|
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] |
Expansion Fan
Expansion may refer to: Arts, entertainment and media * ''L'Expansion'', a French monthly business magazine * ''Expansion'' (album), by American jazz pianist Dave Burrell, released in 2004 * ''Expansions'' (McCoy Tyner album), 1970 * ''Expansions'' (Lonnie Liston Smith album), 1975 * ''Expansión'' (Mexico), a Mexican news portal linked to CNN * Expansion (sculpture) (2004) Bronze sculpture illuminated from within * ''Expansión'' (Spanish newspaper), a Spanish economic daily newspaper published in Spain * Expansion pack in gaming, extra content for games, often simply "expansion" Science, technology, and mathematics * Expansion (geometry), stretching of geometric objects with flat sides * Expansion (model theory), in mathematical logic, a mutual converse of a reduct * Expansion card, in computing, a printed circuit board that can be inserted into an expansion slot * Expansion chamber, on a two-stroke engine, a tuned exhaust system that enhances power output * Expansion joi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mach Angle
In fluid dynamics, a Mach wave is a pressure wave traveling with the speed of sound caused by a slight change of pressure added to a compressible flow. These weak waves can combine in supersonic flow to become a shock wave if sufficient Mach waves are present at any location. Such a shock wave is called a Mach stem or Mach front. Thus, it is possible to have shockless compression or expansion in a supersonic flow by having the production of Mach waves sufficiently spaced (''cf.'' isentropic compression in supersonic flows). A Mach wave is the weak limit of an oblique shock wave where time averages of flow quantities don't change; (a normal shock is the other limit). If the size of the object moving at the speed of sound is near 0, then this domain of influence of the wave is called a Mach cone. Mach angle A Mach wave propagates across the flow at the Mach angle ''μ'', which is the angle formed between the Mach wave wavefront and a vector that points opposite to the vector of mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shadowgraph
Shadowgraph is an optical method that reveals non-uniformities in transparent media like air, water, or glass. It is related to, but simpler than, the schlieren and schlieren photography methods that perform a similar function. Shadowgraph is a type of flow visualisation. In principle, a difference in temperature, a different gas, or a shock wave in the transparent air cannot be seen by the human eye or cameras. However, all these disturbances refract light rays, so they can cast shadows. The plume of hot air rising from a fire, for example, can be seen by way of its shadow cast upon a nearby surface by the uniform sunlight. Sunlight shadowgraph Some aquatic predators detect their transparent prey by way of their shadows cast upon the ocean floor. It was Robert Hooke who first scientifically demonstrated the sunlight shadowgraph and Jean-Paul Marat who first used it to study fire. A modern account of shadowgraphy is given by Gary S. Settles. Applications Appli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shock Wave
In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a medium but is characterized by an abrupt, nearly discontinuous, change in pressure, temperature, and density of the medium. For the purpose of comparison, in supersonic flows, additional increased expansion may be achieved through an expansion fan, also known as a Prandtl–Meyer expansion fan. The accompanying expansion wave may approach and eventually collide and recombine with the shock wave, creating a process of destructive interference. The sonic boom associated with the passage of a supersonic aircraft is a type of sound wave produced by constructive interference. Unlike solitons (another kind of nonlinear wave), the energy and speed of a shock wave alone dissipates relatively quickly with distance. When a shock wave passes thr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oblique Shock
An oblique shock wave is a shock wave that, unlike a normal shock, is inclined with respect to the incident upstream flow direction. It will occur when a supersonic flow encounters a corner that effectively turns the flow into itself and compresses. The upstream streamlines are uniformly deflected after the shock wave. The most common way to produce an oblique shock wave is to place a wedge into supersonic, compressible flow. Similar to a normal shock wave, the oblique shock wave consists of a very thin region across which nearly discontinuous changes in the thermodynamic properties of a gas occur. While the upstream and downstream flow directions are unchanged across a normal shock, they are different for flow across an oblique shock wave. It is always possible to convert an oblique shock into a normal shock by a Galilean transformation. Wave theory For a given Mach number, M1, and corner angle, θ, the oblique shock angle, β, and the downstream Mach number, M2, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gas Dynamics
Compressible flow (or gas dynamics) is the branch of fluid mechanics that deals with flows having significant changes in fluid density. While all flows are compressible, flows are usually treated as being incompressible when the Mach number (the ratio of the speed of the flow to the speed of sound) is smaller than 0.3 (since the density change due to velocity is about 5% in that case).Anderson, J.D., ''Fundamentals of Aerodynamics'', 4th Ed., McGraw–Hill, 2007. The study of compressible flow is relevant to high-speed aircraft, jet engines, rocket motors, high-speed entry into a planetary atmosphere, gas pipelines, commercial applications such as abrasive blasting, and many other fields. History The study of gas dynamics is often associated with the flight of modern high-speed aircraft and atmospheric reentry of space-exploration vehicles; however, its origins lie with simpler machines. At the beginning of the 19th century, investigation into the behaviour of fired bullets led to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
No-slip Condition
In fluid dynamics, the no-slip condition for viscous fluids assumes that at a solid boundary, the fluid will have zero velocity relative to the boundary. The fluid velocity at all fluid–solid boundaries is equal to that of the solid boundary. Conceptually, one can think of the outermost molecules of fluid as stuck to the surfaces past which it flows. Because the solution is prescribed at given locations, this is an example of a Dirichlet boundary condition. Physical justification Particles close to a surface do not move along with a flow when adhesion is stronger than cohesion. At the fluid-solid interface, the force of attraction between the fluid particles and solid particles (Adhesive forces) is greater than that between the fluid particles (Cohesive forces). This force imbalance brings down the fluid velocity to zero. The no slip condition is only defined for viscous flows and where continuum concept is valid. Exceptions As with most of the engineering approximations, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tangential Component
In mathematics, given a vector at a point on a curve, that vector can be decomposed uniquely as a sum of two vectors, one tangent to the curve, called the tangential component of the vector, and another one perpendicular to the curve, called the normal component of the vector. Similarly, a vector at a point on a surface can be broken down the same way. More generally, given a submanifold ''N'' of a manifold ''M'', and a vector in the tangent space to ''M'' at a point of ''N'', it can be decomposed into the component tangent to ''N'' and the component normal to ''N''. Formal definition Surface More formally, let S be a surface, and x be a point on the surface. Let \mathbf be a vector at x. Then one can write uniquely \mathbf as a sum : \mathbf=\mathbf_\parallel + \mathbf_\perp where the first vector in the sum is the tangential component and the second one is the normal component. It follows immediately that these two vectors are perpendicular to each other. To calculate the ta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Streamlines, Streaklines And Pathlines
Streamlines, streaklines and pathlines are field lines in a fluid flow. They differ only when the flow changes with time, that is, when the flow is not steady. Considering a velocity vector field in three-dimensional space in the framework of continuum mechanics, we have that: * Streamlines are a family of curves whose tangent vectors constitute the velocity vector field of the flow. These show the direction in which a massless fluid element will travel at any point in time. * Streaklines are the loci of points of all the fluid particles that have passed continuously through a particular spatial point in the past. Dye steadily injected into the fluid at a fixed point extends along a streakline. * Pathlines are the trajectories that individual fluid particles follow. These can be thought of as "recording" the path of a fluid element in the flow over a certain period. The direction the path takes will be determined by the streamlines of the fluid at each moment in time. * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Component
In mathematics, given a vector at a point on a curve, that vector can be decomposed uniquely as a sum of two vectors, one tangent to the curve, called the tangential component of the vector, and another one perpendicular to the curve, called the normal component of the vector. Similarly, a vector at a point on a surface can be broken down the same way. More generally, given a submanifold ''N'' of a manifold ''M'', and a vector in the tangent space to ''M'' at a point of ''N'', it can be decomposed into the component tangent to ''N'' and the component normal to ''N''. Formal definition Surface More formally, let S be a surface, and x be a point on the surface. Let \mathbf be a vector at x. Then one can write uniquely \mathbf as a sum : \mathbf=\mathbf_\parallel + \mathbf_\perp where the first vector in the sum is the tangential component and the second one is the normal component. It follows immediately that these two vectors are perpendicular to each other. To calculate the ta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Turning Angle
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the ''local'' or ''relative'' extrema), or on the entire domain (the ''global'' or ''absolute'' extrema). Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions. As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum. Definition A real-valued function ''f'' defined on a domain ''X'' has a global (or absolute) maximum point at ''x''∗, if for all ''x'' in ''X''. Similarly, the function has a global (or absolute) minimum point at ''x''∗, if for all ''x'' in ''X''. The value of the function at a m ... [...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] |
