| dc.description.abstract | The mathematical modelling of unsteady boundary layers is investigated. The non-linear time dependent boundary layer equations are linearised by an asymptotic expansion method in powers of freestream velocity fluctuation amplitude. A differential-difference technique in conjunction with a series method is developed to solve the linearised equations for the characteristics of two-dimensional periodic laminar and turbulent boundary layers in a stream in which there is a simple harmonic travelling wave with a zero mean pressure gradient and a non-zero fluctuating pressure gradient. This technique is general except that it is subject to the restriction of small freestream perturbation amplitude. The turbulent boundary layer equations are closed by a two-layer eddy viscosity model based on the steady Cebeci-Smith formulation or by a new single layer eddy viscosity model. Calculations using the latter are found to be numerically stable and efficient for any wave convection velocity. Both laminar and turbulent theories are in excellent agreement with other theories and measurements for freestream oscillations with infinite wave speed. The laminar results for oscillations with finite wave speed, less than the mean freestream speed, are in poor agreement with measured amplitudes but fairly good agreement with measured phase angles. The computational method is numerically very accurate and the results are in good agreement with the analytic solutions obtained from an asymptotic high frequency theory. The results are shown to be highly sensitive to the value of wave speed assumed, and much better agreement with measurements can be obtained by small changes of this quantity, which is subject to some experimental uncertainties. The more reliable turbulent results for oscillations with finite wave speed are obtained by using the new single layer eddy viscosity model, the Cebeci-Smith model being subject to difficulties in implementation in this case. They are in reasonable agreement with measurements and are again sensitive to the value of wave speed. Some errors in the low and high frequency laminar theories, and high frequency turbulent theory reported in Patel (1975, 1977) are pointed out and corrected. | en_US |
