CONTRIBUTION TO THE STUDY OF THE ISENTROPIC FLOW IN THE LAVAL NOZZLE

B. ACHOUR, L. AMARA

Abstract


The isentropic flow in the Laval nozzle has been the subject of investigations and theoretical development. In the literature, the flow parameters are expressed as a function of the Mach number M calculated in any cross-sectional area of the flow. In the present study, the flow parameters such as the cross-sectional area A related to the sonic cross-sectional area A*, the mean velocity V of the flow and mass flow rate are expressed as a function of the flow conditions of the generator state. The important relationship between the Mach number M* in the sonic section versus the Mach number M in any cross-sectional area of the flow in the nozzle is also presented. Its graphic representation makes it possible to discuss the behaviour of the flow in the nozzle. On the other hand, the normal shock zone has been examined from a theoretical point of view, the development of which has led to the relations which govern the flow parameters in this zone.

The study first concerned the case where the velocity of the flow, subsonic upstream, becomes sonic in the narrowed section of the nozzle and for which the temperature, the pressure and the volume mass are critical. The flow immediately changes to supersonic and to become again further downstream in subsonic by the intermediary of a shock wave. For this case, a detailed numerical example is considered, showing the procedure to be followed to solve the problem.

Through a practical numerical example, the case where the flow remains subsonic over the entire length of its path is considered. It was introduced in this case study the concept of the cross-sectional area of the hypothetical section where the velocity would become sonic and where the temperature, pressure, and density would reach their critical values.

The study ends with the examination of the borderline cases of the flow in the nozzle, as well as the criteria of classification of the flow.

The most important established relationships are represented graphically and interesting conclusions are drawn.


Keywords


Fluid mechanics, fluid flows, parameterization, compressible flow, Laval Nozzle, shock wave.

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