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Oblique Shock Wave
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] |
Shockwave Pattern Around A T-38C Observed With Background-Oriented Schlieren Photography (1)
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 through ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grumman F-14 Tomcat 2
The Grumman Aircraft Engineering Corporation, later Grumman Aerospace Corporation, was a 20th century American producer of military and civilian aircraft. Founded on December 6, 1929, by Leroy Grumman and his business partners, it merged in 1994 with Northrop Corporation to form Northrop Grumman. History Leroy Grumman worked for the Loening Aircraft Engineering Corporation beginning in 1920. In 1929, Keystone Aircraft Corporation bought Loening Aircraft and moved its operations from New York City to Bristol, Pennsylvania. Grumman and three other ex-Loening Aircraft employees,Jordan, Corey C"Grumman's Ascendency: Chapter One." ''Planes and Pilots Of World War 2,'' 2000. Retrieved: July 22, 2011. (Edmund Ward Poor, William Schwendler, and Jake Swirbul) started their own company in an old Cox-Klemin Aircraft Co. factory in Baldwin on Long Island, New York. The company registered as a business on December 6, 1929, and officially opened on January 2, 1930. While maintaining the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
McGraw-Hill
McGraw Hill is an American educational publishing company and one of the "big three" educational publishers that publishes educational content, software, and services for pre-K through postgraduate education. The company also publishes reference and trade publications for the medical, business, and engineering professions. McGraw Hill operates in 28 countries, has about 4,000 employees globally, and offers products and services to about 140 countries in about 60 languages. Formerly a division of The McGraw Hill Companies (later renamed McGraw Hill Financial, now S&P Global), McGraw Hill Education was divested and acquired by Apollo Global Management in March 2013 for $2.4 billion in cash. McGraw Hill was sold in 2021 to Platinum Equity for $4.5 billion. Corporate History McGraw Hill was founded in 1888 when James H. McGraw, co-founder of the company, purchased the ''American Journal of Railway Appliances''. He continued to add further publications, eventually establishin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dover Publications
Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward and Blanche Cirker. It primarily reissues books that are out of print from their original publishers. These are often, but not always, books in the public domain. The original published editions may be scarce or historically significant. Dover republishes these books, making them available at a significantly reduced cost. Classic reprints Dover reprints classic works of literature, classical sheet music, and public-domain images from the 18th and 19th centuries. Dover also publishes an extensive collection of mathematical, scientific, and engineering texts. It often targets its reprints at a niche market, such as woodworking. Starting in 2015, the company branched out into graphic novel reprints, overseen by Dover acquisitions editor and former comics writer and editor Drew Ford. Most Dover reprints are photo facsimiles of the originals, retaining the original paginatio ... [...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 throug ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shock Polar
The term ''shock polar'' is generally used with the graphical representation of the Rankine–Hugoniot equations in either the hodograph plane or the pressure ratio-flow deflection angle plane. The polar itself is the locus of all possible states after an 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 comp .... Shock polar in the (''φ'', ''p'') plane The minimum angle, \theta, which an oblique shock can have is the Mach angle \mu =\sin^(1/M), where M is the initial Mach number before the shock and the greatest angle corresponds to a normal shock. The range of shock angles is therefore \sin^(1/M)\leq\theta\leq\pi /2. To calculate the pressures for this range of angles, the Rankine–Hugoniot equations are solved for pressure: \frac = 1 + \frac \left(M^\sin^\theta - 1\ri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moving Shock
In fluid dynamics, a moving shock is a shock wave that is travelling through a fluid (often gaseous) medium with a velocity relative to the velocity of the fluid already making up the medium.Shapiro, Ascher H., ''Dynamics and Thermodynamics of Compressible Fluid Flow,'' Krieger Pub. Co; Reprint ed., with corrections (June 1983), . As such, the normal shock relations require modification to calculate the properties before and after the moving shock. A knowledge of moving shocks is important for studying the phenomena surrounding detonation, among other applications. Theory To derive the theoretical equations for a moving shock, one may start by denoting the region in front of the shock as subscript 1, with the subscript 2 defining the region behind the shock. This is shown in the figure, with the shock wave propagating to the right. The velocity of the gas is denoted by ''u'', pressure by ''p'', and the local speed of sound by ''a''. The speed of the shock wave relative to the ga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mach Reflection
Mach reflection is a supersonic fluid dynamics effect, named for Ernst Mach, and is a shock wave reflection pattern involving three shocks. Introduction Mach reflection can exist in steady, pseudo-steady and unsteady flows. When a shock wave, which is moving with a constant velocity, propagates over a solid wedge, the flow generated by the shock impinges on the wedge thus generating a second reflected shock, which ensures that the velocity of the flow is parallel to the wedge surface. Viewed in the frame of the reflection point, this flow is locally steady, and the flow is referred to as pseudosteady. When the angle between the wedge and the primary shock is sufficiently large, a single reflected shock is not able to turn the flow to a direction parallel to the wall and a transition to Mach reflection occurs. In a steady flow situation, if a wedge is placed into a steady supersonic flow in such a way that its oblique attached shock impinges on a flat wall parallel to the free s ... [...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] |
Bow Shock (aerodynamics)
A bow shock, also called a detached shock or bowed normal shock, is a curved propagating disturbance wave characterized by an abrupt, nearly discontinuous, change in pressure, temperature, and density. It occurs when a supersonic flow encounters a body, around which the necessary deviation angle of the flow is higher than the maximum achievable deviation angle for an attached oblique shock (see detachment criterion). Then, the oblique shock transforms in a curved detached shock wave. As bow shocks occur for high flow deflection angles, they are often seen forming around blunt bodies, because of the high deflection angle that the body impose to the flow around it. The thermodynamic transformation across a bow shock is non-isentropic and the shock decreases the flow velocity from supersonic velocity upstream to subsonic velocity downstream. Applications The bow shock significantly increases the drag in a vehicle traveling at a supersonic speed. This property was utilized in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Limit (mathematics)
In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value. Limits are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals. The concept of a limit of a sequence is further generalized to the concept of a limit of a topological net, and is closely related to limit and direct limit in category theory. In formulas, a limit of a function is usually written as : \lim_ f(x) = L, (although a few authors may use "Lt" instead of "lim") and is read as "the limit of of as approaches equals ". The fact that a function approaches the limit as approaches is sometimes denoted by a right arrow (→ or \rightarrow), as in :f(x) \to L \text x \to c, which reads "f of x tends to L as x tends to c". History Grégoire de Saint-Vincent gave the first definition of limit (terminus) of a geometric series in his work ''Opus Geometricum'' (1647): "The ''terminus'' of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
