The Receptivity of a Laminar Boundary Layer to External Disturbances

Leehey, Patrick; Gedney, Charles; Her, Jen‐Yuan

doi:10.1007/978-3-642-82462-3_36

Cited by 5 publications

(3 citation statements)

References 6 publications

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“…It can be defined as the ratio of the amplitude of the T-S wave in the boundary layer to the amplitude of the local or free-stream disturbance field. Leehey, Gedney & Her (1984) considered a free-stream disturbance and defined receptivity as the ratio of the maximum amplitude of the T-S-wave response in the boundary layer to that of the free-stream disturbance. Murdock (1980) used the amplitude of the T-S wave at Branch I in his definition of receptivity.…”

Section: Receptivity Resultsmentioning

confidence: 99%

Boundary layer receptivity to free-stream sound on parabolic bodies

Haddad

Corke

1998

J. Fluid Mech.

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We use a numerical approach to study the receptivity of the boundary layer flow over a slender body with a leading edge of finite radius of curvature to small streamwise velocity fluctuations of a given frequency. The body of interest is a parabola in order to exclude jumps in curvature, which are known sites of receptivity and which occur on elliptic leading edges matched to finite-thickness at plates. The infinitesimally thin flat plate is the limiting solution for the parabola as the nose radius of curvature goes to zero. The formulation of the problem allows the two-dimensional unsteady Navier–Stokes equations in stream function and vorticity form to be converted to two steady systems of equations describing the basic (nonlinear) flow and the perturbation (linear) flow. The results for the basic flow are in excellent agreement with those in the literature. As expected, the perturbation flow was found to be a combination of an unsteady Stokes flow and Orr–Sommerfeld modes. To separate these, the unsteady Stokes flow was solved separately and subtracted from the total perturbation flow. We found agreement with the streamwise wavelengths and locations of Branches I and II of the linear stability neutral growth curve for Tollmien–Schlichting waves. The results showed an increase in the leading-edge receptivity with decreasing nose radius, with the maximum occurring for an infinitely sharp flat plate. The receptivity coefficient was also found to increase with angle of attack. These results were in qualitative agreement with the asymptotic analysis of Hammerton & Kerschen (1992). Good quantitative agreement was also found with the recent numerical results of Fuciarelli (1997), and the experimental results of Saric, Wei & Rasmussen (1994).

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Section: Receptivity Resultsmentioning

confidence: 99%

Boundary layer receptivity to free-stream sound on parabolic bodies

Haddad

Corke

1998

J. Fluid Mech.

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“…Experiments on the TS-instability in twodimensional flat plate flows found sound waves of defined frequency and direction to be very efficient in promoting the transition process (see e.g. Leehey, Gedney & Her 1984;Kosorygin, Levchenko & Polyakov 1984). For TS-instabilities receptivity theories concerning long-wavelength acoustic disturbances have been developed (Goldstein & Hultgren 1989).…”

Section: Soundmentioning

confidence: 99%

Disturbance growth in an unstable three-dimensional boundary layer and its dependence on environmental conditions

1996

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Experimental investigations in the three-dimensional boundary layer of a swept flat plate with the pressure gradient induced from outside are aimed at enhancing knowledge of the transition process in the presence of pure crossflow instability. The development of disturbances is characterized by the occurrence of both stationary and travelling instability modes, by early nonlinear development and by complex dependence upon the environmental conditions. Experiments under natural conditions of transition showed a good correspondence of the identified modes with those predicted by local linear stability theory. The disturbance growth, however, is generally overpredicted. Controlled excitation of crossflow vortices allowing measurements closer to the linear range of amplification confirmed this result. Nonlinear effects such as interaction between stationary disturbances and base flow and between travelling and stationary modes have already been observed when the naturally excited instabilities become of measurable size.The most striking feature of the disturbance development is the complex dependence on initial conditions. Experiments under systematically varied environments showed that surface roughness represents the key parameter responsible for the initiation of stationary crossflow vortices. In contrast to two-dimensional boundary layers, free-stream turbulence influences the transition process indirectly. Only for turbulence levels Tu > 0.2% and smooth surfaces do the travelling instability waves dominate. The location of the final breakdown of laminar flow is clearly determined by the saturation amplitude of crossflow vortices. The receptivity to sound, two-dimensional surface roughness and non-uniformities of the test-section mean flow was found to be very weak.

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“…In general, the receptivity coefficient is defined as the ratio of the instability wave (T-S) amplitude, at some location in the boundary layer, to the acoustic amplitude in the free stream. Leehey, Gedney & Her (1984) used the maximum amplitude in the boundary layer, which for a linear mode occurs at the location of the upper neutral-growth curve (Branch II). Murdock (1980), Saric, Wei & Rasmussen (1995), and Saric & White (1998) preferred to use the location of Branch I.…”

Section: Introductionmentioning

confidence: 99%

Boundary layer receptivity to free-stream sound on elliptic leading edges of flat plates

Wanderley

Corke

2001

J. Fluid Mech.

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The leading-edge receptivity to acoustic waves of two-dimensional bodies is investigated using a spatial solution of the Navier–Stokes equations in vorticity/stream function form in general curvilinear coordinates. The free stream is composed of a uniform flow with a superposed periodic velocity fluctuation of small amplitude. The method follows that of Haddad & Corke (1998), in which the solution for the basic flow and the linearized perturbation flow are solved separately. The initial motivation for the work comes from past physical experiments for flat plates with elliptic leading edges, which indicated narrow frequency bands of higher neutral-curve Branch I receptivity. We investigate the same conditions in our simulations, as well as on a parabolic leading edge. The results document the importance of the leading edge, junction between the ellipse and flat plate, and pressure gradient to the receptivity coefficient at Branch I. Comparisons to the past experiments and other numerical simulations showed the influence of the elliptic leading-edge/flat-plate joint as an additional site of receptivity which, along with the leading edge, provides a wavelength selection mechanism which favours certain frequencies through linear superposition.

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The Receptivity of a Laminar Boundary Layer to External Disturbances

Cited by 5 publications

References 6 publications

Boundary layer receptivity to free-stream sound on parabolic bodies

Boundary layer receptivity to free-stream sound on parabolic bodies

Disturbance growth in an unstable three-dimensional boundary layer and its dependence on environmental conditions

Boundary layer receptivity to free-stream sound on elliptic leading edges of flat plates

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