Compressible flow convergent/divergent nozzles

Pressure profiles for compressible flow through a convergent-divergent nozzle... 

For the delivery of atomization gas, different types of nozzles have been employed, such as straight, converging, and converging-diverging nozzles. Two major types of atomizers, i.e., free-fall and close-coupled atomizers, have been used, in which gas flows may be subsonic, sonic, or supersonic, depending on process parameters and gas nozzle designs. In sonic or supersonic flows, the mass flow rate of atomization gas can be calculated with the following equation based on the compressible fluid dynamics ... 

The vapor flow in a heat pipe is analogous to the compressible fluid flow in a converging-diverging nozzle (see Figure 13.10). In curve A of Figure 13.10, at back pressure (PJ, the pressure decreases in the converging section with an increase in velocity up to the throat. In the divergent section, a pressure recovery occurs with a decrease in velocity. In curve B, at back pressure (Fj), the velocity becomes sonic at the throat, and the maximum mass flow rate... 

Figure 13.10 Compressible flow characteristic in a converging-diverging nozzle...

Equations (7.14), (7.15), and (7.20), combined with the relations between the thermodynamic properties at constant entropy, determine how the velocity varies with cross-sectional area of the nozzle. The variety of results for compressible fluids (e.g., gases), depends in part on whether the velocity is below or above the speed of sound in the fluid. For subsonic flow in a converging nozzle, the velocity increases and pressure decreases as the cross-sectional area diminishes. In a diverging nozzle with supersonic flow, the area increases, but still the velocity increases and the pressure decreases. The various cases are summarized elsewhere.t We limit the rest of this treatment of nozzles to application of the equations to a few specific cases. 

The area-velocity relation provides important insight regarding the behavior of a quasi-ID compressible flow in a channel of varying cross section. It states that for a subsonic flow (M < 1) to increase velocity, a decrease in cross-sectional area is required. This is an intuitive and familiar result similar to incompressible flow theory. In contrast, acceleration of a supersonic flow (M > 1), requires an increase in area a counter-intuitive result when viewed from an incompressible flow perspective. This relation also indicates that sonic velocity (M = 1) can only occur at a nozzle throat where the area is a minimum. It thus follows for a gas to expand from subsonic to supersonic velocities, it must flow through a convergent-divergent channel arrangement. 

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