Jet Flow

Jet flow

A fluid flow in which a stream of one fluid mixes with a surrounding medium, at rest or in motion. Such flows occur in a wide variety of situations, and the geometries, sizes, and flow conditions cover a large range. Jet flows vary greatly, depending on the values of two numbers. The first is the Reynolds number, defined in Eq. (1),

(1) 
where &rgr; is the density, V is a characteristic velocity (for example, the jet exit velocity), L is a characteristic length (for example, the jet diameter), and μ is the viscosity. The second is the Mach number, defined in Eq. (2),
(2) 
where a is the speed of sound. See Mach number, Reynolds number

For conditions where Re < 2300 and M << 1, jet flows take on a simple character. An example is the water jet formed by a household tap when the valve is partially opened to produce a low flow. If the flow or the diameter is increased or the viscosity is decreased so that Re > 2300, the jet will change dramatically. For example, a water jet exiting into water at rest with Re &ap; 2300 is initially in the simple laminar state, but at this Reynolds number that state is unstable and the flow undergoes a transition to the more chaotic turbulent state. Turbulent structures called eddies are formed with a large range of sizes. The large-scale structures are responsible for capturing fluid from the surroundings and entraining it into the jet. However, the jet and external fluids are not thoroughly mixed until diffusion is completed by the small-scale structures. See Diffusion, Laminar flow, Turbulent flow

When the velocities in the jet are greater than the speed of sound (M > 1) the flow is said to be supersonic, and important qualitative changes in the flow occur. The most prominent change is the occurrence of shock waves. For example, a supersonic air jet exhausting from a nozzle at low pressure into higher-pressure air at rest is said to be overexpanded. As the jet leaves the nozzle, it senses the higher pressure around it and adjusts through oblique shock waves emanating from the edges of the nozzle. See Shock wave, Supersonic flow

Another class of jet flows is identified by the fact that the motion of the jet is induced primarily by buoyancy forces. A common example is a hot gas exhaust rising in the atmosphere. Such jet flows are called buoyant plumes, or simply plumes, as distinct from the momentum jets, or simply jets, discussed above. See Fluid flow

Jet Flow

 

a type of fluid flow in which a liquid or gas passes through a fluid with properties, such as velocity, temperature, or density, different from those of the jet. Jet flow is an extremely common phenomenon that exists in many forms, from the stream ejected through the exhaust nozzle of a rocket engine to the jet stream in the earth’s atmosphere. It is studied by examining changes in the velocity, density, temperature, and concentration of the component fluids both in the jet and in the ambient fluid.

Jet flows are classified according to the chief characteristics of interest for simplifying various problems. An important category of jet flow comprises jets issuing from a nozzle or orifice in the wall of a container. Such jets are classified as round, rectangular, plane, and so forth, depending on the cross-sectional shape of the orifice or nozzle. If the streamlines of a jet are parallel at the nozzle exit, the jet is said to exhibit axial flow. Fan-shaped and convoluted jets are also known.

Jets are described as liquid, gas, or plasma flows, depending on the material properties of the fluid. In a jet composed of compressible gases, the ratio of the exhaust velocity v of the gas to the propagation velocity a of sound waves is important. This ratio is called the Mach number M = v/a. Jet streams are classified as subsonic (M < 1) or supersonic (M > 1), depending on the value of M. Two-phase jets, such as a gas containing liquid or solid particles, constitute a special category. The medium through which a jet stream passes may be classified in a similar manner.

Depending on the direction of the streamlines of the ambient fluid, a jet is said to issue into a coflowing stream (one flowing in the same direction), a counterflowing stream, or an obliquely flowing stream; for example, a liquid discharged through a pipe into a river in the direction of the river’s current, against the current, and at an angle to the current, respectively. A stream entering a reservoir is an example of jet flow in a stationary medium. When the composition of the fluid in the jet is identical with that of the surrounding stationary medium, the jet is said to be submerged; air currents in a still atmosphere are an example of submerged flow. Free jet flow is said to exist when a jet passes through an unbounded medium; the flow is called semicontained if the jet passes along a flat surface, and confined if it exists in a medium bounded by solid surfaces, for example, the flow through a pipe having a diameter larger than that of the inlet. A jet flowing past an obstacle is treated as a special case.

Jet flows can also be classified as miscible or immiscible, depending on the physical properties of the substances composing the jet and the ambient fluid. An example of miscible flow is a gas jet flowing into air; a water jet issuing into the atmosphere is a case of immiscible flow. An immiscible jet has unstable boundaries, and the stream breaks up into spray at some distance downstream from the nozzle. The range of such flow, that is, the distance over which the flow remains coherent, depends on the physical properties of the substances and the amount of initial turbulence at the nozzle. The range of the jet of water expelled by a fire hose is increased by contouring and carefully polishing the inner surface of the nozzle. In the case of the jet issuing from a flamethrower, special admixtures are also added to the charge liquid in order to increase the liquid’s surface tension. The range of an atomizer stream is decreased by inducing turbulence, con-voluting the flow, and, sometimes, by mixing in a gas before spraying.

If the material in a jet is freely miscible with the material in the external medium, a monotonically expanding region of viscous mixing forms along the jet boundary. This region is called a boundary layer. Jets may be classified as either laminar or turbulent, depending on the flow regime of the boundary layer. The flow from the exhaust nozzle of a jet airplane in flight is an example of turbulent, supersonic jet flow issuing into a coflowing stream, which may be either subsonic or supersonic, depending on the speed of the aircraft.

In subsonic turbulent flow—a form of isobaric flow with wide technical application in ventilation equipment, industrial furnaces, and other engineering systems—the static pressure at any point in the jet is constant and equal to the pressure in the surrounding region. At the orifice of a nozzle that represents the source of a coflowing, isobaric jet (section AA in Figure 1), the velocity Vo of the jet flow differs from the velocity Vn of the external parallel flow. At the boundary between the jet flow and the external flow the boundary layer T is formed, consisting of the gas in the jet and the ambient gas entrained by the jet. Divergence of the gas in the jet, limited by the dimension b, increases monotonically with increasing distance from the nozzle orifice. However, the total momentum of the gas as determined from the excess velocities remains constant.

Figure 1. Coflowing, isobaric gas jet: (bo) radius of the nozzle, (b) radius of the jet, (xn) length of the initial region, (xp) length of the transition region, (vn) flow velocity at the nozzle orifice, (vn) flow velocity of the ambient fluid, (vm < vo) velocity of axial flow, (T) boundary layer

In the initial region of the jet, where x < xn, the boundary layer expands but does not reach the axis of flow. The velocity v is constant near the axis and is equal to the velocity at the nozzle orifice. In the transition region (xn < xxp), viscous mixing spreads over the entire jet flow and the flow velocity along the axis decreases, but the velocity profiles are not yet stabilized. In the main region (x > xp), the flow velocity along the axis continues decreasing, but the profiles of the relative velocity Δvvm = f(y/b) become constant. In these profiles, Δv = vvn and Δvm = vmvn correspond to the excess velocities at a particular point in the flow and along the jet axis. The jet expands in the main region in the same way that the boundary layer expands in the initial region of turbulent flow, that is, in proportion to the average amount of flow turbulence

where C is a constant. In other words, the jet expansion depends on the difference between the velocities along the flow axis and the flow velocity of the ambient fluid. Similar relations have been established for changes in the temperature of the gas and in the concentrations of the gas’s components where these are different for the jet gas and for the ambient fluid.

The treatment of nonideal supersonic turbulent jet flow is similar, although the problem is more complicated. This type of jet flow issues from the supersonic exhaust nozzles of jet and rocket engines, gas and steam turbines, and similar devices. The initial dynamic region of nonideal supersonic jet flow (the first bulb-shaped region in Figure 2) xxng is defined as the distance from the nozzle orifice to the point where the shock waves (2) intersect the boundaries of the jet. The size and configuration of this region depend on the degree to which the flow departs from that of an ideal fluid jet and are characterized by the parameter n = pa/pn (where pa is the pressure in the flow at the nozzle orifice and pn is the pressure in the ambient fluid), on the Mach number Ma at the nozzle orifice, on the Mach number Mn of the ambient fluid, and on the physical properties of the gases in the jet and ambient fluid. The layer of viscous mixing that forms on the boundaries of the jet reaches the axis of flow at a distance xnv. Pressure waves die out and constant relative profiles for the velocity, temperature, and component concentration become established in the transition region xp, beyond which the flow becomes isobaric. In the case where the coflowing ambient stream is supersonic (Mn > 1), a shock wave (1) forms ahead of the jet.

Figure 2. Nonideal supersonic jet in a supersonic, coflowing stream: (xng) initial dynamic region of jet flow (first bulb-shaped section), (xp) transition region, (xnu) distance at which the layer of viscous mixing reaches the axis of flow, (T) region of viscous mixing (boundary layer) of the jet; (1) shock wave arising in the coflowing stream, (2) shock waves in the jet

Although the preceding representations of jet flow differ from real-life examples, which are more complex, they can be used to formulate sufficiently accurate methods of calculating the fields of velocities, temperature, and component concentration in the jet and ambient fluid. A solution to this problem is essential for determining the quantity of matter that a jet stream entrains from the ambient fluid, the mechanical and thermal interactions between the jet and a surface located at a given distance from the nozzle orifice, and the radiation from a jet.

REFERENCES

Abramovich, G. N. Teoriia turbulentnykh strui. Moscow, 1960.
Vulis, L. A., and V. P. Kashkarev. Teoriia strui viazkoi zhidkosti. Moscow, 1965.
Sverkhzvukovye strui ideal’nogo gaza, parts 1–2. Moscow, 1970–71.

M. IA. IUDELOVICH

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