Singularities of 3D laminar boundary layer equations and flow structure in their vicinity on conical bodies

3D Boundary Layer Theory

“…This indicates that a singularity can arise in the near-wall region. The series decomposition of the near-wall solution in the runoff plane showed the presence of a parameter α, the linear combination of skin friction components, and the sign change of which leads to the change of the physical flow topology near this plane [24]. The analysis of BL equations in the near-wall region showed that α ¼ 0 corresponds to the critical value k c , and it was confirmed by all published numerical calculations [16][17][18]20].…”

“…It had been shown numerical solutions provided incorrect results near the singularity due to the accuracy loss. Similar but more complex results were obtained for arbitrary cones; they allow defining the sufficient conditions of the singularity arising [10,22]. The asymptotic flow structure at large Reynolds number near the singularity on the base of Navier-Stokes equations was constructed, and analytical solutions in different asymptotic regions were obtained, which were matched with BL solutions.…”

“…The asymptotic flow structure at large Reynolds number near the singularity on the base of Navier-Stokes equations was constructed, and analytical solutions in different asymptotic regions were obtained, which were matched with BL solutions. The analysis of the viscous-inviscid interaction region, in particular, revealed that the singularity can arise not only in selfsimilar but in full 3D BL equations [10,22]. The theory showed that the singularity appearance relates with eigensolutions of the BL equations appearing near the runoff plane; it also explained numerical modeling results on the base of parabolized Navier-Stokes equations.…”

“…The 3D laminar boundary layer on a conical surface in the orthogonal coordinate system xyφ ( Figure 3) is described by following self-similar equations and boundary conditions [10,22]:…”

“…The singular behavior of boundary layer characteristics (the skin friction tends to the infinity in the symmetry plan) was found for the boundary layer on the small span delta wing [8,10]. The explanation of these phenomena was found on the base of analytical solutions of laminar boundary layer equations on conical surfaces [10,[21][22][23][24]. The asymptotic flow structure on the base of Navier-Stocks equations in the singularity vicinity is constructed.…”