Turbulent pipe flows are encountered in a multitude of engineering applications. Some of the examples include removal of moisture, odors, and other harmful gases using exhaust pipes; transporting crude oil and cooling water in oil reneries; circulation of coolants through the engine in automobiles and motorcycles; etc. They have been studied experimentally for more than a century and by direct numerical simulations (DNS) for more than two decades. Over the past twenty years, there has been an increase in the involvement of computation in studying turbulent flows, including turbulent pipe flows. The low cost and time consumption of computer simulations, along with the ability to study complex dynamic processes that are practically intractable at all scales, have resulted in the increase in their use in research. At the same time, the presence of curved boundary remains a challenge for accurate DNS of this simple flow. ☐ In the recent past, lattice Boltzmann method (LBM) has emerged as an attractive option for simulating wall-bounded turbulent flows. It offers several advantages compared to the conventional models of computational fluid dynamics, due to the local nature of operations involved and easy implementation of boundary conditions. Despite the advantages posed by the LBM, no DNS of turbulent pipe flow has been reported using LBM. Hence, the objective of this study is to develop a lattice Boltzmann model to simulate turbulent pipe flow and implement it into a computer code using FORTRAN and MPI. This code is then used to simulate fully developed turbulent pipe flow and validate the results with the existing benchmark data. ☐ In this thesis, the lattice Boltzmann model in three spatial dimensions using 27 mesoscopic velocities on a cubic grid was designed using an "inverse design" analysis. Yu et al.'s double interpolation scheme was used to satisfy the no-slip condition at the solid-liquid interface. ☐ The code was first validated by simulating laminar channel and pipe flows. The profiles of streamwise velocity for the laminar pipe and channel flow simulations were observed to be in excellent agreement with the analytical results. Further, the results of the time evolution of the centerline streamwise velocity for the laminar pipe and channel flow also matched the analytical results. Hence, the validity and accuracy of the code was established. ☐ Turbulent pipe flow was then simulated using the D3Q27 model. The first and second order statistics of the turbulent pipe flow simulation from the D3Q27, D3Q19 model were compared with the reference data being obtained from the spectral and finite volume discretizations of the Navier-Stokes equation. The mean velocity profiles of the D3Q27 simulation matched well with the reference data. On the other hand, the D3Q19 model under-predicts the mean velocity, especially near the center. In addition, the contours of the streamwise velocity for the D3Q19 simulation showed a certain preference along particular directions. This was not observed in the D3Q27 simulation. The erroneous results of the D3Q19 model could be explained by the hypothesis stated in White et al., stating that the presence of "defective planes" could be a plausible reason for the errors in the measurement of streamwise velocity in the D3Q19 model. Hence, the D3Q27 model seems like a suitable option to simulate wall-bounded turbulent flows with a curved boundary. The only drawback to using the D3Q27 model is its slower execution speed as it takes 21% more CPU time than the D3Q19 model.

Uma investigação da capacidade de previsão de modelos de turbulência baseados na modelagem estatística clássica e de grandes escalas é apresentada. A modelagem estatística clássica de turbulência (média de Reynolds) foi analisada, através da solução de escoamentos complexos, como, por exemplo, o escoamento turbulento em degrau (backstep). Especial atenção foi dada aos modelos kapa-epsilon de baixo Reynolds e as variantes renormalizadas (RNG). O comportamento dosvários termos da equação da energia cinética turbulenta na região da parede foram analisados em detalhes, especialmente o termo de difusão de pressão. Avaliou-se aimportância da correta modelagem do termo de difusão de pressão sobre as predições dos modelos de baixo número de Reynolds, nas regiões de recirculação. Alguns modelos, propostos na literatura para o termo de difusão de pressão, foram também avaliados teórica e numericamente. A capacidade de previsão da metodologia de simulação de grandes escalas (LES por Large Eddy Simulation) também foi realizada. O desempenho do modelo de Smagorinsky para preverescoamentos limitados por fronteiras sólidas foi avaliado do ponto de vista computacional. Utilizou-se o método de volumes finitos para integrar tanto as equações médias de Reynolds quanto as equações LES. O escoamento turbulentoem canal foi resolvido de modo bidimensional e tridimensional. Já o escoamento em degrau (backstep) foi resolvido exclusivamente de modo bidimensional, enquanto o escoamento em um duto de seção quadrada foi simulado de modotridimensional. Os resultados foram comparados com aqueles obtidos pelos modelos de baixo Reynolds, analisando-se a relação custo-benefício.

This book presents several new findings in the field of turbulent duct flows, which are important for a range of industrial applications. It presents both high-quality experiments and cutting-edge numerical simulations, providing a level of insight and rigour rarely found in PhD theses. The scientific advancements concern the effect of the Earth’s rotation on large duct flows, the experimental confirmation of marginal turbulence in a pressure-driven square duct flow (previously only predicted in simulations), the identification of similar marginal turbulence in wall-driven flows using simulations (for the first time by any means) and, on a separate but related topic, a comprehensive experimental study on the phenomenon of drag reduction via polymer additives in turbulent duct flows. In turn, the work on drag reduction resulted in a correlation that provides a quantitative prediction of drag reduction based on a single, measurable material property of the polymer solution, regardless of the flow geometry or concentration. The first correlation of its kind, it represents an important advancement from both a scientific and practical perspective.