Laminar flow of a gas in a tube with large temperature differences.

The laminar low Mach number flow of a gas in a tube is analyzed for very small and very large values of the inlet-to-wall temperature ratio. When this ratio tends to zero, pressure forces confine the cold gas to a thin core around the axis of the tube. This core is neatly bounded by an ablation front that consumes it at a finite distance from the tube inlet. When the temperature ratio tends to infinity, the temperature of the gas increases smoothly from the wall to the axis of the tube and the shear stress and heat flux are positive at the wall despite the fact that the viscosity and thermal conductivity of the gas scaled with their inlet values tend to zero at the wall

Tranversal motion and flow structure of fully nonlinear streaks in a laminar boundary layer

Typical streak computations present in the literature correspond to linear streaks or to small amplitude nonlinear streaks computed using DNS or nonlinear PSE. We use the Reduced Navier-Stokes (RNS) equations to compute the streamwise evolution of fully non-linear streaks with high amplitude in a laminar flat plate boundary layer. The RNS formulation provides Reynolds number independent solutions that are asymptotically exact in the limit $Re \gg 1$, it requires much less computational effort than DNS, and it does not have the consistency and convergence problems of the PSE. We present various streak computations to show that the flow configuration changes substantially when the amplitude of the streaks grows and the nonlinear effects come into play. The transversal motion (in the wall normal-streamwise plane) becomes more important and strongly distorts the streamwise velocity profiles, that end up being quite different from those of the linear case. We analyze in detail the resulting flow patterns for the nonlinearly saturated streaks and compare them with available experimental results.

Nonlinear description of transversal motion in a laminar boundary layer with streaks

The nonlinear streamwise growth of a spanwise periodic array of steady streaks in a flat plate boundary layer is numerically computed using the well known Reduced Navier-Stokes formulation. It is found that the flow configuration changes substantially when the amplitude of the streaks grows and the nonlinear effects come into play. The transversal motion (in the wall normal-spanwise plane), which is normally not considered, becomes non-negligible in the nonlinear regime, and it strongly distorts the streamwise velocity profiles, which end up being quite different from those predicted by the linear theory. We analyze in detail the resulting flow patterns for the nonlinearly saturated streaks, and compare them with available experimental results.

Influence of open trailing edge on laminar aerofoils at low Reynols number

This article deals with the effect of open trailing edge on the aerodynamic characteristics of laminar aerofoils at low Reynolds numbers, the attention being focussed on the influence of such a trailingedge imperfection on the aerodynamic efficiency. Wind tunnel tests have been performed at different Reynolds numbers and angles of attack, and global aerodynamic as well as pressure distributions were measured (in these tests two types of open trailing edges, either sharp or rounded were considered). From experimental results, a quantitative analysis of the influence of the trailing-edge thickness on the degradation of aerofoil aerodynamic performances has been obtained, which allows the establishment of a criterion for an acceptance limit for this kind of imperfection.

Nonlinear description of transversal motion in a laminar boundary layer with streaks

The nonlinear streamwise growth of a spanwise periodic array of steady streaks in a flat plate boundary layer is numerically computed using the well known Reduced Navier- Stokes formulation. It is found that the flow configuration changes substantially when the amplitude of the streaks grows and the nonlinear effects come into play. The transversal motion (in the wall normal-spanwise plane), which is normally not considered, becomes non-negligible in the nonlinear regime, and it strongly distorts the streamwise velocity profiles, which end up being quite different from those predicted by the linear theory. We analyze in detail the resulting flow patterns for the nonlinearly saturated streaks, and compare them with available experimental results.

Influence of leading edge imperfections on the aerodynamic characterictics of NACA 632-215 laminar aerofoils at low Reynolds number

This article deals with the effect of leading edge imperfections on the aerodynamic characteristics of a NACA 632-215 laminar aerofoil at low Reynolds numbers. Wind tunnel tests have been performed at different Reynolds numbers and angles of attack and global aerodynamic loads were measured. To perform these tests, a NACA 632-215 aerofoil was built up in two halves (corresponding to the upper side and to the lower side), the leading edge imperfection here considered being a slight displacement of half aerofoil with respect to the other. From experimental results, a quantitative measure of the influence of the leading edge displacement on the degradation of the aerofoil aerodynamic performances has been obtained. This allows the establishment of a criterion for an acceptance limit for this kind of imperfection

Laminar-turbulent transition induced by a discrete roughness element in a supersonic boundary layer

The linear instability and breakdown to turbulence induced by an isolated roughness element in a boundary layer at Mach 2:5, over an isothermal flat plate with laminar adiabatic wall temperature, have been analysed by means of direct numerical simulations, aided by spatial BiGlobal and three-dimensional parabolized (PSE-3D) stability analyses. It is important to understand transition in this flow regime since the process can be slower than in incompressible flow and is crucial to prediction of local heat loads on next-generation flight vehicles. The results show that the roughness element, with a height of the order of the boundary layer displacement thickness, generates a highly unstable wake, which is composed of a low-velocity streak surrounded by a three-dimensional high-shear layer and is able to sustain the rapid growth of a number of instability modes. The most unstable of these modes are associated with varicose or sinuous deformations of the low-velocity streak; they are a consequence of the instability developing in the three-dimensional shear layer as a whole (the varicose mode) or in the lateral shear layers (the sinuous mode). The most unstable wake mode is of the varicose type and grows on average 17% faster tan the most unstable sinuous mode and 30 times faster than the most unstable boundary layer mode occurring in the absence of a roughness element. Due to the high growthrates registered in the presence of the roughness element, an amplification factor of N D 9 is reached within 50 roughness heights from the roughness trailing edge. The independently performed Navier–Stokes, spatial BiGlobal and PSE-3D stability results are in excellent agreement with each other, validating the use of simplified theories for roughness-induced transition involving wake instabilities. Following the linear stages of the laminar–turbulent transition process, the roll-up of the three-dimensional shear layer leads to the formation of a wedge of turbulence, which spreads laterally at a rate similar to that observed in the case of compressible turbulent spots for the same Mach number.

Laminar counterflow parallel-plate heat exchangers: Exact and approximate solutions

Multilayered, counterflow, parallel-plate heat exchangers are analyzed numerically and theoretically. The analysis, carried out for constant property fluids, considers a hydrodynamically developed laminar flow and neglects longitudinal conduction both in the fluid and in the plates. The solution for the temperature field involves eigenfunction expansions that can be solved in terms of Whittaker functions using standard symbolic algebra packages, leading to analytical expressions that provide the eigenvalues numerically. It is seen that the approximate solution obtained by retaining the first two modes in the eigenfunction expansion provides an accurate representation for the temperature away from the entrance regions, specially for long heat exchangers, thereby enabling simplified expressions for the wall and bulk temperatures, local heat-transfer rate, overall heat-transfer coefficient, and outlet bulk temperatures. The agreement between the numerical and theoretical results suggests the possibility of using the analytical solutions presented herein as benchmark problems for computational heat-transfer codes.

Exact solution for the conjugate fluid-fluid problem in the thermal entrance region of laminar counterflow heat exchangers

A generalized Lévêque solution is presented for the conjugate fluid–fluid problem that arises in the thermal entrance region of laminar counterflow heat exchangers. The analysis, carried out for constant property fluids, assumes that the Prandtl and Peclet numbers are both large compared to unity, and neglects axial conduction both in the fluids and in the plate, assumed to be thermally thin. Under these conditions, the thermal entrance region admits an asymptotic self-similar description where the temperature varies as a power ϳ of the axial distance, with the particularity that the self-similarity exponent must be determined as an eigenvalue by solving a transcendental equation arising from the requirement of continuity of heat fluxes at the heat conducting wall. Specifically, the analysis reveals that j depends only on the lumped parameter ƙ = (A2/A1)1/3 (α1/α2)1/3(k2/k1), defined in terms of the ratios of the wall velocity gradients, A, thermal diffusivities, α i, and thermal conductivities,k i, of the fluids entering, 1, and exiting, 2, the heat exchanger. Moreover, it is shown that for large (small) values of K solution reduces to the classical first (second) Lévêque solution. Closed-form analytical expressions for the asymptotic temperature distributions and local heat-transfer rate in the thermal entrance region are given and compared with numerical results in the counterflow parallel-plate configuration, showing very good agreement in all cases.

Estudio matemático del comportamiento de un fluido incompresible en flujo laminar

El objetivo de este trabajo es realizar un estudio del comportamiento de un fluido en flujo laminar. En primer lugar se realizará una breve introducción Histórica, con el fin de situar al lector en la época donde suceden los acontecimientos más importantes relativos a la mecánica de fluidos. Se presentarán a las figuras más importantes de la mecánica de fluidos moderna, como Sir Gabriel Stokes o Osborne Reynolds, así como los acontecimientos más importantes. A continuación se expondran las ecuaciones que rigen el comportamiento de un fluido, las ecuaciones de Navier-Stokes y la ecuación de Reynolds, con el objetivo de ayudar al lector a entender los análisis posteriores que se realizarán sobre dichas ecuaciones. En tercer lugar se analizará la ecuación de Reynolds, la existencia y unicidad de soluciones, para seguidamente, realizar una simulación del problema. Dicha simulación se ha realizado en un script, bajo la herramienta Matlab, se explicará como se ha realizado la simulación y se expondrán ejemplos de los casos de un fluido compresible y uno incompresible para diversas ecuaciones. Seguidamente se describe el fenómeno de la capa límite y se explica con un ejemplo en un fluido compresible. Para finalizar se exponen las conclusiones obtenidas en la realización de este trabajo.

Flujo laminar: el cementerio de Igualada y los procesos elásticos en la arquitectura de Enric Miralles y Carme Pinós

La tesis Flujo Laminar, El cementerio de Igualada y los procesos elásticos en la arquitectura de Enric Miralles y Carme Pinós analiza la metodología que utilizan y desarrollan los arquitectos Miralles y Pinós en el proyecto del cementerio de Igualada. Enric Miralles y Carme Pinós comienzan a trabajar juntos en 1983, separándose siete años después. La producción arquitectónica que generan durante este periodo ha sido valorada y considerada por la crítica como una de las de mayor calidad en el último cuarto del siglo XX. Respecto a esta etapa de colaboración existen artículos dispersos que analizan de manera aislada algunos aspectos de sus proyectos. Sin embargo, no se han realizado estudios que analicen su metodología proyectual, sus herramientas, sus estrategias y sus diferentes conexiones y referencias. Tampoco se han analizado hasta el momento, cómo son sus procesos proyectuales, sus tiempos y sus objetivos. En este sentido, el proyecto del cementerio de Igualada será clave en la trayectoria del equipo. El tiempo extenso empleado en el proceso y la singularidad de la obra, además de otros factores del propio imaginario de Miralles y Pinós, marcarán a este proyecto como un punto de inflexión en su trabajo. La investigación plantea, en primer lugar, la descripción del contexto en el cual se comienzan a desarrollar los proyectos iniciales de Miralles y Pinós, además de los antecedentes que generarán la propuesta para el cementerio de Igualada. Seguidamente, se describen y analizan los apoyos y las referencias que los arquitectos utilizan en este proyecto, tanto las vinculadas a la cultura local como las atrapadas desde el imaginario universal. Por otro lado, el bloque central de la investigación aporta doce herramientas que construyen la metodología proyectual de Miralles y Pinós. Esta contribución se ha realizado desde el análisis y el cruce de los documentos originales del proyecto de Igualada y los escritos existentes de los arquitectos. Las herramientas aportadas son: deslizar, desplazar, repetir, enterrar, constreñir, oscilar, estirar, desenredar, desviar, rehacer, hendir y fluir. Todas ellas se describen, analizan e interpretan desde setenta y dos documentos esenciales extraídos del proceso de Igualada. Un último capítulo de conclusiones, define lo que se presenta en la investigación como una metodología propia de Enric Miralles y Carme Pinós, denominada procesos elásticos, en el que se describen sus cualidades y sus tiempos, a la vez que se presenta también una táctica empleada en el proyecto de Igualada denominada flujo laminar. ABSTRACT The thesis Laminar Flow, the Igualada cemetery and the elastic processes in the architecture of Enric Miralles and Carme Pinós analyses the methodology that the architects Miralles and Pinós used in the project for the Igualada cemetery park. Enric Miralles and Carme Pinós began to work together in 1983, and went their different ways seven years later. The architectural production they generated during that period has been valued and considered by critics to be among the greatest quality of production in the final quarter of the twentieth century. There is a scattering of articles about this period which give an independent analysis of some features of their products. However, there are no studies which analyse their project design methodology, their tools, their strategies and their different connections and references. Neither has there been analysis to date of the nature of their project design processes, nor of their times and their aims. Within this context, the Igualada cemetery project was key in the path to be trodden by the team. The great length of time used on the process and the singularity of the work, alongside other factors from Miralles and Pinós's personal imaginarium, were to mark this project as a turning point in their work. This research sets out, first of all, to describe the context in which the early projects by Miralles and Pinós began to be developed, as well as the background to the generation of their proposal for the Igualada cemetery. There follows a description and analysis of the resources and of the references that the architects used in this project, both those linked to local culture and those picked from the universal imaginarium. Furthermore, the central block of the research identifies twelve tools which make up Miralles and Pinós's project design methodology. This contribution has been performed on the basis of analysis and comparison of the original Igualada project documents and of writings extant by the architects. The tools identified are: slide, shift, repeat, bury, constrain, oscillate, stretch, untangle, divert, redo, groove and flow. They are all described, analysed and interpreted on the basis of seventy-two essential documents extracted from the Igualada process. A final chapter of conclusions defines what is presented in the research as a methodology which is specific to Enric Miralles and Carme Pinós, denominated elastic processes, describing their qualities and their times, along with the presentation of a tactic used in the Igualada project which is denominated laminar flow.