The boundary layer of a class of infinite yawed cylinders

Cooke, J. C.

doi:10.1017/s0305004100026220

Cited by 123 publications

(43 citation statements)

References 6 publications

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“…Jones (1947) and Sears (1948) showed that uniform cross flow over a laminar flat plate boundary layer gives rise to an equation which has for its solution the Blasius profile. Cooke (1950) generalized the work of Prandtl (1946) when he found a family of similarity solutions for uniform cross flow over the Falkner-Skan set of pressure gradient driven flows. Rott and Smith (1956) extended the work of Fogarty (1951) to a family cross flows acting on rotating blades.…”

Section: Introductionmentioning

confidence: 91%

New solutions for laminar boundary layers with cross flow

Weidman

1997

Z. angew. Math. Phys.

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In some three-dimensional laminar boundary layer problems a coordinate decomposition reduces the governing equations to a primary nonlinear ordinary differential equation describing the streamwise flow in a semi-infinite domain and a secondary linear equation coupled to the primary solution describing the cross flow of infinite spanwise extent. Five new cross-flow problems of this type are investigated within the confines of laminar boundary layer theory. First, the equation for uniform flow transverse to a planar laminar wall jet is found and solved exactly. Second, two solutions for motion transverse to a uniform shear flow along a flat plate are given. A third problem considered is the transverse motion over a flat plate aligned with the uniform mainstream and advancing toward or receding from the mainstream. In the fourth problem, a family of solutions for transverse uniform streams above and below a planar laminar jet is given in closed form. This solution depends on the momentum J of the planar jet and the velocity ratio κ of the transverse streams. The last problem addresses the motion of transverse uniform streams above and below a planar laminar wake. At leading order the cross flow depends only on the velocity ratio κ and not on the drag D produced by the body forming the wake. The influence of the drag first appears at O(x −1 ln x) in the streamwise coordinate expansion of the cross-flow solution.Mathematics Subject Classification (1991). 35C05, 76D10, 76D25.

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Section: Introductionmentioning

confidence: 91%

New solutions for laminar boundary layers with cross flow

Weidman

1997

Z. angew. Math. Phys.

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“…The FSC similarity solutions are derived in Appendix Appendix A. See also Falkner & Skan (1931); Cooke (1950) for further details. All quantities are non-dimensionalised using the displacement thickness ⇤ 0 and the free-stream streamwise velocity U ⇤ 0 .…”

Section: Baseflowmentioning

confidence: 99%

“…The similarity solutions of Falkner & Skan (1931) and Cooke (1950), subject to boundary conditions f = f 0 = g = 0 at ⌘ = 0 and f 0 ! 1, g !…”

Section: Appendix a Fsc Boundary Layer Equationsmentioning

confidence: 99%

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Stability and sensitivity of a cross-flow-dominated Falkner–Skan–Cooke boundary layer with discrete surface roughness

et al. 2017

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Stability and sensitivity of a crossflow-dominated Falkner-Skan-Cooke boundary layer with discrete surface roughness. Journal of Fluid MechanicsAccess to the published version may require subscription. N.B. When citing this work, cite the original published paper. With the motivation of determining the critical roughness size, a global stability and sensitivity analysis of a three-dimensional Falkner-Skan-Cooke (FSC) boundary layer with a cylindrical surface roughness is performed. The roughness size is chosen such that breakdown to turbulence is initiated by a global version of traditional secondary instabilities of the crossflow (CF) vortices, instead of an immediate flow tripping at the roughness. The resulting global eigenvalue spectra of the systems are found to be very sensitive to numerical parameters and domain size. This sensitivity to numerical parameters is quantified using the "-pseudospectrum, and the dependency on the domain is analysed through an impulse response and an energy budget. It is shown that the growth rates increase with domain size, which originates from the inclusion of stronger CF vortices in the baseflow. This is reflected in a change in the rate of advective energy transport by the baseflow. It is concluded that the onset of global instability in a FSC boundary layer as the roughness height is increased does not correspond to an immediate flow tripping behind the roughness, but occurs for lower roughness heights if su ciently long domains are considered. However, the great sensitivity results in an inability to accurately pinpoint the exact parameter values for the bifurcation, and the large spatial growth of the disturbances in the long domains eventually becomes larger than what can be resolved using finite precision arithmetics.

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“…The base ow eld (U oi ) is given by the Falkner-Skan-Cooke similarity solution (Cooke, 1950). The Reynolds number is Re = Q r =, where Q r is the local edge velocity at the computational inow boundary, and = p x c =U oe is the reference length at the inow.…”

Section: Methodsmentioning

confidence: 99%

Large-eddy simulation of laminar-turbulent transition in a swept-wing boundary layer

Xiaoli

Joslin

Piomelli

1997

35th Aerospace Sciences Meeting and Exhibit

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The spatial development of laminar-turbulent transition in a 45 swept-wing boundary layer is investigated using the large-eddy simulation approach. Both stationary and traveling disturbances are initiated by steady and random forcings. The numerical simulations reproduce the surface shear streaks typical of the crossow instability observed in experiments. Downstream of the transition location the wall shear stress is found to turn towards the streak direction. The strength of the stationary vortices grows exponentially, initially independent of the unsteady forcing amplitude and saturates at dierent levels during the later development, depending on the magnitude of the traveling vortices. Streamwise velocity contours show the evolution from a wave-like structure to the \half-mushroom" structure for the lower-amplitude, traveling-wave case, leading to double inection points in the wallnormal velocity proles prior to transition; the nonlinear interactions involving the stationary vortices are also much stronger, as indicated by the amplication of higher harmonics of the primary mode. The frequency spectrum of the traveling waves show a high frequency secondary instability prior to transition that, however, is not prominent in the higheramplitude traveling-wave case.

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The boundary layer of a class of infinite yawed cylinders

Cited by 123 publications

References 6 publications

New solutions for laminar boundary layers with cross flow

New solutions for laminar boundary layers with cross flow

Stability and sensitivity of a cross-flow-dominated Falkner–Skan–Cooke boundary layer with discrete surface roughness

Large-eddy simulation of laminar-turbulent transition in a swept-wing boundary layer

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