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The results of a complex theoretical and experimental investigation of the flow structure around V-shaped wings at supersonic flow velocities, including the conical center body, are presented. The applicability of the previously established criteria of inviscid vortex structures existence in the cases of the appropriate intensity contact discontinuity formation has been studied. This contact discontinuity proceeds from the -configuration shock wave branching point, which is attendant to the wall turbulent boundary layer separation under the influence of the internal shock wave incident on one of the wing panels. The calculated and experimental data, obtained using the special optical method for the supersonic conical flows visualizing in the conditions of the asymmetric flow around the wing with zero leading edges sweep angle and opening angle γ = 2π/3 by the flow with the Mach number M=3, have been used as the object of the analysis. In the inviscid gas model conditions both the flow regime with shock waves attached to the leading edges and the flow regime with centered expansion wave at the leading edge of the leeward panel have been considered. The variation range of the wing angles of attack and yaw, when the inviscid vortex structures, generated by both the contact discontinuity, proceeding from the bow shock wave branch point, and the -configuration shock wave contact discontinuity can exist, has been determined by using the results of numerical calculations and earlier developed effective semi-empirical intensity calculating method of the contact discontinuity, proceeding from the -configuration shock wave branching point. The inviscid vortex structures existence criteria applicability for the contact discontinuities, generating by the shock wave -configuration, that has been determined, shows that the vortex Ferry singularities formation in the shock layer does not depend on the reason, caused the contact discontinuity existence, and depends only on its intensity. The numerical studies results of the flow structure around the V-shaped wings with a central body in the inviscid gas model at Mach numbers M= 3 and M=6 with the regimes of shock wave, attached to the leading edges, have been presented. The cone angle values, at which the inviscid vortex structures appear for the symmetric flow around the body, has been determined. These vortex structures formation and existence are in good agreement with the previously obtained criteria. However, the flow around the wing with a central body has its own special features: the Ferry singularities disappear with the cone angle increase, despite the vortex structures existence criteria compliance. This is due to the fact, that with increasing body displacement (the cone angle) two bow shock wave branching points approach the leading edges so close, that the contact discontinuities start to get into the corresponding neighborhoods of the salient points of the transverse contour of the body with the high pressure, close to its value in critical points. The gas particles inhibition on both sides of the contact discontinuities in these areas leads to the approach of their total sphere pressure, and, consequently, one of the criteria, that define the vortex structures existence in the shock layer, is not complied. The influence of cone on the lift-to-drag ratio of its configuration with the V-shaped wing at the Mach number M=6 has been studied. The body geometry essential dependence on the lift coefficient has been determined. The configuration with the lift coefficient increase can contain a central body and have γ>π V-shaped wing opening angle, can be the flat delta wing and the V-shaped wing with γ<π. A wide range of the previously not described shock layer flow schemes around the wing with opening angle γ>π, depending on the Mach number, the angles of attack and slip, caused by the breaking point of transverse wing contour, has been detected. These contain the windward panel flow separation and the vortex existence on the slip flow regimes. With the angle of slip increase the sphere flow in the vicinity of the wing central chord changes from subsonic to transonic and supersonic both at the vortex perimeter and in the return flow of vortex around the leeward panel wall with the shock waves formation. This flow structure is confirmed in the experiment while the turbulent boundary layer separation has been detected in the return flow inside the vortex. The work is executed at the partial financial support of RFBR (project № 15-01-02361).