This paper deals with three problems, (1) laminar incompressible viscous flow past a cylinder and a sphere, (2) laminar incompressible viscous flow past a finite flat plate (second-order solutions), and (3) laminar viscous past a sphere at a high Mach number. These problems are solved by using an implicit finite-difference method. The first problem (flow past a sphere and a cylinder) involves the classical boundary-layer equations which are the first approximation to the Navier-Stokes equations in a region near to the body surface for high Reynolds number. The computational results were obtained for the distribution of velocity components in the boundary-layer, and the variation of skin-friction and displacement-thickness along the body. The second problem (second-order flow past a finite flat plate) involves the second-order boundary-layer equations which introduce only the effect of the displacement-thickness in the case of flow past a flat plate. An assumption is made that the displacement-thickness is constant in the wake behind the flat plate. The adequacy of this assumption is checked from solutions based on the calculated displacement-thickness in the wake. The wake behind the finite flat plate is assumed laminar, and its displacement-thickness and the velocity distribution are computed downstream, by using the implicit finite-difference method. In the third problem (high Mach number flow past a sphere), constant density is assumed in the shock layer. This is nearly true in the stagnation-point region, especially if the flow is hypersonic and the temperature of the sphere is nearly the same as the stagnation-temperature. It is also assumed that the shock is nearly spherical, even though it is not spherical as it is in the inviscid case. The numerical results will show that the assumption of a spherical shock will, however, nearly be true. This problem involves the solution of the complete Navier-Stokes equations. These equations are solved for various Reynolds numbers by two methods; namely the truncated series method and the implicit finite-difference method. The solutions by the implicit finite-difference method are in excellent accord with those obtained by the series solutions in the stagnation-point region. As the computation by the finite-difference method proceeds downstream, the deviation of the finite-difference solution from the series solution increases. This is due to the fact that the series is valid only around the stagnation-point, and is thus expected to give inaccurate solutions downstream. The finite-difference method has no such restrictions, however, and gives accurate results in the whole flow field. In conclusion, solutions by the implicit finite-difference method have proven not only to be accurate but also to be stable in all examples computed. / Ph. D.

An oscillating-hot-wire system is developed to allow mean-flow velocity measurements in separated flows. Disturbance velocities can also be measured in regions of interest. An oscillating-arm assembly provides a directional bias to the hot-wire probe, and a linear-step assembly steps the probe through the boundary layer. These assemblies are mounted to a positioning plate which allows profiles to be taken at a discrete number of chord locations. Data sampling is computer regulated using a trigger pulse from an exterior source. A distance proximity probe gives the distance of the hot-wire probe from the model. Series of mean-velocity profiles over an airfoil are measured for R_C 150,000, 200,000, 250,000, and 300,000 with a= 14° and for R_C = 200,000 and 250,000 with α= 12°. / M.S.

M.S.

Following the concepts of stability analysis, a study is made of the pre-breakdown stage of transition to turbulence in boundary layers. The first step consists of a ’decoupling’ of the primary and secondary instabilities. A perturbation method is used to solve for the primary wave, in the absence of any secondary disturbances. Once the wave is calculated, it is decomposed into a basic flow portion and an interaction portion. The basic flow portion acts as a parametric excitation for the secondary wave. The interaction portion then captures the resonance effects of the secondary back onto the primary. A perturbation method is also used for the secondary and interaction components. The results obtained are in three principal forms: Landau constants, amplitude growth curves, and velocity functions. While in good agreement with experiments and simulations, these results offer new explanations to the observed processes. In addition, a physically-based transition criteria is established. / Ph. D.

The linear stability equations which govern the growth of small periodic disturbances for compressible, three-dimensional laminar boundary layer flow are derived in an orthogonal curvilinear coordinate system. The parallel flow assumption is utilized in the derivation. The system of equations is solved using a finite difference scheme similar to that in a current state-of-the-art stability analysis code, COSAL. The LR method and the inverse Rayleigh iteration procedure are used to calculate the eigenvalues. The stability of the three-dimensional compressible laminar boundary layer including the effects of streamline and surface curvature for flows past swept wings where crossflow type disturbances dominate is calculated. A parametric study is performed varying Reynolds number and sweep angle on an airfoil with a concave cutout in the leading edge region of the lower surface. It is known that convex curvature has a stabilizing effect on the laminar boundary layer. Conversely, concave curvature has a destabilizing effect. The magnitude of these effects for swept wing flows is determined. Non-stationary as well as stationary disturbances are calculated, and the most amplified frequencies are identified. N-factor correlations at the measured location of transition are made utilizing flight test data. Results indicate that amplification rates and hence, N-factors, for swept wing flows over convex surfaces are reduced by about 30 to 50 percent when curvature effects are included in the linear stability analysis. In addition, comparisons are made with some experimental results on a swept concave-convex surface. Calculated velocity vector plots show good agreement with observed disturbances in the laminar boundary layer over the concave surface. The results of the calculations show that concave curvature destabilizes "crossflow” type disturbances with a 30 percent increase in amplification rate. / Ph. D.

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.

The aerodynamic benefits of laminar flow have long made it a sought-after attribute in aircraft design. By laminarizing portions of an aircraft, such as the wing or empennage, significant reductions in drag could be achieved, reducing fuel burn rate and increasing range. In addition to environmental benefits, the economic implications of improved fuel efficiency could be substantial due to the upward trend of fuel prices. This is especially true for the commercial aviation industry, where fuel usage is high and fuel expense as a percent of total operating cost is high. Transition from laminar to turbulent flow can be caused by several different transition mechanisms, but the crossflow instability present in swept-wing boundary layers remains the primary obstacle to overcome. One promising technique that could be used to control the crossflow instability is the use of spanwise-periodic discrete roughness elements (DREs). The Flight Research Laboratory (FRL) at Texas A&M University has already shown that an array of DREs can successfully delay transition beyond its natural location in flight at chord Reynolds numbers of 8.0x10^6. The next step is to apply DRE technology at Reynolds numbers between 20x10^6 and 30x10^6, characteristic of transport aircraft. NASA's Environmentally Responsible Aviation Project has sponsored a transonic laminar-flow wing glove experiment further exploring the capabilities of DRE technology. The experiment will be carried out jointly by FRL, the NASA Langley Research Center, and the NASA Dryden Flight Research Center. Upon completion of a wing glove design, a thorough computational evaluation was necessary to determine if the design can meet the experimental requirements. First, representative CAD models of the testbed aircraft and wing glove were created. Next, a computational grid was generated employing these CAD models. Following this step, full-aircraft CFD flowfield calculations were completed at a variety of flight conditions. Finally, these flowfield data were used to perform boundary-layer stability calculations for the wing glove. Based on the results generated by flowfield and stability calculations, conclusions and recommendations regarding design effectiveness were made, providing guidance for the experiment as it moved beyond the design phase.

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.

[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.

[pt] O presente trabalho é um estudo experimental sobre o escoamento laminar de óleos pesados através de dutos longos isolados termicamente e que apresentam forte dependência da viscosidade com a temperatura. O objetivo do estudo é identificar e interpretar o comportamento verificado em operações de campo onde a dependência da queda de pressão ao longo do duto com a vazão afasta-se significativamente da relação linear esperada para escoamentos hidrodinamicamente desenvolvidos. Para o estudo foi montado um experimento em escala de laboratório utilizando como fluido de trabalho uma solução de glicerina e água, que apresenta forte dependência da viscosidade com a temperatura. A solução quente de glicerina era bombeada por um tubo longo imerso em um meio refrigerado. A troca de calor do fluido com o ambiente frio produzia gradientes de temperatura radiais e axiais associados a fortes variações da viscosidade. Os experimentos conduzidos revelaram uma relação linear entre a vazão e a queda de pressão ao longo do duto para baixos e altos valores da vazão. No entanto, para valores intermediários da vazão, a relação entre vazão e queda de pressão afasta-se do comportamento linear, deixando de apresentar uma relação monotônica. Nesta região intermediária, os mesmos valores de queda de pressão foram observados para vazões de ordem de grandeza diferentes. Medidas de perfis radiais de temperatura e velocidade axial foram realizadas para duas diferentes posições axiais no duto. Sondas de termopar e a técnica de velocimetria laser- Doppler foram utilizadas neste estudo. Os perfis de temperatura apresentaram forte assimetria como decorrência da presença de escoamentos secundários originados por convecção natural. Os perfis de velocidade axial foram pouco afetados pelos escoamentos secundários. Acredita-se que o impacto observado na tensão cisalhante na parede e, portanto, na queda de pressão, esteja associado à forte variação da viscosidade junto à parede fria, e não às variações do gradiente de velocidade na parede que não se mostraram significativas. Os resultados experimentais foram comparados com simulações numéricas tridimensionais e unidimensionais fornecidas por outros pesquisadores. A relação de queda de pressão com a vazão foi bem modelada por ambos os modelos. Os perfis radiais de velocidade foram bem previstos pelo modelo tridimensional, ao contrário dos perfis radiais de temperatura que se afastaram das medições. / [en] The present work is an experimental study of laminar flows through long, thermally insulated pipes of heavy oils that present strong dependence of viscosity on temperature. The objective of the study was to reproduce and understand the behavior reported in field operations where the dependence of the pressure drop on the flow rate deviates significantly from the linear relationship expected for hydrodynamically fully developed flow. To this end, a laboratory-scale experiment was constructed employing as working fluid a glycerol-water solution displaying a strong dependence of viscosity on temperature. In the experiments, the heated glycerol solution was pumped through a long isolated pipe immersed in a cold environment. The heat exchange with the cold environment produced radial and axial thermal gradients in the fluid yielding strong viscosity variations. For the low and high ranges of the flow rate the experiments revealed a linear relationship between flow rate and pressure drop from the inlet to the exit of the test section. However, for intermediate values of the flow rate, the relationship between flow rate and pressure drop deviated from the linear behavior. Further, this relationship ceased to be monotonic. In this intermediate flow rate region, the same pressure drop values were measured for flow rates values differing in orders of magnitude. Radial profiles of temperature and axial velocity were measured at different axial positions along the pipe. Thermocouple probes and the laser- Doppler velocimetry technique were employed in this study. Temperature profiles displayed strong asymmetry as a consequence of the presence of secondary flows induced by natural convection. The axial velocity profiles were little affected by the secondary flows. It is believed that the impact observed on the wall shear stress and, as a consequence, on the pressure drop, are associated with the strong viscosity variations close to the cold pipe wall, and not with the variations of the velocity gradient at the wall that were seen to be not too significant. The experimental results obtained were compared with one and tri-dimensional numerical solutions developed by other researchers. The relationship between pressure drop and flow rate was well predicted by both numerical models. The radial velocity profiles were well predicted by the tri-dimensional calculations, while the temperature profiles predictions were seen to deviate from the experiments.