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Von Kármán Swirling Flow
Von Kármán swirling flow is a flow created by a uniformly rotating infinitely long plane disk, named after Theodore von Kármán who solved the problem in 1921. The rotating disk acts as a fluid pump and is used as a model for centrifugal fans or compressors. This flow is classified under the category of steady flows in which vorticity generated at a solid surface is prevented from diffusing far away by an opposing convection, the other examples being the Blasius boundary layer with suction, stagnation point flow etc. Flow description Consider a planar disk of infinite radius rotating at a constant angular velocity \Omega in fluid which is initially at rest everywhere. Near to the surface, the fluid is being turned by the disk, due to friction, which then causes centrifugal forces which move the fluid outwards. This outward radial motion of the fluid near the disk must be accompanied by an inward axial motion of the fluid towards the disk to conserve mass. Theodore von Kármán n ... [...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] |
Vorticity
In continuum mechanics, vorticity is a pseudovector field that describes the local spinning motion of a continuum near some point (the tendency of something to rotate), as would be seen by an observer located at that point and traveling along with the flow. It is an important quantity in the dynamical theory of fluids and provides a convenient framework for understanding a variety of complex flow phenomena, such as the formation and motion of vortex rings. Mathematically, the vorticity \vec is the curl of the flow velocity \vec: :\vec \equiv \nabla \times \vec\,, where \nabla is the nabla operator. Conceptually, \vec could be determined by marking parts of a continuum in a small neighborhood of the point in question, and watching their ''relative'' displacements as they move along the flow. The vorticity \vec would be twice the mean angular velocity vector of those particles relative to their center of mass, oriented according to the right-hand rule. In a two-dimensional fl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blasius Boundary Layer
In physics and fluid mechanics, a Blasius boundary layer (named after Paul Richard Heinrich Blasius) describes the steady two-dimensional laminar boundary layer that forms on a semi-infinite plate which is held parallel to a constant unidirectional flow. Falkner and Skan later generalized Blasius' solution to wedge flow (Falkner–Skan boundary layer), i.e. flows in which the plate is not parallel to the flow. Prandtl's boundary layer equations Using scaling arguments, Ludwig Prandtl argued that about half of the terms in the Navier-Stokes equations are negligible in boundary layer flows (except in a small region near the leading edge of the plate). This leads to a reduced set of equations known as the boundary layer equations. For steady incompressible flow with constant viscosity and density, these read: Mass Continuity: \dfrac+\dfrac=0 x-Momentum: u \dfrac + v \dfrac = - \dfrac \dfrac + \dfrac y-Momentum: 0= - \dfrac \dfrac Here the coordinate system is chosen with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stagnation Point Flow
In fluid dynamics, stagnation point flow represents the flow of a fluid in the immediate neighborhood of a stagnation point (or a stagnation line) with which the stagnation point (or the line) is identified for a potential flow or inviscid flow. The flow specifically considers a class of stagnation points known as saddle points where the incoming streamlines gets deflected and directed outwards in a different direction; the streamline deflections are guided by separatrices. The flow in the neighborhood of the stagnation point or line can generally be described using potential flow theory, although viscous effects cannot be neglected if the stagnation point lies on a solid surface. Stagnation point flow without solid surfaces When two streams either of two-dimensional or axisymmetric nature impinge on each other orthogonally, a stagnation plane is created, where the incoming streams are diverted tangentially outwards; thus on the stagnation plane, the velocity component normal to t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Navier–Stokes Equations
In physics, the Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842–1850 (Stokes). The Navier–Stokes equations mathematically express conservation of momentum and conservation of mass for Newtonian fluids. They are sometimes accompanied by an equation of state relating pressure, temperature and density. They arise from applying Isaac Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term—hence describing ''viscous flow''. The difference between them and the closely related Euler equations is that Navier–Stokes equations take ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Von Karman Swirling Flow With Pressure
The term ''von'' () is used in German language surnames either as a nobiliary particle indicating a noble patrilineality, or as a simple Preposition and postposition, preposition used by commoners that means ''of'' or ''from''. Nobility directories like the ''Almanach de Gotha'' often abbreviate the noble term ''von'' to ''v.'' In medieval or early modern names, the ''von'' particle was at times added to commoners' names; thus, ''Hans von Duisburg'' meant "Hans from [the city of] Duisburg". This meaning is preserved in Swiss toponymic surnames and in the Dutch language, Dutch or Afrikaans ''Van (Dutch), van'', which is a cognate of ''von'' but does not indicate nobility. Usage Germany and Austria The abolition of the Monarchy, monarchies in Germany and Austria in 1919 meant that neither state has a privileged nobility, and both have exclusively republican governments. In Germany, this means that legally ''von'' simply became an ordinary part of the surnames of the people w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
