1998 Heat Transfer Committee Best Paper Award: Complementary Velocity and Heat Transfer Measurements in a Rotating Cooling Passage With Smooth Walls

Abstract

An experimental investigation was conducted on the internal flowfield of a simulated smooth-wall turbine blade cooling passage. The square cross-sectioned passage was manufactured from quartz for optical accessibility. Velocity measurements were taken using Particle Image Velocimetry for both heated and non-heated cases. Thin film resistive heaters on all four exterior walls of the passage allowed heat to be added to the coolant flow without obstructing laser access. Under the same conditions, an infrared detector with associated optics collected wall temperature data for use in calculating local Nusselt number. The test section was operated with radial outward flow and at values of Reynolds number and Rotation number typical of a small turbine blade. The density ratio was 0.27. Velocity data for the non-heated case document the evolution of the Coriolis-induced double vortex. The vortex has the effect of disproportionately increasing the leading side boundary layer thickness. Also, the streamwise component of the Coriolis acceleration creates a considerably thinned side wall boundary layer. Additionally, these data reveal a highly unsteady, turbulent flowfield in the cooling passage. Velocity data for the heated case show a strongly distorted streamwise profile indicative of a buoyancy effect on the leading side. The Coriolis vortex is the mechanism for the accumulation of stagnant flow on the leading side of the passage. Heat transfer data show a maximum factor of two difference in the Nusselt number from trailing side to leading side. A first-order estimate of this heat transfer disparity based on the measured boundary layer edge velocity yields approximately the same factor of two. A momentum integral model was developed for data interpretation, which accounts for coriolis and buoyancy effects. Calculated streamwise profiles and secondary flows match the experimental data well. The model, the velocity data, and the heat transfer data combine to strongly suggest the presence of separated flow on the leading wall starting at about five hydraulic diameters from the channel inlet for the conditions studied.

Flow field investigations in rotating facilities by means of stationary PIV systems

“…where cpr and δ θ are, respectively, the counts per revolution and the angular accuracy of the selected encoder (δ θ ≈ 1 2 (2π)/(cpr)), δ t θ is the time accuracy of the acquisition counter and n is the revolution speed expressed in rpm. Expression (12) is mainly useful to define the maximum value of N that allows a desired level of δω/ω to be achieved when both cpr and n are known. As an example, equation ( 12) is applied to the case n = 10 4 rpm and an encoder with 5000 cpr.…”

“…with the use of a simple meter. An indirect procedure has been used by [1,8,12,14], but unfortunately these works do not provide a complete description of the methodology used and a clear statement of the associated uncertainty. A simple procedure is presented below which allows the desired accuracy to be attained.…”

“…In the indirect approach, once the peripheral velocity has been determined, it must be subtracted from the absolute velocity data acquired by the system to retrieve the relative velocity field. This can be performed either by post-processing the instantaneous absolute velocity fields, as done by most of the authors cited in the introduction, or by pre-processing the PIV image pairs before applying the cross-correlation, as proposed by Bons and Kerrebrock [12]. The former method is by far the most simple and less time consuming, but the results may be affected by high uncertainty when the peripheral velocity is much higher than the relative one, as shown by Di Sante et al [21].…”

“…A first example of PIV investigation of the relative flow field inside cooling channels for gas turbine blades is presented by Bons and Kerrebrock [12]. They used a fixed PIV system synchronized in the phase-locked mode with the test section.…”

“…According to the error propagation theory [22], Di Sante et al [21] concluded that the error associated with an indirect measure grows quadratically with increasing ratio of the absolute and relative velocity moduli, so providing completely unreliable data when the peripheral velocity is much higher than the relative one. However, the error analysis by Di Sante et al [21] suffers the approximation that the uncertainty in the evaluation of the peripheral velocity was completely neglected, and they did not consider the possibility of data pre-processing as done by Bons and Kerrebrock [12].…”