Characteristics of Unsteady Disturbances Due to Streamlinecurvature Instability in a Threedimensional Boundary Layer

Takagi, Shohei; Tokugawa, Naoko; Itoh, Nobutake

doi:10.1007/1-4020-4159-4_52

Cited by 7 publications

(12 citation statements)

References 6 publications

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“…Consequently, the phase velocity of the most unstable CF component is approximately 70 m∕s, which is roughly equivalent to 14% of the main flow velocity Q ∞ 507 m∕s. It is interesting to note that this relation is close to 12%, previously observed for the CF traveling mode in low-speed, subsonic 3-D boundary layers [33].…”

Section: B Detection Of Traveling Modesupporting

confidence: 86%

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

et al. 2015

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Nomenclature Q ∞ = velocity in the freestream direction U ∞ = velocity in the chordwise direction perpendicular to the leading edge V ∞ = velocity in the spanwise direction parallel to the leading edge x = distance in the local external flow direction y = distance in the normal-to-wall direction z = distance in the direction perpendicular to both x and y α = real part of complex wave number in x direction β = real part of complex wave number in z direction λ = wavelength in the wave-number vector direction λ S = wavelength in the spanwise direction ν = kinematic viscosity ϕ = angle measured from the leading edge in the chordwise direction, deg χ = wave-number vector angle measured from local external streamline ψ = angle of external streamline deviation from the chordwise direction

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Section: B Detection Of Traveling Modesupporting

confidence: 86%

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

et al. 2015

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“…The type I mode is due to the wellknown crossflow instability (see for example, Garrett et al 2009a, 2009b, Lingwood 1995, Malik 1986 and references contained therein). The type II mode is attributed to external streamline curvature and has been studied (theoretically and experimentally) by Itoh and coworkers in general 3D-boundary layers (see Itoh 1994, 1996, Takagi et al 2006. However, an understanding of how the maximum growth rates of the types I and II modes change with reduced half-angle will be crucial in determining the dominant mode at each particular halfangle, and this is presented in section 3.…”

Section: Introductionmentioning

confidence: 96%

Linear growth rates of types I and II convective modes within the rotating-cone boundary layer

Garrett¹

2009

Fluid Dyn. Res.

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Experimental observations have shown that the transition characteristics of the boundary-layer flow over rotating cones depends on the cone half-angle. In particular, pairs of counter-rotating Görtler-type vortices are observed over cones with slender half-angles and co-rotating vortices are observed over broad cones. Garrett et al (2009 J. Fluid Mech. 622 209-32) have hypothesized the existence of a centrifugal instability mode over slender cones that is more dangerous than the types I (crossflow) and II (streamline curvature) modes which dominate over rotating disks and broad cones. Work is currently underway to clarify this alternative mode; however, a clear understanding of the growth rates of types I and II modes is crucial to the ultimate understanding of how the dominant mode changes with half-angle. In this paper, we demonstrate that the maximum growth rate for types I and II modes decreases with reduced half-angle, which clears the way for the dominance of the alternative instability mode. Furthermore, it is suggested that vortices travelling at 75% of the cone surface speed will be selected over smooth, clean rotating cones with half-angle such that the type I mode is dominant. Interestingly, this vortex speed has been experimentally observed by Kobayashi and Arai within the rotating-sphere boundary layer.

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“…At low Reynolds numbers first order-theories for circular cylinders predict the effects of sweep quite well. The approach of Takagi et al 8 using hot wire techniques, offers an opportunity to identify both stationary and traveling instability modes.…”

Section: Discussionmentioning

confidence: 99%

“…The λ/λ 0 = 1/cos  theoretical curve is also plotted and demonstrates reasonable agreement with both the Poll data and the new data. At 50 o sweep the theoretical and experimental points of Takagi et al 8 involved ingenious use of theory and hot wire data to discriminate between stability modes. Takagi discovered that at 50 o sweep the crossflow mode dominated; this is the same mode identified by Poll and it is the lateral spacing from the crossflow mode that is plotted in Fig.…”

Section: Transverse Spacingmentioning

confidence: 99%

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Stationary and Traveling Vortical Structures on Swept Cylinders and Turbine Blades

Gostelow

Rona

Garrett

et al. 2013

43rd Fluid Dynamics Conference

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Suction surface flow visualization on turbine blades at subsonic and transonic speeds showed robust streamwise streaks on a lengthy time-average basis. The normal flow past a circular cylinder is a more canonical case and testing was undertaken at high speeds on a 38 mm diameter cylinder and at low speeds on a 152 mm diameter cylinder. The lateral spacing between streaks on cylinders had been predicted by Kestin and Wood and the present tests gave excellent agreement with their theory. Although their work was related to unswept circular cylinders it also provides an excellent benchmark for sweep effects on cylinders and turbomachinery blading. The observations of streaks on turbine blades and unswept cylinders provided a firm basis for referencing the influence of sweep. Experiments on a circular cylinder were performed over a range of sweep angles from zero to 61 o giving results for lateral spacing and angular orientation of the streaks. At high-sweep angles the results are consistent with those of Poll. The introduction of sweep brings consideration of a wide range of instabilities; streamwise and crossflow structures are present on the suction surface of turbine blades. Although the available information on fine structures comes from surface flow visualization, work is now progressing on hot wire measurements away from the surface. The aim is to demonstrate the relationship between the structures and the surface traces. Analysis of the data is complemented by ongoing theoretical work. It is also hoped to provide information on the changing behavior of the vertical structures as the sweep angle is increased. The streamwise disturbance in the unswept case was found to be stationary in nature and to be resilient, often persisting from leading edge to trailing edge. Crossflow instability becomes more significant as sweep is increased. It grows aggressively and rapidly, being predominantly of a traveling nature, and has a major role to play in the transition process. The observed streaks could be of particular concern for the thermal design of turbine blades. It is hoped to give designers confidence about the flow regimes they might anticipate for a given sweep angle and particularly of when and how the aggressive crossflow instability mode is likely to be encountered. Nomenclature

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Characteristics of Unsteady Disturbances Due to Streamlinecurvature Instability in a Threedimensional Boundary Layer

Cited by 7 publications

References 6 publications

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

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

Linear growth rates of types I and II convective modes within the rotating-cone boundary layer

Stationary and Traveling Vortical Structures on Swept Cylinders and Turbine Blades

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