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TECHNICAL PAPERS

# Characterization of the Hydrodynamically Developing Flow in a Microtube Using MTV

[+] Author and Article Information
B. R. Thompson, B. W. Webb

Department of Mechanical Engineering, Brigham Young University, 435 CTB, Provo, UT 84602, USA

D. Maynes

Department of Mechanical Engineering, Brigham Young University, 435 CTB, Provo, UT 84602, USAmaynesrd@et.byu.edu

J. Fluids Eng 127(5), 1003-1012 (May 05, 2005) (10 pages) doi:10.1115/1.1989368 History: Received May 14, 2004; Revised May 05, 2005

## Abstract

Micro-molecular tagging velocimetry $(μMTV)$ has been used to characterize the hydrodynamic developing flow in a microtube inlet with a nominal inner diameter of $180μm$. Velocity profile data at 11 axial locations within the hydrodynamic developing region were acquired using the $μMTV$ approach and the results represent the first characterization of hydrodynamically developing pipe flow at the microscale. The uncertainty in measurements of time-averaged velocity profiles ranged from 6% to 7% of the centerline velocity. The uncertainty in instantaneous measurements is in the range 8%–16% of the peak maximum velocity. Data were taken at Reynolds numbers of 60, 100, 140, 290, and 350. The data suggest the formation of a vena contracta with either locally turbulent flow or unsteady laminar flow separation early in the tube for the larger Reynolds (Re) numbers, which is quite different from macroscale experiment or numerical simulation where a vena-contracta is not observed for $Re<500$. The velocity profiles obtained very near the tube entrance exhibited a uniform velocity core flow surrounded by regions of relatively stagnant fluid in the near wall regions. The size of the inferred recirculation zones, measured velocity rms, and maximum shear rates all exhibit increasing magnitude with increasing Reynolds number. The velocity profiles were observed to evolve in the downstream direction until the classical parabolic distribution existed. The total hydrodynamic entry length agrees well with values published in the literature for laminar flow with a uniform inlet velocity, despite the existence of the observed vena contracta.

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Copyright © 2005 by American Society of Mechanical Engineers
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## Figures

Figure 1

Schematic illustration of flow through a sudden contraction

Figure 2

Illustration of velocity determination from deformed and undeformed MTV lines

Figure 3

Schematic illustration (top) and photograph of the entry length experimental test section and setup

Figure 9

Normalized time averaged velocity profiles for Re=60, 100, 150, 290, and 350, all obtained at the first axial measurement location for each data set, X≈0.5

Figure 10

Average difference from fully developed laminar pipe flow theory (top panel) and the maximum difference from fully developed laminar pipe flow theory (bottom panel) plotted as a function of x∕DRe for all five Reynolds numbers explored

Figure 11

Normalized centerline velocities (top panel) and normalized maximum in the streamwise velocity rms (bottom panel) plotted vs. x∕DRe for all five Reynolds numbers

Figure 4

Normalized measured velocity distribution, U, and induced error due to wall-normal fluid velocity, Un, vs. R for Re=350 and X=1.3

Figure 5

Deformed MTV lines in a 180μm diameter tube at X=0.5 (top), 2.1 (middle), and 23.2 (bottom) for Re=350. Flow is from right to left and each panel represents an average of 190 instantaneous images.

Figure 6

Normalized time averaged velocity profiles at Re=350 and at X=0.5, 1.3, 2.1, 3.0, 3.8, and 6.0 in the top panel, and X=8.2, 10.4, 12.7, 16.3, and 23.2 in the bottom panel

Figure 7

Normalized time averaged velocity profiles at Re=60 and at X=0.4, 0.7, 1.0, 1.8, and 2.4

Figure 8

Normalized profiles of the streamwise velocity rms for Re=350 at axial locations of X=0.5, 2.1, 6.0, and 16.3

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