A numerical method for the simulation of compressible turbulent flows is presented. This method includes a novel hybrid grid generation for airfoil cascades and an unstructured mesh flow solver. The mesh tool incorporates a mapping technique and a grid smoothing method. The mapping technique is used to build an initial volume mesh and the grid smoothing method is used to improve the quality of the initial mesh. The grid smoothing is based on the optimization of mesh-quality parameters. The further improvement of the smoothed mesh is achieved by an edge-swapping and node-insertion technique. The unstructured flow solver is developed for a hybrid grid. This flow solver uses a rotational frame of reference. The convective and viscous fluxes are numerically solved by an upwind scheme and an averaged nodal gradient. A higher-order spatial accuracy is achieved by a piece-wise linear reconstruction. An explicit multi-stage method is employed for integration in time. The Menter’s k −τ model is implemented to simulate the turbulence effects. The flow solver is validated against the analytical and experimental results. A parametric study is performed for a high speed centrifugal compressor.

A numerical method for the simulation of compressible turbulent flows is presented. This method includes a novel hybrid grid generation for airfoil cascades and an unstructured mesh flow solver. The mesh tool incorporates a mapping technique and a grid smoothing method. The mapping technique is used to build an initial volume mesh and the grid smoothing method is used to improve the quality of the initial mesh. The grid smoothing is based on the optimization of mesh-quality parameters. The further improvement of the smoothed mesh is achieved by an edge-swapping and node-insertion technique. The unstructured flow solver is developed for a hybrid grid. This flow solver uses a rotational frame of reference. The convective and viscous fluxes are numerically solved by an upwind scheme and an averaged nodal gradient. A higher-order spatial accuracy is achieved by a piece-wise linear reconstruction. An explicit multi-stage method is employed for integration in time. The Menter’s k −τ model is implemented to simulate the turbulence effects. The flow solver is validated against the analytical and experimental results. A parametric study is performed for a high speed centrifugal compressor.

The objective of this thesis is to develop an easy-to-use and computationally economical numerical tool to investigate the flow field in the Pulsed Pressure Chemical Vapour Deposition (PP-CVD) reactor. The PP-CVD process is a novel thin film deposition technique with some advantages over traditional CVD methods. The numerical modelling of the PP-CVD flow field is carried out using the Quiet Direct Simulation (QDS) method, which is a flux-based kinetic-theory approach. Two approaches are considered for the flux reconstruction, which are the true directional manner and the directional splitting method. Both the true directional and the directional decoupled QDS codes are validated against various numerical methods which include EFM, direct simulation, Riemann solver and the Godunov method. Both two dimensional and axisymmetric test problems are considered. Simulations are conducted to investigate the PP-CVD reactor flow field at 1 Pa and 1 kPa reactor base pressures. A droplet flash evaporation model is presented to model the evaporation and transport of the liquid droplets injected. The solution of the droplet flash evaporation model is used as the inlet conditions for the QDS gas phase solver. The droplet model is found to be able to provide pressure rise in the reactor at the predicted rate. A series of parametric studies are conducted for the PP-CVD process. The numerical study confirms the hypothesis that the flow field uniformity is insensitive to the reactor geometry. However, a sufficient distance from the injection inlet is required to allow the injected precursor solution to diffuse uniformly before reaching the substrate. It is also recommended that placement of the substrate at the reactor’s centre axis should be avoided.

This thesis discusses the application, evaluation, and extension of dimensionally adaptive meshing to the numerical solution of velocity and pressure fields inside cylindrical reactors. Due to the high length to diameter ratios of many cylindrical reactor vessels the flow field can become axisymmetric, allowing for simplification of the governing equations and significant reduction in computational time required for solution. A fully 3D solver is developed from existing computational tools at BYU and validated against theoretical velocity profiles for pipe flow at various Reynolds numbers, as well as with experimental data for an axial-fired center jet with recirculating flow. Dimensionally adaptive meshing is then incorporated into the validated 3D solver. The boundary conditions and assumptions at the dimensional boundary are discussed. The flow information is passed across the boundary through spatial mass-weighted averaging. The 3D and axisymmetric computational domains are decoupled from one another so information can only be passed from the 3D domain downstream to the axisymmetric domain. The dimensional boundary placement must meet two main requirements, the flow must be one-way and axisymmetric. It is found that the flow becomes axisymmetric early on in the reactor (~0.3-0.4 m), but recirculation exists farther downstream (until ~0.61 m) and thus governs the placement of the dimensional boundary. The resulting computational tool capable of running simulations using dimensionally adaptive meshes is called CEDAR (Computationally Efficient Dimensionally Adaptive Recirculating flow solver). Several studies are then undertaken to examine CEDAR's ability to reproduce exit velocity profiles comparable to those produced by a fully 3D mesh, including variations in pressure, firing rate, and geometry. It is found that the flow structure inside the reactor is self-similar over a wide range of operating parameters as long as the burner jets are turbulent. This observation is supported by free and confined jet theory. These theories also provide a method for placing the dimensional boundary, which is a linear function of the confining geometry diameter only (assuming that the jet diameter is less than 1/10 the diameter of the confining geometry). All exit velocity profiles produced by CEDAR are on average within 5% of the fully 3D profiles. Timing studies reveal an average 5.16 times speedup in computational time over fully 3D computations.

Distributed memory systems have gained immense popularity due to their favorable price/performance ratios. This study seeks to reduce the complexities, involved in developing parallel applications for distributed memory systems. The Loci system is a coordination framework which was developed to eliminate most of the accidental complexities involved in numerical simulation software development. A distributed memory version of Loci is developed and has been tested and validated using a finite-rate chemically reacting flow solver developed in the sequential Loci framework. The application developed in the original sequential version of Loci was parallelized with minimal changes in its source code. A comparison with the results from the original sequential version guarantees a correct implementation. The performance measurements indicate that an efficient implementation has been achieved.

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In gas stirred steelmaking ladles, entrainment of slag into metal and vice versa takes place. The slag entrainment has been shown to abruptly increase the mass transfer rates of refining reactions through high temperature and water modeling studies of the past. However such an effect has not been correlated with the degree of entrainment, since the latter has not been quantified in terms of operating parameters like gas injection rate and fluid properties. Much of the past works are limited to finding the critical conditions for onset of entrainment. The difficulty lies in measuring the degree of entrainment in industrial ladles or even in a water model. Mathematical modeling is also challenging due to the complexity of the multiphase phenomena. So in this thesis, a modular mathematical modeling approach is presented wherein the phenomena of slag entrainment into metal is resolved into four aspects, models developed for each and finally integrated to study its role. The individual models are (1) multiphase large eddy simulations to simulate slag entrainment in a narrow domain that receives its boundary conditions from (2) single phase RANS simulation of a full ladle, (3) a Lagrangian particle tracking method to compute the residence times of slag droplets in metal phase and (4) a kinetic model that integrates the above three models to compute mass transfer rate as a function of degree of entrainment. Mass transfer rate predictions comparable to a literature correlation were obtained. This supports the modeling approach and also the assessment of role of various system parameters on entrainment characteristics. In essence, the present work shows a systematic approach to model and study the complex multiphase phenomena. / Thesis / Doctor of Philosophy (PhD) / The entrainment of liquid slag into liquid steel in gas stirred-steelmaking ladles is known to increase the rate of refining drastically. However, there is lack of correlation between degree of entrainment and ladle operating conditions, which this thesis addresses through mathematical modeling.

Micro Aerial Vehicles (MAVs) are battery operated, remote controlled miniature flying vehicles. MAVs are required in military missions, traffic management, hostage situation surveillance, sensing, spying, scientific, rescue, police and mapping applications. The essential characteristics required for MAVs are: light weight, maneuverability, ease of launch in variety of conditions, ability to operate in very hostile environments, stealth capabilities and small size. There are three main classes of MAVs : fixed, rotary and flapping wing MAV’s. There are some MAVs which are combinations of these main classes. Each class has its own advantage and disadvantage. Different scenarios may call for different types of MAV. Amongst the various classes, flapping wing class of MAVs offer the required potential for miniaturisation and maneuverability, necessitating the need to understand flapping wing flight. In the case of flapping winged flight, the thrust required for the vehicle flight is obtained due to the flapping of the wing. Hence for efficient flapping flight, optimising the flap motion is necessary. In this thesis work, an algorithm for motion optimisation of plunging airfoils is developed in a parallel framework. An evolutionary optimisation algorithm, PSO (Particle Swarm Optimisation), is coupled with an unsteady flow solver to develop a generic motion optimisation tool for plunging airfoils. All the unsteady flow computations in this work are done with the HIFUN1 code, developed in–house in the Computational Aerodynamics Laboratory, IISc. This code is a cell centered finite volume compressible flow solver. The motion optimisation algorithm involves starting with a population of motion curves from which an optimal curve is evolved. Parametric representation of curves using NURBS is used for efficient handling of the motion paths. In the present case, the motion paths of a plunging NACA 0012 airfoil is optimised to give maximum flight efficiency for both inviscid and laminar cases. Also, the present analysis considers all practically achievable plunge paths, si- nusoidal and non–sinusoidal, with varying plunge amplitudes and slopes. The results show promise, and indicate that the algorithm can be extended to more realistic three dimension motion optimisation studies.

Computing 3D high lift flows has been a challenge to the CFD community because of three important reasons: complex physics, complex geometries and large computational requirements. In the recent years, considerable progress has been made in understanding the suitability of various CFD solvers in computing 3D high lift flows, through the systematic studies carried out under High Lift Prediction workshops. The primary focus of these workshops is to assess the ability of the CFD solvers to predict CLmax and αmax associated with the high lift flows, apart from the predictability of lift and drag of such flows in the linear region. Now there is a reasonable consensus in the community about the ability of the CFD solvers to predict these quantities and fresh efforts to further understand the ability of the CFD solvers to predict more complex physics associated with these flows have already begun. The goal of this thesis is to assess the capability of the computational methods in predicting such complex flow phenomena associated with the 3D High-Lift systems. For evaluation NASA three element Trapezoidal wing configuration which poses a challenging task in numerical modeling was selected. Unstructured data based 3D RANS solver HiFUN (HiFUN stands for High Resolution Flow Solver for UNstructured Meshes) is used in investigating the high lift flow. The computations were run fully turbulent, using the one equation Spalart-Allmaras turbulence model. A summary of the results obtained using the flow solver HiFUN for the 3D High lift NASA Trapezoidal wing are presented. Hybrid unstructured grids have been used for the computations. Grid converged solution obtained for the clean wing and the wing with support brackets, are compared with experimental data. The ability of the solver to predict critical design parameters associated with the high lift flow, such as αmax and CLmax is demonstrated. The utility of the CFD tools, in predicting change in aerodynamic parameters in response to perturbational changes in the configuration is brought out. The solutions obtained for the high lift configuration from two variants of the Spalart-Allmaras turbulence model are compared. To check the unsteadiness in the flow, particularly near stall, unsteady simulations were performed on static grid. Lastly, hysteresis on lower leg of lift curve is discussed, the results obtained for quasi-steady and dynamic unsteady simulations are presented. Inferences from the study on useful design practices pertaining to the 3D high lift flow simulations are summarized.

A high resolution spectrally accurate three-dimensional flow solver is developed in order to simulate convection dominated fluid flows. The governing incompressible Navier Stokes equations along with the energy equation for temperature are discretized using a second-order accurate projection method which utilizes Adams Bashforth and Backward Differentiation formula for temporal discretization of the non-linear convective and linear viscous terms, respectively. Spatial discretization is performed using a Fourier/Chebyshev spectral method. Extensive tests on three-dimensional Taylor Couette flow are performed and it is shown that the method successfully captures the different states ranging from formation of Taylor vortices to wavy vortex regime. Next, the code is validated for convection dominated flows through a comprehensive comparison of the results for two dimensional Rayleigh Benard convection with the theoretical and experimental results from the literature. Finally, fully parallel simulations, with efficient utilization of computational resources and memory, are performed on a model three-dimensional axially homogeneous Rayleigh Benard convection problem in order to explore the high Rayleigh number flows and to test the scaling of global properties.