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Time Resolved PIV Measurements of Low Reynolds Number Flow in Rotating Channels

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VKI PHDT 2008-02, Time Resolved PIV Measurements of Low Reynolds Number Flow in Rotating Channels, ISBN 978-2-930389-29-X

Time resolved PIV measurements of low Reynolds number flow in ro

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Time Resolved PIV Measurements of Low Reynolds Number Flow in Rotating Channels
By Alberto di Sante
PhD Thesis from the von Karman Institute/Università Politecnica delle Marche, Italy, December 2007
ISBN 978-2-930389-29-X
Abstract

The present work consists of two parts: the first one is the design and construction of the new RC-1 facility and its instrumentation at the von Karman Institute, the second one is the creation of a well documented data-base for the detailed flow in a rotating diverging channel at low Reynolds number and at rotation numbers that are relevant for radial impellers and cooling channels.

The newly built Rotating Channel facility allows accurate 2-D, Time-Resolved PIV measurements by acquiring the data directly in the rotating frame. This task was very innovative and there are no similar test-rigs documented in the scientific community capable to perform this type of measurements.

The selection of the instrumentation was driven by the desire to mount it together with the channel on a rotating disk. Preliminary analysis have made clear that it would not be possible to do this with the ‘standard’ PIV syatems (i.e. with a CCD camera and high-power pulsed laser). A compact air-cooled laser diode was selected to illuminate the seeding particles. The high-speed camera selected for this work made the direct measurement of the velocity possible thanks to the possibility to record and store the images in the internal memory. It was proven that the direct acquisition of the relative velocity allows a large improvement of the instantaneous PIV flow field measurement accuracy.

The continuous laser light in combination with a high-speed camera allowed the acquisition of time-resolved PIV measurements. The error assessment of the statistical quantities from the series of measurements indicated the need for a novel approach. Well-established methods in the PIV community allow determining the error in the computation of the mean velocity and turbulence intensity only for not time-resolved measurements. The sampling frequency in conventional PIV is generally very low, typically of the order of 10 Hz, so that each instantaneous flow field is independent. The sampling frequency in the order of kHz, allowed by the high-speed camera, causes dependency between the instantaneous flow fields, and excludes the use of classical techniques to determine the error. In the present work the measurement error on the mean velocity and mean turbulence intensity was retrieved by an original application to PIV data of an existing technique known in the econometric community as dependent circular block bootstrapping.

The flow in a low aspect-ratio diverging channel was investigated at one Reynolds number and three rotational speeds. 2-D PIV measurements were taken in nine planes at the channel inlet and in nine planes halfway between the channel inlet and outlet. In total, 135 single PIV measurements were acquired, each consisting of 2,778 single pictures of the instantaneous flow field. Automated data processing on the VKI cluster made possible to obtain processed results in a reasonable time. Each of the 135 measurements required in fact approximately 10 hours to obtain the mean velocity, the mean turbulence intensity distributions and the errors from the bootstrapping technique.

The mean flow field analysis showed a fairly uniform inlet flow which was only little affected by rotational speed. The boundary layer thickness and the turbulence intensity increased noticeably only on the suction side corners, where a large zone of low momentum flow exists already in stationary conditions.

The boundary layer thickness on the SS, at a location halfway between channel inlet and outlet, increased almost linearly with rotation Conversely, the boundary layer thickness on the PS decreased for low rotation speed and then remained almost constant at higher rotation speeds. Secondary flows generated by rotation caused a re-distribution of the mass flow over the channel height: the mass flow decreased in the channel central part and slightly increased close to the bottom and top walls. Previous studies reported in the literature concluded that rotation causes a stabilization of the SS boundary layer flow and a decrease in turbulence. This work confirmed that the turbulence intensity decreases close to the SS wall, but it also showed that there exists a turbulence peak in the SS boundary layer distant from the wall whose value is little affected by rotation. The distance of that turbulence peak from the wall increases with increasing rotation speed. The turbulence intensity peak slightly increases with increasing rotation on the pressure side wall and remains close to the wall.

The Richardson number distribution showed negative values on the pressure side, indicating a destabilized boundary layer with an increased turbulence activity. Positive values of the Richardson number on the suction side correspond to a boundary layer stabilization with an enhanced risk for separation.

The effects of rotation on 2-D boundary layer turbulence structures have for the first time been reported in the literature with high spatial and temporal resolution. In stationary channels the lateral wall boundary layers as well as the boundary layers on the bottom and top walls are characterized by hairpin vortices. They have been explained according to the model of Adrian. Hairpin vortices characterize the boundary layer also in rotation on the pressure side. Differently, the thick boundary layer on the suction side shows circular coherent structures developing relatively distant from the wall.

The analysis of the velocity spectra both in stationary conditions and with rotation showed low frequency velocity variations at the location of the turbulence peaks. They are related to the passage of the coherent vortical structures recognized by the instantaneous flow field analysis.

A well-documented test case for low Reynolds number flow in rotating diverging channels has been created and allows testing the reliability of the turbulence models implemented in Navier-Stokes solvers.

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