No description available.

No description available.

No description available.

In this work, we investigate the performance limitations characterizing certain common closure models for nonlinear models of fluid flow. The need for closures arises when for computational reasons first-principles models, such as the Navier-Stokes equations, are replaced with their simplified (filtered) versions such as the Large-Eddy Simulation (LES). In the present work, we focus on a simple model problem based on the 1D Kuramoto-Sivashinsky equation with a Smagorinsky-type eddy-viscosity closure model. The eddy viscosity is assumed to be a function of the state (flow) variable whose optimal functional form is determined in a very general form in the continuous setting. It is found by solving a PDE-constrained optimization problem in which the least-squares error between the output of the LES and the true flow evolution is minimized with respect to the functional form of the eddy viscosity. This problem is solved using a gradient-based technique utilizing a suitable adjoint-based variational data-assimilation approach implemented in the optimize-then-discretize setting using state-of-the-art techniques. The numerical computations are thoroughly validated. The obtained results indicate how the standard Smagorinsky closure model can be refined such that the corresponding LES evolution approximates more accurately the evolution of the original (unfiltered) flow. / Thesis / Master of Science (MSc)

The accurate and efficient numerical simulation of geophysical flows is of great interest in numerical weather prediction and climate modeling as well as in numerous critical areas and industries, such as agriculture, construction, tourism, transportation, weather-related disaster management, and sustainable energy technologies. Oceanic and atmospheric flows display an enormous range of temporal and spatial scales, from seconds to decades and from centimeters to thousands of kilometers, respectively. Scale interactions, both spatial and temporal, are the dominant feature of all aspects of general circulation models in geophysical fluid dynamics. In this thesis, to decrease the cost for these geophysical flow computations, several types of multiscale methods were systematically developed and tested for a variety of physical settings including barotropic and stratified wind-driven large scale ocean circulation models, decaying and forced two-dimensional turbulence simulations, as well as several benchmark incompressible flow problems in two and three dimensions. The new models proposed here are based on two classes of modern multiscale methods: (i) interpolation based approaches in the context of the multigrid/multiresolution methodologies, and (ii) deconvolution based spatial filtering approaches in the context of large eddy simulation techniques. In the first case, we developed a coarse-grid projection method that uses simple interpolation schemes to go between the two components of the problem, in which the solution algorithms have different levels of complexity. In the second case, the use of approximate deconvolution closure modeling strategies was implemented for large eddy simulations of large-scale turbulent geophysical flows. The numerical assessment of these approaches showed that both the coarse-grid projection and approximate deconvolution methods could represent viable tools for computing more realistic turbulent geophysical flows that provide significant increases in accuracy and computational efficiency over conventional methods. / Ph. D.

Wakes of lifting bodies contain vortex sheets that roll up into strong streamwise vortices. The long time behavior of such vortices depends on the turbulence in the wake and the stability characteristics of the vortices themselves. In the near wake of a rectangular wing the flow field consists of a spiraling wake that winds around a pair of vortex cores. The study of the turbulence structure and life of wing tip vortices is of great importance to air traffic control in congested airports. In this dissertation a computer code is developed for the temporal as well as spatial simulations of trailing vortices. A sixth-order compact finite-difference method is used in the cross plane. The streamwise derivatives are represented either by a Fourier series for temporal simulations (periodic flow) or by a sixth-order compact scheme for spatial simulations. The time marching scheme is a third-order Runge-Kutta method. The code is used to study the nonlinear development of temporal helical instability waves in a trailing vortex. Contours of a passive scalar are used to study the entrainment process that redistributes angular and axial momenta between the core and its surroundings. Such a process leads to quenching of the instability waves in the vortex core. The code is also used to predict the spatial development of mean flow in the wake of a rectangular wing. New treatment of the outflow boundary condition on the pressure is formulated so that a strong streamwise vortex can exit the computational domain without distortion. Temporal large-eddy simulation (LES) is performed to study the development of large scale structures in the wake and their interaction with the tip vortex. A modified MacCormack scheme developed by Gottlieb and Turkel(1976) has been used to solve the LES equations. A model of the initial conditions in the near wake of a rectangular wing is devised to investigate mechanisms of turbulence production in the spiral wake around the core of a tip vortex. The model consists of a streamwise vortex sheet whose strength is found from Prandtl lifting line theory. A Gaussian streamwise velocity profile is superimposed on the field of the vortex sheet. This profile represents the spanwise vorticity. The integrated spanwise vorticity of this profile is zero. A novel feature of this study is that the mean flow contains both streamwise and spanwise vorticity. The model is then used to initialize the flow field for temporal LES of the instabilities of the spanwise vorticity during roll up. The results show that the sinuous mode prevails in the spiral wake around the core. The strength and streamwise length scale of the instability vary along the span because of the continuous variation of the wake thickness due to stretching by the tip vortex. The large scale structures produced by the instability of the spiral wake cause the formation of undulations on the core - consistent with the hypothesis of Devenport et al. (1996). / Ph. D.

Increasing the turbine inlet temperature of gas turbine engines significantly increases their power output and efficiency, but it also increases the likelihood of thermal failure. Internal passages with tiny ribs are typically cast into turbine blades to cool them, and the ability to accurately predict the flow and heat transfer within these channels leads to higher design reliability and prevention of blade failure resulting from local thermal loading. Prediction of the flow through these channels is challenging, however, because the flow is highly turbulent and anisotropic, and the presence of rotational body forces further complicates the flow. Large Eddy Simulations are used to study these flows because of their ability to predict the unsteady flow effects and anisotropic turbulence more reliably than traditional RANS closure models. Calculations in a stationary duct are validated with experiments in the developing flow, fully developed, and 180° bend regions to establish the accuracy and prediction capability of the LES calculations and to aid in understanding the major flow structures encountered in a ribbed duct. It is found that most flow and heat transfer calculations come to within 10-15% of the measurements, typically showing excellent agreement in all comparisons. In the developing flow region, Coriolis effects are found to destabilize turbulence and increase heat transfer along the trailing wall (pressure side), while decreasing leading wall heat transfer by stabilizing turbulence. Coriolis forces improve flow turning in the 180° bend by shifting the shape of the separated recirculation zone at the tip of the dividing wall and increasing the mainstream flow area. In addition, turbulence is attenuated near the leading wall throughout the bend, while Coriolis forces have little effect on trailing wall turbulence in the bend. Introducing and increasing centrifugal buoyancy in the developing flow region increases trailing wall heat transfer monotonically. Along the leading wall, buoyancy increases the size of the recirculation zones, shifting the peak heat transfer to a region upstream of the rib, which decreases heat transfer at low buoyancy parameters but increases it as the buoyancy parameter is increased beyond a value of 0.3. Centrifugal buoyancy in the 180° bend initially decreases the size of the recirculation zone at the tip of the dividing wall, increasing flow area and decreasing flow impingement. At high buoyancy, however, the recirculation zone shifts to the middle of the bend, increasing flow resistance and causing strong flow impingement on the back wall. The Boussinesq approximation is used in the buoyancy calculations, but the accuracy of the approximation comes into question in the presence of large temperature differences. A variable property algorithm is developed to calculate unsteady low speed flows with large density variations resulting from large temperature differences. The algorithm is validated against two test cases: Rayleigh-Bénard convection and Poiseuille-Bénard flow. Finally, design issues in rotating ribbed ducts are considered. The fully developed assumption is discussed with regard to the developing flow region, and controlling the recirculation zone in the 180° bend is considered as a way to determine the blade tip heat transfer and pressure drop across the bend. / Ph. D.

Studying the effects of free stream turbulence on noise, vibration, and heat transfer on structures is very important in engineering applications. The problem of the interaction of large scale turbulence with a flat-plate cascade is a model of important problems in propulsion systems. Addressing the problem of large scale turbulence interacting with a flat plate cascade requires flow simulation over a large number of plates (6-12 plates) in order to be able to represent numerically integral length scales on the order of blade-to-blade spacing. Having such a large number of solid surfaces in the simulation requires very large computational grid points to resolve the boundary layers on the plates, and that is not possible with the current computing resources. In this thesis we develop a computational technique to predict the distortion of homogeneous isotropic turbulence as it passes through a cascade of thin flat plates. We use Large-Eddy Simulation (LES) to capture the spatial development of the incident turbulence and its interaction with the plates which are assumed to be inviscid walls. The LES is conducted for a linear cascade composed of six plates. Because suppression of the normal component of velocity is the main mechanism of distortion, we neglect the presence of mean shear in the boundary layers and wakes, and allow slip velocity on the plate surfaces. We enforce the zero normal velocity condition on the plates. This boundary condition treatment is motivated by rapid distortion theory (RDT) in which viscous effects are neglected, however, the present LES approach accounts for nonlinear and turbulence diffusion effects by a sub-grid scale model. We refer to this type of turbulence-blade interaction as shear-free interaction. To validate our calculations, we computed the unsteady loading and radiated acoustic pressure field from flat plates interacting with vortical structures. We consider two fundamental problems: (1) A linear cascade of flat plates excited by a vortical wave (gust) given by a 2D Fourier mode, and (2) The parallel interaction of a finite-core vortex with a single plate. We solve the nonlinear Euler equations by a high-order finite-differece method. We use nonreflecting boundary conditions at the inflow and outflow boundaries. For the gust problem, we found that the cascade response depends sensitively on the frequency of the convicted gust. The unsteady surface pressure distribution and radiated pressure field agree very well with predictions of the linear theory for the tested range of reduced frequency. We have also investigated the effects of the incident gust frequency on the undesirable wave reflection at the inflow and outflow boundaries. For the vortex-plate interaction problem, we investigate the effects of the internal structure of the vortex on the strength and directivity of radiated sound. Then we solved the turbulence cascade interaction problem. The normal Reynolds stresses and velocity spectra are analyzed ahead, within, and downstream of the cascade. Good agreement with predictions of rapid distortion theory in the region of its validity is obtained. Also, the normal Reynolds stress profiles are found to be in qualitative agreement with available experimental data. As such, this dissertation presents a viable computational alternative to rapid distortion theory (RDT) for the prediction of noise radiation due to the interaction of free stream turbulence with structures. / Ph. D.

The issue of the effects of free stream turbulence on the flow field over a surface-mounted prism is examined through experimental and numerical investigations. In the experimental studies, particle image velocimetry measurements are conducted in the ESM water tunnel at Reynolds number of $9,600$ and under two cases of turbulent inflow conditions. The results show that the mean flow separation, reattachment and parameters such as mean velocity, root mean square, Reynolds stresses and turbulent kinetic energy are affected by the turbulence characteristics of the incident flow. The instantaneous dynamics of the interactions between the separating shear layer and the solid wall and between the shear layer and the turbulence in the incident flow are detailed. In the numerical studies, large eddy simulations of the flow over a surface-mounted prism under two inflow conditions, namely, smooth inflow and isotropic homogeneous turbulence inflow, are performed. The use of a fifth-order scheme (CUD-II-5), which is a member of a family of Compact Upwind Difference schemes, in large eddy simulations of this flow is assessed. The performance of this scheme is validated by comparing the rate of temporal decay of isotropic turbulence with available experimental measurements for grid-generated turbulence. The results show that the spectra are sensitive to the method of flux vector splitting needed for the implementation of the upwind scheme. With van Leer splitting, the CUD-II-5 scheme is found to be too dissipative. On the other hand, using the Lax-Friedrichs vector splitting yields good agreement with experiments by controlling the level of artificial dissipation. This led us to recommend a new procedure, we denote by C6CUD5 scheme, that combines a compact sixth-order scheme with the CUD-II-5 scheme for large eddy simulation of complex flows. The simulation results, including flow patterns, pressure fields and turbulence statistics show that the CUD-II-5 scheme, with Lax-Friedricks flux vector splitting, provides high resolution of local flow structures. The results present new physical aspects of the flow topology over surface-mounted prisms. The effects of the incident homogeneous turbulence on the size of the separation region and suction pressures are determined by pointing out differences in the flow topologies between the two incident flow cases. / Ph. D.

This dissertation investigates the flow physics, turbulence structure, and particle classification process in hydrocyclones using large-eddy simulations of turbulent multiphase flow. Two types of hydrocyclones are considered. The first is a classifying hydrocyclone, and the second is a mineral flotation hydrocyclone, also known as an air-sparged hydrocyclone (ASH). Large-eddy simulations (LES) are conducted for multi-phase flow (air, water, and sand particles) so that the complex anisotropic turbulence of a swirling flow is computed correctly. The effects of mesh refinements on the mean flow and turbulence stresses are investigated, and (LES) results are validated by comparisons with experimental data for classifying hydrocyclone. The two-phase flow in air-sparged hydrocyclone has not been analyzed before. ANSYS CFX software V17.2 has been used to conduct the simulations. Firstly, large-eddy simulations have been conducted for two-phase flow (water and air) in a conventional hydrocyclone using the Eulerian two-fluid (Eulerian-Eulerian) and Volume-of- Fluid (VOF) models. Subgrid stresses are modeled using a dynamic eddy–viscosity model, and results are compared to those using the Smagorinsky model. The effects of grid resolutions on the mean flow and turbulence statistics have been thoroughly investigated. Five block-structured grids of 0.72, 1.47, 2.4, 3.81, and 7.38 million elements have been used for the simulations of a typical conventional hydrocyclone designed and tested by Hsieh (75 mm hydrocyclone) [1]. Mean velocity profiles and normal Reynolds stresses have been compared with experimental data. The results of the Eulerian two-fluid model agree with those of the VOF model. A fine mesh in the axial and radial directions is necessary for capturing the turbulent vortical structures. Turbulence structures in the hydrocyclone are dominated by helical vortices around the air core. Energy spectra are analyzed at different points in the hydrocyclone, and regions of low turbulent kinetic energy are identified and attributed to stabilizing effects of the swirling velocity component. Turbulent energy spectra in the different regions of the hydrocyclone have been analyzed. The energy spectra are calculated at two points near the air-water interface. They show a short inertial subrange where energy decays as f−5/3, followed by viscous damping where energy drops as f−7, where f is frequency. However, for the points located near the boundary where high turbulent kinetic energy is found, the energy spectra exhibit f^(−4) decay. Secondly, the two-fluid (Eulerian two-fluid) model and large-eddy simulation are used to compute the turbulent two-phase flow of air and water in a cyclonic flotation device known as an Air-Sparged Hydrocyclone (ASH). In the operation of ASH, the air is injected through a porous cylindrical wall. The study considers a 48-mm diameter hydrocyclone and uses a block-structured fine mesh of 10.5 million hexahedral elements. The air-to-water injection ratio is 4, and a uniform air bubble diameter of 0.5 mm has been specified. The flow field in ASH has been investigated for the inlet flow rate of water of 30.6 L/min at different values of underflow exit pressure. The present simulations show that the value of static pressure imposed at the underflow section strongly affects the distribution of air volume fraction, water axial velocity, tangential velocity, and swirling layer thickness in ASH. The loci of zero-axial velocity surfaces have been determined for different exit pressures. The water split ratio through the overflow opening varies with underflow exit pressure as 6%, 8%, 16%, and 26% for 3, 4, 5, and 6 kPa, respectively. These results indicate that regulating the pressure at the underflow exit can be used to optimize ASH's performance. Turbulent energy spectra in different regions of the hydrocyclone have been analyzed. Small-scale turbulence spectra at near-wall points exhibit f^(−4) law, where f is frequency. Whereas for points at the air-column interface, the energy spectra show an inertial subrange f^(−5/3) followed by a dissipative range of f^(−7) law. Thirdly, large-eddy simulation (LES) has been used to investigate the flow separation in multi-phase flow (gas, liquid, and solid) in a classifying hydrocyclone using the multi-fluid (Eulerian multi-fluid) model. The results of the CFD simulation are compared with the Hsieh [1] experimental data. The water phase is considered a continuous phase, while air and solid particles are considered dispersed phases. Drag between water-air and water-sand is the only considered interfacial force. The Schiller-Naumann and Wen-Yu models are used to model the drag, and the Gidaspow model is used to calculate the solid pressure term. Various particle sizes are tested in the hydrocyclone to investigate the underflow recovery percentages. The results agree with the experimental data for the particles of a diameter smaller than 20 μm, while the results vary based on the model for the large particles. Therefore, using the Wen Yu and Schiller-Naumann model for the drag model and the Gidaspow model for the solid pressure in the three-fluid model could give acceptable results for the small particles underflow recovery and volume fraction distribution. However, the models failed for large particles. Finally, the large particle size separation needs more investigation. / Doctor of Philosophy / Hydrocyclones are widely used in mining and chemical industries. They can be used as separation devices to separate solid or fluid particles based on their size or/and weight. They can also be used as flotation devices to capture certain mineral particles from a slurry of water and solid particles. The flow field within a hydrocyclone is complex as it involves flow of different phases of matter (liquid, gas, and solid). It is also a turbulent flow in which the velocity and pressure fluctuate in time with many frequencies. The efficiency of the hydrocyclone depends on its geometry and distribution of the velocity. Computer simulations are very efficient tools to predict and study the flow field in hydrocyclones. This dissertation used a computer simulations to explain how turbulence could affect the particle separation from the slurry inside the hydrocyclones. The water's velocity fields, swirling flow, air behavior, pressure distribution and turbulence statistics are analysed. Understanding the turbulence structure and statistics in hydrocyclones is important for particle tracking and dispersion. Also, turbulent structure affects the motion of the air bubbles and solid particles in the flow field, which eventually will affect the hydrocyclone's performance. In short, a more comprehensive understanding of the behavior of turbulence of hydrocyclones represents an important tool that can guide the design of hydrocyclones according to their use goals and will help engineers who model these processes to develop a better model.