On the Calibration of Irwin Probes for Flow in Rectangular Ducts With Different Aspect Ratios

Abstract

In this work, the suitability of pressure probes, commonly known as Irwin probes, to determine the local wall shear stress was evaluated for steady turbulent flow in rectangular ducts. Pressure measurements were conducted in the fully developed flow region of the duct and both the influence of duct aspect ratio (AR) (from 1:1.03 to 1:4.00) and Reynolds number (from 104 to 9 × 104) on the mean characteristics of the flow were analyzed. In addition, the sensitivity of the longitudinal and transversal placement of the Irwin probes was verified. To determine the most appropriate representation of the experimental data, three different characteristic lengths (l*) to describe Darcy's friction coefficient were investigated, namely: hydraulic diameter (Dh), square root of the cross section area (√A), and laminar equivalent diameter (DL). The comparison of the present experimental data for the range of tested Re numbers against the results for turbulent flow in smooth circular tubes indicates similar trends independently of the AR. The selection of the appropriate l* to represent the friction coefficient was found to be dependent on the AR of the duct, and the three tested scales present similar performance. However, the hydraulic diameter, being the commonly employed to compute turbulent flow in rectangular ducts, is the selected characteristic length scale to be used in the present study. A power function-based calibration equation is proposed for the Irwin probes, which is valid for the range of ARs and Reynolds numbers tested.