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Research Papers: Techniques and Procedures

Wall Shear Stress Determination in a Small-Scale Parallel Plate Flow Chamber Using Laser Doppler Velocimetry Under Laminar, Pulsatile and Low-Reynolds Number Turbulent Flows

[+] Author and Article Information
Hamed Avari

Advanced Fluid Mechanics Research Group,
Department of Mechanical and
Materials Engineering,
University of Western Ontario,
London, ON N6A 5B8, Canada
e-mail: havari@uwo.ca

Kem A. Rogers

Department of Anatomy and Cell Biology,
University of Western Ontario,
London, ON N6A 5B8, Canada
e-mail: kem.rogers@schulich.uwo.ca

Eric Savory

Advanced Fluid Mechanics Research Group,
Department of Mechanical and
Materials Engineering,
University of Western Ontario,
London, ON N6A 5B8, Canada
e-mail: esavory@eng.uwo.ca

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received April 6, 2017; final manuscript received January 5, 2018; published online March 13, 2018. Assoc. Editor: Elias Balaras.

J. Fluids Eng 140(6), 061404 (Mar 13, 2018) (15 pages) Paper No: FE-17-1212; doi: 10.1115/1.4039158 History: Received April 06, 2017; Revised January 05, 2018

The parallel plate flow chamber (PPFC) has gained popularity due to its applications in fields such as biological tissue engineering. However, most of the studies using PPFC refer to theoretical relations for estimating the wall shear stress (WSS) and, hence, the accuracy of such quantifications remains elusive for anything other than steady laminar flow. In the current study, a laser Doppler velocimetry (LDV) method was used to quantify the flow in a PPFC (H = 1.8 mm × W = 17.5 mm, Dh = 3.26 mm, aspect ratio = 9.72) under steady Re = 990, laminar pulsatile (carotid Re0-mean = 282 as well as a non-zero-mean sinusoidal Re0-mean = 45 pulse) and low-Re turbulent Re = 2750 flow conditions. A mini-LDV probe was applied, and the absolute location of the LDV measuring volume with the respect to the wall was determined using a signal monitoring technique with uncertainties being around ±27 μm. The uniformity of the flow across the span of the channel, as well as the WSS assessment for all the flow conditions, was measured with the uncertainties all being less than 16%. At least two points within the viscous sublayer of the low-Re turbulent flow were measured (with the y+ for the first point < 3) and the WSS was determined using two methods with the differences between the two methods being within 5%. This paper for the first time presents the experimental determination of WSS using LDV in a small-scale PPFC under various flow conditions, the challenges associated with each condition, and a comparison between the cases. The present data will be useful for those conducting biological or numerical modeling studies using such devices.

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Figures

Grahic Jump Location
Fig. 1

Layout of the LDV system components and probe positioning with respect to the PPFC test section

Grahic Jump Location
Fig. 2

Reference coordinate system, working section dimensions, and measurement location for spanwise u-velocity at x/L = 0, 0.5 and 1, 2y/H = 0.33 (A, B, and C) and measurement location for streamwise u-velocity x/L = 0, 0.5 and 1, z/W = 0 (D, E, and F)

Grahic Jump Location
Fig. 3

Percent shear rate (defined as γ=dU/dy) error for a second-order polynomial fit (np = 2) using Np = 3, 4, 5, and 6 points for various initial points d1 = 0.04, 0.09, 0.13, 0.18, and 0.22 (d1 = 2y1/H)

Grahic Jump Location
Fig. 4

(a) Comparison of streamwise time-averaged mean velocity U normalized by Ub across the width of the channel with the analytical solution from Eq. (13) for −1 < 2z/W < 1 at locations A, B, and C for Re = 990. The average deviation of the experimental data points from the analytical solution at locations A, B, and C is ±2.4, ±2.9, and ±4.4%, respectively; (b) Comparison of streamwise time-averaged mean velocity U normalized by bulk velocity Ub with the analytical solution from Eq. (13) for 0 < 2y/H < 1 at locations D, E, and F for Re = 990. The average deviation of the experimental data points from the analytical solution at locations D, E, and F is ±1.8, ±3.2, and ±6.2%, respectively.

Grahic Jump Location
Fig. 5

(a) Bulk velocity (Ub) and phase-averaged streamwise velocity <u> normalized by Ub,max at location E and 2y/H = 1 versus normalized time (t*) for the carotid pulse; (b) Phase-averaged streamwise velocity profiles <u> normalized by Ub,max at 2y/H = 0.33, 0.66, and 1 for location E for the carotid pulse (error bars are indication of experimental uncertainty)

Grahic Jump Location
Fig. 6

(a) Streamwise phase-averaged velocity profiles <u> normalized by Ub,max at locations A, B and C for the phases t1* = 0.19, t2* = 0.33, and t3* = 0.85 across the span of the channel −1 < 2z/W < 1 for the carotid pulse; (b) Streamwise phase-averaged velocity profiles <u> normalized by Ub,max at locations D, E, and F for the phases t1*, t2* and t3* = 0.19, 0.63, and 0.85 across the channel half height 0 < 2y/H < 1 for the carotid pulse (error bars are indication of experimental uncertainty and are drawn on one data set only for the clarity of the graph)

Grahic Jump Location
Fig. 7

Phase-averaged WSS <τw> versus normalized time at locations D, E, and F for the carotid pulse

Grahic Jump Location
Fig. 8

(a) Bulk velocity (Ub) and phase-averaged streamwise velocity <u> normalized by Ub,max at location E and 2y/H = 1 versus normalized time (t*) for the non-zero-mean sinusoidal pulse and (b) Phase-averaged streamwise velocity profiles <u> by Ub,max at 2y/H = 0.33, 0.66 and 1 for location E versus normalized time (t*) for the non-zero-mean sinusoidal pulse (error bars are indication of experimental uncertainty)

Grahic Jump Location
Fig. 9

(a) Streamwise phase-averaged velocity profiles <u> normalized by Ub,max at locations A, B, and C for the phases t1* = 0.28, t2* = 0.50, and t3* = 0.72 across the span of the channel −1 < 2z/W < 1 for the non-zero-mean sinusoidal pulse; (b) streamwise phase-averaged velocity profiles <u> normalized by Ub,max at locations D, E, and F for the phases t1* = 0.28, t2* = 0.50, and t3* = 0.72 across the channel half height 0 < 2y/H < 1 for the non-zero-mean sinusoidal pulse (error bars are indication of experimental uncertainty and are drawn on one data set only for the clarity of the graph). Solid and dashed lines representing the velocity profiles from Hale et al. [75] for a cosine pressure pulse at phase angles of 0 deg, 90 deg, and 180 deg (the values are not drawn to scale) for comparison between the profile shapes between the current versus Hale et al. [75].

Grahic Jump Location
Fig. 10

Phase-averaged WSS <τw> versus normalized time (t*) at locations D, E, and F for the non-zero-mean sinusoidal pulse

Grahic Jump Location
Fig. 11

(a) Mean streamwise velocity U profiles normalized by bulk velocity Ub at locations D, E and F at 0 < 2y/H < 1 for the low-Re turbulent flow (Re0 = 1830); (b) Streamwise mean velocity distribution in the near wall region of the channel (y < 280 μm, 0 < 2y/H < 0.311) along with polynomial fitting with np = 2 for both the measured and corrected profile at y = 0 (location E; Re0 = 1830)

Grahic Jump Location
Fig. 12

Turbulence intensities in x and y directions (urms and vrms, respectively) normalized by the friction velocity across the channel half-height in wall units (y+) at locations D, E, and F for the low-Re turbulent flow with Re = 2750 (Re0 = 1830) compared with experimental data from Kim et al. [84]

Grahic Jump Location
Fig. 13

NRSS (−u′v′¯/uτ2) versus y+ at locations D, E, and F for the low-Re turbulent flow with Re0 = 1830 (Re = 2750) compared with results reported by Li et al. for Re0 = 1837 [88]

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