Aerodynamics: a time dependent flow model for the inner region of a turbulent boundary layer

Abstract

Response of the flow variables to external driving forces is non-linear for shear flows. For the turbulent boundary layer case, surface shear stress fluctuations of magnitude as great as the mean value are observed. For flow near the surface Prandtl's turbulent boundary layer approach of employing averaged Reynolds equation and a turbulence closure model is insufficient to account for surf ace shear fluctuations. A model which incorporates a discrete time dependent solution for the inner region of the turbulent boundary layer is proposed. The model requires stochastic averaging of the time dependent solution to account for the random aspect of the flow. The physical model for the flow near the surface is based on the bursting cycle observed in the inner region of a turbulent boundary layer. Localized pressure gradients created in the valleys of the large scale structures of the outer region of the flow are assumed to be the origin of the bursting process. This model treats the sweep motion as an impulsively started flow over a flat plate. An averaging technique is demonstrated to predict the important features of the surface shear stress. In order to confirm the time dependent model assumptions, measurements of the probability distribution and cross-correlation of the longitudinal turbulent velocity and the surface shear stress were evaluated. The sweep-scale, sweep-direction, and origin of the instability are determined from isocorrelation maps. The shape of the probability density distributions of the velocity near the surface and the surface shear stress are found to be similar. However, the velocity probability distribution changes rapidly with increasing distance from the surface. As implied by the time dependent model for the surface shear stress, the magnitude of the large surface shear stress would be substantially changed if the sweep motion could be modified. A series of thin, metal plates were employed to block the instability from reaching the surface. Results show that the mean value of surface shear and the large magnitude fluctuations of surface shear stress were reduced significantly. The variation in surface shear was found to be extremely sensitive to slight angle of attacks of the plates.