Flow nozzles

Flow nozzles are commonly used in the measurement of steam and other high velocity fluids where erosion can occur. Nozzle flow coefficients are insensitive to small contour changes and reasonable accuracy can be maintained for long periods under difficult measurement conditions that would create unacceptable errors using an orifice installation. 

Adiabatic Frictionless Nozzle Flow In process plant pipelines, compressible flows are usually more nearly adiabatic than isothermal. Solutions for adiabatic flows through frictionless nozzles and in channels with constant cross section and constant friction factor are readily available. 

The equations for nozzle flow, Eqs. (6-114) through (6-118), remain valid for the nozzle section even in the presence of the discharge pipe. Equations (6-116) and (6-120), for the temperature variation, may also be used for the pipe, with Mo, po replacing Mi, pi since they are valid for adiabatic flow, with or without friction. 

Choked and unchoked flow situations arise in pipes and nozzles in the same fashion for homogeneous equihbrium flashing flow as for gas flow. For nozzle flow from stagnation pressure po to exit pressure pi, the mass flux is given by... 

Ideal (Frictionless) Flow in Nozzles The flow path in well-formed nozzles follows smoothly along the nozzle contour without separating from the wall. The effects of small imperfections and small frictional losses are accounted for by correcting the ideal nozzle flow by an empirically determined coefficient of mscharge. The acceleration of a fluid initially at rest to flowing conditions in an ideal nozzle is given by ... 

HEM for Two-Phase Orifice Discharge For orifice or nozzle flow, the friction term and the potential energy term in Eq. (26-82) are negligible, so it can be integrated in general across both subcooled and flashing regions thusly ... 

This is a low value, therefore, the possibility exists of an up-rate relative to any nozzle flow limits. At this point, a comment or two is in order. There is a rule of thumb that sets inlet nozzle velocity limit at approximately 100 fps. But because the gases used in the examples have relatively high acoustic velocities, they will help illustrate how this limit may be extended. Regardless of the method being used to extend the velocity, a value of 150 fps should be considered maximum. When the sonic velocity of a gas is relatively low, the method used in this example may dictate a velocity for the inlet nozzle of less than 100 fps. The pressure drop due to velocity head loss of the original design is calculated as follows ... 

McRee, D. I., and H. L. Moses. 1967. The effect of aspect ratio and offset on nozzle flow and jet reattachment. In Advances in Fluidics The 1967 Fluidics Symposium. ASME. 

The velocity of the nozzle flow is found by equation 4-81. The total area of the nozzle openings is... 

Introducing the nozzle flow coefficient of 0.95 and using field system of units, Equation 4-117 becomes... 

Nb205 F (NH4)20 Type Plasma Nozzles flow g/sec Yield, % F content, % wt g/1 Nb205 F (NH4)20... 

A link between laminar and turbulent lifted flames has been demonstrated based on the observation of a continuous transition from laminar to turbulent lifted flames, as shown in Figure 4.3.13 [56]. The flame attached to the nozzle lifted off in the laminar regime, experienced the transition by the jet breakup characteristics, and became turbulent lifted flames as the nozzle flow became turbulent. Subsequently, the liftoff height increased linearly and finally blowout (BO) occurred. This continuous transition suggested that tribrachial flames observed in laminar lifted flames could play an important role in the stabilization of turbulent lifted flames. Recent measurements supported the existence of tribrachial structure at turbulent lifted edges [57], with the OH zone indicating that the diffusion reaction zone is surrounded by the rich and lean reaction zones. 

The axial velocity profiles, calculated on the basis of Tollmien similarity and experimental measurement in Yang and Kcaims (1980) were integrated across the jet cross-section at different elevations to obtain the total jet flow across the respective jet cross-sections. The total jet flows at different jet cross-sections are compared with the original jet nozzle flow, as shown in Fig. 31. Up to about 50% of the original jet flow can be entrained from the emulsion phase at the lower part of the jet close to the jet nozzle. This distance can extend up to about 4 times the nozzle diameter. The gas is then expelled from the jet along the jet height. 

The subscript s denotes an isentropic path for ideal nozzle flow. For ideal gas with Pok = constant, substitution of this isentropic expansion law into Eq. (23-98) yields the following critical pressure ratio PJP and critical flow rate Gc ... 

Equation (1.54) indicates that A/A becomes minimal at M = 1. The flow Mach number increases as A/A decreases when M < 1, and also increases as A/A increases when M > 1. When M = 1, the relationship A = A is obtained and is independent of Y- It is evident that A is the minimum cross-sectional area of the nozzle flow, the so-called nozzle throat", in which the flow velocity becomes the sonic velocity, furthermore, it is evident that the velocity increases in the subsonic flow of a convergent part and also increases in the supersonic flow of a divergent part. 

Since Cp indicates the efficiency of the expansion process in the nozzle flow and c indicates the efficiency of the combustion process in the chamber, gives an indication of the overall efficiency of a rocket motor. 

Fig. 12.16 Temperature along the exhaust nozzle flow and effect of the concentration of K2SO4.

A nozzle used for a rocket is composed of a convergent section and a divergent section. The connected part of these two nozzle sections is the minimum cross-sectional area termed the throat The convergent part is used to increase the flow velocity from subsonic to sonic velocity by reducing the pressure and temperature along the flow direction. The flow velocity reaches the sonic level at the throat and continues to increase to supersonic levels in the divergent part. Both the pressure and temperature of the combustion gas flow decrease along the flow direction. This nozzle flow occurs as an isentropic process. 

When a supersonic flow emerges from a rocket nozzle, several oblique shock waves and expansion waves are formed along the nozzle flow. These waves are formed repeatedly and form a brilliant diamond-Uke array, as shown in Fig. C-5. When an under-expanded flow, i. e., having pressure higher than the ambient pressure is formed at the nozzle exit, an expansion wave is formed to decrease the pressure. This expansion wave is reflected at the interface between the flow stream and the ambient air and a shock wave is formed. This process is repeated several times to form a diamond array, as shown in Fig. C-6 (a). 

Figure C-6. Structures of (a) an under-expanded nozzle flow and (b) an over-expanded nozzle flow.

If the flow process is an isentropic change, the total pressure poa remains unchanged throughout the nozzle flow. However, the process of the generation of a shock wave in the divergent part increases the entropy and the total pressure becomes Pq2- It is evident that the inlet performance increases as po2 approaches Po. ... 

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