Supersonic nozzle flow

When gas flows from stagnation conditions through a nozzle, thereby undergoing an isoentropic change, the enthalpy change is represented by Eq. (1.23). The flow velocity is obtained by substitution of Eq. (1.14) into Eq. (1.24) as 

The mass flux can also be expressed as a function of Mach number using Eqs. (1.25) and (1.26) as follows  

It is evident that m is maximal at M = 1. The maximum mass flux, is ob- 

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. 

For example, TITq = 0.833, p /To = 0.528, and p /Po = 0.664 are obtained when y = 1.4. The temperature Tq at the stagnation condition decreases by 17 % and the pressure Po decreases by 50% in the nozzle throat. The pressure decrease is more rapid 

---

Westenberg, A., Favin, R.M., Complex Kinetics in Supersonic Nozzle Flow, Ninth Symp. Int. on Combustion, Academic Press, New York, 1963, pages 785-798. 

Meyer, R.E. (1956). Perturbations of supersonic nozzle flows. Aeronautical Quarterly 7 71-84. Meyer, R.E. (1962). ALiouville theorem in rmsteady gas dynamics. Applied mechanics. 224-226, F. Rolla, W.T. Koiter, eds. Elsevier Amsterdam. 

The influence of an admixture of air on the onset and the progress of spontaneous condensation of carbon dioxide in a stationary supersonic nozzle flow has been studied for mixtures with C02 niole fractions ranging from 5 to 75 per cent. For mole fractions of 75 and 50 per cent, the supersaturation of the carbon dioxide at the Wilson point is scarcely influenced by the addition of air. In the range of lower COp-concentrations, the condensation of carbon dioxide is promoted by the presence of the non-condensing component, as was to be expected from various results reported in the literature. 

The phenomenon of spontaneous condensation in a supersaturated vapour is of interest in different fields of natural science and in various technical applications, e.g. wind tunnels and steam turbines. Expecially with respect to Organic Rankine Cycles for heat recovery there exists some interest in the conditions for the onset of spontaneous condensation in the so-called Wilson point and in the influence of the released heat of condensation on the flow field for different working fluids. From this point of view, we started systematic investigations on spontaneous condensation of pure vapours in stationary supersonic nozzle flow with the intention to cover a wide range of thermodynamic state for substances of different molecular structure. In this paper we present experimental results for carbon dioxide and compare them in a first step with results... 

The Wilson points obtained with this nozzle match very well with comparable literature data. Therefore, it seemed to be justified to include further literature data for water vapour into the intended comparison. After an accurate re-evaluation of the relevant literature data for water vapour, using Poliak s equation of state [b] and the same criterion for defining the Wilson point, we obtained an extended average Wilson line which is representative for the relative high expansion rates realized in supersonic nozzle flow [4]. 

Derived from an analytical model for flat, infinitely thick liquid layer Effects of gas compressibility included Effects of gas/liquid ratio, liquid viscosity, and nozzle geometry not included X and Xm can be determined from the universal curves for metals in P29] for subsonic gas flow and in [330] for sonic/supersonic gas flow ... 

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. 

The FJ test is similar to an aerodynamic wind-turmel test used for supersonic aircraft, except for the airflow condition. A ducted rocket projectile is mounted on a thrust stand and the projectile and thmst stand are placed in a test chamber. A supersonic airflow simulating the flight conditions is suppHed to the projectile through a supersonic nozzle attached to the front-end of the test chamber. The pressure and temperature in the test chamber are kept equivalent to the flight alHtude conditions. The aerodynamic drag on the projectile and the thmst generated by the ducted rocket are measured directly by the FJ test. The airflow surrounding the projectile and the combustion gas expelled from the ramburner flow out from the exhaust pipe attached to the rear-end of the test chamber. 

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). 

At or near sonic velocity, as at the C-J plane and beyond, a minute divergence had a marked effect. Similarly, at the throat of supersonic nozzle, an infinitesimal change in cross-sectional area produced a finite acceleration of the flow. Objection was raised, however, by Duff Knight (Ref 17a) that evidence of a large density gradient at the end of the reaction zone is lacking. Wood Kirkwood (Ref 17b) suggested that even in normal detonation, the reactions are incomplete at the C-J point in a tube of finite diameter (Ref 22, p lid)... 

---