Self-similar problem of separated ideal-fluid flow over an expanding plate

Ideal gas flows with separation zones and time-dependent contact discontinuities of complicated shape

“…Before presenting the results obtained for ideal gas flows, we note that unsteady separated flows of an ideal fluid have been constructed by many researchers using simplifying assumptions of one kind or another (see [7][8][9][10][11][12][13][14][15] and the references therein). As for the ideal gas flows studied below, in considering the flow FLUID DYNAMICS Vol.…”

“…5 past configurations of one type (in particular, separated flow past a divergent plate [7][8][9]) we can restrict ourselves to half the flow plane, whereas for the flows past other configurations, such as separated flows past a divergent cylinder or its combination with a plate [10][11][12], the entire flow should be considered starting from a certain value of the analog of the angle of attack. The fundamental difference between modeling steady separated flows of an ideal fluid [1][2][3][4][5][6] and unsteady separated flows of, again, an ideal fluid [7][8][9][10][11][12][13][14][15] consists in that in the latter case certain "singular" objects are used, such as vortex filaments, vortex cuts, vortex sheets infinitely rolled up at their ends, etc., which, strictly speaking, are far from having a physical meaning. Moreover, though making it possible to reveal many features of the flows under study (for example, the inviscid nature of the asymmetry of the flow around the analog of a circular cone at high angles of attack [10][11][12]) and to calculate, like the discrete vortex method [15], the parameters of two-dimensional and three-dimensional configurations important for practical applications, these approaches evoke a certain feeling of dissatisfaction.…”

“…Moreover, though making it possible to reveal many features of the flows under study (for example, the inviscid nature of the asymmetry of the flow around the analog of a circular cone at high angles of attack [10][11][12]) and to calculate, like the discrete vortex method [15], the parameters of two-dimensional and three-dimensional configurations important for practical applications, these approaches evoke a certain feeling of dissatisfaction. For example, instead of an infinite velocity and a minus infinite pressure at sharp edges, in [7][8][9]14] similar infinities appear in vortex filaments, that is, two-dimensional vortices which replace the no more physical, infinitely rolled-up ends of vortex sheets. The distinctive feature of the results obtained for an ideal gas by numerical integration of the time-dependent Euler equations is the absence of such helpful but nonphysical "chimeras".…”

“…In the case of an ideal incompressible fluid, plane-parallel, axisymmetric, and even three-dimensional flows with separation zones and contact discontinuities shed from the sharp edges or smooth regions of body surfaces have long been fairly usual hydrodynamic objects [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. One of the reasons for this is that the construction of such flows is based on analytical or, to be more precise, partially analytical approaches.…”