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Research Papers: Techniques and Procedures

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

[+] Author and Article Information
Raquel Faria

Polytechnic Institute of Coimbra,
ISEC,
Rua Pedro Nunes—Quinta da Nora,
Coimbra 3030-199, Portugal;
ADAI-LAETA,
Department of Mechanical Engineering,
University of Coimbra,
Polo II,
Coimbra 3030-788, Portugal
e-mail: rfaria@isec.pt

Almerindo D. Ferreira

ADAI-LAETA,
Department of Mechanical Engineering,
University of Coimbra,
Polo II,
Coimbra 3030-788, Portugal
e-mail: almerindo.ferreira@dem.uc.pt

A. M. G. Lopes

ADAI-LAETA,
Department of Mechanical Engineering,
University of Coimbra,
Polo II,
Coimbra 3030-788, Portugal
e-mail: antonio.gameiro@dem.uc.pt

Antonio C. M. Sousa

Mem. ASME
Department of Mechanical Engineering,
University of New Brunswick,
P.O. Box 4400,
Fredericton, NB E3B 5A3, Canada
e-mail: asousa@unb.ca

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received October 4, 2016; final manuscript received April 10, 2017; published online July 6, 2017. Assoc. Editor: Mark R. Duignan.

J. Fluids Eng 139(10), 101401 (Jul 06, 2017) (10 pages) Paper No: FE-16-1651; doi: 10.1115/1.4036668 History: Received October 04, 2016; Revised April 10, 2017

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.

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Figures

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Fig. 1

Schematic of experimental apparatus—top view (dimensions in meters)

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Fig. 2

Geometry of the Irwin probes used (dimensions in millimeters)

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Fig. 3

Irwin probes (patterned dots) positioning. Test section with mean pressure sections (dashed lines) and static pressure taps (solid dots) (Fig. 1) (dimensions in meters).

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Fig. 4

Repeatability tests of representative case AR4 for different values of Re (five tests for each Re). Normalized standard deviation (symbols—left vertical axis) and absolute deviation (bars—right vertical axis): (a) mean static pressure and (b) Irwin probe (top face at x/Lmax = 0.64).

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Fig. 5

Influence of the Reynolds number on the normalized pressure at x/Lmax = 0.20 (all cases). Pressure coefficient (markers) and power law Cp∝Re−2 (solid lines).

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Fig. 6

Cp distribution along the streamwise direction of the duct for different values of Re (case AR3 and case AR4)

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Fig. 7

Comparison of the present experimental data against smooth circular tube predictions [36]—Eq. (13)

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Fig. 9

Assessment of the effect of longitudinal placement (a) and (b), transversal placement (c), and comparison between top and bottom faces (d) on the pressure measurement by the Irwin probes of representative case AR3

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Fig. 8

Assessment of the influence of the characteristic length scale on the friction coefficient; markers correspond to the experimental values, and lines (legend) represent values obtained with a semi-empirical relation [26]—Eq. (4)

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Fig. 10

Calibration curve (τw=0.0257×ΔpI0.818, with  R2=0.9881) for the Irwin probes located at x/Lmax = 0.64 (hollow markers correspond to top face and filled markers to the bottom face)

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Fig. 11

Comparison between experimental and correlated values of the wall shear stress; lines correspond to the calibration curve, Eq. (15), and markers were obtained with Eq. (10)

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