Correlations of the Convection Heat Transfer in Annular Channels With Rotating Inner Cylinder

Abstract

In the internal air system of gas turbine engines or generators, a large variety of different types of annular channels with rotating cylinders are found. Even though the geometry is very simple, the flow field in such channels can be completely three-dimensional and also unsteady. From the literature it is well-known that the basic two-dimensional flow field breaks up into a pattern of counter-rotating vortices as soon as the critical speed of the inner cylinder is exceeded. The presence of a superimposed axial flow leads to a helical shape of the vortex pairs that are moving through the channel. For the designer of cooling air systems there are several open questions. Does the formation of a Taylor-vortex flow field significantly affect the convective heat transfer behavior of the channel flow? Is there a stability problem even for high axial Reynolds-numbers and where is the location of the stability boundary? After all, the general influence of rotation on the heat transfer characteristics has to be known. By the results of flow field and heat transfer measurements, the impact of rotation and the additional influence of Taylor-vortex formation on the heat transfer characteristics in annular channels with axial throughflow will be discussed. The flow field was investigated by time-dependant LDA-measurements, which revealed detailed information about the flow conditions. By a spectral analysis of the measured data, the different flow regimes could be identified. Based on these results, the heat transfer from the hot gas to the rotating inner shaft was determined with a steady-state method. Thus, the influence of the different physical phenomena such as rotation with and without Taylor-vortex formation or the flow development could be separated and quantified. Finally, correlations of the measured results were derived for technical applications.

A review of heat transfer between concentric rotating cylinders with or without axial flow

“…On the other hand, the results of experiments by Yamada [34] show that the transition from turbulent flow to turbulent flow with vortices is punctuated by a critical zone and not by an analytically defined separation. Jakoby et al [46] have likewise confirmed the existence of a transition area rather than a pronounced boundary between flows with as opposed to flows without vortices; one may consult their frequency study for high axial Reynolds and Taylor numbers (2 Â 10 4 < Re < 3 Â 10 4 et 10 5 < Ta < 2 Â 10 8 ). Most of the publications cited involve relatively low Taylor numbers, that is to say approximately 0 < Ta/Ta c < 100.…”

“…It mention that the flow's nature has already been established by the different authors cited [34,43e45] if: 0 Re a 10 4 and 0 Ta 10 6 . The study by Jakoby et al [46] bears special mention on account of a particularly high axial Reynolds number: 2 Â 10 4 < Re < 3 Â 10 4 ; this entails equally high critical Taylor numbers, which may reach 4 Â 10 7 and even 2 Â 10 9 .…”

Flow visualization in an annulus between co-axis rotating cylinders with a circular jet on stationary outer cylinder

“…They indicated that the Couette flow could change into the Taylor vortex flow and then transfer to the pure turbulent flow after several transition processes, respectively. Jakoby et al [8] used LDA (Laser Doppler Anemometry) measurement technology to investigate the convective heat transfer characteristics inside the co-axis rotating annular channel. Their results indicated that the flow field became very complex when the rotational speed of the inner cylinder exceeded a critical value.…”

Temperature distributions in rotary-blade coupling of a 4WD vehicle with longitudinal ribbed turbulators

“…Empirical equations for the dimensionless flux of the filtrate were derived in terms of the Taylor number and the ratio of the annular gap to the radius of the inner cylinder, respectively. Jakoby et al [5] examined the convective heat-transfer in annular channels with a rotating inner cylinder. Their experimental data established the effects of rotation on the formation of a Taylor vortex on the heat-transfer characteristics in annular channels with axial through flow.…”