|
Prandtl Meyer Function
Ludwig Prandtl (4 February 1875 – 15 August 1953) was a German fluid dynamicist, physicist and aerospace scientist. He was a pioneer in the development of rigorous systematic mathematical analyses which he used for underlying the science of aerodynamics, which have come to form the basis of the applied science of aeronautical engineering. In the 1920s, he developed the mathematical basis for the fundamental principles of subsonic aerodynamics in particular; and in general up to and including transonic velocities. His studies identified the boundary layer, thin- airfoils, and lifting-line theories. The Prandtl number was named after him. Early years Prandtl was born in Freising, near Munich, on 4 February 1875. His mother suffered from a lengthy illness and, as a result, Ludwig spent more time with his father, a professor of engineering. His father also encouraged him to observe nature and think about his observations. Prandtl entered the Technische Hochschule Munich in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Freising
Freising () is a university town in Bavaria, Germany, and the capital of the Freising (district), with a population of about 50,000. Location Freising is the oldest town between Regensburg and Bolzano, and is located on the Isar river in Upper Bavaria, north of Munich and near the Munich International Airport. The city is built on and around two prominent hills: the Cathedral Hill with the former Bishop's Residence and Freising Cathedral, and Weihenstephan Hill with the former Weihenstephan Abbey, containing the oldest working brewery in the world. It was also the location of the first recorded tornado in Europe. The city is 448 meters above sea level. Cultural significance Freising is one of the oldest settlements in Bavaria, becoming a major religious centre in the early Middle Ages. It is the centre of an important diocese. Some important historical documents were created between 900 and 1200 in its monastery: * Freising manuscripts written in Slovenian, being th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Walter Tollmien
Walter Tollmien (13 October 1900, in Berlin Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population withi ... – 25 November 1968, in Göttingen) was a German fluid dynamicist. Life Walter Tollmien studied mathematics and physics for the winter semester in 1920–1921 with Ludwig Prandtl in Göttingen and then from 1924 onwards worked under Prandtl at the Kaiser Wilhelm Institute. After some research in Germany, he went to the United States and stayed there between 1930 and 1933. He became a professor in 1937 at Technische Hochschule Dresden. In 1957, he took over the post of director at the Max-Planck Institute for fluid mechanics research. Achievements Through his pioneering work as a researcher and a teacher, Walter Tollmien brought fluid mechanics into the lime light and as an inter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pitot Tube
A pitot tube ( ; also pitot probe) measures fluid flow velocity. It was invented by French engineer Henri Pitot during his work with aqueducts and published in 1732, and modified to its modern form in 1858 by Henry Darcy. It is widely used to determine the airspeed of aircraft; the water speed of boats; and the flow velocity of liquids, air, and gases in industry. Theory of operation The basic pitot tube consists of a tube pointing directly into the oncoming fluid flow. Pressure in the tube can be measured as the moving fluid cannot escape and stagnates. This pressure is the stagnation pressure of the fluid, also known as the total pressure or (particularly in aviation) the pitot pressure. The measured stagnation pressure cannot just by itself be used to determine the fluid flow velocity (airspeed in aviation) directly. However, with a measured static pressure as well it can be determined by the use of Bernoulli's equation which states: :Stagnation pressure = static pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stress Functions
In linear elasticity, the equations describing the deformation of an elastic body subject only to surface forces (or body forces that could be expressed as potentials) on the boundary are (using index notation) the equilibrium equation: :\sigma_=0\, where \sigma is the stress tensor, and the Beltrami-Michell compatibility equations: :\sigma_+\frac\sigma_=0 A general solution of these equations may be expressed in terms of the Beltrami stress tensor. Stress functions are derived as special cases of this Beltrami stress tensor which, although less general, sometimes will yield a more tractable method of solution for the elastic equations. Beltrami stress functions It can be shown that a complete solution to the equilibrium equations may be written as :\sigma=\nabla \times \Phi \times \nabla Using index notation: :\sigma_=\varepsilon_\varepsilon_\Phi_ : where \Phi_ is a symmetric but otherwise arbitrary second-rank tensor field that is at least twice differentiable, and is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prandtl Number
The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity. The Prandtl number is given as:where: * \nu : momentum diffusivity ( kinematic viscosity), \nu = \mu/\rho, ( SI units: m2/s) * \alpha : thermal diffusivity, \alpha = k/(\rho c_p), (SI units: m2/s) * \mu : dynamic viscosity, (SI units: Pa s = N s/m2) * k : thermal conductivity, (SI units: W/(m·K)) * c_p : specific heat, (SI units: J/(kg·K)) * \rho : density, (SI units: kg/m3). Note that whereas the Reynolds number and Grashof number are subscripted with a scale variable, the Prandtl number contains no such length scale and is dependent only on the fluid and the fluid state. The Prandtl number is often found in property tables alongside other properties such as viscosity and thermal conductivity. The mass transfer analog of the Prandtl number is the Schmidt number and the ratio of the Pran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prandtl Condition
In fluid mechanics the Prandtl condition was suggested by the German physicist Ludwig Prandtl to identify possible boundary layer separation points of incompressible fluid In fluid mechanics, or more generally continuum mechanics, incompressible flow is a flow in which the material density does not vary over time. Equivalently, the divergence of an incompressible flow velocity is zero. Under certain conditions, t ... flows. Prandtl condition-in normal shock In the case of normal shock, flow is assumed to be in a steady state and thickness of shock is very small. It is further assumed that there is no friction or heat loss at the shock (because heat transfer is negligible because it occurs on a relatively small surface). It is customary in this field to denote x as the upstream and y as the downstream condition. Since the mass flow rate from the two sides of the shock are constant, the mass balance becomes, \rho_.U_=\rho_.U_ As there is no external force applied, momentum is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closed Wing
A closed wing is a wing that effectively has two main planes that merge at their ends so that there are no conventional wing tips. Closed Wing configuration, wing designs include the annular wing (commonly known as the cylindrical or ring wing), the joined wing, the box wing, and spiroid tip devices. Like many wingtip devices, the closed wing aims to reduce the wasteful effects associated with wingtip vortices that occur at the tips of conventional wings. Although the closed wing has no unique claim on such benefits, many closed wing designs do offer structural advantages over a conventional cantilever wing, cantilever monoplane. Characteristics Wingtip vortices form a major component of wake turbulence and are associated with induced drag, which is a significant contributor to total drag in most regimes. A closed wing avoids the need for wingtips and thus might be expected to reduce wingtip drag (physics), drag effects. In addition to potential structural advantages over open ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Membrane Analogy
The elastic membrane analogy, also known as the soap-film analogy, was first published by pioneering aerodynamicist Ludwig Prandtl in 1903. It describes the stress distribution on a long bar in torsion. The cross section of the bar is constant along its length, and need not be circular. The differential equation that governs the stress distribution on the bar in torsion is of the same form as the equation governing the shape of a membrane under differential pressure. Therefore, in order to discover the stress distribution on the bar, all one has to do is cut the shape of the cross section out of a piece of wood, cover it with a soap film, and apply a differential pressure across it. Then the slope of the soap film at any area of the cross section is directly proportional to the stress in the bar at the same point on its cross section. Application to thin-walled, open cross sections While the membrane analogy allows the stress distribution on any cross section to be determine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lifting-line Theory
The Lanchester–Prandtl lifting-line theoryAnderson, John D. (2001), ''Fundamentals of Aerodynamics'', p. 360. McGraw-Hill, Boston. . is a mathematical model in aerodynamics that predicts lift distribution over a three-dimensional wing from the wing's geometry. The theory was expressed independently by Frederick W. Lanchester in 1907, and by Ludwig Prandtl in 1918–1919 after working with Albert Betz and Max Munk. In this model, the vortex bound to the wing develops along the whole wingspan because it is shed as a vortex-sheet from the trailing edge, rather than just as a single vortex from the wing-tips. Introduction It is difficult to predict analytically the overall amount of lift that a wing of given geometry will generate. When analyzing a three-dimensional finite wing, a traditional approach slices the wing into cross-sections and analyzes each cross-section independently as a wing in a two-dimensional world. Each of these slices is called an airfoil, and it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mixing Length Model
In fluid dynamics, the mixing length model is a method attempting to describe momentum transfer by turbulence Reynolds stresses within a Newtonian fluid boundary layer by means of an eddy viscosity. The model was developed by Ludwig Prandtl in the early 20th century. Prandtl himself had reservations about the model, describing it as, "only a rough approximation," but it has been used in numerous fields ever since, including atmospheric science, oceanography and stellar structure. Also, Ali and Dey hypothesized an advanced concept of mixing instability. Physical intuition The mixing length is conceptually analogous to the concept of mean free path in thermodynamics: a fluid parcel will conserve its properties for a characteristic length, \ \xi' , before mixing with the surrounding fluid. Prandtl described that the mixing length, In the figure above, temperature, \ T, is conserved for a certain distance as a parcel moves across a temperature gradient. The fluctuation in tempe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boundary Layer
In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a Boundary (thermodynamic), bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a No-slip condition, no-slip boundary condition (zero velocity at the wall). The flow velocity then monotonically increases above the surface until it returns to the bulk flow velocity. The thin layer consisting of fluid whose velocity has not yet returned to the bulk flow velocity is called the velocity boundary layer. The air next to a human is heated, resulting in gravity-induced convective airflow, which results in both a velocity and thermal boundary layer. A breeze disrupts the boundary layer, and hair and clothing protect it, making the human feel cooler or warmer. On an aircraft wing, the velocity boundary layer is the part of the flow close to the wing, where viscosity, viscous forces distort the surrounding non-viscous flow. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vishnu Madav Ghatage
Vishnu Madav Ghatage (24 October 1908 – 6 December 1991) was an Indian aeronautical engineer, known for his pioneering conceptual and engineering contributions to Indian aeronautics. He led the team which designed and developed HAL HT-2, the first Indian designed and built aircraft. He was honoured by the Government of India in 1965, with the award of Padma Shri, the fourth highest Indian civilian award for his services to the nation. Biography Vishnu Madav Ghatage was born on 24 October 1908 at Hasur, Maharashtra, Hasur, a small village in the princely state of Kolhapur, now in the western Indian state of Maharashtra. His early schooling was at Kolhapur after which he graduated (BSc) from Sir Parshurambhau College, Pune and joined The Institute of Science, Mumbai, Institute of Science, Mumbai (formerly known as Royal Institute of Science) for post graduate studies. He passed MSc from there with distinction which made him eligible for scholarship for overseas studies. Aft ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
