Theoretical and numerical studies of laminar jet diffusion flames have been conducted in the limit of infinitely fast chemistry for unity oxygen Lewis number LO = 1, providing information on flame shapes and flame temperatures for different reactant-feed dilution, fuel Lewis number LF, and coflow-to-jet velocity ratios U0. Shvab-Zel'dovich coupling functions are used to write the conservation equations for planar and axisymmetric jet flames in the boundary-layer approximation. Specific consideration is given to the mixing-layer solution near the injector rim, where differential-diffusion effects are seen to result in the expected superadiabatic/subadiabatic temperature for LF smaller/larger than 1. These effects are more pronounced for U0 = 0 and at intermediate values of Zs. The evolution of the temperature along the flame is found to exhibit an unexpected behavior, in that irrespective of the dilution and coflow velocity the flame temperature always transitions from superadiabatic to subadiabatic when LF < 1 and from subadiabatic to superadiabatic for LF > 1. The variation with LF of the flame shape relative to the enthalpy eld is reasoned as the cause for the observed transition. Additional computations are performed for inverse diffusion flames with LO = 1 and LF ~= 1. These do not exhibit reversed differential-diffusion behaviors, indicating that the diffusivity of the abundant (co-flow) reactant is less critical than that of the deficient (central-jet) reactant.

El objetivo de este artículo teórico es rastrear algunos elementos ecológicos en el pensamiento de los pueblos originarios que nos pueden servir en la construcción de una nueva matriz civilizatoria y una racionalidad ambiental menos agresiva con la biodiversidad de la naturaleza. En la primera parte se analiza cómo la ciencia moderna y la separación cartesiana del hombre-naturaleza han generado gran parte de la crisis ambiental y civilizatoria. En segundo término, se examina la noción de racionalidad ambiental y la importancia de los diálogos de saberes para descolonizar el eurocentrismo del pensamiento colonial, dualista, instrumental y antropocéntrico que ha torturado al planeta. Finalmente, se retoman algunos aportes ontológicos encontrados en el núcleo duro del pensamiento mesoamericano que contribuyen a la descolonización epistémica y el diseño de una nueva matriz civilizatoria a favor de la coexistencia, convivencia y profundización de las diferencias en armonía con el medio ambiente y la vida. 

This thesis addresses the aerodynamics of Tsuji burners, involving a flame developing from the forward stagnation region of a cylindrical porous fuel injector placed in an air stream. Attention is focused on cases when the fuel-injection velocity is comparable to the outer air velocity, so that the boundary layer is blown off from the cylinder surface. In the resulting flow, the flame is embedded in the thin mixing layer that forms about the stream surface separating the outer air stream from the fuel stream, both having in general different density. The flow structure, nearly inviscid outside the mixing layer, is investigated here for cases where the porous fuel injector is placed in a uniform air stream or at the center of a symmetrical planar counterflow configuration. In both cases the velocity on the air side of the mixing layer is potential, while the velocity found on the fuel side is rotational, because fuel injection generates vorticity through the requirement that fuel emerges normal to the cylinder surface. It is shown that introduction of a density-weighted streamfunction reduces the problem to the case of constant-density flow, with the density-square-root-weighted ratio of injection velocity to free-stream velocity Lambda emerging as the only controlling parameter. The numerical solution, involving the determination of the vorticity distribution through an iterative scheme, provides the structure of the flow, including the location of the flame and associated strain-rate distribution. Numerical results are presented for values of Lambda ranging from small injection velocities Lambda << 1 to large injection velocities Lambda >> 1. The inviscid results reported here in the limit of vanishingly small injection velocities Lambda << 1 indicate that the outer air velocity never approaches the classical solution corresponding to potential flow with Lambda=0, a result with important implications for the analysis of flames stabilized in Tsuji burners.

Characterization of cerebrospinal fluid (CSF) dynamics in the central nervous system is fundamental for the study of CSF-related disorders, such as normal pressure hydrocephalus, Chiari malformation, and syringomyelia, which can help guide clinical diagnosis and treatment therapy. In this thesis, phase contrast, a non-invasive magnetic resonance imaging (MRI) technique that can map the phase accrual of the moving fluid region to velocity, is combined with rigorously derived simplified models of the CSF motion to enable patient-specific quantitative descriptions of the fluid flow and associated pressure variations for clinical use. Attention is focused on two specific problems, namely, flow in the cerebral aqueduct, a slender canal connecting the third and fourth ventricles of the brain, and flow in the spinal canal. In the former case, special attention is given to the relation between the predicted flow rate and the interventricular pressure variation, which is subsequently used in a volunteer study to obtain indirect evaluations of the transmantle pressure from direct MRI flow measurements corresponding to 77 subjects. The model for the pulsating viscous motion in the spinal canal assumes a linearly elastic compliant tube of slowly varying section, with a Darcy pressure-loss term included to model the fluid resistance introduced by the microanatomy. As shown by the preliminary computations presented here, this simple one-dimensional model can serve as a basis for quantitative analyses targeting predictions of intracranial pressure temporal fluctuations based on MRI measurements of spinal-canal anatomy and CSF flow rate. Future directions are proposed concerning both flow problems, including further validation exercises involving in-vitro and in-vivo experiments.

This dissertation investigates the fluid–structure dynamics involved in squeeze-film levitation, in pursuit of a theoretical explanation for the anomalously large, attractive load-bearing forces observed in recent experiments.

Consider a rigid disk vibrating rapidly along its axis of symmetry near a parallel wall, inducing oscillatory airflow in the thin film of air separating the disk and the wall as well as its periphery. Due to the nonlinear effects of fluid inertia and compressibility, the air pressure within the film varies in time asymmetrically about its ambient value, providing a nonzero time-averaged pressure force on the disk. Prior studies of this “squeeze-film” effect report that the time-averaged force typically repels the disk from the wall, making it a suitable mechanism for bearing lubrication. The strong attractive forces reported recently thus constitute a radical departure from this historical norm, expanding the range of possible applications to include wall-climbing robots and versatile contactless grippers. This dissertation aims to understand the fluid–structure physics underlying the emergence of strong attraction, through the derivation of reduced mathematical formulations that may ultimately aid the development of such novel systems.

Gas-lubricated systems represent an exceptional family of slender fluid flows for which the effects of compressibility and viscous shear enter simultaneously while maintaining small values of the Knudsen number, thereby guaranteeing applicability of the continuum hypothesis in describing the flow. Thus, the classical Navier–Stokes equations are used here to investigate the gas dynamics in the thin film as well as the effectively incompressible discharge and entrainment of air across a small region surrounding its edge. An approximate solution obtained using the method of matched asymptotic expansions indicates that the augmented attractive forces observed in recent experiments can be attributed to the pronounced dynamic bending of the highly flexible disks utilized. The theoretical formulation is then generalized to describe two-way fluid–structure coupling between the undulating disk and the thin-film airflow, thereby yielding predictions of system behavior that exhibit greatly improved agreement with experimental data. The canonical problems outlined herein can be readily extended to describe more complex configurations of practical interest—in particular, those involving transportation of the levitated object.

Combustion in scramjet engines is faced with the limitation of brief residence time in the combustion chamber, requiring fuel and preheated air streams to mix and ignite in a matter of milliseconds. Accurate predictions of autoignition times are needed to design reliable supersonic combustion chambers. Most efforts in estimating non-premixed autoignition times have been de- voted to hydrogen-air mixtures. The present work addresses hydrocarbon-air combustion, which is of interest for future scramjet engines.

Computation of ignition in supersonic flows requires adequate characterization of ignition ix

chemistry and description of the flow, both of which are derived in this work. In particular, we have shown that activation energy asymptotics combined with a previously derived reduced chemical kinetic mechanism provides analytic predictions of autoignition times in homogeneous systems. Results are compared with data from shock tube experiments, and previous expressions which employ a fuel depletion criterion.

Ignition in scramjet engines has a strong dependence on temperature, which is found by perturbing the chemically frozen mixing layer solution. The frozen solution is obtained here, accounting for effects of viscous dissipation between the fuel and air streams. We investigate variations of thermodynamic and transport properties, and compare these to simplified mixing layers which neglect these variations. Numerically integrating the mixing layer problem reveals a nonmonotonic temperature profile, with a peak occurring inside the shear layer for sufficiently high Mach numbers.

These results will be essential in computation of ignition distances in supersonic combus- tion chambers.

Flow that develops over a semi-infinite horizontal plate has been studied over the past decades. In this particular case, a boundary-layer flow over a horizontal hot plate is chosen and its stability characteristics at a finite distance from the leading edge are analyzed. A critical value of the Grashof number Gr based on the local boundary-layer thickness is defined and used to analyze the resulting instability.

Due to the nature of the hot plate, the Boussinesq approximation used in previous linear stability analyses becomes less desirable since wall-to-ambient temperature differences are not close to unity. And as a result, a non-Boussinesq analysis is needed and presented here for two instability modes: vortex, i.e. Gortler-like streamwise vortices, and wave, i.e. spanwise traveling waves.

Numerical results are presented such as the neutral stability curve, and critical Grashof number for Prandtl numbers of 0.7 over a wide range of wall-to-ambient temperature ratios. It is found that as this ratio increases, the susceptibility of the flow to the vortex mode of instability decreases while the wave mode instability becomes more prominent. The present study provides an approach suitable for both the vortex and wave instability modes with different wall-to-ambient temperature ratio. The results for the two modes are compared with each other as well as to other available instability data.

Cerebrospinal fluid (CSF) is a water-like fluid that surrounds the brain and the spinal cord, together known as the central nervous system (CNS). CSF provides a physical cushion for the CNS and also plays an important physiological role by maintaining the electrolytic environment, transporting hormones, circulating nutrients and chemicals filtered from the blood, and removing waste products from cell metabolism of the CNS. It is generally accepted that the absence of CSF circulation may compromise the normal physiological functions of the CNS. CSF circulation also provides a mechanism for the delivery of potent analgesics and chemotherapy to the CNS, a drug delivery procedure often referred to as intrathecal drug delivery (ITDD). Despite significant efforts, most of these processes remain poorly understood.

This dissertation analyzes CSF flow and solute transport along the spinal canal by using asymptotic methods based on the disparity of length and time scales associated with this problem. In addition to the oscillatory flow induced by the cardiac and respiratory cycles, with zero time- averaged velocity at any location, it is found that small corrections associated with the convective acceleration and canal deformation lead to a nonzero steady-streaming velocity. This small steady velocity, together with Stokes drift caused by the non-uniform oscillatory flow, determines the slow time-averaged Lagrangian motion of the CSF, which is found to be responsible for the transport of solutes along the canal. A key outcome of the analysis is a time-averaged transport equation that describes solute dispersion in the long-time scale. The use of this simplified equation circumvents the need to compute concentration fluctuations resulting from the fast oscillatory motion in the short-time scale, drastically reducing the associated computational times. The accuracy and limitations of the time-averaged description are tested by comparison to the results of direct numerical simulations spanning hundreds of oscillation cycles, as needed to generate significant dispersion of the solute. The analysis is extended to study effects of buoyancy-induced motion, arising when the injected solute has a density that differs from that of the CSF. For the small density differences that characterize ITDD drugs, buoyancy is found to have a significant effect on the convective transport, leading to large changes in the resulting solute-dispersion patterns. Finally, the classical problem of oscillatory flow past a circular cylinder is extended to the case of a streamwise periodic array of cylinders, providing insight regarding the effects of spinal-canal micro-anatomical features, such as trabeculae, ligaments, and nerve roots, on the flow and transport in the spinal canal.

Theoretical and numerical techniques are used to investigate three different problems involving non-isothermal fluid flow.

The first part of the dissertation investigates flame dynamics in a strained mixing layer established between two-dimensional counterflowing streams of fuel and oxidizer. When a one-step Arrhenius chemistry model is employed for the chemistry description, the numerical computations for small values of the stoichiometric mixture fraction yield a C-shaped premixed front with a trailing diffusion flame attached to one of its ends, a structure that is markedly different to the tri-brachial structure found in previous studies. Analytic predictions from the G equation are found to agree well with the numerical results. An explanation for these unexpected shapes is obtained by analyzing the variation with dilution of the burning velocity of planar premixed flames. Detailed-chemistry results are presented next for H$_2$-O$_2$-N$_2$ systems with high degrees of N$_2$ dilution, such that the resulting flame temperature lies close to the crossover value. Under these near-critical conditions, the flame dynamics is found to be strongly dependent on the initial conditions. A bifurcation diagram is presented in the stoichiometric mixture-fraction vs. strain-rate plane that identifies six different combustion regimes involving four different flame types, namely, one-dimensional diffusion flames, propagating/retreating edge flames, broken flame tubes, and isolated flame tubes.

A spherically symmetric heterogeneous fuel-oxidizer system is investigated next as an ignition model for hypergolic gelled propellants. Depending on the conditions, the fuel-oxidizer system may approach an explosive mode or it may settle into a steady-state mode. The critical condition defining the transition between these two states is determined analytically and the ignition time for the explosive mode is approximated by solving an integral equation for the interface temperature, employing activation-energy asymptotics.

A non-Boussinesq stability analysis of natural-convection boundary-layer flows over hot inclined surfaces is presented in the last part of the dissertation. Depending on the inclination angle, the disturbances are seen to evolve into either streamwise vortices or spanwise traveling waves. The critical inclination angle at which transition between the two instability modes occurs is calculated as a function of wall-to-ambient temperature ratio. For sufficiently large values of this ratio, wave modes are found to be always predominant, regardless of the inclination angle.

Cross-shore exchange processes are of critical importance for coastal ecosystems such as coral reefs with implications for transport of nutrients, larvae and heat. We present an analytical study of two-dimensional flow in a wedge driven by a time-dependent surface heat flux as a model problem to understand buoyancy-induced cross-shore flow. Besides the turbulent Prandtl number and the Rayleigh number, both assumed to be of order unity, the solution is seen to depend on the geometry through a small parameter ß measuring the bottom slope. Following previous efforts (e.g. [1]) an analytic solution is sought in the asymptotic limit ß << 1 for a water layer bounded by an adiabatic bottom surface subject to a harmonic heat flux on the upper surface. The analysis reveals that the motion at leading order can be expressed as the sum of a harmonic component and a steady component, the latter driven by the nonlinear advection terms. This steady-streaming motion includes a nearshore and alongshore oriented vortex with associated counterclockwise recirculating motion that could have a signicant effect on the near-short transport dynamics.