The linear stability of Hagen-Poiseuille flow (Poiseuille pipe flow) with superimposed rigid rotation against small three-dimensional disturbances is examined at finite and infinite axial Reynolds numbers. The neutral curve, which is obtained by numerical solution of the system of perturbation equations (derived from the Navier-Stokes equations), has been confirmed for finite axial Reynolds numbers by a few simple experiments. The results suggest that, at high axial Reynolds numbers, the amount of rotation required for destabilization could be small enough to have escaped notice in experiments on the transition to turbulence in (nominally) non-rotating pipe flow.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112076001304

Stability of Hagen-Poiseuille flow with superimposed rigid rotation

Convective heat transfer inside a rotating cylinder with an axial air flow

Heat transfer and friction characteristics in decaying swirl flow generated by different radial guide vane swirl generators

The effects of swirl on internal turbulent flows are studied by conducting experiments on turbulent pipe flow with variable initial swirl. This first part of the study is primarily concerned with similarity laws. The mean velocity profiles, both away from and close to the wall, are found to admit similarity representations at sufficiently large Reynolds numbers, provided that flow reversal does not take place near the entrance. While the wall law is not sensibly dependent on swirl, the velocity defect law in its extended form is sensitive to swirl. Further, a logarithmic skin-friction law is obtained in which only the additive coefficient depends on swirl. This coefficient is found to vary linearly with the swirl angle in the range of the present experiments.

Experiments on swirling turbulent flows. Part 1. Similarity in swirling flows

An investigation of the hydrodynamic stability of swirling flows having arbitrary Rossby numbers is described A necessary condition for instability is derived for rigidly rotating flows and this condition is further refined in the specific case of a parabolic axial flow Numerical results are presented for two azimuthal wave-numbers corresponding to the maximum growth rates of unstable perturbations as a function of Rossby number It is found that the largest growth rates occur when the Rossby number is O(1) and that instability persists for surprisingly large values of this parameter Previous explanations of the instability mechanism are discussed and it is concluded that these are only adequate in the limit of small Rossby number

Instability of rigidly rotating flows to non-axisymmetric disturbances

The stability of a flow consisting of solid body rotation superposed on an entrance‐type pipe flow profile is investigated experimentally. Increasing the swirl ratios from zero to four reduced the axial Reynolds number at which laminar flow breaks down from 2500 to 900.

L. Wolf

Papers

Stability of Pipe Flow with Superposed Solid Body Rotation

Measurements of the decay of swirl in turbulent flow.

Transpiration cooling in an arc-jet environment.

Mass transfer cooling in laminar hypersonic cavity flow