Nozzles and diffusers

Pressure-distance plot for various flow rates in a converging-diverging nozzle. 

Throughout the calculation we hold the upstream reservoir pressure constant. We begin to lower the downstream reservoir pressure / 2. As long as the exiting gas is in subsonic flow, the exit pressure will be the same as the downstream pressure so if we set the downstream pressure, we have set the pressure at the exit of the nozzle. From this pressure and the area of the nozzle, we can calculate the pressure at the throat or at any other point whose cross-sectional area we know, as shown in the following example.. 

Example 8.13. We now set the downstream reservoir pressure at 0.9506 times the upstream reservoir pressure (point B in Fig. 8.14). What is the pressure at the throat of the nozzle  

We look in App. A.5 for F/P = 0.9506 and find that the exit Mach number is 0.27. We also observe that A JA is 2.2385. Then we can find 

We see in App, A.5 that this corresponds to a Mach number of about 0.43 at the throat, and therefore we have PIPn = 0.88 at the throat. In the same way, we could calculate PIP at any point in the nozzle at which A was known, thereby completing the entire curve AB in Fig, 8.14.  

It is important to remember that the examples in this section are restricted to cases when steady-state can be applied. If we are interested in start-up or shutdown of these processes, or the case where there are fluctuations in feed or operating conditions, we must use the unsteady form of the energy balance. 

These process devices convert between internal energy and kinetic energy by changing the cross-sectional area through which a fluid flows. In a nozzle the flow is constricted, increasing e - A diffuser increases the cross-sectional area to decrease the bulk flow velocity. An example of a process calculation through a diffuser follows. 

The intake to the engine of a jet airliner consists of a diffuser that must reduce the air velocity to zero so that it can enter the compressor. Consider a jet flying at a cruising speed of 350 m/s at an altitude of 10,000 m where the temperature is 10°C. What is the temperature of the air upon exiting the diffuser and entering the compressor  

This steady-state process occurs in an open system with one stream in and one stream out. In this case, we can write the first law using Equation (2.50)  

Using the definition of heat capacity, we get the following integral expression  

---

The ejector is widely used as a vacuum pump, where it is staged when required to achieve deeper vacuum levels. If the motive fluid pressure is sufficiently high, the ejector can compress gas to a slightly positive pressure. Ejectors are used both as subsonic and supersonic devices. The design must incorporate the appropriate nozzle and diffuser compatible with the gas velocity. The ejector is one of the ( to liquid carryover in the suction gas. 

When the aim is to build a cheap fan system and have a small pressure rise, then the nozzle and diffuser are not usually installed in the system. 

Figure 6-1. Basic ejector components and diagram of energy conversion in nozzle and diffuser. By permission, Ingersoll-Rand Co.

An increase in steam pressure over design will not increase vapor handling capacity for the usual fixed capacity ejector. The increased pressure usually decreases capacity due to the extra steam in the diffuser. The best ejector steam economy is attained when the steam nozzle and diffuser are proportioned for a specified performance [8]. This is the reason it is difficult to keep so-called standard ejectors in stock and expect to have the equivalent of a custom designed unit. The throttling type ejector has a family of performance curves depending upon the motive steam pressure. This type has a lower compression ratio across the ejector than the fixed-type. The fixed-type unit is of the most concern in this presentation. 

A reversible adiabatic process is isentropic, meaning that a substance will have the same entropy values at the beginning and end of the process. Systems such as pumps, turbines, nozzles, and diffusers are nearly adiabatic operations and are more efficient when irreversibilities, such as friction, are reduced, and hence operated under isentropic conditions. 

Co., October 15, 1956 from Leitinger, H., Research on the Design of Hypersonic Nozzles and Diffusers at High Stagnation Temperatures, Part 1, Appendix 4 (WADC 55-507). 

Fig. 19. Schematic representation of an HF (DF) laser with supersonic flow (a). In part (b) nozzle and diffusion details are shown...

Jet ejectors require very little attention and maintenance and are especially valuable with corrosive gases that would damage mechanical vacuum pumps. For difficult problems the nozzles and diffusers can be made of corrosion-resistant metal, graphite, or other inert material. Ejectors, particularly when multistage, use large quantities of steam and water. They arc rarely used to produce absolute pressures below 1 mm Hg, Steam jets are no longer as popular as they once were, because of the dramatic increase in the cost of steam. In many instances where corrosion is not a serious consideration, they have been replaced by mechanical vacuum pumps, which use much less energy for the same service. 

Fig. 9.19 Conical nozzle and diffuser elements. Reprinted from (Lee and Kim (2006a). ...

A flow field is laminar, when it is governed by the viscous properties. That applies to very slow fluid velocities or very high viscosities, which are typical for polymer composites or highly concentrated suspensions (e.g. paints). There are three ideal types of laminar flow uniform flow (e.g. experienced by settling particles), shear flow (e. g in rheometers or pipes), and elongational flow (e.g. in nozzles and diffusers). Only the latter two are relevant for deagglomeration. 

The very high velocities that the ejector is exposed to subject the nozzle and diffuser throat to excessive wear. Low-quality steam will accelerate this erosion. A gradual loss in vacuum may be due to enlargement of the ejector clearances. It is a good practice to caliper these clearances when the system is out of service. A fuller description of ejector operation, steam requirements, and pressure capabilities can be found in Robert Frumerman s "Steam Jet Ejectors," Chemical Engineering, June 1956. 

---