factors have shown favorable agreement with the superpipe data, and the LES estimates of the Karman constant and additive constant of the log-law closely match values obtained from experiment.

Optical intrinsically fuzzy mathematical morphology for gray-scale image processing

Intrinsically fuzzy morphological erosion and dilation are extended to a total of eight operations that have been formulated in terms of a single morphological operation--biased dilation. Based on the spatial coding of a fuzzy variable, a bidirectional projection concept is proposed. Thus, fuzzy logic operations, arithmetic operations, gray-scale dilation, and erosion for the extended intrinsically fuzzy morphological operations can be included in a unified algorithm with only biased dilation and fuzzy logic operations. To execute this image algebra approach we present a cellular two-layer processing architecture that consists of a biased dilation processor and a fuzzy logic processor. (C) 1996 Optical Society of America

Fuzzy reasoning morphological operators and their optical implementation

Fuzzy-reasoning theory is widely used in industrial control. Mathematical morphology is a powerful tool to perform image processing. We apply fuzzy-reasoning theory to morphology and suggest a scheme of fuzzy-reasoning morphology, including fuzzy-reasoning dilation and erosion functions. These functions retain more fine details than the corresponding conventional morphological operators with the same structuring element. An optical implementation has been developed with area-coding and thresholding methods. (C) 1997 Optical Society of America.

Measurement of small vibration amplitudes of a rough surface by an interferometer with a self-pumped phase-conjugate mirror

The application of a Michelson interferometer with a self-pumped phase-conjugate mirror to measure small vibration amplitudes of a rough surface is described. The distorted wave front of the light that is diffusely reflected from the rough surface is restored by phase conjugation to provide an interference signal with a high signal-to-noise ratio. The vibration amplitudes of a stainless-steel sample are measured with a precision of similar to 5 nm. (C) 2000 Optical Society of America OCIS codes: 120.3180, 190.5040, 120.7280.

FUZZY SOLID SETS FOR MATHEMATICAL MORPHOLOGY AND OPTICAL IMPLEMENTATION

Fuzzy sets in the subject space are transformed to fuzzy solid sets in an increased object space on the basis of the development of the local umbra concept. Further, a counting transform is defined for reconstructing the fuzzy sets from the fuzzy solid sets, and the dilation and erosion operators in mathematical morphology are redefined in the fuzzy solid-set space. The algebraic structures of fuzzy solid sets can lead not only to fuzzy logic but also to arithmetic operations. Thus a fuzzy solid-set image algebra of two image transforms and five set operators is defined that can formulate binary and gray-scale morphological image-processing functions consisting of dilation, erosion, intersection, union, complement, addition, subtraction, and reflection in a unified form. A cellular set-logic array architecture is suggested for executing this image algebra. The optical implementation of the architecture, based on area coding of gray-scale values, is demonstrated. (C) 1995 Optical Society of America

Fuzzy inferring mathematical morphology and optical implementation

Fuzzification is introduced into gray-scale mathematical morphology by using two-input one-output fuzzy rule-based inference systems. The fuzzy inferring dilation or erosion is defined from the approximate reasoning of the two consequences of a dilation or an erosion and an extended rank-order operation. The fuzzy inference systems with numbers of rules and fuzzy membership functions are further reduced to a simple fuzzy system formulated by only an exponential two-input one-output function. Such a one-function fuzzy inference system is able to approach complex fuzzy inference systems by using two specified parameters within it-a proportion to characterize the fuzzy degree and an exponent to depict the nonlinearity in the inferring. The proposed fuzzy inferring morphological operators tend to keep the object details comparable to the structuring element and to smooth the conventional morphological operations. Based on digital area coding of a gray-scale image, incoherently optical correlation for neighboring connection, and optical thresholding for rank-order operations, a fuzzy inference system can be realized optically in parallel. (C) 1996 Society of Photo-Optical Instrumentation Engineers.

IQAFAL - Índice Fuzzy de Qualidade de Água para Ambiente Lótico.

A divulgação de informação sobre qualidade das águas para um público não especialista é fundamental para subsidiar ações políticas e institucionais de gestão dos ambientes aquáticos. Para tanto, índices de qualidade de água têm sido propostos por serem capazes de sintetizar em um único valor ou categoria a informação normalmente descrita a partir de um conjunto extenso de variáveis químicas, físicas e biológicas de qualidade de água. A maioria das metodologias propostas para o desenvolvimento de índices de qualidade de água é baseada no conhecimento de especialistas quanto à escolha das variáveis a serem utilizadas, a ponderação da importância relativa de cada variável e métodos utilizados para agregar os dados das variáveis em um único valor. Este trabalho propõe um novo índice de qualidade de água, baseado em lógica nebulosa e direcionado para o ambiente lótico. Esse índice, o IQAFAL, foi desenvolvido com a colaboração de especialistas com ampla e comprovada experiência na área de qualidade de água. A essência do desenvolvimento de um índice, usando-se lógica nebulosa, está na capacidade dessa metodologia representar, de forma mais eficiente e clara, os limites dos intervalos de variação dos parâmetros de qualidade de água para um conjunto de categorias subjetivas, quando esses limites não são bem definidos ou são imprecisos. O índice proposto neste trabalho foi desenvolvido com base no conhecimento dos especialistas em qualidade de água do Instituto Estadual do Ambiente - INEA e aplicado aos dados de qualidade de água do Rio Paraíba do Sul, obtidos pelo INEA, nos anos de 2002 a 2009. Os resultados do IQAFAL mostraram que esse índice foi capaz de sintetizar a qualidade da água deste trecho do Rio Paraíba do Sul correspondendo satisfatoriamente às avaliações de qualidade de água descritas nos relatórios disponíveis. Verificou-se também que com essa metodologia foi possível evitar que a influência de uma variável em condições críticas fosse atenuada pela influência das outras variáveis em condições favoráveis produzindo um resultado indesejável no índice final.