Development of a lattice boltzmann based flow solver for large eddy simulation of turbulent flows

Abstract

Turbulence is recognized as one of the most complex unsolved problems in classical physics. Its chaotic and multi-scale nature is characterized by irregular fluctuations in flow variables across a wide range of spatial and temporal scales. Analyzing turbulence theoretically is quite challenging. Although experimental methods provide valuable data, they can be costly, difficult to set up, and limited in their ability to replicate extreme conditions. Consequently, numerical approaches have become crucial tools for investigating the complex physics of turbulent flows. The development of efficient numerical approaches is vital for turbulent flow analyses since simulations can quickly become computationally expensive due to fine mesh resolution requirements to resolve a wide range of scales and model complex physical phenomena. Several computational strategies exist to handle turbulent flows. The Reynolds Averaged Navier Stokes (RANS) method offers a computationally efficient approach that models all of the turbulent fluctuations. It is useful for many engineering applications where mean flow properties are important. However, RANS inherently loses details about instantaneous turbulent structures, and its accuracy is heavily dependent on the chosen turbulence model. At the other extreme, direct numerical simulation (DNS) resolves all scales of turbulence without any modeling. Therefore, it provides the highest possible accuracy and serves as a benchmark for other methods. However, the computational cost of DNS is enormous, and it scales prohibitively with the Reynolds number. Thus, DNS is impractical for most engineering problems. Large eddy simulation (LES) offers a compromise by directly resolving the large, energy-carrying turbulent eddies while modeling the effects of the smaller, subgrid-scale (SGS) eddies. This approach significantly reduces computational cost compared to DNS while retaining more detailed information about the unsteady nature of the turbulent flow than RANS. In recent years, the lattice Boltzmann method (LBM) has emerged as a promising alternative to traditional Navier-Stokes methods for fluid dynamics. LBM operates on a mesoscopic scale by simulating fluid flow by tracking the collective behavior of fictitious particles on lattice structures. Its algorithmic simplicity and locality provide excellent suitability for parallel computing and make it computationally efficient. Coupling LBM with LES creates an efficient framework for simulating turbulent flows. This framework can overcome some classical limitations of LBM, such as the numerical stability problem at high Reynolds numbers, by incorporating SGS models that introduce an effective eddy viscosity. The primary objective of this study was to develop a solver that highlights the advantages of the lattice Boltzmann method while systematically addressing inherent LBM limitations for enabling high-accuracy simulations of wall-bounded turbulent flows. In this context, the large eddy simulation approach is employed for accurately capturing turbulent dynamics. A non-uniform lattice structure is implemented to improve computational efficiency by refining the grid only where necessary. The immersed boundary method with an interpolated bounce-back scheme is incorporated to accurately represent complex, curved geometries within the structured lattice framework of LBM. The in-house parallel solver, lbmles, is written in FORTRAN and utilizes the D3Q19 lattice configuration. The relaxation process is modeled with 2 different approaches: single relaxation time (SRT) and multiple relaxation time (MRT). For turbulence, it employs the LES approach with Smagorinsky and one-equation (k-sgs) subgrid scale models. Parallelization is achieved using the Message Passing Interface (MPI) which enables efficient execution on high-performance computing clusters. The solver utilizes non-uniform mesh generation and handles complex boundaries via IBM coupled with a Bouzidi interpolated bounce-back scheme. The solver's capabilities were extensively validated and demonstrated through a series of numerical investigations. Laminar flow cases included the lid-driven cavity (LDC) flow at various Reynolds numbers (Re = 100, 400, 1000), flow around a circular cylinder (Re = 10, 20, 40), and flow around the NACA0012 airfoil (Re = 1000). Fundamental accuracy and stability of the LBM framework are validated with the laminar LDC flow. The capability of handling curved geometries within a structured grid by immersed boundary via bounce-back scheme is assessed through flow around cylinder simulations. Characteristic flow parameters such as recirculation length behind the cylinder, separation angle, and drag coefficient are evaluated in good agreement with other numerical approaches. Moreover, the handling complex geometry ability of the developed LBM-IBM framework is also tested with an arbitrary curved geometry: NACA0012 Airfoil. Unsteady flow simulation is successfully conducted with the solver by various angles of attack. After 7 degrees of angle of attack, a vortex shedding is observed, which is expected for the flow around NACA0012 airfoil at Re = 1000. Moreover, the mean pressure coefficient distribution is calculated in harmony with other numerical simulations. After the solver was validated on curved geometries, its capabilities in turbulent flows were assessed with decaying homogeneous isotropic turbulence (DHIT) and turbulent lid-driven cavity flow (Re = 12000) problems. To initially assess whether the LES methodology was properly implemented within the LBM framework, the decaying homogeneous isotropic turbulence (DHIT) problem, which is an idealized case without any complex boundary conditions, was analyzed. When DHIT was investigated using the LBM-LES framework, it was observed that the decay trends of energy and dissipation spectrum aligned well with the literature, which means that the solver produces physically consistent results. To evaluate the performance of the implemented subgrid-scale (SGS) models, direct numerical simulation (DNS) was conducted at a very low initial Taylor's scale Reynolds number (Re_lambda = 18) using a fine mesh with a lattice structure of 128x128x128. Subsequently, LES simulations were performed at the same initial Taylor Reynolds number but with a coarser mesh with a lattice structure of 32x32x32. LES results showed good agreement with the DNS data, demonstrating that the SGS models produce physically consistent results. Following the validation of the SGS models under ideal conditions, numerical investigation of the turbulent lid-driven cavity flow is conducted by the solver. In this analysis, a 129x129x129 lattice structure was used with both uniform and stretched configurations. It was particularly observed that the flow physics near the walls was captured more accurately with the stretched mesh. Hence, increasing the mesh resolution in near-wall regions with high gradients had a direct impact on the simulation results. Both the mean flow characteristics and the fluctuation features obtained from the simulations were in good agreement with DNS data reported in the literature. Numerical investigation of non-reacting turbulent flow inside a swirl-stabilized combustor geometry is considered as a key application in the scope of this thesis. This challenging case served as a benchmark to evaluate the MRT-LBM-LES framework's ability to handle intricate geometries and turbulent flow physics at the same time. The solver successfully captured key flow features such as inner and outer shear layers, the central recirculation zone, and vortical structures. Mean flow features showed good agreement with experimental data. In conclusion, a new lattice Boltzmann solver is successfully developed with the LES approach. Conducted simulations demonstrate that the solver, developed by non-uniform mesh capability, immersed boundary method, and LES approach, is a capable and efficient tool for analyzing wall-bounded turbulent flows by overcoming inherent LBM limitations. It provides consistent results with established numerical data and experimental measurements.