Nozzle divergent part

Equation (1.54) indicates that A/A becomes minimal at M = 1. The flow Mach number increases as A/A decreases when M < 1, and also increases as A/A increases when M > 1. When M = 1, the relationship A = A is obtained and is independent of Y- It is evident that A is the minimum cross-sectional area of the nozzle flow, the so-called nozzle throat", in which the flow velocity becomes the sonic velocity, furthermore, it is evident that the velocity increases in the subsonic flow of a convergent part and also increases in the supersonic flow of a divergent part. 

A nozzle used for a rocket is composed of a convergent section and a divergent section. The connected part of these two nozzle sections is the minimum cross-sectional area termed the throat The convergent part is used to increase the flow velocity from subsonic to sonic velocity by reducing the pressure and temperature along the flow direction. The flow velocity reaches the sonic level at the throat and continues to increase to supersonic levels in the divergent part. Both the pressure and temperature of the combustion gas flow decrease along the flow direction. This nozzle flow occurs as an isentropic process. 

Fig. D-2 shows the shock-wave formation at a supersonic diffuser composed of a divergent nozzle. Three types of shock wave are formed at three different back-pressures downstream of the diffuser. When the back-pressure is higher than the design pressure, a normal shock wave is set up in front of the divergent nozzle and the flow velocity becomes a subsonic flow, as shown in Fig. D-2 (a). Since the streamline bends outwards downstream of the shock wave, some air is spilled over from the air-intake. The cross-sectional area upstream of the duct becomes smaller than the cross-sectional area of the air-intake, and so the efficiency of the diffuser is reduced. The subsonic flow velocity is further reduced and the pressure is increased in the divergent part of the diffuser.

If the flow process is an isentropic change, the total pressure poa remains unchanged throughout the nozzle flow. However, the process of the generation of a shock wave in the divergent part increases the entropy and the total pressure becomes Pq2- It is evident that the inlet performance increases as po2 approaches Po. ... 

For example, T /T0 = 0.833, p /po = 0.528, and p /po = 0.634 are obtained when y = 1.4. The temperature T0 at the stagnation condition decreases 17 % and the pressure p0 decreases 50% at the nozzle throat. The pressure decrease is more rapid than the temperature decrease when the flow expands through a convergent nozzle. The maximum flow velocity is obtained at the exit of the divergent part of the nozzle. When the pressure at the nozzle exit is vacuum, the maximum velocity is obtained by the use of Eqs. (1.48) and (1.6) as... 

It is shown in specialized texts on fluid dynamics that a convergent-diveigent nozzle is needed to accelerate a gas from subsonic to supersonic conditions, since gas acceleration in the subsonic regime requires the flow area to diminish with speed, while gas acceleration from sonic to supersonic speeds requires the flow area to expand with speed. The subsonic, convergent part of the nozzle is linked to the supersonic, divergent part of the nozzle by a duct of constant flow area, known as the throat, which is kept very short in practice in order to avoid frictional losses. The throat is the only section of the nozzle in which sonic flow can occur, and it is impossible for the throat to support any speed greater than sonic. The above remarks apply to all polytropic... 

The motive nozzle is shaped like a Laval nozzle. This means there is an enlargement of the diameter after the smallest cross section. This is necessary to achieve velocities higher than sonic speed. For steam an expansion pressure ratio of only Pi/Po = is sufficient to just achieve sonic velocity (critical pressure ratio). At higher expansion ratios (supercritical pressure ratios), the exact critical pressure and sonic speed is achieved in the smallest cross section. In these cases in the divergent part of the motive nozzle, a supersonic velocity results from a continuing expansion. Owing to the blocking of the velocity to the sonic speed in the smallest cross section, the mass flow rate of such a supersonic nozzle only depends on the state of the motive media in front of the nozzle and of course on the diameter d.. Here the mass flow rate is proportional to the motive pressurep. ... 

Beyond the significant mass flow rates that must be introduced to generate a uniform supersonic flow downstream of a Laval nozzle, it is also important to stress that the inner shape of the divergent part of the Laval nozzle and the temperature of the reservoir completely constrain the flow conditions i.e. nature of the buffer gas, gas flow rate, supersonic temperature and pressure. In other words, for a given Laval nozzle, the temperature in the supersonic flow is not a timeable parameter. Hence, a series of different Laval nozzles are required to match the range of temperature that needs to be explored. The typical temperatures that can be achieved in the present working CRESU apparatuses are usually in the range 15-300 K. This temperature is directly linked to the reservoir temperature by the relation ... 

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. 

Nozzles are placed in series along tubular reactor and have on the outside surface the flutes forming with inside surface of box wall screw canal (Fig. 6.6), and inside surface of nozzles has on flanks conical lugs with diameter in 1,3-3 times lower than in cylindrical part of inside cavity of nozzles and forming tubular turbulent reactor of divergent-convergent design (Fig. 6.5). Screw canal and inside cavity of nozzle are connected by holes and/or cuts, and beyond last nozzle in the course of gas-iiquid flow one or more static mixers are placed. 

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