Flow in the wake of self-propelled bodies and related sources of turbulence

Abstract

In the steady-state counterpart of the wake behind a totally immersed, self-propelled body, simulated in an air tunnel by a concentric nozzle and disk, measurements were made of mean-flow velocity and pressure, turbulence intensities in the three co-ordinate directions, turbulent shear, and mean temporal gradient and auto-correlation of the axial-velocity fluctuations. Through the equations of momentum and energy for the mean and the turbulent motion, the experimental data were used to verify the condition of self-propulsion and the accuracy of measurement, and to provide a picture of the force field and the process of energy transformation.The variation of the principal flow characteristics was analysed with the aid of appropriate hypotheses as to the transport mechanism and the structure of the turbulence. Two hypotheses proved to be most useful: a more general concept of self-preservation than is known from elementary free-turbulence flows; and the assumption that beyond an intial shear zone the turbulence can be regarded as having originated at a point source in the flow. Extension of the analysis to flows past line and plane sources of turbulence then permitted its validity to be tested with the extensive experimental information available on decaying homogeneous turbulence behind a grid. The rates of diffusion and decay were first deduced in terms of the conventional power laws and thereafter, on the assumption of proportionality of all length scales for any one flow, in terms of more elaborate relationships. The most noteworthy results of the latter approach are the asymptotic development of wake widths and eddy scales toward constant values and the elimination of the subdivision of the flow field into a number of decay zones of vaguely defined limits that has been customary in the theory of homogeneous turbulence. Agreement with corresponding experimental results for a self-propelled body and a grid (i.e. for a point and a plane source of turbulence) was obtained over the entire available ranges of measurement.