The specific turbulent kinetic energy, root-mean-square fluctuating vorticity, and mean-vortexwavelength distributions are presented for fully rough pipe flow. The distributions of these turbulence variables are obtained from a proposed turbulence model. Many of the turbulence models commonly used for computational fluid dynamics are based on an analogy between molecular and turbulent transport. However, traditional k-ε and k-ω models fail to exhibit proper dependence on the molecular viscosity. Based on a rigorous application of the Boussinesq’s hypothesis, Phillips proposed a vorticity-based transport equation for the turbulent kinetic energy. The foundation for this vorticity-based transport equation is presented. In future development of this model, a transport equation for the fluctuating vorticity is needed. In order to assess the model and evaluate closure coefficients, the resulting turbulent vorticity distribution must be compared to reference distributions. This dissertation presents reference distributions for the mean fluctuating vorticity and mean turbulent wavelength obtained for fully rough pipe flow. These distributions are obtained from a turbulence model, which involves the proposed transport equation for the turbulent kinetic energy and an empirical relation for the mean vortex wavelength. The empirical relation for the mean vortex wavelength requires numerous closure coefficients. These closure coefficients are determined through gradient-based optimization techniques. The current model gives excellent agreement with well established relations obtained for both the friction factor and velocity distribution.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第19288号 / 工博第4085号 / 新制||工||1630(附属図書館) / 32290 / 京都大学大学院工学研究科都市社会工学専攻 / (主査)教授 細田 尚, 教授 戸田 圭一, 教授 後藤 仁志 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

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<p dir="ltr">The kinetic-based lattice Boltzmann method (LBM) is a specialized computational fluid dynamics (CFD) technique that resolves intricate flow phenomena at the mesoscale level. The LBM is particularly suited for large-scale parallel computing on Graphic Processing Units (GPU) and simulating multi-phase flows. By incorporating a volume fraction parameter, LBM becomes a volumetric lattice Boltzmann method (VLBM), leading to advantages such as easy handling of complex geometries with/without movement. These capabilities render VLBM an effective tool for modeling various complex flows. In this study, we investigated the computational modeling of complex flows using VLBM, focusing particularly on pulsatile flows, the transition to turbulent flows, and pore-scale porous media flows. Furthermore, a new discrete dynamical system (DDS) is derived and validated for potential integration into large eddy simulations (LES) aimed at enhancing modeling for turbulent and pulsatile flows. Pulsatile flows are prevalent in nature, engineering, and the human body. Understanding these flows is crucial in research areas such as biomedical engineering and cardiovascular studies. However, the characteristics of oscillatory, variability in Reynolds number (Re), and shear stress bring difficulties in the numerical modeling of pulsatile flows. To analyze and understand the shear stress variability in pulsatile flows, we first developed a unique computational method using VLBM to quantify four-dimensional (4-D) wall stresses in image-based pulsatile flows. The method is validated against analytical solutions and experimental data, showing good agreement. Additionally, an application study is presented for the non-invasive quantification of 4-D hemodynamics in human carotid and vertebral arteries. Secondly, the transition to turbulent flows is studied as it plays an important role in the understanding of pulsatile flows since the flow can shift from laminar to transient and then to turbulent within a single flow cycle. We conducted direct numerical simulations (DNS) using VLBM in a three-dimensional (3-D) pipe and investigated the flow at Re ranging from 226 to 14066 in the Lagrangian description. Results demonstrate good agreement with analytical solutions for laminar flows and with open data for turbulent flows. Key observations include the disappearance of parabolic velocity profiles when Re>2300, the fluctuation of turbulent kinetic energy (TKE) between laminar and turbulent states within the range 2300</p>

L'étude théorique de la transition vers la turbulence d'écoulements en tuyau de fluides non newtoniens rhéofluidifiants (fluides de Carreau) est menée, avec l'approche consistant à calculer des «~structures très cohérentes~» sous la forme d'«~ondes non linéaires~». Pour cela un code pseudo-spectral de type Petrov-Galerkin, permettant de suivre des solutions ondes non linéaires tridimensionnelles dans l'espace des paramètres par continuation, est développé. Ce code est validé par comparaison à des résultats existants en fluide newtonien, et grâce à un test de consistance en fluide non newtonien. Une convergence spectrale exponentielle est obtenue dans tous les cas. Ce code est utilisé pour chercher (guidé par des résultats expérimentaux récents) de nouvelles solutions de nombre d'onde azimutal fondamental égal à 1, sans succès pour l'instant. Par contre des solutions de nombre d'onde azimutal fondamental égal à 2 ou 3 sont obtenues par continuation à partir du cas newtonien. La rhéofluidification induit, en termes de nombres de Reynolds critiques, un retard à l'apparition de ces ondes par rapport au cas newtonien. Ce retard est caractérisé, et le parallèle est fait avec divers résultats expérimentaux qui montrent un retard à l'apparition de bouffées turbulentes en fluides non newtoniens / The transition to turbulence in pipe flows of shear-thinning fluids is studied theoretically. The method used is the computation of `exact coherent structures' that are tridimensional nonlinear waves. For this purpose a pseudo-spectral Petrov-Galerkin code is developped, which also allows to follow solution branches in the parameter space with continuation methods. This code is validated by recovering already published results in the Newtonian case, and by a consistency test in the non-Newtonian case. A spectral exponential convergence is obtained in all cases. This code is used to seek (guided by recent experimental results) new solutions of fundamental azimuthal wavenumber equal to 1,without success at the time being. On the contrary solutions with a fundamental azimuthal wavenumber equal to 2 and 3 are obtained by continuation from the Newtonian case. The shear-thinning effects induce, in terms of critical Reynolds numbers, a delay for the onset of these waves, as compared with the Newtonian case. This delay is characterized. An analogy is made with various experimental results that show a delay in the transition to turbulence, more precisely, in the onset of `puffs', in non-Newtonian fluids