Streamline-curvature Instability Research Articles

Laminar-Turbulence Transition over the Rotor Disk in an Enclosed Rotor-Stator Cavity

Large eddy simulation (LES) of transitional and turbulent flow are performed for a range of rotational Reynolds numbers, 4 × 104 ≤ Reω = b2ω/ν ≤ 4 × 105, in both an enclosed rotor-stator annular and an enclosed rotor-stator cylindrical cavities of aspect ratio G = (b − a)/h = 5, where a and b are, respectively, the inner and outer radii of the rotor disk and h is the distance between the rotor and stator disks. Although it is well-known that the Cross-Flow instability plays an important role in the transition process to turbulence in the rotor boundary-layer, the spiral patterns related to the Streamline-Curvature (S-C) instability became dominant in this study. In addition, the structures due to secondary instability appear in the outward side of the primary spiral patterns. These structures obtained from LES are in agreement with experimental visualizations performed in this study. The results suggest that S-C instability is excited and becomes dominant in the rotor side since the rotor boundary-layer is perturbed by disturbances emanating from the stator side. Subsequently, secondary instabilities result from the interaction of the dominant S-C instability with the main flow. These instabilities seem to be the probable source of laminar-turbulence transition in the rotor boundary-layer for the present case.

Experimental investigation of the flow instability near the attachment-line boundary layer on a yawed cylinder

The behavior of small disturbances in a 3-D laminar boundary layer on a yawed cylinder was experimentally investigated. This setup simulates the flow around the leading edge of swept wings. Since multiple instability modes appear near the attachment-line region, a point-source disturbance was artificially introduced to separate these modes. Amplitude and phase distributions of the disturbances originating from the point source were measured using a hotwire probe near the attachment-line flow to test existing theoretical predictions. Hotwire measurements show that two instability modes definitely coexist and overlap in the middle portion of the wedge-shaped region developing downstream of the point source. Decomposition by 2-D fast Fourier transform (FFT) analysis enables us to separate one oblique wave from the other. One of the oblique waves belongs to the cross-flow instability mode, which travels to the attachment line and grows even at Reynolds numbers that are slightly lower than the critical Reynolds number for the attachment-line instability. The origin of the other mode is not identifiable, because it has peculiar characteristics different from both the streamline-curvature instability mode and the cross-flow instability mode. This mode decays in the downstream direction for all frequencies examined. By investigating the spatial characteristics of the small disturbance, the critical Reynolds number for cross-flow instability was successfully determined in the off-attachment-line region. The value, Rc = 543, was lower than the critical Reynolds number of Rc = 583 for the attachment-line flow. Furthermore, the critical frequency and wavenumber were in good agreement with existing predictions based on linear stability theory.

Experiments on Streamline-Curvature Instability in Boundary Layers on a Yawed Cylinder

Instability of the three-dimensional boundary layer on a yawed circular cylinder placed in a uniform flow is investigated experimentally by introducing acoustic disturbances from a point near the attachment line. To exemplify the flow dominated by streamline-curvature instability rather than crossflow instability, which has been often observed in many swept-wing flows, is the aim here. In upstream regions of the disturbance wedge originating from the point source, both streamline-curvature and crossflow disturbances are superposed on each other and yield complicated amplitude distributions. A newly proposed method enables the decomposition of the distorted amplitude distribution into contributions from the two instability modes. Detailed observations, however, show that the crossflow mode decays with the distance from the source much faster than the streamline-curvature mode and allows the latter to be dominant in a region further downstream. A fundamental characteristic of the streamline-curvature instability wave is confirmed by examining its phase distribution in the spanwise and normal directions.

Stability of the boundary layer on a sphere rotating in still fluid

A theoretical study of the transition of a three-dimensional boundary layer on a sphere rotating in still fluid is carried out by a linear stability analysis. A set of perturbation equations governing the instability of the flow field is derived assuming the perturbations to be consisting of spiral vortices. It is shown that the critical Reynolds numbers obtained in the present analytical study are close to those observed in experiments. It has been found that the streamline-curvature instability appears in the rotating sphere flow. It is also shown that the cross-flow instability is dominant near the poles of a sphere while the streamline-curvature instability overtakes near the equator.

Development of an axisymmetric wave packet in rotating-disk flow

The three-dimensional flow on a rotating disk admits two kinds of wavy disturbances induced by the cross-flow instability and the streamline-curvature instability. Their separate appearances by some artificial forcing are very desirable for experimental investigation of differences in dynamics and structure between the two instabilities. Thus the present study considers an instantaneous excitation of the boundary-layer flow through an annular slit on the disk surface and describes temporal and spatial development of the excited wavy disturbances by applying the method of complex characteristics to eigensolutions of approximate stability equations. Computational results show that observation at a downstream station will first catch the streamline-curvature disturbances with smaller circumferential wavenumbers and then the familiar cross-flow ones, because of a definite difference in propagation speed of the two modes. This study provides evidence to show that the method of complex characteristics is a very useful tool for theoretical prediction of dispersive properties of such instability waves.

Streamline-Curvature Instability of the Flow on a Rotating Disk with Uniform Suction

Linear stability analysis of the rotating-disk flow is made with a very simple model of disturbance equations consisting of the parallel-flow approximation and an additional term associated with the curvature of flow field. Numerical solutions of the resulting eigenvalue problem indicate the existence of two instabilities and reveal their entirely different mechanisms. One is the well-known cross-flow instability and the other is the instability due to the curvature of external streamlines, which was recently predicted to occur in three-dimensional boundary layers on a swept wing. The streamline-curvature mode is in fact identical with the classical one called `parallel' or `type 2' instability in atomospheric literature.

Simple cases of the streamline-curvature instability in three-dimensional boundary layers

A new instability of the centrifugal type due to the curvature of external streamlines was theoretically predicted in a recent study on boundary layers along a swept wing. It is, however, not clear how this instability relates to already-known instability phenomena in various three-dimensional flows. So the basic idea developed in the analysis of boundary layers is applied to the simpler problems of the flow on a rotating disk and along the leading edge of a yawed circular cylinder, and the resulting eigenvalue problems are numerically solved to show multiple stability characteristics of the flows. Computational results confirm that the streamline-curvature instability does appear in the rotating-disk flow and that it is in fact identical with the instability called the ‘parallel’ or ‘type 2’ mode in the atmospheric literature. This instability is also found to occur in the steady flow near the attachment line and to give the lowest values of the critical Reynolds number except for a very narrow region close to the attachment line, where the viscous and cross-flow instabilities are dominant. These facts provide evidence to show that the same mode of instability as the classical one observed in rotating flows can appear in general three-dimensional boundary layers without rotation.