The convergent-divergent nozzle

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. 

Figure 8.16 Cross-sectional diagram of a single-use disposable powder injection system highlighting the major components. When the actuator button is depressed, the driver gas (He) is released into the surrounding rupture chamber. At a specific pressure, the plastic membranes of the drug cassette burst and the drug particles are entrained in the gas flow, which is accelerated through the convergent-divergent nozzle. [From Hickey (2001). Reproduced with permission from Euromed Communications.]...

It has been shown above that sonic flow will occur when the throat pressure has reached the critical value given in equation (14.54), but this begs the question of how we determine the throat pressure given only the inlet and outlet pressures for the nozzle, which will be the usual case. The answer may be stated easily for the case of the convergent-only nozzle, where the nozzle throat and the nozzle outlet are adjacent. Here the throat pressure will be the same as the outlet pressure until the ratio of the outlet to inlet pressures falls below the critical value, and thereafter the throat pressure will remain at the critical value. The case for the convergent-divergent nozzle is more complicated, and requires the fuller treatment given later in this chapter. 

We shall discuss in Section 14.7 the nozzle efficiency for the convergent-only nozzle and hence calculate the outlet velocity and mass flow. We shall then develop similar methods for the convergent-divergent nozzle in Section 14.8. 

Figure A6.6 Measured versus calculated efficiency for the convergent-divergent nozzle of 2.34 nominal divergence ratio.

This is the location of the minimum cross-sectional area in the converging/diverging nozzle where sonic flow conditions exist (tmity Mach number). 

Note that both the plain orifice and the convergent-divergent nozzle are assumed to undergo an isentropic expansion from the same initial conditions thus, the velocities and densities in each device are identical. The denominator a3xcd/of2cd in Eq. (49) can be calculated with Eq. (47) if the Mach number that the flow attains when entering the Mach disk is known. To calculate aM/ot2, one needs to know only the diameter of the Mach disk Dm and of the nozzle exit D2 ... 

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

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. 

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... 

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 ... 

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. 

---