In this two-part paper, time-accurate solutions of the Reynolds-averaged Navier-Stokes equations are presented, which address through model problems, the response of turbulent propeller-blade boundary layers and wakes to external-flow traveling waves. In Part 1, the Massachusetts Institute of Technology flapping-foil experiment was simulated and the results validated through comparisons with data. The response was shown to be significantly more complex than classical unsteady boundary layer and unsteady lifting flows thus motivating further study. In Part 2, the effects of frequency, waveform, and foil geometry are investigated. The results demonstrate that uniquely different response occurs for low and high frequency. High-frequency response agrees with behavior seen in the flapping-foil experiment, whereas low-frequency response displays a temporal behavior which more closely agrees with classical inviscid-flow theories. Study of waveform and geometry show that, for high frequency, the driving mechanism of the response is a viscous-inviscid interaction created by a near-wake peak in the displacement thickness which, in turn, is directly related to unsteady lift and the oscillatory wake sheet. Pressure waves radiate upstream and downstream of the displacement thickness peak for high frequency flows. Secondary effects, which are primarily due to geometry, include gust deformation due to steady-unsteady interaction and trailing-edge counter-rotating vortices which create a two-layered amplitude and phase-angle profile across the boundary layer.

1.
Basu, B. C., and Hancock, G. J., 1978, “The Unsteady Motion of a Two-Dimensional Aerofoil in Incompressible Inviscid Flow,” Journal of Fluid Mechanics, Vol. 87.
2.
Chen, B., and Stern, F., 1994, “Computation of Unsteady Viscous Marine Propeller Blade and Wake Flow,” Proceedings of ONR Symposium on Naval Hydrodynamics, Santa Barbara, CA.
3.
Choi, J. E., Sreedhar, M., and Stern, F., 1996, “Stokes Layers in Horizontal-Wave Outer Flows,” ASME JOURNAL OF FLUIDS ENGINEERING, Vol. 118, No. 3.
4.
Goldstein, M. E., and Attasi, H. A., 1976, “A Complete Second-Order Theory for the Unsteady Flow About an Airfoil Due to a Periodic Gust,” Journal of Fluid Mechanics, Vol. 74.
5.
Horlock, J., 1968, “Fluctuating Lift Forces on Aerofoils Moving Through Transverse and Chordwise Gusts,” ASME Journal of Basic Engineering, pp. 494–500.
6.
Horwich-Lurie, B., 1993, “Unsteady Response of a Two-Dimensional Hydrofoil Subject to High Reduced Frequency Gust Loading,” M. S. thesis, Massachusetts Institute of Technology.
7.
Jessup, S., 1990, “Measurement of Multiple Blade Rate Unsteady Propeller Forces,” David Taylor Research Center, Hydromechanics Department, Research and Development Report DTRC-90/015.
8.
Kerwin, J. E., and Lee, C. S., 1978, “Prediction of Steady and Unsteady Marine Propeller Performance by Numerical Lifting-Surface Theory,” Transactions SNAME, Vol. 86.
9.
Lewis, E. V., editor, 1988, Principles of Naval Architecture, 2nd Revision, Volume II—Resistance, Propulsion, and Vibration, The Society of Naval Architects and Marine Engineers, pp. 291–305.
10.
Lurie, E. A., 1996, “Investigation of High Reduced Frequency, Separated Trailing Edge Flows,” Sc. D. thesis, Massachusetts Institute of Technology.
11.
Naumann, H., and Yeh, H., 1973, “Lift and Pressure Fluctuations of a Cambered Airfoil Under Periodic Gusts and Applications in Turbomachinery,” ASME Journal of Engineering for Power, Jan., pp. 1–10.
12.
Patel
M. H.
,
1977
, “
On Turbulent Boundary Layers in Oscillatory Flow
,”
Proceedings of the Royal Society of London A
, Vol.
353
, pp.
121
143
.
13.
Paterson, E. G., and Stern, F., 1997, “Computation of Unsteady Viscous Marine-Propulsor Blade Flows—Part 1: Validation and Analysis,” ASME JOURNAL OF FLUIDS ENGINEERING, Vol. 119, No. 1.
14.
Paterson, E. G., Wilson, R. V., and Stern, F., 1998, “Verification/Validation of Steady Flow RANS Simulation of DTMB Model 5415,” Proceedings 1st Symposium on Marine Applications of CFD, May 19–21, McLean, VA.
15.
Poling, D. R., and Telionis, D. P., 1986, “The Response of Airfoils to Periodic Disturbances—The Unsteady Kutta Condition,” AIAA Journal, Vol. 24, No. 2.
16.
Sears, W. R., 1941, “Some Aspects of Non-Stationary Airfoil Theory and Its Practical Application,” Journal of Aeronautical Sciences, Vol. 8.
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