Brief History of the Early Development of Theoretical and Experimental Fluid Dynamics
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Gustave Eiffel, a Pioneer of Aerodynamics
Int. J. Engineering Systems Modelling and Simulation, Vol. 5, Nos. 1/2/3, 2013 3 Gustave Eiffel, a pioneer of aerodynamics Bruno Chanetz* Onera, 8 rue des Vertugadins, F-92 190 Meudon, France Fax: +33-1-46-23-51-58 and University Paris-Ouest, LTIE-GTE, EA 4415, 50 rue de Sèvres, F-92410 Ville d’Avray, France Fax: +33-1-40-97-48-73 E-mail: [email protected] E-mail: [email protected] *Corresponding author Martin Peter Laboratoire Aérodynamique Eiffel, 68 rue Boileau, F-75016 Paris E-mail: [email protected] Abstract: At the beginning of the 20th century, Gustave Eiffel contributes with Ludwig Prandtl to establish a new science: aerodynamics. He was going to study the forces to which he was confronted as engineer during his life: gravity and wind. Keywords: Eiffel wind tunnel; diffuser; laminar regime; turbulent regime; transition; drag of the sphere; Eiffel chamber. Reference to this paper should be made as follows: Chanetz, B. and Peter, M. (2013) ‘Gustave Eiffel, a pioneer of aerodynamics’, Int. J. Engineering Systems Modelling and Simulation, Vol. 5, Nos. 1/2/3, pp.3–7. Biographical notes: Bruno Chanetz joins Onera in 1983 as a Research Engineer. He was the Head of Hypersonic Group in 1990, Head of Hypersonic Hyperenthalpic Project in 1997 and Head of Experimental Simulation and Physics of Fluid Unit in 1998, then Deputy Director of the Fundamental and Experimental Aerodynamics Department in 2003. He was a Lecturer in Charge of the course ‘Boundary Layer’ at the Ecole Centrale de Paris from 1996 to 2003, then Associate Professor at the University of Versailles from 2003 to 2009. -
In Classical Fluid Dynamics, a Boundary Layer Is the Layer I
Atm S 547 Boundary Layer Meteorology Bretherton Lecture 1 Scope of Boundary Layer (BL) Meteorology (Garratt, Ch. 1) In classical fluid dynamics, a boundary layer is the layer in a nearly inviscid fluid next to a surface in which frictional drag associated with that surface is significant (term introduced by Prandtl, 1905). Such boundary layers can be laminar or turbulent, and are often only mm thick. In atmospheric science, a similar definition is useful. The atmospheric boundary layer (ABL, sometimes called P[lanetary] BL) is the layer of fluid directly above the Earth’s surface in which significant fluxes of momentum, heat and/or moisture are carried by turbulent motions whose horizontal and vertical scales are on the order of the boundary layer depth, and whose circulation timescale is a few hours or less (Garratt, p. 1). A similar definition works for the ocean. The complexity of this definition is due to several complications compared to classical aerodynamics. i) Surface heat exchange can lead to thermal convection ii) Moisture and effects on convection iii) Earth’s rotation iv) Complex surface characteristics and topography. BL is assumed to encompass surface-driven dry convection. Most workers (but not all) include shallow cumulus in BL, but deep precipitating cumuli are usually excluded from scope of BLM due to longer time for most air to recirculate back from clouds into contact with surface. Air-surface exchange BLM also traditionally includes the study of fluxes of heat, moisture and momentum between the atmosphere and the underlying surface, and how to characterize surfaces so as to predict these fluxes (roughness, thermal and moisture fluxes, radiative characteristics). -
The Bernoulli Edition the Collected Scientific Papers of the Mathematicians and Physicists of the Bernoulli Family
Bernoulli2005.qxd 24.01.2006 16:34 Seite 1 The Bernoulli Edition The Collected Scientific Papers of the Mathematicians and Physicists of the Bernoulli Family Edited on behalf of the Naturforschende Gesellschaft in Basel and the Otto Spiess-Stiftung, with support of the Schweizerischer Nationalfonds and the Verein zur Förderung der Bernoulli-Edition Bernoulli2005.qxd 24.01.2006 16:34 Seite 2 The Scientific Legacy Èthe Bernoullis' contributions to the theory of oscillations, especially Daniel's discovery of of the Bernoullis the main theorems on stationary modes. Johann II considered, but rejected, a theory of Modern science is predominantly based on the transversal wave optics; Jacob II came discoveries in the fields of mathematics and the tantalizingly close to formulating the natural sciences in the 17th and 18th centuries. equations for the vibrating plate – an Eight members of the Bernoulli family as well as important topic of the time the Bernoulli disciple Jacob Hermann made Èthe important steps Daniel Bernoulli took significant contributions to this development in toward a theory of errors. His efforts to the areas of mathematics, physics, engineering improve the apparatus for measuring the and medicine. Some of their most influential inclination of the Earth's magnetic field led achievements may be listed as follows: him to the first systematic evaluation of ÈJacob Bernoulli's pioneering work in proba- experimental errors bility theory, which included the discovery of ÈDaniel's achievements in medicine, including the Law of Large Numbers, the basic theorem the first computation of the work done by the underlying all statistical analysis human heart. -
Leonhard Euler: His Life, the Man, and His Works∗
SIAM REVIEW c 2008 Walter Gautschi Vol. 50, No. 1, pp. 3–33 Leonhard Euler: His Life, the Man, and His Works∗ Walter Gautschi† Abstract. On the occasion of the 300th anniversary (on April 15, 2007) of Euler’s birth, an attempt is made to bring Euler’s genius to the attention of a broad segment of the educated public. The three stations of his life—Basel, St. Petersburg, andBerlin—are sketchedandthe principal works identified in more or less chronological order. To convey a flavor of his work andits impact on modernscience, a few of Euler’s memorable contributions are selected anddiscussedinmore detail. Remarks on Euler’s personality, intellect, andcraftsmanship roundout the presentation. Key words. LeonhardEuler, sketch of Euler’s life, works, andpersonality AMS subject classification. 01A50 DOI. 10.1137/070702710 Seh ich die Werke der Meister an, So sehe ich, was sie getan; Betracht ich meine Siebensachen, Seh ich, was ich h¨att sollen machen. –Goethe, Weimar 1814/1815 1. Introduction. It is a virtually impossible task to do justice, in a short span of time and space, to the great genius of Leonhard Euler. All we can do, in this lecture, is to bring across some glimpses of Euler’s incredibly voluminous and diverse work, which today fills 74 massive volumes of the Opera omnia (with two more to come). Nine additional volumes of correspondence are planned and have already appeared in part, and about seven volumes of notebooks and diaries still await editing! We begin in section 2 with a brief outline of Euler’s life, going through the three stations of his life: Basel, St. -
Chapter 5 Frictional Boundary Layers
Chapter 5 Frictional boundary layers 5.1 The Ekman layer problem over a solid surface In this chapter we will take up the important question of the role of friction, especially in the case when the friction is relatively small (and we will have to find an objective measure of what we mean by small). As we noted in the last chapter, the no-slip boundary condition has to be satisfied no matter how small friction is but ignoring friction lowers the spatial order of the Navier Stokes equations and makes the satisfaction of the boundary condition impossible. What is the resolution of this fundamental perplexity? At the same time, the examination of this basic fluid mechanical question allows us to investigate a physical phenomenon of great importance to both meteorology and oceanography, the frictional boundary layer in a rotating fluid, called the Ekman Layer. The historical background of this development is very interesting, partly because of the fascinating people involved. Ekman (1874-1954) was a student of the great Norwegian meteorologist, Vilhelm Bjerknes, (himself the father of Jacques Bjerknes who did so much to understand the nature of the Southern Oscillation). Vilhelm Bjerknes, who was the first to seriously attempt to formulate meteorology as a problem in fluid mechanics, was a student of his own father Christian Bjerknes, the physicist who in turn worked with Hertz who was the first to demonstrate the correctness of Maxwell’s formulation of electrodynamics. So, we are part of a joined sequence of scientists going back to the great days of classical physics. -
The Atmospheric Boundary Layer (ABL Or PBL)
The Atmospheric Boundary Layer (ABL or PBL) • The layer of fluid directly above the Earth’s surface in which significant fluxes of momentum, heat and/or moisture are carried by turbulent motions whose horizontal and vertical scales are on the order of the boundary layer depth, and whose circulation timescale is a few hours or less (Garratt, p. 1). A similar definition works for the ocean. • The complexity of this definition is due to several complications compared to classical aerodynamics: i) Surface heat exchange can lead to thermal convection ii) Moisture and effects on convection iii) Earth’s rotation iv) Complex surface characteristics and topography. Atm S 547 Lecture 1, Slide 1 Sublayers of the atmospheric boundary layer Atm S 547 Lecture 1, Slide 2 Applications and Relevance of BLM i) Climate simulation and NWP ii) Air Pollution and Urban Meteorology iii) Agricultural meteorology iv) Aviation v) Remote Sensing vi) Military Atm S 547 Lecture 1, Slide 3 History of Boundary-Layer Meteorology 1900 – 1910 Development of laminar boundary layer theory for aerodynamics, starting with a seminal paper of Prandtl (1904). Ekman (1905,1906) develops his theory of laminar Ekman layer. 1910 – 1940 Taylor develops basic methods for examining and understanding turbulent mixing Mixing length theory, eddy diffusivity - von Karman, Prandtl, Lettau 1940 – 1950 Kolmogorov (1941) similarity theory of turbulence 1950 – 1960 Buoyancy effects on surface layer (Monin and Obuhkov, 1954). Early field experiments (e. g. Great Plains Expt. of 1953) capable of accurate direct turbulent flux measurements 1960 – 1970 The Golden Age of BLM. Accurate observations of a variety of boundary layer types, including convective, stable and trade- cumulus. -
Continuity Example – Falling Water
Continuity example – falling water Why does the stream of water from a tap get narrower as it falls? Hint: Is the water accelerating as it falls? Answer: The fluid accelerates under gravity so the velocity is higher down lower. Since Av = const (i.e. A is inversely proportional to v), the cross sectional area, and the radius, is smaller down lower Bernoulli’s principle Bernoulli conducted experiments like this: https://youtu.be/9DYyGYSUhIc (from 2:06) A fluid accelerates when entering a narrow section of tube, increasing its kinetic energy (=½mv2) Something must be doing work on the parcel. But what? Bernoulli’s principle resolves this dilemma. Daniel Bernoulli “An increase in the speed of an ideal fluid is accompanied 1700-1782 by a drop in its pressure.” The fluid is pushed from behind Examples of Bernoulli’s principle Aeroplane wings high v, low P Compressible fluids? Bernoulli’s equation OK if not too much compression. Venturi meters Measure velocity from pressure difference between two points of known cross section. Bernoulli’s equation New Concept: A fluid parcel of volume V at pressure P has a pressure potential energy Epot-p = PV. It also has gravitational potential energy: Epot-g = mgh Ignoring friction, the energy of the parcel as it flows must be constant: Ek + Epot = const 1 mv 2 + PV + mgh = const ) 2 For incompressible fluids, we can divide by volume, showing conservation of energy 1 density: ⇢v 2 + P + ⇢gh = const 2 This is Bernoulli’s equation. Bernoulli equation example – leak in water tank A full water tank 2m tall has a hole 5mm diameter near the base. -
Boundary Layers
1 I-campus project School-wide Program on Fluid Mechanics Modules on High Reynolds Number Flows K. P. Burr, T. R. Akylas & C. C. Mei CHAPTER TWO TWO-DIMENSIONAL LAMINAR BOUNDARY LAYERS 1 Introduction. When a viscous fluid flows along a fixed impermeable wall, or past the rigid surface of an immersed body, an essential condition is that the velocity at any point on the wall or other fixed surface is zero. The extent to which this condition modifies the general character of the flow depends upon the value of the viscosity. If the body is of streamlined shape and if the viscosity is small without being negligible, the modifying effect appears to be confined within narrow regions adjacent to the solid surfaces; these are called boundary layers. Within such layers the fluid velocity changes rapidly from zero to its main-stream value, and this may imply a steep gradient of shearing stress; as a consequence, not all the viscous terms in the equation of motion will be negligible, even though the viscosity, which they contain as a factor, is itself very small. A more precise criterion for the existence of a well-defined laminar boundary layer is that the Reynolds number should be large, though not so large as to imply a breakdown of the laminar flow. 2 Boundary Layer Governing Equations. In developing a mathematical theory of boundary layers, the first step is to show the existence, as the Reynolds number R tends to infinity, or the kinematic viscosity ν tends to zero, of a limiting form of the equations of motion, different from that obtained by putting ν = 0 in the first place. -
Leonhard Euler - Wikipedia, the Free Encyclopedia Page 1 of 14
Leonhard Euler - Wikipedia, the free encyclopedia Page 1 of 14 Leonhard Euler From Wikipedia, the free encyclopedia Leonhard Euler ( German pronunciation: [l]; English Leonhard Euler approximation, "Oiler" [1] 15 April 1707 – 18 September 1783) was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function.[2] He is also renowned for his work in mechanics, fluid dynamics, optics, and astronomy. Euler spent most of his adult life in St. Petersburg, Russia, and in Berlin, Prussia. He is considered to be the preeminent mathematician of the 18th century, and one of the greatest of all time. He is also one of the most prolific mathematicians ever; his collected works fill 60–80 quarto volumes. [3] A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is our teacher in all things," which has also been translated as "Read Portrait by Emanuel Handmann 1756(?) Euler, read Euler, he is the master of us all." [4] Born 15 April 1707 Euler was featured on the sixth series of the Swiss 10- Basel, Switzerland franc banknote and on numerous Swiss, German, and Died Russian postage stamps. The asteroid 2002 Euler was 18 September 1783 (aged 76) named in his honor. He is also commemorated by the [OS: 7 September 1783] Lutheran Church on their Calendar of Saints on 24 St. Petersburg, Russia May – he was a devout Christian (and believer in Residence Prussia, Russia biblical inerrancy) who wrote apologetics and argued Switzerland [5] forcefully against the prominent atheists of his time. -
A Method That Lends Wings
FLASHBACK_Aerodynamics A method that lends wings Mathematician Irmgard Flügge-Lotz was one of the first female researchers in the field of aerodynamics and automatic control. While working at the Kaiser Wilhelm Institute for Flow Research, she succeeded in simplifying the calculations required for aircraft construction. Flügge-Lotz was later appointed the first female Professor of Engineering at Stanford University. In the U.S., her work is still held in high esteem. In Germany, however, she has been all but forgotten. TEXT KATJA ENGEL Goettingen, 1931. Leading flow researcher could only be tested by means of complex Ludwig Prandtl was astonished. His colleague, wind tunnel measurements. Ludwig Prandtl, at 28 just half his age, had just handed him who is generally thought to be the founder of the solution to a mathematical puzzle that no- aircraft aerodynamics, and his team in Goet- body had been able to crack for more than ten tingen carried out pioneering work on the years. This conundrum was on his “menu”, as theoretical description of lift. However, math- he called his list of uncompleted research ematical calculations of his wing theory tasks. The result went down in the history of turned out to be difficult. In 1919, Albert Betz, aerodynamic research together with the a doctoral student in Goettingen who was young researcher's name. The "Lotz method" later to become Prandtl’s successor at the In- makes it possible to calculate the lift on an air- stitute, finally succeeded in the describing lift plane wing with comparative ease. by means of differential equations. However, Prandtl soon made the woman who had so his formulae were too complex for practical impressed him an (unofficial) Head of Depart- use when constructing new profiles. -
Bernoulli? Perhaps, but What About Viscosity?
Volume 6, Issue 1 - 2007 TTTHHHEEE SSSCCCIIIEEENNNCCCEEE EEEDDDUUUCCCAAATTTIIIOOONNN RRREEEVVVIIIEEEWWW Ideas for enhancing primary and high school science education Did you Know? Fish Likely Feel Pain Studies on Rainbow Trout in the United Kingdom lead us to conclude that these fish very likely feel pain. They have pain receptors that look virtually identical to the corresponding receptors in humans, have very similar mechanical and thermal thresholds to humans, suffer post-traumatic stress disorders (some of which are almost identical to human stress reactions), and respond to morphine--a pain killer--by ceasing their abnormal behaviour. How, then, might a freshly-caught fish be treated without cruelty? Perhaps it should be plunged immediately into icy water (which slows the metabolism, allowing the fish to sink into hibernation and then anaesthesia) and then removed from the icy water and placed gently on ice, allowing it to suffocate. Bernoulli? Perhaps, but What About Viscosity? Peter Eastwell Science Time Education, Queensland, Australia [email protected] Abstract Bernoulli’s principle is being misunderstood and consequently misused. This paper clarifies the issues involved, hypothesises as to how this unfortunate situation has arisen, provides sound explanations for many everyday phenomena involving moving air, and makes associated recommendations for teaching the effects of moving fluids. "In all affairs, it’s a healthy thing now and then to hang a question mark on the things you have long taken for granted.” Bertrand Russell I was recently asked to teach Bernoulli’s principle to a class of upper primary students because, as the Principal told me, she didn’t feel she had a sufficient understanding of the concept. -
Analysis of Boundary Layers Through Computational Fluid Dynamics and Experimental Analysis
Analysis of Boundary Layers through Computational Fluid Dynamics and Experimental analysis By Eugene O’Reilly, B.Eng This thesis is submitted as the fulfilment of the requirement for the award of degree of Master of Engineering Supervisors Dr Joseph Stokes and Dr Brian Corcoran School of Mechanical and Manufacturing Engineering, Dublin City University, Ireland. October 2006 DECLARATION I hereby certify that this material, which I now submit for assessment on the programme of study leading to the award of Degree of Master of Engineering is entirely my own work and has not been taken from the work of others save and to the extent that such work has been cited and acknowledged within the text of my own work Signed ID Number 99604434 Date 2&j \Oj 2QOG I ACKNOWLEDGEMENTS I would like to thank Dr Joseph Stokes and Dr Brian Corcoran of the School of Mechanical and Manufacturing Engineering, Dublin City University, for their advice and guidance through this work Their helpful discussions and availability to discuss any problems I was having has been the cornerstone of this research Thanks also, to Mr Michael May of the School of Mechanical and Manufacturing Engineering for his invaluable help and guidance in the design and construction of the experimental equipment To Mr Cian Meme and Mr Eoin Tuohy of the workshop for their technical advice and excellent work in the production of the required parts and to Mr Keith Hickey for his help with all my software queries and computer issues Thanks also to Mr Ben Austin and Mr David Cunningham of the School