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Prandtl–Glauert Singularity
The Prandtl–Glauert singularity is a theoretical construct in flow physics, often incorrectly used to explain vapor cones in transonic flows. It is the prediction by the Prandtl–Glauert transformation that infinite pressures would be experienced by an aircraft as it approaches the speed of sound. Because it is invalid to apply the transformation at these speeds, the predicted singularity does not emerge. The incorrect association is related to the early-20th-century misconception of the impenetrability of the sound barrier. Reasons of invalidity around Mach 1 The Prandtl–Glauert transformation assumes linearity (i.e. a small change will have a small effect that is proportional to its size). This assumption becomes inaccurate toward Mach 1 and is entirely invalid in places where the flow reaches supersonic speeds, since sonic shock waves are instantaneous (and thus manifestly non-linear) changes in the flow. Indeed, one assumption in the Prandtl–Glauert transformation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vapor Cone
A vapor cone (also known as a Mach diamond, shock collar, or shock egg) is a visible cloud of condensed water that can sometimes form around an object moving at high speed through moist air, for example, an aircraft flying at transonic speeds. When the localized air pressure around the object drops, so does the air temperature. If the temperature drops below the saturation temperature, a cloud forms. In the case of aircraft, the cloud is caused by expansion fans decreasing the air pressure, density, and temperature below the dew point. Then pressure, density, and temperature suddenly increase across the stern shock wave associated with a return to subsonic flow behind the aircraft. Since the local Mach number is not uniform over the aircraft, parts of the aircraft may be supersonic while others remain subsonic—a flight regime called transonic flight. In addition to making the shock waves themselves visible, water condensation can also occur in the trough between two crests o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
FA-18 Hornet Breaking Sound Barrier (7 July 1999)
The McDonnell Douglas F/A-18 Hornet is an all-weather, twin-engine, supersonic, carrier-capable, multirole combat aircraft, designed as both a fighter and attack aircraft (hence the F/A designation). Designed by McDonnell Douglas (now part of Boeing) and Northrop (now part of Northrop Grumman), the F/A-18 was derived from the latter's YF-17 in the 1970s for use by the United States Navy and Marine Corps. The Hornet is also used by the air forces of several other nations, and formerly by the U.S. Navy's Flight Demonstration Squadron, the Blue Angels. The F/A-18 was designed to be a highly versatile aircraft due to its avionics, cockpit displays, and excellent aerodynamic characteristics, with the ability to carry a wide variety of weapons. The aircraft can perform fighter escort, fleet air defense, suppression of enemy air defenses, air interdiction, close air support, and aerial reconnaissance. Its versatility and reliability have proven it to be a valuable carrier asset ... [...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] |
Speed Of Sound
The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends strongly on temperature as well as the medium through which a sound wave is propagating. At , the speed of sound in air is about . The speed of sound in an ideal gas depends only on its temperature and composition. The speed has a weak dependence on frequency and pressure in ordinary air, deviating slightly from ideal behavior. In colloquial speech, ''speed of sound'' refers to the speed of sound waves in air. However, the speed of sound varies from substance to substance: typically, sound travels most slowly in gases, faster in liquids, and fastest in solids. For example, while sound travels at in air, it travels at in water (almost 4.3 times as fast) and at in iron (almost 15 times as fast). In an exceptionally stiff material such as diamond, sound travels a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sound Barrier
The sound barrier or sonic barrier is the large increase in aerodynamic drag and other undesirable effects experienced by an aircraft or other object when it approaches the speed of sound. When aircraft first approached the speed of sound, these effects were seen as constituting a barrier, making faster speeds very difficult or impossible. The term ''sound barrier'' is still sometimes used today to refer to aircraft approaching Supersonic speed, supersonic flight in this high drag regime. Flying faster than sound produces a sonic boom. In dry air at 20 °C (68 °F), the speed of sound is 343 metres per second (about 767 mph, 1234 km/h or 1,125 ft/s). The term came into use during World War II when pilots of high-speed fighter aircraft experienced the effects of compressibility, a number of adverse aerodynamic effects that deterred further acceleration, seemingly impeding flight at speeds close to the speed of sound. These difficulties represented a bar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Singularity (mathematics)
In mathematics, a singularity is a point at which a given mathematical object is not defined, or a point where the mathematical object ceases to be well-behaved in some particular way, such as by lacking differentiability or analyticity. For example, the real function : f(x) = \frac has a singularity at x = 0, where the numerical value of the function approaches \pm\infty so the function is not defined. The absolute value function g(x) = , x, also has a singularity at x = 0, since it is not differentiable there. The algebraic curve defined by \left\ in the (x, y) coordinate system has a singularity (called a cusp) at (0, 0). For singularities in algebraic geometry, see singular point of an algebraic variety. For singularities in differential geometry, see singularity theory. Real analysis In real analysis, singularities are either discontinuities, or discontinuities of the derivative (sometimes also discontinuities of higher order derivatives). There are four kinds of discon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pressure Coefficient
The pressure coefficient is a dimensionless number which describes the relative pressures throughout a flow field in fluid dynamics. The pressure coefficient is used in aerodynamics and hydrodynamics. Every point in a fluid flow field has its own unique pressure coefficient, C_p. In many situations in aerodynamics and hydrodynamics, the pressure coefficient at a point near a body is independent of body size. Consequently, an engineering model can be tested in a wind tunnel or water tunnel, pressure coefficients can be determined at critical locations around the model, and these pressure coefficients can be used with confidence to predict the fluid pressure at those critical locations around a full-size aircraft or boat. Definition The pressure coefficient is a parameter for studying both incompressible/compressible fluids such as water and air. The relationship between the dimensionless coefficient and the dimensional numbers is :C_p = = where: : p is the static pressure a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Incompressible
In fluid mechanics or more generally continuum mechanics, incompressible flow ( isochoric flow) refers to a flow in which the material density is constant within a fluid parcel—an infinitesimal volume that moves with the flow velocity. An equivalent statement that implies incompressibility is that the divergence of the flow velocity is zero (see the derivation below, which illustrates why these conditions are equivalent). Incompressible flow does not imply that the fluid itself is incompressible. It is shown in the derivation below that (under the right conditions) even compressible fluids can – to a good approximation – be modelled as an incompressible flow. Incompressible flow implies that the density remains constant within a parcel of fluid that moves with the flow velocity. Derivation The fundamental requirement for incompressible flow is that the density, \rho , is constant within a small element volume, ''dV'', which moves at the flow velocity u. Mathematic ... [...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 through ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compressible Flow
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] |
Vapor Cone
A vapor cone (also known as a Mach diamond, shock collar, or shock egg) is a visible cloud of condensed water that can sometimes form around an object moving at high speed through moist air, for example, an aircraft flying at transonic speeds. When the localized air pressure around the object drops, so does the air temperature. If the temperature drops below the saturation temperature, a cloud forms. In the case of aircraft, the cloud is caused by expansion fans decreasing the air pressure, density, and temperature below the dew point. Then pressure, density, and temperature suddenly increase across the stern shock wave associated with a return to subsonic flow behind the aircraft. Since the local Mach number is not uniform over the aircraft, parts of the aircraft may be supersonic while others remain subsonic—a flight regime called transonic flight. In addition to making the shock waves themselves visible, water condensation can also occur in the trough between two crests o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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