Problems of minimal aerodynamic resistance

Nesta tese estamos preocupados com o problema da resistência mínima primeiro dirigida por I. Newton em seu Principia (1687): encontrar o corpo de resistência mínima que se desloca através de um médio. As partículas do médio não interagem entre si, bem como a interação das partículas com o corpo é perfeitamente elástica. Diferentes abordagens desse modelo foram feitas por vários matemáticos nos últimos 20 anos. Aqui damos uma visão geral sobre estes resultados que representa interesse independente, uma vez que os autores diferentes usam notações diferentes. Apresentamos uma solução do problema de minimização na classe de corpos de revolução geralmente não convexos e simplesmente conexos. Acontece que nessa classe existem corpos com resistência menor do que o mínimo da resistência na classe de corpos convexos de revolução. Encontramos o infimum da resistência nesta classe e construimos uma sequência regular de corpos que aproxima este infimum. Também apresentamos um corpo de resistência nula. Até agora ninguém sabia se tais corpos existem ou não, evidentemente o nosso corpo não pertence a nenhuma classe anteriormente analisado. Este corpo é não convexo e não simplesmente conexo; a forma topológica dele é um toro, parece um UFO extraterrestre. Apresentamos aqui várias famílias de tais corpos e estudamos as suas propriedades. Também apresentamos um corpo que é natural de chamar um corpo "invisíveis em uma direção", uma vez que a trajectória de cada partícula com a certa direcção coincide com a linha recta fora do invólucro convexo do corpo. ABSTRACT: In this thesis we are concerned with the problem of minimal resistance first addressed by I. Newton in his Principia (1687): find the body of minimal resistance moving through a medium. The medium particles do not mutually interact, and the interaction of particles with the body is perfectly elastic. Different approaches to that model have been tried by several mathematicians during the last 20 years. Here we give an overview of these results that represents interest in itself since all authors use different notations. We present a solution of the minimization problem in the class of generally non convex, simply connected bodies of revolution. It happens that in this class there are bodies with smaller resistance than the minimum in the class of convex bodies of revolution. We find the infimum of the resistance in this class, and construct a sequence of bodies which approximates this infimum. Also we present a body of zero resistance. Since earlier it was unknown if such bodies exists or not, evidently our body does not belong to any class previously examined. The zero resistance body found by us is non-convex and non-simply connected; topologically it is a torus, and it looks like an extraterrestrial UFO. We present here several families of such bodies and study their properties. We also present a body which is natural to call a body "invisible in one direction", since the trajectory of each particle with the given direction, outside the convex hull of the body, coincides with a straight line.

On the role of surface roughness in the aerodynamic performance and energy conversion of horizontal wind turbine blades:a review

Summary: Renewable energy is one of the main pillars of sustainable development, especially in developing economies. Increasing energy demand and the limitation of fossil fuel reserves make the use of renewable energy essential for sustainable development. Wind energy is considered to be one of the most important resources of renewable energy. In North African countries, such as Egypt, wind energy has an enormous potential; however, it faces quite a number of technical challenges related to the performance of wind turbines in the Saharan environment. Seasonal sand storms affect the performance of wind turbines in many ways, one of which is increasing the wind turbine aerodynamic resistance through the increase of blade surface roughness. The power loss because of blade surface deterioration is significant in wind turbines. The surface roughness of wind turbine blades deteriorates because of several environmental conditions such as ice or sand. This paper is the first review on the topic of surface roughness effects on the performance of horizontal-axis wind turbines. The review covers the numerical simulation and experimental studies as well as discussing the present research trends to develop a roadmap for better understanding and improvement of wind turbine performance in deleterious environments.

不同光照条件下作物蒸腾量计算的研究

作物蒸腾量的计算是水资源开发利用和农业生产运筹的关键参数之一 .本文以彭曼 -蒙特斯方程为基础 ,通过引入临界阻力 ,根据实测资料建立冠层阻力和空气动力学阻力比值与临界阻力和空气动力学阻力比值二者之间的函数关系 ,得到一个只需气象参数就能计算作物蒸腾量的简单方法 .文章对该方法进行了理论分析 ,并用实例给予验证 .结果表明 ,该方法在理论上和实践上都是可行的 ,是一个值得研究和发展的新方法 .作物蒸腾量的日变化表明 ,炎热夏季晴天中午遮光处理后作物蒸腾量的增大是可能的

Modelling of urban sensible heat flux at multiple spatial scales : a demonstration using airborne hyperspectral imagery of Shanghai and a temperature–emissivity separation approach

Urbanization related alterations to the surface energy balance impact urban warming (‘heat islands’), the growth of the boundary layer, and many other biophysical processes. Traditionally, in situ heat flux measures have been used to quantify such processes, but these typically represent only a small local-scale area within the heterogeneous urban environment. For this reason, remote sensing approaches are very attractive for elucidating more spatially representative information. Here we use hyperspectral imagery from a new airborne sensor, the Operative Modular Imaging Spectrometer (OMIS), along with a survey map and meteorological data, to derive the land cover information and surface parameters required to map spatial variations in turbulent sensible heat flux (QH). The results from two spatially-explicit flux retrieval methods which use contrasting approaches and, to a large degree, different input data are compared for a central urban area of Shanghai, China: (1) the Local-scale Urban Meteorological Parameterization Scheme (LUMPS) and (2) an Aerodynamic Resistance Method (ARM). Sensible heat fluxes are determined at the full 6 m spatial resolution of the OMIS sensor, and at lower resolutions via pixel aggregation and spatial averaging. At the 6 m spatial resolution, the sensible heat flux of rooftop dominated pixels exceeds that of roads, water and vegetated areas, with values peaking at ∼ 350 W m− 2, whilst the storage heat flux is greatest for road dominated pixels (peaking at around 420 W m− 2). We investigate the use of both OMIS-derived land surface temperatures made using a Temperature–Emissivity Separation (TES) approach, and land surface temperatures estimated from air temperature measures. Sensible heat flux differences from the two approaches over the entire 2 × 2 km study area are less than 30 W m− 2, suggesting that methods employing either strategy maybe practica1 when operated using low spatial resolution (e.g. 1 km) data. Due to the differing methodologies, direct comparisons between results obtained with the LUMPS and ARM methods are most sensibly made at reduced spatial scales. At 30 m spatial resolution, both approaches produce similar results, with the smallest difference being less than 15 W m− 2 in mean QH averaged over the entire study area. This is encouraging given the differing architecture and data requirements of the LUMPS and ARM methods. Furthermore, in terms of mean study QH, the results obtained by averaging the original 6 m spatial resolution LUMPS-derived QH values to 30 and 90 m spatial resolution are within ∼ 5 W m− 2 of those derived from averaging the original surface parameter maps prior to input into LUMPS, suggesting that that use of much lower spatial resolution spaceborne imagery data, for example from Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) is likely to be a practical solution for heat flux determination in urban areas.

Formulation of a tropical town energy budget (t-TEB) scheme

This work describes the tropical town energy budget (t-TEB) scheme addressed to simulate the diurnal occurrence of the urban heat island (UHI) as observed in the Metropolitan Area of Rio de Janeiro (MARJ; -22A degrees S; -44A degrees W) in Brazil. Reasoning about the tropical urban climate have guided the scheme implementation, starting from the original equations from Masson (Bound-Lay Meteorol 94:357-397, 2000). The modifications include (a) local scaling approaches for obtaining flux-gradient relationships in the roughness sub-layer, (b) the Monin-Obukhov similarity framework in the inertial sub-layer, (c) increasing aerodynamic conductance toward more unstable conditions, and (d) a modified urban subsurface drainage system to transfer the intercepted rainwater by roofs to the roads. Simulations along 2007 for the MARJ are obtained and compared with the climatology. The t-TEB simulation is consistent with the observations, suggesting that the timing and dynamics of the UHI in tropical cities could vary significantly from the familiar patterns observed in mid-latitude cities-with the peak heat island intensity occurring in the morning than at night. The simulations are suggesting that the thermal phase shift of this tropical diurnal UHI is a response of the surface energy budget to the large amount of solar radiation, intense evapotranspiration, and thermal response of the vegetated surfaces over a very humid soil layer.

Sulla ricerca del minimo dei consumi per vetture sportive

La ricerca oggetto di questa tesi, come si evince dal titolo stesso, è volta alla riduzione dei consumi per vetture a forte carattere sportivo ed elevate prestazioni specifiche. In particolare, tutte le attività descritte fanno riferimento ad un ben definito modello di vettura, ovvero la Maserati Quattroporte. Lo scenario all’interno del quale questo lavoro si inquadra, è quello di una forte spinta alla riduzione dei cosiddetti gas serra, ossia dell’anidride carbonica, in linea con quelle che sono le disposizioni dettate dal protocollo di Kyoto. La necessità di ridurre l’immissione in atmosfera di CO2 sta condizionando tutti i settori della società: dal riscaldamento degli edifici privati a quello degli stabilimenti industriali, dalla generazione di energia ai processi produttivi in senso lato. Nell’ambito di questo panorama, chiaramente, sono chiamati ad uno sforzo considerevole i costruttori di automobili, alle quali è imputata una percentuale considerevole dell’anidride carbonica prodotta ogni giorno e riversata nell’atmosfera. Al delicato problema inquinamento ne va aggiunto uno forse ancor più contingente e diretto, legato a ragioni di carattere economico. I combustibili fossili, come tutti sanno, sono una fonte di energia non rinnovabile, la cui disponibilità è legata a giacimenti situati in opportune zone del pianeta e non inesauribili. Per di più, la situazione socio politica che il medio oriente sta affrontando, unita alla crescente domanda da parte di quei paesi in cui il processo di industrializzazione è partito da poco a ritmi vertiginosi, hanno letteralmente fatto lievitare il prezzo del petrolio. A causa di ciò, avere una vettura efficiente in senso lato e, quindi, a ridotti consumi, è a tutti gli effetti un contenuto di prodotto apprezzato dal punto di vista del marketing, anche per i segmenti vettura più alti. Nell’ambito di questa ricerca il problema dei consumi è stato affrontato come una conseguenza del comportamento globale della vettura in termini di efficienza, valutando il miglior compromesso fra le diverse aree funzionali costituenti il veicolo. Una parte consistente del lavoro è stata dedicata alla messa a punto di un modello di calcolo, attraverso il quale eseguire una serie di analisi di sensibilità sull’influenza dei diversi parametri vettura sul consumo complessivo di carburante. Sulla base di tali indicazioni, è stata proposta una modifica dei rapporti del cambio elettro-attuato con lo scopo di ottimizzare il compromesso tra consumi e prestazioni, senza inficiare considerevolmente queste ultime. La soluzione proposta è stata effettivamente realizzata e provata su vettura, dando la possibilità di verificare i risultati ed operare un’approfondita attività di correlazione del modello di calcolo per i consumi. Il beneficio ottenuto in termini di autonomia è stato decisamente significativo con riferimento sia ai cicli di omologazione europei, che a quelli statunitensi. Sono state inoltre analizzate le ripercussioni dal punto di vista delle prestazioni ed anche in questo caso i numerosi dati rilevati hanno permesso di migliorare il livello di correlazione del modello di simulazione per le prestazioni. La vettura con la nuova rapportatura proposta è stata poi confrontata con un prototipo di Maserati Quattroporte avente cambio automatico e convertitore di coppia. Questa ulteriore attività ha permesso di valutare il differente comportamento tra le due soluzioni, sia in termini di consumo istantaneo, che di consumo complessivo rilevato durante le principali missioni su banco a rulli previste dalle normative. L’ultima sezione del lavoro è stata dedicata alla valutazione dell’efficienza energetica del sistema vettura, intesa come resistenza all’avanzamento incontrata durante il moto ad una determinata velocità. Sono state indagate sperimentalmente le curve di “coast down” della Quattroporte e di alcune concorrenti e sono stati proposti degli interventi volti alla riduzione del coefficiente di penetrazione aerodinamica, pur con il vincolo di non alterare lo stile vettura.

Estudio paramétrico del conjunto tractor-trailer mediante aplicación de mecánica de fluidos computacional

La mejora del comportamiento aerodinámico de vehículos pesados en la carretera ha adquirido una mayor importancia estos últimos años debido a la crisis y su consecuente aumento del precio de los combustibles. Dado que una reducción en la resistencia aerodinámica del vehículo conlleva un menor empleo de combustible, el objetivo de este proyecto es realizar un estudio paramétrico del conjunto tractor-tráiler mediante la mecánica de fluidos computacional (CFD) para así obtener la geometría que proporciona un menor gasto de combustible cuando ésta es expuesta a viento frontal. La influencia de 3 parámetros, que son la separación existente entre cabina y remolque, la altura del remolque y el radio de curvatura de las aristas frontales de la cabina, es analizada en este estudio dividido en varias etapas que implican el uso de programas específicos como son: la parametrización y creación de las geometrías en 3D que es llevada a cabo mediante CATIA, el mallado del dominio (realizado con Gambit) y resolución de las ecuaciones mediante FLUENT. Finalmente se obtendrá una relación entre la resistencia aerodinámica (representada mediante el coeficiente de arrastre) y la combinación de los 3 parámetros, que nos permitirá decidir que geometría es la óptima. Abstract The improvement of the heavy vehicle’s aerodynamic behavior on the road has gained a great importance for these last years because of the economic crisis and the consequent increase of the price of the fuels. Due to the fact that a reduction in the aerodynamic resistance of the vehicle involves using a smaller amount of fuel, the objective of this project is to carry out a parametric study about the ensemble tractor-trailer by computational fluid dynamics methods (CFD) in order to obtain the geometry which expense of fuel is the lowest when it’s exposed to frontal wind. The influence of the three parameters, which are the space between cab and trailer, the height of the trailer and the curvature of the frontal cab edges, is analysed in this study which is divided into different parts involving specific programs: choosing the parameters and building the geometries, which is done by using CATIA, the mesh is built by Gambit, and the program equations-solver is FLUENT. Finally a ratio between aerodynamic resistance and a combination of the three parameters will be obtained and it will allow us to choose the best geometry.

Tridimensional simulation of the speed, pressure and turbulence fields of the air flow on the geometry of a freight truck inside a wind tunnel

This study shows the air flow behavior through the geometry of a freight truck inside a AF6109 wind tunnel with the purpose to predict the speed, pressure and turbulence fields made by the air flow, to decrease the aerodynamic resistance, to calculate the dragging coefficient, to evaluate the aerodynamics of the geometry of the prototype using the CFD technique and to compare the results of the simulation with the results obtained experimentally with the “PETER 739 HAULER” scaled freight truck model located on the floor of the test chamber. The Geometry went through a numerical simulation process using the CFX 5,7. The obtained results showed the behavior of the air flow through the test chamber, and also it showed the variations of speed and pressure at the exit of the chamber and the calculations of the coefficient and the dragging force on the geometry of the freight truck. The evaluation of the aerodynamics showed that the aerodynamic deflector is a device that helped the reduction the dragging produced in a significant way by the air. Furthermore, the dragging coefficient and force on the prototype freight truck could be estimated establishing an incomplete similarity.

Problems of optimal transportation on the circle and their mechanical applications

We consider a mechanical problem concerning a 2D axisymmetric body moving forward on the plane and making slow turns of fixed magnitude about its axis of symmetry. The body moves through a medium of non-interacting particles at rest, and collisions of particles with the body's boundary are perfectly elastic (billiard-like). The body has a blunt nose: a line segment orthogonal to the symmetry axis. It is required to make small cavities with special shape on the nose so as to minimize its aerodynamic resistance. This problem of optimizing the shape of the cavities amounts to a special case of the optimal mass transfer problem on the circle with the transportation cost being the squared Euclidean distance. We find the exact solution for this problem when the amplitude of rotation is smaller than a fixed critical value, and give a numerical solution otherwise. As a by-product, we get explicit description of the solution for a class of optimal transfer problems on the circle.

Fluid-dynamic drag; practical information on aerodynamic drag and hydrodynamic resistance

Mode of access: Internet.

Newton's aerodynamic problem in media of chaotically moving particles

Plakhov, A.Y.; Torres, D., (2005) 'Newton's aerodynamic problem in media of chaotically moving particles', Sbornik: Mathematics 196(6) pp.885-933 RAE2008

Aerodynamic Optimization of a High-speed Train using Genetic Algorithms

Genetic algorithms (GA) have been used for the minimization of the aerodynamic drag of a train subject to front wind. The significant importance of the external aerodynamic drag on the total resistance a train experiments as the cruise speed is increased highlights the interest of this study. A complete description of the methodology required for this optimization method is introduced here, where the parameterization of the geometry to be optimized and the metamodel used to speed up the optimization process are detailed. A reduction of about a 25% of the initial aerodynamic drag is obtained in this study, what confirms GA as a proper method for this optimization problem. The evolution of the nose shape is consistent with the literature. The advantage of using metamodels is stressed thanks to the information of the whole design space extracted from it. The influence of each design variable on the objective function is analyzed by means of an ANOVA test.

Smoothing a Discrete Hazard Function for the Number of Patients Colonized with Methicillin-Resistance Staphylococcus Aureus in an Intensive Care Unit

A new method for estimating the time to colonization of Methicillin-resistant Staphylococcus Aureus (MRSA) patients is developed in this paper. The time to colonization of MRSA is modelled using a Bayesian smoothing approach for the hazard function. There are two prior models discussed in this paper: the first difference prior and the second difference prior. The second difference prior model gives smoother estimates of the hazard functions and, when applied to data from an intensive care unit (ICU), clearly shows increasing hazard up to day 13, then a decreasing hazard. The results clearly demonstrate that the hazard is not constant and provide a useful quantification of the effect of length of stay on the risk of MRSA colonization which provides useful insight.