Absolute and Convective Instabilities in the Compressible Boundary Layer on a Rotating Disk

Türkyılmazoğlu, Mustafa; Cole, Jim; Gajjar, Jitesh S. B.

doi:10.1007/s001620050123

Cited by 63 publications

(70 citation statements)

References 42 publications

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“…Hence, decreasing ψ is found to destabilize the flow. Similar comparisons for the rotating disk have been given recently for stationary and non-stationary neutral solutions by Turkyilmazoglu (2006Turkyilmazoglu ( , 2007. Figure 12 shows a comparison between the predicted onset of the two instability modes found in the numerical investigation for stationary vortices and the observed onset of spiral vortices as measured in three experimental investigations: Kreith et al (1962), Kappesser et al (1973) and Kobayashi & Izumi (1983).…”

Section: Comparison Between the Asymptotic And Numerical Investigationssupporting

confidence: 75%

“…An alternative numerical investigation into the rotating disk boundary layer by Turkyilmazoglu & Gajjar (1998) appears to demonstrate that disturbances arising from the type II mode can move at different speeds relative to the disk surface and with considerably lower critical Reynolds numbers than for the type I mode. Under their formulation in the rotating frame, the value of γ is fixed for each neutral curve plot and β is treated as an independent variable; fixing γ at different values then enables the analysis of vortices which rotate at different speeds relative to the disk surface.…”

Section: Non-stationary Vorticesmentioning

confidence: 99%

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The cross-flow instability of the boundary layer on a rotating cone

2009

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Experimental studies have shown that the boundary-layer flow over a rotating cone is susceptible to cross-flow and centrifugal instability modes of spiral nature, depending on the cone sharpness. For half-angles (ψ) ranging from propeller nose cones to rotating disks (ψ > 40• ), the instability triggers co-rotating vortices, whereas for sharp spinning missiles (ψ < 40• ), counter-rotating vortices are observed. In this paper we provide a mathematical description of the onset of co-rotating vortices for a family of cones rotating in quiescent fluid, with a view towards explaining the effect of ψ on the underlying transition of dominant instability. We investigate the stability of inviscid cross-flow modes (type I) as well as modes which arise from a viscous-Coriolis force balance (type II), using numerical and asymptotic methods. The influence of ψ on the number and orientation of the spiral vortices is examined, with comparisons drawn between our two distinct methods as well as with previous experimental studies. Our results indicate that increasing ψ has a stabilizing effect on both the type I and type II modes. Favourable agreement is obtained between the numerical and asymptotic methods presented here and existing experimental results for ψ > 40• . Below this half-angle we suggest that an alternative instability mechanism is at work, which is not amenable to investigation using the formulation presented here.

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Section: Comparison Between the Asymptotic And Numerical Investigationssupporting

confidence: 75%

Section: Non-stationary Vorticesmentioning

confidence: 99%

The cross-flow instability of the boundary layer on a rotating cone

2009

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“…The effect of wall heating is to enhance the absolute instability properties. On the other hand, cooling the wall greatly decreases the region of absolute instability regime for the studied Mach number range [30] [31].…”

Section: Xenosmentioning

confidence: 93%

Thermal Radiation Effect on the MHD Turbulent Compressible Boundary Layer Flow with Adverse Pressure Gradient, Heat Transfer and Local Suction

Xenos¹

2017

OJFD

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The combined effect of magnetic field, thermal radiation and local suction on the steady turbulent compressible boundary layer flow with adverse pressure gradient is numerically studied. The magnetic field is constant and applied transversely to the direction of the flow. The fluid is subjected to a localized suction and is considered as a radiative optically thin gray fluid. The Reynolds Averaged Boundary Layer (RABL) equations with appropriate boundary conditions are transformed using the compressible Falkner Skan transformation. The nonlinear and coupled system of partial differential equations (PDEs) is solved using the Keller box method. For the eddy-kinematic viscosity the Baldwin Lomax turbulent model and for the turbulent Prandtl number the extended Kays Crawford model are used. The numerical results show that the flow field can be controlled by the combined effect of the applied magnetic field, thermal radiation, and localized suction, moving the separation point, s x , downstream towards the plate's end, and increasing total drag, D . The combined effect of thermal radiation and magnetic field has a cooling effect on the fluid at the wall vicinity. The combined effect has a greater influence in the case of high free-stream temperature.

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“…The steady flows used were those previously obtained by Towers & Garrett (2016) and are known to be consistent with the compressible rotating-disk flows obtained by Seddougui (1990) and Turkyilmazoglu et al (2000). The analysis presented here was formulated using scalings consistent with the equivalent but incompressible analysis of Garrett et al (2009).…”

Section: Resultsmentioning

confidence: 86%

Viscous modes within the compressible boundary-layer flow due to a broad rotating cone

et al. 2016

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We investigate the effects of compressibility and wall cooling on the stationary, viscous (Type II) instability mode within the three-dimensional boundary layer over rotating cones with half-angle greater than 40 • . The stationary mode is characterised by zero shear stress at the wall and a triple-deck solution is presented in the isothermal case. Asymptotic solutions are obtained which describe the structure of the wavenumber and the orientation of this mode as a function of local Mach number. It is found that a stationary mode is possible only over a finite range of local Mach number. Our conclusions are entirely consistent with the results of Seddougui [Q. J. Mech. Appl. Math. 43]. It is suggested that wall cooling has a significant stabilising effect, while reducing the half-angle is marginally destabilising. Solutions are presented for air.

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Absolute and Convective Instabilities in the Compressible Boundary Layer on a Rotating Disk

Cited by 63 publications

References 42 publications

The cross-flow instability of the boundary layer on a rotating cone

The cross-flow instability of the boundary layer on a rotating cone

Thermal Radiation Effect on the MHD Turbulent Compressible Boundary Layer Flow with Adverse Pressure Gradient, Heat Transfer and Local Suction

Viscous modes within the compressible boundary-layer flow due to a broad rotating cone

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