Boundaries of non-separation flow-around of bodies of rotation, with the nose part in the form of Riabouchinsky half-cavity

Aeronautical and Space-Rocket Engineering

Aerodynamics and heat-exchange processes in flying vehicles


Kuznetsov E. N., Lunin V. Y.*, Panyushkin A. V.**, Chernyshev I. L.***

Central Aerohydrodynamic Institute named after N.E. Zhukovsky (TsAGI), 1, Zhukovsky str., Zhukovsky, Moscow Region, 140180, Russia



Bodies that are optimal at the so-called low critical Mach number M*, at which at least one sonic point on the body flown-over surface occurs, were studied theoretically in Ref. [1]. It was confirmed that M* achieves its maximum value and, consequently, the wave drag minimum value occurred for the body identical to the Riabouchinsky finite cavity in the classical theory of incompressible fluids. It was experimentally studied in Ref. [12], which demonstrated that in the transonic velocities range the Riabouchinsky half- cavity had the smallest drag among the bodies of rotation with the same aspect ratio  λ=L/D=0.87(where L is the nose part length and D is the diameter of its mid-section). This conclusion is incorrect for aspect ratios λ>2 due to the friction impact the drag as it follows fr om Ref. [24]. The absence of turbulent boundary layer separation from the side surface of the body of rotation under study at zero angle of attack in the range of Mach numbers 0.8≤M≤0.95 was demonstrated in Ref [17].

The main objective of this work is determination of angles of attack αsep at which turbulent boundary layer separation from the side surface of the studied body occurs. The study was performed with NUMECA FINE/Open software based on Reynolds Averaged Navier-Stokes equations (RANS). The solution of the problem was performed in the framework of fully turbulent flow model without accounting for laminar-turbulent transition using Spalart-Allmaras (SA) and k-ω SST turbulence models. To determine the boundaries of the non-separated flow-around computation was performed in stationary problem setting at various angles of attack. With that, the flow separation indicator was the presence of the zone on the model surface wh ere the friction coefficient Cf < 0. The results obtained with two turbulence models are close to each other, and the difference between the two separation angles does not exceed 1°.

The results of the study obtained for αsep for the nose part with aspect ratio of are as follows:

αsep=15° for М=0.5, αsep=9° for М=0.65,

αsep=12° for М=0.8, αsep=13° for М=0.85,

αsep=5° for М=0.9, αsep=11° for М=0.95.

Computing results for the longer nose part with aspect ratio are:

αsep=20° for М=0.5, αsep=13° for М=0.7, αsep=21° for М=0.9, αsep=18° for М=0.95.

The angles of attack αsep which realize turbulent boundary layer separation from the side surface of the investigated body at free-stream Mach numbers 0.5≤M≤0.95 were obtained. Separation zones location is shown for various models and modes.


Riabouchinsky semi-cavity, body of rotation, transonic flow-around, boundary layer


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