Convergent nozzles

By feeding the mixture through a converging nozzle, the velocity profile may be made nearly flat or uniform. A Bunsen flame in such a flow has a smaller range of stabiUty but the mechanism is essentially the same and the flame very closely approximates a cone. If the apex angle of the flame is , then S can be obtained from equation 21... 

The shape of the converging section is a smooth trumpet shape similar to the simple converging nozzle. However, special shapes of the diverging section are required to produce the maximum supersonic-exit velocity. Shocks result if the divergence is too rapid and excessive boundary layer friction occurs if the divergence is too shallow. See Liepmann and Roshko (Elements of Gas Dynamic.s, Wiley, New York, 1957, p. 284). If the nozzle is to be used as a thrust device, the diverg-... 

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. 

The experimental setup sketched in Figure 5.2.3 comprises a burner with ad = 22 mm nozzle exit diameter and a driver unit (loudspeaker) fixed at its base. The burner body is a cylindrical tube of 65 mm inner diameter containing a set of grids and a honeycomb followed by a convergent nozzle with an area contraction ratio of cr= 9 1. 

Air is fed from a reservoir through a converging nozzle into a 1 /2 in. ID drawn steel tube that is 15 ft long. The flow in the tube is adiabatic, and the reservoir temperature and pressure are 70°F and lOOpsia. 

Pressure profiles for compressible flow through a convergent nozzle... 

If the back pressure is reduced below P, there is no increase in the flow rate through the nozzle, ie the flow is choked. In a convergent nozzle it is impossible for the gas speed to exceed the speed of sound. This case is... 

Nitrogen contained in a large tank at a pressure P = 200000 Pa and a temperature of 300 K flows steadily under adiabatic conditions into a second tank through a converging nozzle with a throat diameter of 15 mm. The pressure in the second tank and at the throat of the nozzle is P, = 140000 Pa. Calculate the mass flow rate, M, of nitrogen assuming frictionless flow and ideal gas behaviour. Also calculate the gas speed at the nozzle and establish that the flow is subsonic. The relative molecular mass of nitrogen is 28.02 and the ratio of the specific heat capacities y is 1.39. 

Consider the case in which an ideal gas flows from one tank to another tank at a lower pressure through a convergent nozzle. The second tank is assumed to be at a constant pressure. The flow may be assumed to be isentropic so that the mass flow rate is given by equation 6.107. 

Air at a pressure of 5 bar in a closed tank is to be vented by allowing it to discharge through a convergent nozzle straight to the atmosphere. Show that the mass flow rate M is given by... 

Nitrogen is to be vented to the atmosphere from a closed tank at a pressure of 2 atm gauge and a temperature of 20 °C through a convergent nozzle with an exit diameter of 15 mm. 

Derived from spray data for wax melts with a single convergent nozzle (air converged and expanded through an annulus around a liquid nozzle) and a double concentric nozzle (a secondary air nozzle inserted axially in a liquid nozzle) Counted using a microscope ... 

It should be noted that the gas flow process in the port is not isentropic because mass and heat addihons occur in the port. This implies that there is stagnation pressure loss and so the specific impulse is reduced for nozzleless rockets. When a convergent nozzle is attached to the rear end of port, the static pressure at the port exit, Pj, continues to decrease to the atmospheric pressure and the specific impulse of the nozzleless rocket motor is increased. The expansion process in a divergent nozzle is an isentropic process, as described in Section 1.2. 

Metering of Powdered Solids. Powdered solids have been successfully metered by use of a simple converging nozzle. Farbar (1V), using a constant air flow for suspending and carrying the particles, has found that the pressure differential across such a nozzle varies linearly over a range of solids to gas flow ratios. Particles ranging between 12 and 208 microns were tested. 

Kwauk, X. Debenedetti, P. G. Mathematical Modeling of Aerosol Formation by Rapid Expansion of Supercritical Solutions in a Converging Nozzle. J. Aerosol Sci. 1993, 24, 445-469. 

The corresponding pressure is the minimum obtainable in the converging nozzle. Initial property values are as in the preceding problem. 

Since the maximum fluid velocity obtainable in a converging nozzle is speed of sound, a nozzle of this kind can deliver a constant flow rate into a regi of variable pressure. Suppose a compressible fluid enters a converging nozzle pressure Pi and discharges from the nozzle into a chamber of variable press P2. If this discharge pressure is P)t the flow is zero. As P2 decreases below the flow rate and velocity increase. Ultimately, the pressure ratio P2/Pi reach a critical value at which the velocity in the throat is sonic. Further reduction i P2 has no effect on the conditions in the nozzle. The flow remains constant, ah the velocity in the throat is that given by Eq. (7.21), regardless of the value P2/P , provided it is always less than the critical value. For steam, the criti value of this ratio is about 0.55 at moderate temperatures and pressures. 

Steam enters a converging nozzle at 700 kPa and 260°C with negligible velocity. If expansi is isentropic, what is the minimum pressure that can be reached in such a nozzle and what is cross-sectional area at the nozzle throat at this pressure for a flow Tate of 0.5 kg s-1 ... 

A gas enters a converging nozzle at pressure with negligible velocity, expands isentropie in the nozzle, and discharges into a chamber at pressure P2. Sketch graphs showing the velocity the throat and the mass flow rate as functions of the pressure ratio P2/ Pj ... 

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. 

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