AIAA 2000–2538 Acoustic Receptivity of a Blasius Boundary Layer with 2-D and Oblique Surface Waviness

An experimental investigation was conducted to examine acoustic receptivity and subsequent boundary-layer instability evolution for a Blasius boundary layer formed on a flat plate in the presence of two-dimensional (2-D) and oblique (3-D) surface waviness. The effect of the non-localized surface roughness geometry and acoustic wave amplitude on the receptivity process was explored. The surface roughness had a well defined wavenum-ber spectrum with fundamental wavenumber kw. A planar downstream-traveling acoustic wave was created to temporally excite the flow near the resonance frequency of an unstable eigenmode corresponding to kts = kw. The range of acoustic forcing levels, , and roughness heights, ∆h, examined resulted in a linear dependence of receptivity coefficients; however, the larger values of the forcing combination · ∆h resulted in subsequent non-linear development of the Tollmien-Schlichting (T-S) wave. This study provided the first experimental evidence of a marked increase in the receptivity coefficient with increasing obliqueness of the surface waviness in excellent agreement with theory. Detuning of the 2-D and oblique disturbances was investigated by varying the streamwise wall-roughness wavenumber αw and measuring the T-S response. For the configuration where laminar-to-turbulent breakdown occurred, the breakdown process was found to be dominated by energy at the fundamental and harmonic frequencies, indicative of K-type breakdown. Nomenclature C receptivity coefficient, u ts,I /u ac. c ph phase speed of boundary-layer disturbance. F nondimensional frequency, 2πfν/U 2 ∞. f frequency in Hz. h normalized step height, ∆h n /∆h 1 (n = 1, 2, 3). k wavenumber, (α 2 + β 2) 1/2. N amplification factor, x xI −α i (x; f)dx. R Reynolds number base on δ r , U ∞ x v /ν. Re l Reynolds number base on length scale l, U ∞ l/ν. U mean streamwise velocity. u rms streamwise fluctuating velocity. x streamwise distance from model leading edge. x v streamwise distance from virtual origin. y wall-normal distance from model surface. α streamwise wavenumber. α i spatial amplification rate. β spanwise wavenumber. ∆h surface roughness step height. δ r nondimensional length scale, x v /R. δ * displacement thickness. normalized acoustic wave amplitude, u ac /U ∞. φ phase of disturbance velocity. γ coherence function. η normalized wall-normal coordinate, (y/x v) · R. λ wavelength, 2π/k. ν kinematic viscosity. σ detuning parameter, (α w − α ts,I)/α ts,I. ψ wave angle. Subscripts ac freestream acoustic field. I, II lower and upper branch locations. t total disturbance …