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

Abstract

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.

Observation of Cross-Flow Instability Mode over a Yawed Cylinder at Mach 2

“…To quantify the surface roughness condition, it should be noted that the uncoated surface roughness was approximately 0.06 μm in arithmetic average of the distance of roughness profile from its mean line, whereas the buffed coated surface was finished to 0.11 μm. However, in recognition of previous findings, surface finish has little influence on the growth of the traveling mode, as observed in low subsonic 3-D boundary-layer transition for a similar geometric configuration with different sweep angle [5,9]. A circular brass ring rounded at the upstream edge was installed to hold a hot-wire probe.…”

“…Although the SC mode has a lower critical Reynolds number than that of the CF mode and appears first, the coexistence of these two traveling instability modes within the boundary layer makes it difficult to distinguish them in any natural transition process. However, by taking into consideration the differing features and wave structures present in these two modes, namely different traveling directions and dominant wave number between the CF mode and SC mode, the two modes can be successfully separated in the wedge-shaped region that develops downstream from the artificial forcing of a point source [7,9]. Of course, all three-dimensional boundary layers in naturally occurring laminar to turbulent transition are inherently exposed to both instabilities.…”

“…5, although those components tend to decay downstream. Because inviscid external streamlines are highly curved near the attachment line, it might be speculated that this minor peak originates from the streamline-curvature instability [9]. Confirmation of this speculation, however, rests upon additional experimental measurements and the calculation of analytical results from a theory that includes the streamline-curvature terms in the stability analysis.…”

Observation of Cross-Flow Instability Mode over a Yawed Cylinder at Mach 2

“…To quantify the surface roughness condition, it should be noted that the uncoated surface roughness was approximately 0.06 μm in arithmetic average of the distance of roughness profile from its mean line, whereas the buffed coated surface was finished to 0.11 μm. However, in recognition of previous findings, surface finish has little influence on the growth of the traveling mode, as observed in low subsonic 3-D boundary-layer transition for a similar geometric configuration with different sweep angle [5,9]. A circular brass ring rounded at the upstream edge was installed to hold a hot-wire probe.…”

“…Although the SC mode has a lower critical Reynolds number than that of the CF mode and appears first, the coexistence of these two traveling instability modes within the boundary layer makes it difficult to distinguish them in any natural transition process. However, by taking into consideration the differing features and wave structures present in these two modes, namely different traveling directions and dominant wave number between the CF mode and SC mode, the two modes can be successfully separated in the wedge-shaped region that develops downstream from the artificial forcing of a point source [7,9]. Of course, all three-dimensional boundary layers in naturally occurring laminar to turbulent transition are inherently exposed to both instabilities.…”

“…5, although those components tend to decay downstream. Because inviscid external streamlines are highly curved near the attachment line, it might be speculated that this minor peak originates from the streamline-curvature instability [9]. Confirmation of this speculation, however, rests upon additional experimental measurements and the calculation of analytical results from a theory that includes the streamline-curvature terms in the stability analysis.…”

Non-parallel stability analysis of three-dimensional boundary layers along an infinite attachment line

“…On most swept wings of conventional high-speed aircraft, the boundary-layer instability and transition occurs in the wind-facing region near the leading edge. Experimental observations by Poll (1979) identiÿed the spanwise-traveling Tollmien-Schlichting waves in the attachment-line boundary layer on a yawed circular cylinder, while Takagi and Itoh (1998), Tokugawa et al (1999) experimentally investigated the development of both cross-ow and streamline-curvature modes in a fully developed boundary layer slightly downstream on a yawed cylinder. For physical understanding of the early transition in swept-wing boundary layers, however, more detailed experiments should be conducted on stability characteristics of the ow ÿeld between the attachment line and the downstream region.…”

Observation of Cross-Flow Instability Mode over a Yawed Cylinder at Mach 2

“…To quantify the surface roughness condition, it should be noted that the uncoated surface roughness was approximately 0.06 μm in arithmetic average of the distance of roughness profile from its mean line, whereas the buffed coated surface was finished to 0.11 μm. However, in recognition of previous findings, surface finish has little influence on the growth of the traveling mode, as observed in low subsonic 3-D boundary-layer transition for a similar geometric configuration with different sweep angle [5,9]. A circular brass ring rounded at the upstream edge was installed to hold a hot-wire probe.…”

“…Although the SC mode has a lower critical Reynolds number than that of the CF mode and appears first, the coexistence of these two traveling instability modes within the boundary layer makes it difficult to distinguish them in any natural transition process. However, by taking into consideration the differing features and wave structures present in these two modes, namely different traveling directions and dominant wave number between the CF mode and SC mode, the two modes can be successfully separated in the wedge-shaped region that develops downstream from the artificial forcing of a point source [7,9]. Of course, all three-dimensional boundary layers in naturally occurring laminar to turbulent transition are inherently exposed to both instabilities.…”

“…5, although those components tend to decay downstream. Because inviscid external streamlines are highly curved near the attachment line, it might be speculated that this minor peak originates from the streamline-curvature instability [9]. Confirmation of this speculation, however, rests upon additional experimental measurements and the calculation of analytical results from a theory that includes the streamline-curvature terms in the stability analysis.…”

Non-parallel stability analysis of three-dimensional boundary layers along an infinite attachment line

“…On most swept wings of conventional high-speed aircraft, the boundary-layer instability and transition occurs in the wind-facing region near the leading edge. Experimental observations by Poll (1979) identiÿed the spanwise-traveling Tollmien-Schlichting waves in the attachment-line boundary layer on a yawed circular cylinder, while Takagi and Itoh (1998), Tokugawa et al (1999) experimentally investigated the development of both cross-ow and streamline-curvature modes in a fully developed boundary layer slightly downstream on a yawed cylinder. For physical understanding of the early transition in swept-wing boundary layers, however, more detailed experiments should be conducted on stability characteristics of the ow ÿeld between the attachment line and the downstream region.…”

Observation of Cross-Flow Instability Mode over a Yawed Cylinder at Mach 2

“…To quantify the surface roughness condition, it should be noted that the uncoated surface roughness was approximately 0.06 μm in arithmetic average of the distance of roughness profile from its mean line, whereas the buffed coated surface was finished to 0.11 μm. However, in recognition of previous findings, surface finish has little influence on the growth of the traveling mode, as observed in low subsonic 3-D boundary-layer transition for a similar geometric configuration with different sweep angle [5,9]. A circular brass ring rounded at the upstream edge was installed to hold a hot-wire probe.…”

“…Although the SC mode has a lower critical Reynolds number than that of the CF mode and appears first, the coexistence of these two traveling instability modes within the boundary layer makes it difficult to distinguish them in any natural transition process. However, by taking into consideration the differing features and wave structures present in these two modes, namely different traveling directions and dominant wave number between the CF mode and SC mode, the two modes can be successfully separated in the wedge-shaped region that develops downstream from the artificial forcing of a point source [7,9]. Of course, all three-dimensional boundary layers in naturally occurring laminar to turbulent transition are inherently exposed to both instabilities.…”

“…5, although those components tend to decay downstream. Because inviscid external streamlines are highly curved near the attachment line, it might be speculated that this minor peak originates from the streamline-curvature instability [9]. Confirmation of this speculation, however, rests upon additional experimental measurements and the calculation of analytical results from a theory that includes the streamline-curvature terms in the stability analysis.…”

Non-parallel stability analysis of three-dimensional boundary layers along an infinite attachment line

“…On most swept wings of conventional high-speed aircraft, the boundary-layer instability and transition occurs in the wind-facing region near the leading edge. Experimental observations by Poll (1979) identiÿed the spanwise-traveling Tollmien-Schlichting waves in the attachment-line boundary layer on a yawed circular cylinder, while Takagi and Itoh (1998), Tokugawa et al (1999) experimentally investigated the development of both cross-ow and streamline-curvature modes in a fully developed boundary layer slightly downstream on a yawed cylinder. For physical understanding of the early transition in swept-wing boundary layers, however, more detailed experiments should be conducted on stability characteristics of the ow ÿeld between the attachment line and the downstream region.…”