# Pipe flow - rotating

## Best Practice Advice for the UFR

Choosing the length of the computational box for direct simulations of wall turbulent flows is an important issue. EUW used axial two point correlations of the rms velocity components to show that for N=0 a length of the pipe is sufficient to allow these correlation to drop to zero. In contrast, when the pipe rotates, flow visualizations by Nishibori et al.(1987), at high rotation (), showed that in the central part of the pipe elongated coherent structures form and that, at even higher rotation rates, the variations in the stream-wise direction disappear, in agreement with the Taylor-Proudman theorem. These flow visualizations induced us to verify whether the length is sufficient when the pipe is rotating. The check was done at N=2, the highest N in this study, and it was observed that with the turbulent stresses and did not converge to the statistical steady state after 200 time units. On the contrary, when the length was increased to and to , by keeping the same , a convergence to the statistical steady state was reached. Furthermore it has been observed that the elongated structures in the central region of the pipe have long time scales, requiring a longer time to reach statistical steady state than in the non-rotating case. Although at N<2 a length is sufficient, the simulations were performed with the same length used for N=2 ( )

The second advise concern the sub grid modelling. Although in simple flows, eddy viscosity models produce results comparable to those by Reynolds-stress models, the latter are necessary in a variety of flows that simpler models () could not describe. The turbulent rotating pipe is one of them. Hirai et al. (1988) proved that the conventional model does not work for this flow.

The two major effects in this flow, a rotationally dependent axial mean velocity and the presence of mean swirl velocity relative to the rotating pipe, cannot be predicted by traditional two-equation models such as the standard model with conventional near-wall treatments. Two-dimensional explicit algebraic stress models are able to predict the rotationally dependent axial mean velocity. However, they are unable to predict the presence of a nonzero mean swirl velocity, approximately a 15% effect, when conventional near-wall treatments, such as those used in the model, are implemented. This effect, however, can be predicted by three-dimensional explicit algebraic stress models where it arises from a frame-dependent cubic nonlinearity. Second-order closure models provide a good description of this flow, in that the two principal effects discussed above can be described by virtually any second order closure, since they arise from Coriolis effects which are automatically present in these models. Quadratic pressure-strain models, as embodied by the SSG model, performed the best overall when detailed comparisons were made with experiments. The Launder et al. model, with its linear pressure-strain, yields a reasonably good description of this flow, but does not perform quite as well.

There is no question that three-dimensional frame-dependent models are needed to adequately describe turbulent flow in an axially rotating pipe. These can be either three-dimensional algebraic models with a cubic nonlinearity or full second-order closures, although there are some problems with the former.