Abstract
This paper presents linear biglobal stability analysis of axisymmetric boundary layer over a circular cone. An incompressible flow over a sharp circular cone is considered with zero angle of attack. The base flow velocity profile is fully non-parallel and non-similar. Linearized Navier-Stokes (LNS) equations are derived for disturbance flow quantities using the standard procedure. The LNS equations are discretized using Chebyshev spectral collocation method. The governing equations along with boundary conditions form a general eigenvalues problem. The numerical solution of general eigenvalues problem is obtained using ARPACK subroutine, which uses Arnoldis iterative algorithm. The global temporal modes are computed for the range of Reynolds number and semi-cone angles(α)for the axisymmetric mode(N=0). The flow is found temporally and spatially stable for 1° semi-cone angle and the range of Reynolds numbers considered. However, flow becomes temporally unstable and spatially stable with the increase in semi-cone angle(α). The wave-like behaviour of the disturbances is found at small semi-cone angles (α).
Highlights
The laminar-turbulent transition in boundary layers has been a subject of interest to many researchers in past few decades
The main aim of this paper is to study the Global stability characteristics of the axisymmetric boundary layer on a circular cone and the effect of the transverse curvature and pressure gradient on the stability characteristics
The standard procedure is followed for the derivation of the Linearized Navier-Stokes equations(LNS) for the disturbance flow quantities
Summary
The laminar-turbulent transition in boundary layers has been a subject of interest to many researchers in past few decades. It is important to understand the onset of transition in boundary layers as the flow pattern and its effects are very different in laminar and turbulent flows. At low free-stream levels the boundary layers undergo transition through the classical TS wave mechanism. The amplification of the disturbance waves is the primary step in the transition process and this is studied in linear stability analysis. The results from stability analysis and the prediction of transition onset is very useful in hydrodynamics and aerodynamics applications like submarines, torpedoes, rockets, missiles etc. The linear stability analysis of shear flows with parallel flow assumption is well understood by the solution of the Orr-Sommerfeld equation [1]. It is known that the stability characteristics in a boundary layer is strongly influenced by various factors such as pressure gradient, surface curvature free-stream turbulence level
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