Nozzles converging/diverging, flow

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... 

This is identical to the equation derived in physics for the speed of so in the fluid. Therefore, the maximum fluid velocity obtainable in a pipe of const cross-sectional area is the speed of sound. This does not imply that higt velocities are impossible they are, in fact, readily obtained in converg diverging nozzles (Sec. 7.3). However, the speed of sound is the maximum val that can be reached in a conduit of constant cross section, provided the entran velocity is subsonic. The sonic velocity must be reached at the exit of the pi-If the pipe length is increased, the mass rate of flow decreases so that the so velocity is still obtained at the outlet of the lengthened pipe. 

For a converging/diverging nozzle with negligible entrance velocity in which expansion isentropic, sketch graphs of mass flow rate m, velocity u, and area ratio A/A, vs. the pressure i P/ P,. Here, A is the cross-sectional area of the nozzle at the point in the nozzle where the press" is P, and subscript 1 denotes the nozzle entrance. 

Steam expands isentropically in a converging/diverging nozzle from inlet conditions of200(p 600(, F), and negligible velocity to a discharge pressure of 50(psia). At the throat, the cross-seeds area is I (in)2. Determine the mass flow rate of the steam and the state of the steam at the exit of 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 speed of sound is attained at the throat of a converging/diverging nozzle only when the pressure at the throat is low enough that the critical value of P-JP is reached. If insufficient pressure drop is available in the nozzle for the velocity to become sonic, the diverging section of the nozzle acts as a diffuser. That is, after the throat is reached the pressure rises and the velocity decreases this is the conventional behavior for subsonic flow in diverging sections. The relationships between velocity, area, and pressure in a nozzle are illustrated numerically in Example 7.3. 

---