Gedaechtniseffekte in der Turbulenz

Gedaechtniseffekte in der Turbulenz

Hinze, J.O.

Civil Engineering and Geosciences

Hydraulic Engineering

1975-09-01

NOTE: REPORT IN GERMAN, ONLY THE ABSTRACT IS IN ENGLISH Memory effects in the flow of fluids are known long since. One has to reckon with such effects when studying the flow of non-Newtonian fluids, for instance when they exhibit a visco-elastic behaviour. Certain phenomena in turbulence also seem to point towards a visco-elastic behaviour. If, however, turbulence is considered as a hypothetical non-Newtonian fluid, there are essential differences with actual non-Newtonian fluids. First the requirement of objectivity concerning invariance of any constitutive equation against a time-dependent bodily rotation, has to be dropped. Second, in rheology the principle of local action is used. This means that in the case of a simple fluid any deformation-history can be described completely in terms of the local velocity gradient. In turbulence, action is not restricted to small regions, and higher derivatives of the mean velocity are often required to describe this action. In flows with a preferred main-flow direction, a distinction can be made between transport in axial and in transverse direction, when considering a "memory" behaviour that determines the degree of localness of action. If, for instance, turbulence shear-stress is expressed in the transverse gradient of the mean velocity with an eddy viscosity (Boussinesq), this gradient may well vary in the transverse direction across "memory" distances, where the contribution to the total transport of momentum is still of importance. In some cases negative values may be obtained in a small region around a maximum of the mean velocity with an asymmetric distribution (wall jet) if the variation of this gradient is neglected. This would result in a "negative turbulence energy production ." These "memory" distances are of the order of the Lagrangian integral length-scale or of the size of the bigger eddies. The action can then no longer be considered as being local in the rheological sense. In the axial, main flow direction, the situation may be different. Because of the relatively large convection velocity in this direction the memory distance is much larger than in transverse direction, i.e. many times the size of the bigger eddies. Though often the action may be described satisfactorily as if it were local, because of the size of the eddies involved the action is not strictly local. If we consider in those flows the effect of a non-constant mean-velocity gradient on the turbulence shear stress by extending the simple Boussinesq relation with a term giving the change in axial direction of this velocity gradient. The obtained equations have been applied to a wake flow generated by a hemi-spherical cap on the wall of a constant-pressure turbulent boundary layer, and the wake-flow of a circular cylinder in a uniform free stream. The result is that the extra-memory effects are important in both the disturbed boundary-layer and the developing part of the wake at short distances from the cylinder. In the first case the eddy viscosity when corrected for the extra-memory effect and rendered dimensionless with the local wall-friction velocity and boundary-layer thickness, still follows the same distribution as for the undisturbed boundary-layer. When applying the obtained equations to actual flows, an uncertainty is presented concerning the quantitative evaluation of the length Lambda_1 and of the function G, because of lack of knowledge of the Lagrangian autocorrelation and the relaxation time or memory function. In the present paper the function G has been approximated by an exponential function, and a relation for Lambda_1. As an estimate it has proven to be useful, at least for the time being.

Turbulenz
Gedaechtniseffekte
memory effects
turbulence
Boussinesq
viscosity

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