Divergent nozzle

Convergent/Divergent Nozzles (De Laval Nozzles) During frictionless adiabatic one-dimensional flow with changing cross-sectional area A the following relations are obeyed ... 

Figure 4.5. Flow through converging-diverging nozzles...

With a converging-diverging nozzle, the velocity increases beyond the sonic velocity only if the velocity at the throat is sonic and the pressure at the outlet is lower than the throat pressure. For a converging nozzle the rate of flow is independent of the downstream pressure, provided the critical pressure ratio is reached and the throat velocity is sonic. 

A practical example of flow through a converging-diverging nozzle is given in Example 4.4... 

Air passes from a large reservoir at 70°F through an isentropic converging-diverging nozzle into the atmosphere. The area of the throat is 1 cm2, and that of the exit is 2 cm2. What is the reservoir pressure at which the flow in the nozzle just reaches sonic velocity, and what are the mass flow rate and exit Mach number under these conditions ... 

The case of flow through a convergent-divergent nozzle is shown in Figure 6.2. On reducing the back pressure PB, while keeping the supply... 

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

Air flows from a large reservoir where the temperature and pressure are 25°C and 10 atm, through a convergent-divergent nozzle and discharges to the atmosphere. The area of the nozzle s exit is twice that of its throat. Show that under these conditions a shock wave must occur, (y = 1.4.)... 

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 ... 

It should be noted that the gas flow process in the port is not isentropic because mass and heat addihons occur in the port. This implies that there is stagnation pressure loss and so the specific impulse is reduced for nozzleless rockets. When a convergent nozzle is attached to the rear end of port, the static pressure at the port exit, Pj, continues to decrease to the atmospheric pressure and the specific impulse of the nozzleless rocket motor is increased. The expansion process in a divergent nozzle is an isentropic process, as described in Section 1.2. 

Nozzleless rockets are very simplified and low-cost rockets because no nozzles are used. Their specific impulse is lower than that of conventional rockets even when the same mass of propellant is used. Normally, a convergent-divergent nozzle is used to expand the chamber pressure to the atmospheric pressure through an isentropic change, which is the most effective process for converting pressure into propulsive thrust The flow process without a nozzle increases entropy and there is stagnahon pressure loss. 

The supersonic air induced into the air-intake is converted into a pressurized subsonic airflow through the shock wave in the air-intake. The fuel-rich gas produced in the gas generator pressurizes the combustion chamber and flows into the ramburner through a gas flow control system. The pressurized air and the fuel-rich gas produce a premixed and/or a diffusional flame in the ramburner. The combustion gas flows out through the convergent-divergent nozzle and is accelerated to supersonic flow. 

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.

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