Sharon Stephen

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

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°. 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.

Boundary-Layer Transition on Broad Cones rotating in an Imposed Axial Flow

We present stability analyses for the boundary-layer flow over broad cones (half-angle > 40 ◦ ) rotating in imposed axial flows. Preliminary convective instability analyses are presented that are based on the Orr–Sommerfeld equation for a variety of axial-flow speeds. The results are discussed in terms of the limited existing experimental data and previous stability analyses on related bodies. The results of an absolute instability analysis are also presented which are intended to further those by Garrett & Peake 21 through the use of a more rigorous steady-flow formulation. Axial flow is seen to delay the onset of both convective and absolute instabilities.

The instability of the boundary layer over a disk rotating in an enforced axial flow

We consider the convective instability of stationary and traveling modes within the boundary layer over a disk rotating in a uniform axial flow. Complementary numerical and high Reynolds number asymptotic analyses are presented. Stationary and traveling modes of type I (crossflow) and type II (streamline curvature) are found to exist within the boundary layer at all axial flow rates considered. For low to moderate axial flows, slowly traveling type I modes are found to be the most amplified, and quickly traveling type II modes are found to have the lower critical Reynolds numbers. However, near-stationary type I modes are expected to be selected due to a balance being struck between onset and amplification. Axial flow is seen to stabilize the boundary layer by increasing the critical Reynolds numbers and reducing amplification rates of both modes. However, the relative importance of type II modes increases with axial flow and they are, therefore, expected to dominate for sufficiently high rates. The application to chemical vapour deposition(CVD) reactors is considered.

The centrifugal instability of a slender rotating cone.

In this study, we provide a mathematical description of the onset of counter-rotating circular vortices observed for a family of slender rotating cones (of half-angles 15° or less) in quiescent fluid. In particular, we apply appropriate scalings in order to simplify the basic-flow profiles, which are subsequently perturbed, accounting for the effects of streamline curvature. A combined large Reynolds number and large vortex wavenumber analysis is used to obtain an estimate for the asymptotic right-hand branch of neutral stability for a slender rotating cone. Our results confirm our earlier predictions pertaining to the existence of the new Görtler mode and capture the effects of the governing centrifugal instability mechanism. Meanwhile, favourable comparisons are drawn with existing numerical neutral stability curve results.

Eects of Porous Walls on Hypersonic Boundary Layers over a Sharp Cone

of curvature and of the attached shock are included for axisymmetric and non-axisymmetric disturbances. The ow in the hypersonic boundary layer is coupled to the ow in the porous layer. The theoretical model of a porous wall developed by Fedorov and his coworkers is used for regular microstructures. The physical parameters chosen correspond to those of their studies. The resulting transcendental equations are solved numerically. Neutral solutions are presented, indicating a destabilizing eect of the porous wall. The spatial growth rates determined demonstrate that the porous wall leads to a signicant increase in growth rates for non-axisymmetric modes.

The effect of non-Newtonian viscosity on the stability of the Blasius boundary layer

We consider, for the first time, the stability of the non-Newtonian boundary layer flow over a flat plate. Shear-thinning and shear-thickening flows are modelled using a Carreau constitutive viscosity relationship. The boundary layer equations are solved in a self-similar fashion. A linear asymptotic stability analysis, that concerns the lower-branch structure of the neutral curve, is presented in the limit of large Reynolds number. It is shown that the lower-branch mode is destabilised and stabilised for shear-thinning and shear-thickening fluids, respectively. Favourable agreement is obtained between these asymptotic predictions and numerical results obtained from an equivalent Orr-Sommerfeld type analysis. Our results indicate that an increase in shear-thinning has the effect of significantly reducing the value of the critical Reynolds number, this suggests that the onset of instability will be significantly advanced in this case. This postulation, that shear-thinning destabilises the boundary layer flow, is further supported by our calculations regarding the development of the streamwise eigenfunctions and the relative magnitude of the temporal growth rates.

Delaying transition in rotating boundary-layer flows

We investigate both the type I and II modes of stationary instability within the boundarylayer flow over a rotating disk. Extending the work of previous studies we find that the flow can be stabilised via the introduction of shear-thinning non-Newtonian fluids. Laminar-flow profiles are determined from a generalised von Karman similarity solution. An asymptotic study is presented in the limit of large Reynolds number and a numerical investigation which includes the effects of streamline curvature and Coriolis force is also conducted. Favourable agreement is obtained between solutions from the two schemes. Results indicate that the transition process from laminar to turbulent flow can be significantly delayed, in this case at least. Such a study is presented with a view to suggesting potential control mechanisms in aerodynamically-significant flows.

Effects of regular and random microstructures on hypersonic boundary layers

of curvature and of the attached shock are included for axisymmetric and non-axisymmetric disturbances. The ow in the hypersonic boundary layer is coupled to the ow in the porous layer. The theoretical model of a porous wall developed by Fedorov and his co-workers is used for a random microstructure. The physical parameters chosen correspond to those of their experiments for ow over a felt-metal coating. The resulting transcendental equations are solved numerically. Results for neutrally stable disturbances are presented together with spatial growth rates. These are compared to the case of a regular microstructure. Results are also obtained for a porous wall comprising of layers of regular meshes. The eect of the thickness of the layer is investigated.

Effects of Passive Porous Walls on Hypersonic Boundary Layers

A theoretical linear stability analysis is used to consider the effect of a porous wall on the first mode of a hypersonic boundary layer on a sharp slender cone. The effect of curvature and of the attached shock are included. The flow in the hypersonic boundary layer is coupled to the flow in the porous layer. The theoretical model of a porous wall developed by Fedorov and his co-workers is used for regular microstructures. The resulting transcendental equations are solved numerically. Neutral solutions are presented, indicating a destabilizing effect of the porous wall. The spatial growth rates determined demonstrate that the porous wall leads to a significant increase in growth rates.

Centrifugal instabilities in curved compressible wakes

This investigation is concerned with the linear development of Gortler vortices in the high-Reynolds-number laminar compressible wake behind a flat plate which is aligned with the centerline of a curved mixing-layer system. The Gortler modes were previously found to exist within curved compressible mixing layers by Owen et al. [Phys. Fluids 8, 2506 (1997)]. This study extends that investigation and demonstrates the effect a wake has on the growth rate and location of such modes. The investigations were made by examining the growth rate and the location of the Gortler modes in the limit of large Gortler number and high wave number within the wake-dominated curved compressible mixing-layer systems based on three wake flow models. An analytic Gaussian wake profile is first used to model the behavior of the basic flow within the mixing layer at the trailing edge of the splitter plate. It is found that the wake has an amplification effect on the growth of the Gortler instability within the concavely curved or ...