Shohei Takagi

Observation of traveling waves in the three-dimensional boundary layer along a yawed cylinder

Experimental investigations are made of crossflow instability of the three-dimensional boundary layer along a yawed circular cylinder. To explore the effect of environmental disturbances on transition, comparative experiments are performed in high- and low-turbulence wind tunnels. Independent of turbulence level, unsteady disturbances with definite frequencies instead of stationary vortices are observed in hot-wire surveys of the unstable flow filed. Detailed measurements with the aid of hot-wire arrays have confirmed that the unsteady disturbances are identical with the so-called crossflow traveling waves predicted by linear stability theory as the most unstable disturbances, although some discrepancies still remain between experimental results and theoretical predictions.

Dispersive evolution of crossflow disturbances excited by an airjet column in a three-dimensional boundary layer

An experimental study is made to show that dispersive properties of disturbances originating from a point source lead to the separate appearance of stationary vortices and travelling waves of the crossflow instability in a three-dimensional boundary layer. The spatial development of disturbances induced by a weak airjet issuing from a small surface hole near the attachment line of a yawed circular cylinder is observed at several downstream stations. Experimental results show that the disturbances evolve into a wedge-shaped distribution, which includes both stationary and nonstationary modes of the crossflow instability. The observed behavior of those disturbances is shown to be in fairly good agreement with recent results of a linear stability theory based on the method of complex characteristics, although there are some incongruities in frequency and growth rate of the most unstable disturbances. The experiment also shows the existence of a new instability due to the curvature of external streamlines, which was simultaneously predicted by the theory.

Characteristic features of traveling disturbances originating from a point source in rotating-disk flow

An experimental investigation of rotating-disk flow was made to separate the cross-flow traveling mode from the streamline-curvature mode by introducing a point-source disturbance through a hole on the disk. A glue-on hotwire probe was successfully applied to discriminate between the introduced traveling modes and the stationary modes, which contaminate the measurement using a conventional probe fixed in the laboratory frame, because of no sensitivity to cross-flow stationary vortices. The experimental results show a definite separation of the two modes appearing in wedge-shaped region downstream of the point source in accordance with the dispersion relation. The characteristic features, such as wavenumber, wave-crest inclination, and phase velocity of the observed disturbances are in good agreement with the linear stability theory making use of the method of complex characteristics, although there is slight disagreement in the spatial growth rate of cross-flow mode.

On Similarity Law of the Crossflow Instability in Three-Dimensional Boundary Layers on Yawed Cylinders

Three-dimensional boundary layers are unstable to both stationary and traveling crossflow disturbances. Early experiments show the center frequency of traveling disturbances to shift according to experimental conditions such as freestream turbulence and surface roughness. A natural speculation is that the observed shift of the center frequency of traveling disturbances is due mainly to the presence of stationary vortices, which surely deform the basic flow; no frequency shift should be observed in the flow with no stationary vortices. On this speculation, special cares are paid to establish traveling-mode dominated flows free from the stationary mode on yawed-circular cylinders. Then, a series of parametric studies focusing on the center frequency of traveling disturbances is conducted in combination of three yawed cylinders with different size and three wind tunnels with different turbulence levels under a constant Reynolds number. Experimental results show that the nondimensional center frequencies in totally six cases tested are almost independent of freestream turbulence levels and their spectra, and of the size of models with different surface conditions, providing a strong support to the above speculation.

Excitation of streamline-curvature instability in three-dimensional boundary layer 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. The aim is to exemplify the flow cbminated by streamlinecurvature instability, rather than cross-flow instability which is often observed in many swept-wing flows. In upstream regions of the disturbance wedge originating from the source point, both streamlinecurvature and cross-flow disturbances arc superposed on each other to yield so complicated results of hot-wire measurements that cannot be compared with theoretical pre&tions. Detailed observations, however, show that the crossflow mcde decaysmuch faster with the distance from the source and allows the streamline-curvature mode to bc dominant in a far &wnstmam region. Some fundamental characteristicsof the two instability waves are confirmed by examining the phase distributions in the spanwise and normal directions. from the usual process governed by C-F streamwise vortices. On the other hand, we have very poor knowledge of S-C instability in boundary layers on swept wings, becausethe phenomenon has beenignored or unrecognizeduntil the recentthcoretical prediction by Itoh and the following experimental confirmation by Takagi et al.” It is highly desirable to investigate. roles of SC instability in the transitional process of such wing flows. As a first step of such investigations, the present study is drected to the pmblem of whether SC disturbance can have a magnitude comparable to or larger than C-F mo& or not. Fortunately, linear stability theory has predrcted some geometrical conditions under which S-C m& is unstable but C-F mode is always stable in the swept-cylinder flow’. Artificial excitation is made to clarify the characteristics of the flow by acoustically intro&ing a point-source disturbance through a tiny hole near the leading edgeof the model.

Dispersive Disturbances due to Cross-Flow and Streamline- Curvature Instabilities in 3-D Boundary Layers

Three-dimensional laminar boundary layers are susceptible to cross-flow instability and streamline-curvature instability, both of which lead to growth of longitudinal vortices. It is practically difficult to distinguish one instability mode from the other in the natural process of laminar-turbulent transition. Unlike plane-wave disturbances, however, the point-source disturbances evolve into dispersive development of their different components, which will result in separate appearance of two instability modes downstream of a point source. Continuous excitation from a small hole is applied to the boundary layer on a yawed circular cylinder evolving into a wedge-shaped pattern downstream of the hole, while a pulsed jet through a tiny hole is used to generate disturbances of a wave-packet type in the flow on a rotating-disk. Spatial development of localized disturbances corresponding to these experimental configurations can be described by linear stability analysis based on the complex ray theory. Comparison between experimental results and theoretical calculations shows qualitative and even quantitative agreement for either case.

Characteristics of streamline-curvature disturbances in a rotating-disk flow

An experimental investigation of rotating-disk flow is made to reveal the fundamental characteristics of a centrifugal instability caused by curvature of inviscid external streamlines. This was recently shown to be identical to the so-called Type n or parallel instability hi atmospheric sciences. Small but clearly observable disturbances of this instability are successfully produced by means of artificial excitation through the annular slit of the disk in a low Reynolds number region, where crossflow instability is subcriticaL Acoustic forcing simulating various environmental fluctuations is also used to investigate contribution of the streamlinecurvature instability to transition. Experimental results show that streamline-curvature disturbances initiated at the slit behave like annular waves travelling in the outboard direction, whose characteristics are in good agreement with linear stability theory. Anotherimportant result is that the introduction of a weak streamlinecurvature wavepacketoverwhelmspre-existing cross-flow stationary vortices, suggesting that a gust or turbulent patch hi surrounding fluid may cause the transition location to shift downward. On the contrary, continuously strong forcing of streamline-curvature instability leadsto another transition route, which is differentfrom the usual transition dominated by streamwise vortices.