Geometrical parameters effect of recessed nozzle inlet section on the flow coefficient

Aeronautical and Space-Rocket Engineering

Thermal engines, electric propulsion and power plants for flying vehicles


Sabirzyanov A. N.*, Kirillova A. N.**, Khamatnurova C. B.***

Kazan National Research Technical University named after A.N. Tupolev, KNRTU-KAI, 10, Karl Marks str., Kazan, 420111, Russia



Rocket engine energy performance improvement is an actual task for modern researchers. The article considers rocket solid propellant engines, which distinctive feature consists in the recessed nozzle.

Recommendations on designing the inlet sections geometry of the recessed nozzles are few and inconsistent. The purpose of the presented work is studying the nozzle inlet shape effect on the flow-rate characteristics and developing appropriate recommendations on nozzle designing.

The flow coefficient is one of perfection indicators of the flow processes. Advanced methods of computational fluid dynamics (CFD) were employed for studying the flow coefficient of the recessed nozzles. The problem was being considered in quasi-stationary axisymmetric adiabatic approximation of the ideal gaseous setting. The RNG k- å two-parameter turbulence model with standard set of model constants, being passed verification while computing classic nozzles consumption and the specific impulse losses of the recessed nozzle, was employed for the flow structure modelling.

The computational geometrical model contained:

– combustion chamber;

– charging duct, from which surface the working medium was being supplied;

– various options of the nozzle recessed part shapes;

– the conical expanding part;

– as well as extra volume behind the nozzle cut.

The grid quality maintained constant while varying the recessed part sizes, and the nozzle degree of submergence.

The gas dynamic component of the flow coefficient was being studied. Nozzle inlet geometry formed by ellipse and by Vitoshinsky curve were being examined. The dependences of the flow coefficient on the nozzle inlet shape and degree of submergence coefficient were obtained.

The results of the flow characteristics of the inlet sections under study are being compared with the previously obtained results for the radius inlet. It was demonstrated that the best values of the flow coefficient corresponded to the inlet section formed by the Vitoshinsky curve. The distinctive feature of the inlet section designed by the Vitoshinsky equation is high stability of the gas-dynamic losses irrespective of its geometrical parameters changes.

Elliptical inlet nozzles allow improving flow coefficients indicators even for the worst option of the radius nozzles by 7%. The article presents recommendations on designing the inlet section of the recessed nozzle.


solid propellant rocket engine, recessed nozzle, gas-dynamic component of the flow coefficient, nozzle recessed part shape, numerical modelling


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