Supersonic slot injection problems were studied by a finite volume method. The numerical technique used is the upwind method of Roe’s flux difference splitting (FDS) with vertical line Gauss-Seidel relaxation applied to the thin layer Navier-Stokes equations. To test the accuracy of the numerical methods without the complications and uncertainties of turbulence modeling, two sample cases were chosen with laminar flows. The sample problems were the compressible laminar boundary layer flow over a flat plate and the laminar boundary layer - shock interaction problem. For these problems, both the results from Roe’s FDS and van Leer’s flux vector splitting (FVS) are compared with exact solutions and experimental data. For the sample problems, comparisons showed that Roe’s FDS method is more accurate than van Leer’s FVS method. Because of the very complicated wave patterns and strong viscous-inviscid interaction produced by supersonic slot injection, an adaptive grid based on the equidistribution law was combined with the solution algorithm. The results from Roe’s FDS method with the adaptive grid showed good results for the supersonic slot injection over a flat plate. For the slot injection over a 10-degree wedge surface case, there is a significant difference between the numerical and experimental wall pressure distribution. Some potential reasons for the discrepancy including 3D effects and/or transition in the reattachment region in the experiments and possibly a need for a much finer grid in the calculations are discussed. / Ph. D.

The majority of this work is concerned with the local-linear convective instability analysis of the incompressible boundary-layer flows over prolate spheroids and oblate spheroids rotating in otherwise still fluid. The laminar boundary layer and the perturbation equations have been formulated by introducing two distinct orthogonal coordinate systems. A cross-sectional eccentricity parameter e is introduced to identify each spheroid within its family. Both systems of equations reduce exactly to those already established for the rotating sphere boundary layer. The effects of viscosity and streamline-curvature are included in each analysis. We predict that for prolate spheroids at low to moderate latitudes, increasing eccentricity has a strong stabilizing effect. However, at high latitudes of ϴ ≥ 60, increasing eccentricity is seen to have a destabilizing effect. For oblate spheroids, increasing eccentricity has a stabilizing effect at all latitudes. Near the pole of both types of spheroids, the critical Reynolds numbers approach that for the rotating disk boundary layer. However, in prolate spheroid case near the pole for very large values of e, the critical Reynolds numbers exceed that for the rotating disk. We show that high curvature near the pole of prolate spheroids is responsible for the increase in critical Reynolds number with increasing eccentricity. For both types of spheroids at moderate eccentricity, we predict that the most amplified modes travel at approximately 76% of the surface speed at all latitudes. This is consistent with the existing studies of boundary-layer flows over the related rotating-disk, -sphere and -cone geometries. However, for large values of eccentricity, the traveling speed of the most amplified modes increases up to approximately 90% of the surface speed of oblate spheroids and up to 100% in the prolate spheroid case.

Dispositivos de reação miniaturizados tendem a ganhar espaço na indústria de processos químicos por elevarem o transporte de massa e de calor e a segurança dos processos. Para compreender o papel de cada elemento constituinte de um microrreator sobre seu campo de velocidades e fenômenos de mistura, foram simulados um conjunto de dois canais, uma junção em T, 30 canais em formato de serpentina e um microchip completo através da fluidodinâmica computacional. A seção transversal destes microdispositivos têm dimensões entre 100 e 300 µm, enquanto o comprimento dos canais varia de 3000 a 25190 µm. Os modelos computacionais foram discretizados por malhas hexaédricas e os campos de velocidade em estado estacionário foram calculados para vazões de alimentação entre 12,5 e 2000 µL min-1, considerando regime laminar. A mistura foi avaliada pela injeção de traçadores não-reativos e distribuição das respectivas frações mássicas. As simulações foram validadas usando microvelocimetria por imagens de partículas. Os campos de velocidade possuem magnitudes significativas apesar das dimensões reduzidas e baixas vazões de operação dos sistemas. As imagens experimentais do escoamento evidenciaram o formato parabólico do campo de velocidades e o deslocamento de seu ponto máximo nas regiões curvas causado pela força centrífuga, como estimado pelo modelo computacional. Tal força, em conjunto com as forças viscosas na parede, gera fluxos secundários no escoamento. A distribuição de traçadores não-reativos evidenciou a importância dos fluxos secundários para promover mistura na direção ortogonal ao escoamento principal, ocorrendo sob o regime estacionário nas vazões analisadas. O estudo aqui realizado evidencia o emprego da fluidodinâmica computacional como ferramenta para melhor compreensão da fluidodinâmica e como apoio ao projeto de microdispositivos. / Miniaturized reaction vessels are drawing attention of chemical industries because they promote better mass and heat transfer and also enhance process safety. To understand the relevance of each element of a microreactor on the velocity field of the equipment and the corresponding mixing processes, several microdevices were simulated using computational fluid dynamics: an assembly of two channels, a T-junction, 30 channels in a serpentine assembly and a full microreactor. The cross section of the devices is 100 - 300 µm wide and the length of the channels varies between 3000 and 25190 µm. Computational domains were discretized using hexahedral meshes and steady-state velocity fields were computed considering laminar flow for flow rates between 12,5 and 2000 µL min-1. Mixing was evaluated by injecting inert tracers and monitoring their distribution. Simulations were validated against experimental micro particle image velocimetry data. Velocities throughout the devices are relatively high despite the small dimensions of the cross sections and small flow rates. Experimental images of the flow elucidated the parabolic shape of the velocity profile and its distortion on curved segments caused by centrifugal forces, matching predictions of the computational model. Tracer maps indicated secondary flows play an important role in mixing stream perpendicular to the main flow direction. This study emphasizes the use of computational fluid dynamics as a tool for understating flow throughout microdevices and supporting their design.

"New, economical semi-solid metal (SSM) processes rely on forced convection during solidification to influence non-dendritic growth. The fundamental mechanisms that produce SSM microstructures in the presence of forced convection (due to fluid flow) are not fully understood. The objective of this work is to elucidate these mechanisms through the use of a new semi-solid slurry-making technique. Employing an apparatus developed at WPI, two alloy melts are mixed within a static reactor that induces convection and rapid cooling. Experiments carried out with this apparatus, named the “Continuous Rheoconversion Process” (CRP), result in globular semi-solid microstructures throughout a wide range of processing conditions. These conditions include the superheat in the melts before mixing, cooling rate of the slurry through the SSM range, and the presence or absence of inoculants in the melts. The results comprise repeatable sets of semi-solid microstructures having fine particle size and shape factors approaching unity. Even in the absence of melt inoculants, uniform distributions of α-Al particle sizes of about 60µm are attainable. Entrapped liquid is not present in the majority of the samples obtained with the CRP, and irregular particles that form in the process are of a limited distribution. Variation of slurry analysis methods indicates that these structures can be obtained consistently for both thixocasting and rheocasting applications. The design of the mixing reactor leads to turbulent fluid flow just as solidification commences. The results suggest that the following factors must be considered in identifying the mechanisms operating under the above conditions: copious nucleation of the primary phase; dispersion of nuclei throughout the bulk liquid; and inhibited remelting of nuclei due to temperature uniformity. In the CRP, these factors consistently lead to suppression of dendritic growth, significant grain refinement, and globular slurries. The exact fundamental mechanism leading to this effect is yet to be uncovered; however it is clear that temperature gradients ahead of the liquid are such that a cellular, non-dendritic morphology is the most stable growth form. Through further exploration of the process and identification of the operating mechanisms, future development of economical, continuous rheocasting methods will be facilitated."

<div>To reduce the risk of using suction in a hypersonic quiet-tunnel nozzle design, this project tested micro-perforated suction sections to remove the boundary layer on an axisymmetric model in the Boeing/AFOSR Mach-6 Quiet Tunnel. The model was a cone-flare geometry tested at 0° angle of attack. The turn from the 7° half-angle cone to the flare was designed to prevent flow separation. The flare was designed to amplify the Görtler instability.</div><div><br></div><div>Five suction sections were designed with different perforation patterns and porosities. Four were successfully manufactured, but only the first of the four sections has been tested so far. The first suction section has pores drilled along straight lines with a nominal 5% porosity.</div><div><br></div><div>Measurements were made with temperature-sensitive paint and oil-flow visualization on a non-perforated blank to measure the baseline development of Görtler vortices on the flare. Although the signal-to-noise ratio of the measurement techniques were insufficient to measure the vortices, it was confirmed that the boundary layer is laminar for the entire model. Measurements with suction also did not show the Görtler vortices.</div><div><br></div><div>Surface pressure fluctuations were measured on the flare. Apparent second-mode waves were detected. The suction measurements showed a slight increase in second-mode peak frequency over the baseline results, as expected.</div><div><br></div><div>Concerns had been raised about acoustic noise that might be radiated from the suction section. Thus, fluctuations above the suction section were measured using a pitot probe and using focused-laser differential interferometry. The measurements during suction showed no noticeable increase in fluctuations compared to the baseline results.</div>

The Generation IV Very High Temperature Reactor (VHTR) design is being actively studied in various countries for application due to its inherent passive safe design, higher thermal efficiencies, and proposed capability of providing high temperature process heat. The pebble bed core is one of two core designs used in gas reactors. In the pebble bed core there are mechanisms present which can cause the flow to laminarize, thus reducing its heat transfer effectiveness. Wind tunnel experiments were conducted using Particle Image Velocimetry (PIV) to investigate boundary layer laminarization due to flow acceleration and convex curvature effects. The flow was subject to acceleration and curvature both separately and together and the flow behavior characterized with velocity flow profiles, mean boundary layer parameters, and turbulence quantities. Laminarization was identified and the influence of acceleration and curvature was characterized. / Graduation date: 2013

In this investigation, the flow friction associated with laminar pulsating flows through porous media was numerically studied. The problem is of interest for understanding the regenerators of Stirling and pulse tube cryocoolers. Two-dimensional flow in a system composed of a number of unit cells of generic porous structures was simulated using a CFD tool, with sinusoidal variations of flow with time. Detailed numerical data representing the oscillating velocity and pressure variations for five different generic porous structure geometries in the porosity range of 0.64 to 0.84, with flow pulsation frequency of 40 Hz were obtained, and special attention was paid to the phase shift characteristics between the velocity and pressure waves. Based on these detailed numerical data, the standard unsteady volume-averaged momentum conservation equation for porous media was then applied in order to obtain the instantaneous as well as cycle-averaged permeability and Forchheimer coefficients. It was found that the cycle-averaged permeability coefficients were nearly the same as those for steady flow, but the cycle-averaged Forchheimer coefficients were about two times larger than those for steady flow. Significant phase lags were observed with respect to the volume-averaged velocity and pressure waves. The parametric trends representing the dependence of these phase lags on porosity and flow Reynolds number were discussed. The phase difference between pressure and velocity waves, which is important for pulse tube cryocooling, depended strongly on porosity and flow Reynolds number.

Thesis (MScEng (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2006. / An analytical modelling procedure for predicting the streamwise pressure gradient for steady laminar incompressible flow of a Newtonian fluid through homogeneous isotropic granular porous media is introduced. The modelling strategy involves the spatial volume averaging of a statistical representative portion of the porous domain to obtain measurable macroscopic quantities from which macroscopic transport equations can be derived. A simple pore-scale model is introduced to approximate the actual complex granular porous microstructure through rectangular cubic geometry. The sound physical principles on which the modelling procedure is based avoid the need for redundant empirical coefficients. The model is generalized to predict the rheological flow behaviour of non-Newtonian purely viscous power law fluids by introducing the dependence of the apparent viscosity on the shear rate through the wall shear stress. The field of application of the Newtonian model is extended to predict the flow behaviour in fluidized beds by adjusting the Darcy velocity to incorporate the relative velocity of the solid phase. The Newtonian model is furthermore adjusted to predict fluid flow through Fontainebleau sandstone by taking into account the effect of blocked throats at very low porosities. The analytical model as well as the model generalizations for extended applicability is verified through comparison with other analytical and semi-empirical models and a wide range of experimental data from the literature. The accuracy of the predictive analytical model reveals to be highly acceptable for most engineering designs.

[pt] O escoamento de suspensões concentradas tem grande importância em diversos segmentos da indústria, representando uma maneira econômica de transportar grandes quantidades de materiais sólidos particulados. Uma das aplicações inclui a etapa de perfuração de poços de petróleo direcionais. No decorrer do processo são gerados sedimentos originários do corte da formação, que são removidos através da operação de limpeza do poço. Durante a limpeza, no trecho de maior inclinação esses sedimentos tendem a se separar da suspensão, pelo efeito gravitacional, formando um leito na parte inferior do anular. Esse leito formado pode causar vários problemas, como redução da taxa de penetração, desgaste prematuro da broca, prisão da coluna de perfuração, fraturamento da formação e torque excessivo na coluna de perfuração. O entendimento do escoamento de suspensões de partículas se torna relevante para o aperfeiçoamento desses processos. Nesse sentido, o objetivo deste trabalho é analisar o escoamento de suspensões de partículas entre duas placas paralelas para estudar a formação de um leito de sedimentos na parte inferior do canal e determinar o efeito dos diferentes mecanismos de migração de partículas neste processo. A formulação matemática do problema inclui as equações de conservação de massa e quantidade de movimento linear e equação de transporte de partículas. Para descrever o transporte de partículas no escoamento foi usado o modelo de fluxo difusivo proposto por Phillips et al. (1992). As equações diferenciais parciais, que descrevem o escoamento de uma suspensão de partículas, são resolvidas pelo método de Elementos Finitos de Galerkin e o sistema não-linear é resolvido através do método de Newton. Os resultados obtidos mostram como a distribuição das partículas sólidas varia com os parâmetros do problema e determina as condições para a formação de um leito de partículas. / [en] The flow of solid particles suspended in a liquid medium have great importance in several industry segments representing an economical way to transport large quantities of solid materials. One of the applications includes the flow during directional well drilling. During the process sediments are generated from the formation cutting, which are removed through the wellbore cleaning. During the cleaning, step near the horizontal section of the well, these sediments tend to separate from the suspension by the action of gravity, forming a stationary bed in the bottom of the annular. This stationary bed can cause problems, such as reducing the penetration rate, premature wear of the drill bit, trapping column, fracturing of the formation and high torque. The complete understanding of the flow of solid particles suspension becomes relevant to the improvement of these processes. In this sense, the main goal of this work is to analyze the flow of solid particle suspensions between two parallel plates to investigate the formation of a stationary bed in the bottom of the channel and to determine the effect of different particle migration mechanisms in this process. The mathematical formulation includes the equations of mass (continuity equation) and momentum conservation. The Diffusive Flux Model proposed by Phillips et al. (1992) was used to describe the particle transport in the flow. The partial differential equations, which describe the flow of solid particles suspension, are solved by the Galerkin/Finite Element Method (GFEM) and the non-linear system is solved using Newton s Method. The results show how the distribution of solid particles varies with the problem parameters and determines the conditions for the formation of a stationary bed.

Thesis submitted in fulfillment of the requirements for the degree Doctor of Technology: Mechanical Engineering Cape Peninsula University of Technology, 2013 / Fluid flow through a porous channel and cylindrical pipe walls are important area of research due to its wide applications in transpiration cooling, gaseous diffusion technology, cooling of rocket, mechanized irrigation and filtration processes. It is therefore necessary to examine the effect of Navier slip, combined effects of buoyancy forces and variable viscosity on the entire flow structure. Analyzing the magneto- hydrodynamics (MHD) of unsteady flow with buoyancy effect and also investigate numerically the entropy generation in an unsteady flow through porous pipe. We have also examined the thermal stability and entropy generation in the system. The problems were investigated theoretically using appropriate mathematical models for both transient and steady state scenario. Both analytical techniques and numerical methods are employed to tackle the model nonlinear equations derived from the law of conservation of mass, momentum and energy balance. Some definitions of terms to come across and introduction to fluid flow are given in chapter 1, together with literature reviews, statement of problem and objectives of the study. Chapter 2 lays the foundation for basic fundamental equations governing fluid flow. In chapter 3, the combined effect of suction/injection and asymmetric Navier slip on the entropy generation rate for steady flow of an incompressible viscous fluid through a porous channel subjected to different temperature at the walls are investigated. Chapter 4 analyze combined effects of buoyancy forces together with Navier slip on the entropy generation in a vertical porous channel wall with suction/injection wall. Analysis of MHD unsteady flow through a porous pipe with buoyancy effects are carried out in chapter 5, while chapter 6 investigates numerically entropy generation of unsteady flow through a porous pipe with suction and chapter 7 gives concluding remarks.