Spatial Evolution of Resonant Harmonic Mode Triads in a Blasius Boundary Layer 37th AIAA Fluid Dynamics Conference and Exhibit José B. Dávila Department of Engineering Trinity College Rudolph A. King Flow Physics and Control Branch NASA Langley Research Center June 25, 2007

Spatial Evolution of Resonant Harmonic Mode Triads in a Blasius Boundary Layer Blasius boundary layer evolution is studied by means of bicoherence calculations. The layer is acoustically excited at the T-S frequency to provide a controlled transition. Measurements are made using a smooth surface as well as various roughness patterns. The bicoherence calculations are used to determine the extent to which frequency resonant velocity fluctuation waves can participate in energy exchange. The emphasis is on downstream variation of the individual interactions among harmonic modes. A limited picture of the role of quadratic wave interactions is revealed. 37th AIAA Fluid Dynamics Conference and Exhibit

Objectives Determine the effect of surface roughness height and orientation angle on mode growth and quadratic interactions Determine the role of quadratic interactions in energy transfer to harmonic modes.

Transition Process 37th AIAA Fluid Dynamics Conference and Exhibit

Top and side views of wind tunnel 37th AIAA Fluid Dynamics Conference and Exhibit

Top and side views of flat plate model Data x = 1.52 m 37th AIAA Fluid Dynamics Conference and Exhibit

Two-Dimensional Roughness x Flow 37th AIAA Fluid Dynamics Conference and Exhibit

Oblique Roughness x  Flow 37th AIAA Fluid Dynamics Conference and Exhibit

Bispectrum Bicoherence square X = Fast Fourier Transform of the streamwise velocity fluctuation Calculations 37th AIAA Fluid Dynamics Conference and Exhibit

Time Series Parameters Sampling frequency = 1000 Hz Points per realization = 2048 Frequency resolution = Hz Number of realizations = 20 37th AIAA Fluid Dynamics Conference and Exhibit Acoustic Parameters f o = 71 Hz ε low = u ac /U ∞ = 3.8 ×10 -5 ε high = u ac /U ∞ = 7.6 ×10 -5 Roughness Parameters  h low = 36  m  h high = 72  m x ≈ 50.3 mm

37th AIAA Fluid Dynamics Conference and Exhibit Fig. 1 R = 1082 Bicohernece Square Energy Spectrum Energy spectrum f/f o

Fig. 2 Medium excitation, smooth plate 37th AIAA Fluid Dynamics Conference and Exhibit

Fig. 3 High excitation, smooth plate 37th AIAA Fluid Dynamics Conference and Exhibit

Fig. 4 Medium excitation, high roughness,  = 0º 37th AIAA Fluid Dynamics Conference and Exhibit

Fig. 5 High excitation, high roughness,  = 0º 37th AIAA Fluid Dynamics Conference and Exhibit

Fig. 6 Medium excitation, medium roughness,  = 0º 37th AIAA Fluid Dynamics Conference and Exhibit

Fig. 7 Medium excitation, medium roughness,  = 15º 37th AIAA Fluid Dynamics Conference and Exhibit

Fig. 8 Medium excitation, medium roughness,  = 30º 37th AIAA Fluid Dynamics Conference and Exhibit

Fig. 9 Medium excitation, medium roughness,  = 45º 37th AIAA Fluid Dynamics Conference and Exhibit

Concluding Remarks The results show that the roughness element thickness and orientation influence the development of quadratic interactions. Only part of the picture is evident from the evolution of energy spectrum values. In conjunction with these, bicoherence calculations can reveal a more complete picture of the evolution of interacting triads. In particular, the energy spectrum and bicoherence calculations show that: (1) in the two-dimensional case, higher surface roughness yields higher fundamental mode amplitudes and promotes quadratic interactions, and (2) that three-dimensionality imposed by surface roughness obliqueness inhibits quadratic interactions. The results confirm those of King and Breuer 1. Also, they suggest that the presence of multiple, effective quadratic interactions are a precondition for transition in the R region studied. 1 King, R. A. and Breuer, K. S., “Acoustic Receptivity and Evolution of Two-Dimensional and Oblique Disturbances in a Blasius Boundary Layer,” J. Fluid Mech., Vol. 432, 2001, pp th AIAA Fluid Dynamics Conference and Exhibit