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a specially shaped enclosed channel designed to accelerate liquids or gases to a given velocity and to impart a given direction to the flow. Nozzles are also used as a means of obtaining gas or liquid jets. The cross section of the nozzle may be rectangular (two-dimensional nozzle), circular (axisymmetric nozzle), or some other shape (spatial nozzle).
Within a nozzle, the velocity v of the liquid or gas increases continuously in the direction of the flow from an initial value v0 at the entry to a maximum velocity v = va at the exit. By virtue of the energy conservation principle, as the velocity v increases in a nozzle, there is a simultaneous continuous drop in the pressure and temperature from initial values p0 and T0 to minimum values pa and Ta at the discharge area. Thus, for flow to occur in a nozzle some pressure drop is necessary, that is, the condition p0 > pa must be fulfilled. When T0 is increased, the velocity in all sections of a nozzle rises because of the higher initial potential energy. As long as the flow velocity is not too high, the corresponding pressure and temperature changes in the nozzle are small; therefore, the property of compressibility—the ability of a liquid or gas to undergo a volume change in response to the application of pressure or a change in temperature—does not manifest itself, and it is possible to disregard any variation in the density p of the flowing medium, that is, to consider the density constant. Under these conditions, a nozzle should have a converging shape if a continuous increase in velocity is desired since by virtue of the continuity equation ρvF = const, the area F of the nozzle cross section must decrease in inverse proportion to the rise in velocity. However, with a further increase in v, the compressibility of the medium begins to manifest itself, and the density decreases in the direction of flow. Consequently, the constancy of the product of the three factors pvF under these new conditions depends on the rate at which p decreases as v increases. When v < a, where a is the local velocity of sound propagation in the moving medium, the rate at which the density of a gas decreases lags behind the rate at which the velocity increases, and therefore, in order to provide acceleration, that is, to increase v, F must be decreased (Figure 1) despite the decrease in the density (subsonic nozzle). But with acceleration to velocities v > a, the density decreases more rapidly than the velocity increases; it therefore becomes necessary in the supersonic part to increase the area F (supersonic nozzle). Thus, a supersonic nozzle, which is also known as a Laval nozzle, has both a convergent section and a divergent portion (Figure 2). The velocity variation through the nozzle depends on the variation of the area of the cross section F with the length.
The pressure at the discharge area of a subsonic nozzle is always equal to the pressure pm of the surrounding medium at the exit (pa = pm). The pressures are equal because any deviation manifests itself as disturbances that propagate inside the nozzle with a velocity equal to that of sound and bring about a rearrangement of the flow that equalizes the pressure at the nozzle’s discharge area. When p0 increases and pm remains constant, the velocity va at the discharge area of a subsonic nozzle first increases, but after p0 reaches a certain value the velocity becomes constant and does not change when p0 is increased further. This phenomenon is referred to as crisis flow in the nozzle. With the onset of crisis flow, the average velocity of the discharge from a subsonic nozzle is equal to the local sound velocity (va = a) and is called the critical discharge velocity. The subsonic nozzle is converted into a sonic nozzle. All the gas parameters in the discharge area of the nozzle in this case are also described as critical. For subsonic nozzles with a smooth contour, the critical pressure ratio when discharging air and other diatomic gases is (P0/pm)cr ≈ 1.9.
In a supersonic nozzle, the narrowest section is described as critical. The relative velocity va/a in the discharge area of a supersonic nozzle depends only on the ratio of the discharge area Fa to the area of the critical section Fa and, within wide limits, is independent of variations in the pressure p0 in the front of the nozzle. Consequently, by varying the area of the critical section Fcr with a mechanical device while the area Fa is left unchanged, it is possible to vary va/la. The adjustable nozzles used in technology that vary the gas discharge velocity are based on this principle. The pressure in the discharge area of a supersonic nozzle can be equal to the pressure of the surrounding medium (pa = pm), and a flow regime of this type is called the design flow; when the pressures are not equal, the regime is called off-design flow. Unlike a subsonic nozzle, the pressure disturbances when pa± pm, which propagate with the velocity of sound, are in the supersonic flow and do not penetrate into the supersonic nozzle; the pressure pa is therefore not equalized with pm. Off-design regimes are characterized by the formation of rarefaction waves when pa > pm and shock waves when pa < pm. When the flow passes through a system of such waves outside the nozzle, the pressure becomes equal to pm. When the pressure in the atmosphere greatly exeeds the pressure at the nozzle’s discharge area, the shock waves may move into the nozzle, and then the continuous increase of the velocity in the supersonic part of the nozzle is disturbed. A sharp drop in the pressure and temperature of a gas in a supersonic nozzle can lead, depending on the composition of the flowing medium, to the occurrence of such physicochemical processes as chemical reactions, phase transformations, and nonequilibrium thermodynamic transitions. These processes must be taken into account when calculating the gas flow in the nozzle.
Nozzles are widely used in technology in, for example, steam and gas turbines, rocket engines, air-breathing jet engines, gas lasers, equipment used in magnetogas dynamics, wind tunnels, test benches used in gas dynamics, jet devices, and flowmeters. They also find use in the creation of molecular beams, in chemical engineering, and in various types of blasting processes. The nozzle must be designed to carry out the particular technical function. For example, wind-tunnel nozzles must provide a uniform, parallel gas flow in the discharge area, while the nozzles used in rocket engines must ensure that the momentum of the gas flow at the discharge area be as high as possible for the given dimensions. These and other technical specifications have brought about a vigorous development of nozzle theory, which studies the presence in the gas flow of liquid and solid particles, as well as such processes as nonequilibrium chemical reactions and the transfer of radiant energy. Computers have been used extensively in this work both to determine nozzle design and to develop complex experimental methods of investigating nozzles.
REFERENCESAbramovich, G. N. Prikladnaia gazovaia dinamika, 3rd ed. Moscow, 1969.
Sternin, L. E. Osnovy gazodinamiki dvukhfaznykh techenii vsoplakh. Moscow, 1974.
S. L. VISHNEVETSKII
A conduit with a variable cross-sectional area in which a fluid accelerates into a high-velocity stream.
The fluid must be compressed to a state of high pressure before it is sent through the nozzle. If the fluid is a gaseous medium, the temperature of the fluid also drops as the fluid accelerates. Since the velocity of sound of the fluid is directly related to the temperature of the fluid, the fluid velocity may exceed the speed of sound of the fluid, so that the fluid is in a state of supersonic flow. Under this condition, the nozzle must have a convergent-divergent geometry, since the supersonic state is realized only in the divergent portion of the nozzle (see illustration). The Mach number, which is the ratio of the velocity of the flowing fluid to the velocity of sound of the fluid, may be employed to characterize the flow. The Mach number is less than unity if the flow is subsonic, unity if the flow is sonic, and larger than unity if the flow is supersonic. If the flow at the throat is sonic, the flow is said to reach the critical state.
A nozzle can be used for a variety of purposes. It is an indispensable piece of equipment in many devices employing fluid as a working medium. The reaction force that results from the fluid acceleration may be employed to propel a jet aircraft or a rocket. In fact, most military jet aircraft employ the simple convergent conical nozzle, with adjustable conical angle, as their propulsive device. If the high-velocity fluid stream is directed to turn a turbine, it may generate electric power or drive an automotive vehicle. The high-velocity stream may also be produced inside a wind tunnel so that the conditions of flight of a missile or an aircraft may be simulated inside the tunnel for research purposes. The nozzle must be carefully designed in this case to provide uniformly flowing fluid with the desired velocity, pressure, and temperature at the test section of the wind tunnel. Nozzles may also be used to disperse fuel into an atomized mist, such as that in diesel engines, for combustion purposes. See Atomization, Impulse turbine, Internal combustion engine, Jet propulsion, Rocket propulsion, Wind tunnel
ii. The primary aperture through which fuel is injected into a gas turbine engine combustion chamber.
iii. A duct with a varying cross-sectional area used to accelerate the fluid flow. This acceleration of fluid causes the pressure to decrease.