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Prandtl
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, in 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. He entered the Technische Hochschule Munich in 1894 and graduated wi ... [...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 bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a 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, 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 viscous forces distort the surrounding non-viscous flow. In the Earth's atmosphere, the atmospheric boun ... [...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: : \mathrm = \frac = \frac = \frac = \frac 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prandtl–Glauert Transformation
The Prandtl–Glauert transformation is a mathematical technique which allows solving certain compressible flow problems by incompressible-flow calculation methods. It also allows applying incompressible-flow data to compressible-flow cases. Mathematical formulation Inviscid compressible flow over slender bodies is governed by linearized compressible small-disturbance potential equation: :\phi_ + \phi_ + \phi_ = M_\infty^2 \phi_ \quad \mbox together with the small-disturbance flow-tangency boundary condition. :V_\infty n_x + \phi_y n_y + \phi_z n_z = 0 \quad \mbox M_\infty is the freestream Mach number, and n_x, n_y, n_z are the surface-normal vector components. The unknown variable is the perturbation potential \phi(x,y,z), and the total velocity is given by its gradient plus the freestream velocity V_\infty which is assumed here to be along x. :\vec = \nabla \phi + V_\infty \hat = (V_\infty + \phi_x) \hat + \phi_y \hat + \phi_z \hat The above formulation is valid only ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prandtl–Meyer Expansion Fan
A supersonic expansion fan, technically known as Prandtl–Meyer expansion fan, a two-dimensional simple wave, is a centered expansion process that occurs when a supersonic flow turns around a convex corner. The fan consists of an infinite number of Mach waves, diverging from a sharp corner. When a flow turns around a smooth and circular corner, these waves can be extended backwards to meet at a point. Each wave in the expansion fan turns the flow gradually (in small steps). It is physically impossible for the flow to turn through a single "shock" wave because this would violate the second law of thermodynamics. Impossibility of expanding a flow through a single "shock" wave: Consider the scenario shown in the adjacent figure. As a supersonic flow turns, the normal component of the velocity increases ( w_2 > w_1 ), while the tangential component remains constant ( v_2 = v_1 ). The corresponding change is the entropy (\Delta s = s_2 - s_1) can be expressed as follows, :\begin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prandtl–Batchelor Theorem
In fluid dynamics, Prandtl–Batchelor theorem states that ''if in a two-dimensional laminar flow at high Reynolds number closed streamlines occur, then the vorticity in the closed streamline region must be a constant''. A similar statement holds true for axisymmetric flows. The theorem is named after Ludwig Prandtl and George Batchelor. Prandtl in his celebrated 1904 paper stated this theorem in arguments, George Batchelor unaware of this work proved the theorem in 1956. The problem was also studied in the same year by Richard Feynman and Paco Lagerstrom and by W.W. Wood in 1957. Mathematical proof At high Reynolds numbers, Euler equations reduce to solving a problem for stream function The stream function is defined for incompressible flow, incompressible (divergence-free) fluid flow, flows in two dimensions – as well as in three dimensions with axisymmetry. The flow velocity components can be expressed as the derivatives of t ..., :\nabla^2\psi = - \omega(\psi), \quad \psi=\p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prandtl–Meyer Function
In aerodynamics, the Prandtl–Meyer function describes the angle through which a flow turns isentropically from sonic velocity (M=1) to a Mach (M) number greater than 1. The maximum angle through which a sonic ( ''M'' = 1) flow can be turned around a convex corner is calculated for M = \infty. For an ideal gas, it is expressed as follows, : \begin \nu(M) & = \int \frac\frac \\ pt& = \sqrt \cdot \arctan \sqrt - \arctan \sqrt \end where \nu \, is the Prandtl–Meyer function, M is the Mach number of the flow and \gamma is the ratio of the specific heat capacities. By convention, the constant of integration is selected such that \nu(1) = 0. \, As Mach number varies from 1 to \infty, \nu \, takes values from 0 to \nu_\text \,, where : \nu_\text = \frac \bigg( \sqrt -1 \bigg) where, \theta is the absolute value of the angle through which the flow turns, M is the flow Mach number and the suffixes "1" and "2" denote the initial and final conditions respectively. See also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Göttingen
The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded in 1734 by George II, King of Great Britain and Elector of Hanover, and starting classes in 1737, the Georgia Augusta was conceived to promote the ideals of the Enlightenment. It is the oldest university in the state of Lower Saxony and the largest in student enrollment, which stands at around 31,600. Home to many noted figures, it represents one of Germany's historic and traditional institutions. According to an official exhibition held by the University of Göttingen in 2002, 44 Nobel Prize winners had been affiliated with the University of Göttingen as alumni, faculty members or researchers by that year alone. The University of Göttingen was previously supported by the German Universities Excellence Initiative, holds memberships ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lifting-line Theory
The Prandtl lifting-line theory is a mathematical model in aerodynamics that predicts lift distribution over a three-dimensional wing based on its geometry. It is also known as the Lanchester–Prandtl wing theory. 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 bound vortex loses strength 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, the first approximation to understanding is to consider slicing the wing into cross-sections and analyzing each cross-section independently as a wing in a two-dimensional world. Each of these slices is called an airfoil, and it is easier to understand an ... [...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 determined ex ... [...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. 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 temperature that the parcel experienced throughout the process is \ T'. So \ T' c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theodore Von Kármán
Theodore von Kármán ( hu, ( szőllőskislaki) Kármán Tódor ; born Tivadar Mihály Kármán; 11 May 18816 May 1963) was a Hungarian-American mathematician, aerospace engineer, and physicist who was active primarily in the fields of aeronautics and astronautics. He was responsible for many key advances in aerodynamics, notably on supersonic and hypersonic airflow characterization. He is regarded as an outstanding aerodynamic theoretician of the 20th century. Early life Theodore von Kármán was born into a Jewish family in Budapest, Austria-Hungary, as Kármán Tódor, the son of Helen (Kohn, hu, Kohn Ilka) and Mór Kármán. One of his ancestors was Rabbi Judah Loew ben Bezalel. He studied engineering at the city's Royal Joseph Technical University, known today as Budapest University of Technology and Economics. After graduating in 1902 he moved to the German Empire and joined Ludwig Prandtl at the University of Göttingen, where he received his doctorate in 1908. He taug ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adolf Busemann
Adolf Busemann (20 April 1901 – 3 November 1986) was a German aerospace engineer and influential Nazi-era pioneer in aerodynamics, specialising in supersonic airflows. He introduced the concept of swept wings and, after emigrating in 1947 to the United States under Operation Paperclip, invented the shockwave-free supersonic Busemann biplane. Education and early life Born in Lübeck, Germany, Busemann attended the Technical University of Braunschweig, receiving his Ph.D. in engineering in 1924. Career and research The next year he was given the position of aeronautical research scientist at the Max-Planck Institute where he joined the famed team led by Ludwig Prandtl, including Theodore von Kármán, Max Munk and Jakob Ackeret. In 1930 he was promoted to professor at University of Göttingen. He held various positions within the German scientific community during this period, and during the war he was the director of the Braunschweig Laboratory, a famous research establishment ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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