Stability of symmetric vortex flow over slender bodies and possibility of control by local gas heating

Abstract

Stability properties of vortex structure over slender bodies at high angles of attack and instability mechanism are the subjects of many experimental and computational studies, most of which are observed in [1,2]. However, the reasons and mechanism of spontaneous symmetric §ow breaking are not established up to now. In the ¦rst part of the present paper, a criterion for asymmetry origin for slender conical bodies is obtained using slender body theory [3] and catastrophe theory [4]. The theoretical results are veri¦ed by comparison with experimental data [5 8]; they helped to explain most of experimental observations and numerical simulations. In the second part, based on the obtained criterion and numerical solutions of boundary layer equations evaluations are made to estimate an e¨ectiveness of global §ow structure control method using local volumetric or surface gas heating. Qualitative con¦rmation of these estimations was done in experiments [7,8] with gas heating by plasma discharge. STABILITY ANALYSISA §ow over a slender pointed body of self-similar cross-section shape r = F (θ)a(X) where a(0) = 0; X is scaled with the body length l; r and θ are the polar radius and angle of the cylindrical coordinates (X, r, θ) scaled with maximal transversal size δl and maximal relative width δ, respectively, is considered.It is assumed that the body is symmetric with respect to the plane Z = 0 where (X, Y, Z) are the Cartesian coordinates; Y and Z are scaled with δl. The freestream velocity is U ∞ ; the vertical freestream velocity component is Progress in Flight Physics 5 (2013) 155-168

3D Boundary Layer Theory

“…Therefore, at these conditions a solution of BL equations cannot exist. This conclusion and also the criterion (26) for the boundary of the existing leeward symmetry plane solution are confirmed by numerical calculations for the slender round cone at an angle of attack [25][26][27][28][29][30][31][32]37], a part of which is presented in Figure 6. In this figure, symbols correspond to calculations of limit Figure 6.…”

“…The method of the global flow stability was developed [27][28][29][30][31] using the asymptotic approach for the flow over slender cones, the separated inviscid flow model [34] and the stability theory of autonomous dynamical systems [35]. Comparison of the calculated criteria for different elliptic slender cones with experimental data for laminar and turbulent boundary layers sowed its efficiency.…”

“…The use as a criterion numerical results and experimental data is restricted as a result of the high sensitivity of the asymmetry origin to different parameters [29]. Solution of these problems was obtained with the development of new models [30][31][32][33][34].…”