Converging-diverging 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 ... 

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. 

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.]...

However, never confuse the lift of the valve with its capacity, as even a perfect convergent/divergent nozzle s flow rate is reduced beyond the medium s critical pressure ratio, as shown in the graph in Figure 5.40. In principle, a perfect nozzle has a KD (flow factor) = 1. 

Figure 6-23 shows a converging/diverging nozzle. When p2/p0 is less than the critical pressure ratio (p a/p ), the flow will be subsonic in the converging portion of the nozzle, sonic at the throat, and supersonic in the diverging portion. At the throat, where the flow is critical and the velocity is sonic, the area is denoted A. The cross-sectional... 

Venturi tubes and converging/diverging nozzles. For these devices,p2 in the equations in the preceding subsection is the pressure at the throat where the velocity is V2. In the following discussion it is assumed that the initial values of p1 and T1 remain constant while P2 varies. 

It must be remembered that Eqs. (10.94) to (10.97) are to be used only when the velocity of approach is negligible and when p2 at the throat of a venturi tube or converging/diverging nozzle is reduced to a value pc as obtained from Eq. (10.92). For an orifice p2 is the pressure in the space into which the jet issues, no matter how low this pressure may become. 

If Pi is increased, the acoustic velocity may be shown to remain unaltered, but, since the density of the gas is increased, the rate of disharge is greater. The orifice and the venturi tube are alike insofar as discharge capacity is concerned. The only difference is that with the venturi tube, or a converging/diverging nozzle, a supersonic velocity may be attained at discharge from the device, while with the orifice the acoustic velocity is the maximum value possible at any point. 

Example 10.8 Air enters a converging/diverging nozzle (venturi) at a pressure of 120 psia and a temperature of 90°F. Neglecting the entrance velocity, and assuming a frictionless process, find the Mach number at the cross section where the pressure is 35 psia. 

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