Response of turbulent boundary layers to multiple strain rates

Abstract

Many practical applications, such as in blade cascades and turbomachinery, involve inhomogeneous turbulent shear flows subjected simultaneously to multiple strains. In principle, the applied strain can be combined to yield an effective strain. However, no simple stress–strain relation is capable of establishing turbulent stress or energy balance in the mean or on an instantaneous basis. In the current investigation, a turbulent boundary layer is examined in the presence of convex curvatures of different strengths combined with streamwise (favourable and adverse) pressure gradients, with various values of pressure gradient ratio, (∂P/∂s)/(∂P/∂n). Measurements of the mean and turbulent parameters and flux Richardson number show appreciable changes, mainly in the outer portion of the boundary layer (y⁺ > 100). The turbulent burst frequency, particularly at the location of application of the additional strain rate, also changes relative to its value with wall curvature alone.

Three primary observations from these experiments are as follows: (i) in all cases, the mean velocity profile and all of the measured Reynolds stresses collapse in the near-wall region using standard inner scaling; (ii) the applied strains combine nonlinearly, with one of the strains dominating the local flow during its development; (iii) the ratio of the radial to axial pressure gradient magnitude influences both classical turbulence correlations and mean flow, as well as the physical production cycle of turbulence; and (iv) application rate of newly introduced strain rates is at least as important as their magnitudes.