Entropy-vorticity Wave
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Entropy-vorticity Wave
Entropy-vorticity waves (or sometimes entropy-vortex waves) refer to small-amplitude waves carried by the gas within which entropy, vorticity, density but not pressure perturbations are propagated.Landau, L. D., & Lifshitz, E. M. (2013). Fluid Mechanics: Landau and Lifshitz: Course of Theoretical Physics, Volume 6 (Vol. 6). Elsevier. Page 316, section 82. Entropy-vortivity waves are essentially isobaric, incompressible, rotational perturbations along with entropy perturbations. This wave differs from the other well-known small-amplitude wave that is a sound wave, which propagates with respect to the gas within which density, pressure but not entropy perturbations are propagated. The classification of small disturbances into acoustic, entropy and vortex modes were introduced by Leslie S. G. Kovasznay. Entropy-vorticity waves are ubiquitous in supersonic problems, particularly those involving shock waves. Since these perturbations are carried by the gas, they are convected by the flo ...
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Entropy
Entropy is a scientific concept, most commonly associated with states of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory. It has found far-ranging applications in chemistry and physics, in biological systems and their relation to life, in cosmology, economics, sociology, weather science, climate change and information systems including the transmission of information in telecommunication. Entropy is central to the second law of thermodynamics, which states that the entropy of an isolated system left to spontaneous evolution cannot decrease with time. As a result, isolated systems evolve toward thermodynamic equilibrium, where the entropy is highest. A consequence of the second law of thermodynamics is that certain processes are irreversible. The thermodynami ...
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Vorticity
In continuum mechanics, vorticity is a pseudovector (or axial vector) 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 \boldsymbol is the curl of the flow velocity \mathbf v: :\boldsymbol \equiv \nabla \times \mathbf v\,, where \nabla is the nabla operator. Conceptually, \boldsymbol 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 \boldsymbol would be twice the mean angular velocity vector of those particles relative to their center of mass, orie ...
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Density
Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be used: \rho = \frac, where ''ρ'' is the density, ''m'' is the mass, and ''V'' is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume, although this is scientifically inaccurate this quantity is more specifically called specific weight. For a pure substance, the density is equal to its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium is the densest known element at standard conditions for temperature and pressure. To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless quantity "relative den ...
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Pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and even by industry. Further, both spellings are often used ''within'' a particular industry or country. Industries in British English-speaking countries typically use the "gauge" spelling. is the pressure relative to the ambient pressure. Various #Units, units are used to express pressure. Some of these derive from a unit of force divided by a unit of area; the International System of Units, SI unit of pressure, the Pascal (unit), pascal (Pa), for example, is one newton (unit), newton per square metre (N/m2); similarly, the Pound (force), pound-force per square inch (Pound per square inch, psi, symbol lbf/in2) is the traditional unit of pressure in the imperial units, imperial and United States customary units, US customary systems. Pressure ma ...
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Isobaric Process
In thermodynamics, an isobaric process is a type of thermodynamic process in which the pressure of the Thermodynamic system, system stays constant: Δ''P'' = 0. The heat transferred to the system does work (thermodynamics), work, but also changes the internal energy (''U'') of the system. This article uses the physics sign convention for work, where positive work is work (thermodynamics)#Sign convention, work done by the system. Using this convention, by the first law of thermodynamics, : Q = \Delta U + W\, where ''W'' is work, ''U'' is internal energy, and ''Q'' is heat. Pressure-volume work by the closed system is defined as: :W = \int \! p \,dV \, where Δ means change over the whole process, whereas ''d'' denotes a differential. Since pressure is constant, this means that : W = p \Delta V\, . Applying the ideal gas law, this becomes : W = n\,R\,\Delta T with ''R'' representing the gas constant, and ''n'' representing the amount of substance, which is ass ...
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Incompressible Flow
In fluid mechanics, or more generally continuum mechanics, incompressible flow is a flow in which the material density does not vary over time. Equivalently, the divergence of an incompressible flow velocity is zero. Under certain conditions, the flow of compressible fluids can be modelled as incompressible flow to a good approximation. 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. Mathematically, this constraint implies that the material derivative (discussed below) of the density must vanish to ensure incompressible flow. Before introducing this constraint, we must apply the conservation of mass to generate the necessary relations. The mass is calculated by a volume integral of the density, \rho : : = . The conservation of mass requires that the time derivative of the mass inside a control volume be equal to the mass flux, J, acro ...
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Sound Wave
In physics, sound is a vibration that propagates as an acoustic wave through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the brain. Only acoustic waves that have frequencies lying between about 20 Hz and 20 kHz, the audio frequency range, elicit an auditory percept in humans. In air at atmospheric pressure, these represent sound waves with wavelengths of to . Sound waves above 20  kHz are known as ultrasound and are not audible to humans. Sound waves below 20 Hz are known as infrasound. Different animal species have varying hearing ranges, allowing some to even hear ultrasounds. Definition Sound is defined as "(a) Oscillation in pressure, stress, particle displacement, particle velocity, etc., propagated in a medium with internal forces (e.g., elastic or viscous), or the superposition of such propagated oscillation. (b) Auditory sens ...
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Leslie Stephen George Kovasznay
Leslie S. G. Kovasznay (14 April 1918, Budapest – 17 April 1980) was a Hungarian-American engineer, known as one of the world's leading experts in turbulent flow research. Kovasznay earned in 1943 his doctorate in engineering at the Royal Hungarian Institute of Technology in the laboratory of Előd Abody-Anderlik in the faculty of mechanical engineering. After working from 1941 to 1946 at that Faculty, he spent a year at the Cavendish Laboratory working with Sir Geoffrey Taylor. From 1947 to 1978 Kovasznay was a faculty member of the Aeronautics Department organized by Francis H. Clauser (1913–2013) at Johns Hopkins University (JHU). In December, he resigned from JHU to become a professor of mechanical engineering at the University of Houston, where he remained in his professorship until his sudden death in 1980. In the 1970s, he worked with Hajime Fujita on experimental studies of interactions between airfoils and wake turbulence and, with Chih-Ming Ho, on experimental s ...
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Shock Waves
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 ...
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Acoustic Wave
Acoustic waves are types of waves that propagate through matter—such as gas, liquid, and/or solids—by causing the particles of the medium to compress and expand. These waves carry energy and are characterized by properties like acoustic pressure, particle velocity, and acoustic intensity. The speed of an acoustic wave depends on the properties of the medium it travels through; for example, it travels at approximately 343 meters per second in air, and 1480 meters per second in water. Acoustic waves encompass a broad range of phenomena, from audible sound to seismic waves and ultrasound, finding applications in diverse fields like acoustics, engineering, and medicine. Wave properties An acoustic wave is a mechanical wave that transmits energy through the movements of atoms and molecules. Acoustic waves transmit through fluids in a longitudinal manner (movement of particles are parallel to the direction of propagation of the wave); in contrast to electromagnetic waves that tra ...
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Solid-propellant Rocket
A solid-propellant rocket or solid rocket is a rocket with a rocket engine that uses solid propellants (fuel/ oxidizer). The earliest rockets were solid-fuel rockets powered by gunpowder. The inception of gunpowder rockets in warfare can be credited to the ancient Chinese, and in the 13th century, the Mongols played a pivotal role in facilitating their westward adoption. All rockets used some form of solid or powdered propellant until the 20th century, when liquid-propellant rockets offered more efficient and controllable alternatives. Because of their simplicity and reliability, solid rockets are still used today in military armaments worldwide, model rockets, solid rocket boosters and on larger applications. Since solid-fuel rockets can remain in storage for an extended period without much propellant degradation, and since they almost always launch reliably, they have been frequently used in military applications such as missiles. The lower performance of solid propellant ...
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Detonations
Detonation () is a type of combustion involving a supersonic exothermic front accelerating through a medium that eventually drives a shock front propagating directly in front of it. Detonations propagate supersonically through shock waves with speeds about 1 km/sec and differ from deflagrations which have subsonic flame speeds about 1 m/sec. Detonation may form from an explosion of fuel-oxidizer mixture. Compared with deflagration, detonation doesn't need to have an external oxidizer. Oxidizers and fuel mix when deflagration occurs. Detonation is more destructive than deflagrations. In detonation, the flame front travels through the air-fuel faster than sound; while in deflagration, the flame front travels through the air-fuel slower than sound. Detonations occur in both conventional solid and liquid explosives, as well as in reactive gases. TNT, dynamite, and C4 are examples of high power explosives that detonate. The velocity of detonation in solid and liquid explosives ...
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