Compressible Modes of the Rotating-Disk Boundary-Layer Flow Leading to Absolute Instability

• Published in: Studies in applied mathematics (Cambridge) 2005-07, Vol.115 (1), p.1-20
• Main Authors: Turkyilmazoglu, M., Uygun, N.
• Format: Article
• Language: English
• Subjects: Boundary layer; Computational methods in fluid dynamics; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Mathematical analysis; Mathematics; Partial differential equations; Physics; Reynolds equation; Reynolds number; Sciences and techniques of general use; Studies
• ISSN: 0022-2526; 1467-9590
• DOI: 10.1111/j.1467-9590.2005.01549

This work is devoted to the clarification of the viscous compressible modes particularly leading to absolute instability of the three‐dimensional generalized Von Karman's boundary‐layer flow due to a rotating disk. The infinitesimally small perturbations are superimposed onto the basic Von Karman's flow to achieve linearized viscous compressible stability equations. A numerical treatment of these equations is then undertaken to search for the modes causing absolute instability within the principle of Briggs–Bers pinching. Having verified the earlier incompressible and inviscid compressible results of [1–3], and also confirming the correct match of the viscous modes onto the inviscid ones in the large Reynolds number limit, the influences of the compressibility on the subject matter are investigated taking into consideration both the wall insulation and heat transfer. Results clearly demonstrate that compressibility, as the Mach number increases, acts in favor of stabilizing the boundary‐layer flow, especially in the inviscid limit, as far as the absolute instability is concerned, although wall heating and insulation greatly enhances the viscous absolutely unstable modes (even more dramatic in the case of wall insulation) by lowering down the critical Reynolds number for the onset of instability, unlike the wall cooling.