The aim of this thesis is to develop a flow solver that has the ability to obtain an accurate numerical solution fast and efficiently with minimum user intervention. In this study, a two-dimensional viscous, laminar, incompressible flow solver based on Least-Squares Spectral Element Method (LSSEM) is developed. The LSSEM flow solver can work on hp-type nonconforming grids and can perform p-type adaptive refinement. Several benchmark problems are solved in order to validate the solver and successful results are obtained. In particular, it is demonstrated that p-type adaptive refinement on hp-type non-conforming grids can be used to improve the quality of the solution. Moreover, it is found that mass conservation performance of LSSEM can be enhanced by using p-type adaptive refinement strategies while keeping computational costs reasonable.

A spectral element algorithm for solution of the incompressible Navier-Stokes and heat transfer equations is developed, with an emphasis on extending the classical conforming Galerkin formulations to nonconforming spectral elements. The new algorithm employs both the Constrained Approximation Method (CAM), and the Mortar Element Method (MEM) for p-and h-type nonconforming elements. Detailed descriptions, and formulation steps for both methods, as well as the performance comparisons between CAM and MEM, are presented. This study fills an important gap in the literature by providing a detailed explanation for treatment of p-and h-type nonconforming interfaces. A comparative eigenvalue spectrum analysis of diffusion and convection operators is provided for CAM and MEM. Effects of consistency errors due to the nonconforming formulations on the convergence of steady and time dependent problems are studied in detail. Incompressible flow solvers that can utilize these nonconforming formulations on both p- and h-type nonconforming grids are developed and validated. Engineering use of the developed solvers are demonstrated by detailed parametric analyses of oscillatory flow forced convection heat transfer in two-dimensional channels.

Spectral element based numerical solvers are developed to simulate electrokinetically driven flows for micro-fluidic applications. Based on these numerical solvers, basic phenomena and devices for electrokinetic applications in micro and nano flows are systematically studied. As a first application, flow and species transport control in a grooved micro-channel using local electrokinetic forces are studied. Locally applied electric fields, zeta potential patterned grooved surfaces, and geometry are manipulated to control mixed electroosmotic/pressure driven flow in the grooved micro-channel. The controlled flow pattern enables entrapment and release of prescribed amounts of scalar species in the grooves. As another application, hydrodynamic/ electrokinetic focusing in a micro-channel is studied. External electric field, flow rate of pressure driven flow, and geometry in the micro-channel are manipulated to obtain the focusing point, which led to determination of the electrophoretic mobility and (relative) concentration of dilute mixtures. This technique can be used to identify and detect species in dilute mixtures.

abstract: A moving overlapping mesh methodology that achieves spectral accuracy in space and up to second-order accuracy in time is developed for solution of unsteady incompressible flow equations in three-dimensional domains. The targeted applications are in aerospace and mechanical engineering domains and involve problems in turbomachinery, rotary aircrafts, wind turbines and others. The methodology is built within the dual-session communication framework initially developed for stationary overlapping meshes. The methodology employs semi-implicit spectral element discretization of equations in each subdomain and explicit treatment of subdomain interfaces with spectrally-accurate spatial interpolation and high-order accurate temporal extrapolation, and requires few, if any, iterations, yet maintains the global accuracy and stability of the underlying flow solver. Mesh movement is enabled through the Arbitrary Lagrangian-Eulerian formulation of the governing equations, which allows for prescription of arbitrary velocity values at discrete mesh points. The stationary and moving overlapping mesh methodologies are thoroughly validated using two- and three-dimensional benchmark problems in laminar and turbulent flows. The spatial and temporal global convergence, for both methods, is documented and is in agreement with the nominal order of accuracy of the underlying solver. Stationary overlapping mesh methodology was validated to assess the influence of long integration times and inflow-outflow global boundary conditions on the performance. In a turbulent benchmark of fully-developed turbulent pipe flow, the turbulent statistics are validated against the available data. Moving overlapping mesh simulations are validated on the problems of two-dimensional oscillating cylinder and a three-dimensional rotating sphere. The aerodynamic forces acting on these moving rigid bodies are determined, and all results are compared with published data. Scaling tests, with both methodologies, show near linear strong scaling, even for moderately large processor counts. The moving overlapping mesh methodology is utilized to investigate the effect of an upstream turbulent wake on a three-dimensional oscillating NACA0012 extruded airfoil. A direct numerical simulation (DNS) at Reynolds Number 44,000 is performed for steady inflow incident upon the airfoil oscillating between angle of attack 5.6 and 25 degrees with reduced frequency k=0.16. Results are contrasted with subsequent DNS of the same oscillating airfoil in a turbulent wake generated by a stationary upstream cylinder. / Dissertation/Thesis / Doctoral Dissertation Aerospace Engineering 2016

abstract: The effect of reduced frequency on dynamic stall behavior of a pitching NACA0012 airfoil in a turbulent wake using Direct Numerical Simulations is presented in the current study. Upstream turbulence with dynamically oscillating blades and airfoils is associated with ambient flow unsteadiness and is encountered in many operating conditions. Wake turbulence, a more realistic scenario for airfoils in operation, is generated using a small solid cylinder placed upstream, the vortices shed from which interact with the pitching airfoil affecting dynamic stall behavior. A recently developed moving overlapping grid approach is used using a high-order Spectral Element Method (SEM) for spatial discretization combined with a dynamic time-stepping procedure allowing for up to third order temporal discretization. Two cases of reduced frequency (k = 0:16 and 0:25) for airfoil oscillation are investigated and the change in dynamic stall behavior with change in reduced frequency is studied and documented using flow-fields and aerodynamic coefficients (Drag, Lift and Pitching Moment) with a focus on understanding vortex system dynamics (including formation of secondary vortices) for different reduced frequencies and it’s affect on airfoil aerodynamic characteristics and fatigue life. Transition of the flow over the surface of an airfoil for both undisturbed and disturbed flow cases will also be discussed using Pressure coefficient and Skin Friction coefficient data for a given cycle combined with a wavelet analysis using Morse wavelets in MATLAB. / Dissertation/Thesis / Masters Thesis Mechanical Engineering 2017

Red blood cells (RBCs) are the most abundant cells in human blood, representing 40 to 45% of the blood volume (hematocrit). These cells have the particular ability to deform and bridge together to form aggregates under very low shear rates. The theory and mechanics behind aggregation are, however, not yet completely understood. The purpose of this work is to provide a novel method to analyze, understand and mimic blood behaviour in microcirculation. The main objective is to develop a methodology to quantify and characterize RBC aggregates and hence enhance the current understanding of the non-Newtonian behaviour of blood at the microscale. For this purpose, suspensions of porcine blood and human blood are tested in vitro in a Poly-di-methylsiloxane (PDMS) microchannel to characterize RBC aggregates within these two types of blood. These microchannels are fabricated using standard photolithography methods. Experiments are performed using a micro Particle Image Velocimetry ( PIV) system for shear rate measurements coupled with a high speed camera for the flow visualization. Corresponding numerical simulations are conducted using a research Computational Fluid Dynamic (CFD) solver, Nek5000, based on the spectral element method solution to the incompressible non-Newtonian Navier-Stokes equations. RBC aggregate sizes are quantified in controlled and measurable shear rate environments for 5, 10 and 15% hematocrit. Aggregate sizes are determined using image processing techniques. Velocity fields of the blood flow are measured experimentally and compared to numerical simulations using simple non-Newtonian models (Power law and Carreau models). This work establishes for the first time a relationship between RBC aggregate sizes and corresponding shear rates in a microfluidic environment as well as one between RBC aggregate sizes and apparent blood viscosity at body temperature in a microfluidic controlled environment. The results of the investigation can be used to help develop new numerical models for non-Newtonian blood flow, provide a better understanding of the mechanics of RBC aggregation and help determine aggregate behaviour in clinical settings such as for degenerative diseases like diabetes and heart disease.

In the thesis we study incompressible turbulent flow using spectral element method (SEM). We present fundamentals of SEM which can be seen as a combination of spectral method and finite element method. Turbulent flow is described with the help of two-equation k-ω turbulence models. We give reasons for the choice of Kolmogorov's and Wilcox model and implement them in 2D into an existing SEM C++ framework, Nektar++. Analytical solutions of Navier- Stokes equation were found and used as test cases for the implementation of the models. We simulated turbulent flow in channel and compared the results with direct numerical simulation. 1

QC 20101105

The development of adaptive mesh refinement capabilities in the field of computational fluid dynamics is an essential tool for enabling the simulation of larger and more complex physical problems. While such techniques have been known for a long time, most simulations do not make use of them because of the lack of a robust implementation. In this work, we present recent progresses that have been made to develop adaptive mesh refinement features in Nek5000, a code based on the spectral element method. These developments are driven by the algorithmic challenges posed by future exascale supercomputers. First, we perform the study of the strong scaling of Nek5000 on three petascale machines in order to assess the scalability of the code and identify the current bottlenecks. It is found that strong scaling limit ranges between 5, 000 and 220, 000 degrees of freedom per core depending on the machine and the case. The need for synchronized and low latency communication for efficient computational fluid dynamics simulation is also confirmed. Additionally, we present how Hypre, a library for linear algebra, is used to develop a new and efficient code for performing the setup step required prior to the use of an algebraic multigrid solver for preconditioning the pressure equation in Nek5000. Finally, the main objective of this work is to develop new methods for estimating the error on a numerical solution of the Navier–Stokes equations via the resolution of an adjoint problem. These new estimators are compared to existing ones, which are based on the decay of the spectral coefficients. Then, the estimators are combined with newly implemented capabilities in Nek5000 for automatic grid refinement and adaptive mesh adaptation is carried out. The applications considered so far are steady and two-dimensional, namely the lid-driven cavity at Re = 7, 500 and the flow past a cylinder at Re = 40. The use of adaptive mesh refinement techniques makes mesh generation easier and it is shown that a similar accuracy as with a static mesh can be reached with a significant reduction in the number of degrees of freedom. / <p>QC 20171114</p>

No description available.