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Research Papers

Characterization of Transition to Turbulence for Blood in a Straight Pipe Under Steady Flow Conditions

[+] Author and Article Information
Dipankar Biswas, David M. Casey

Department of Mechanical Engineering,
The University of Akron,
Akron, OH 44325

Douglas C. Crowder, Yang H. Yun

Department of Biomedical Engineering,
The University of Akron,
Akron, OH 44325

David A. Steinman

Department of Mechanical and
Industrial Engineering,
University of Toronto,
Toronto, ON M5S3G8, Canada

Francis Loth

Department of Mechanical Engineering,
The University of Akron,
Akron, OH 44325;
Department of Biomedical Engineering,
The University of Akron,
Akron, OH 44325

1Corresponding author.

Manuscript received October 10, 2014; final manuscript received April 4, 2016; published online June 7, 2016. Assoc. Editor: Ender A. Finol.

J Biomech Eng 138(7), 071001 (Jun 07, 2016) (12 pages) Paper No: BIO-14-1507; doi: 10.1115/1.4033474 History: Received October 10, 2014; Revised April 04, 2016

Blood is a complex fluid that, among other things, has been established to behave as a shear thinning, non-Newtonian fluid when exposed to low shear rates (SR). Many hemodynamic investigations use a Newtonian fluid to represent blood when the flow field of study has relatively high SR (>200 s−1). Shear thinning fluids have been shown to exhibit differences in transition to turbulence (TT) compared to that of Newtonian fluids. Incorrect prediction of the transition point in a simulation could result in erroneous hemodynamic force predictions. The goal of the present study was to compare velocity profiles near TT of whole blood and Newtonian blood analogs in a straight rigid pipe with a diameter 6.35 mm under steady flow conditions. Rheology was measured for six samples of whole porcine blood and three samples of a Newtonian fluid, and the results show blood acts as a shear thinning non-Newtonian fluid. Measurements also revealed that blood viscosity at SR = 200 s−1 is significantly larger than at SR = 1000 s−1 (13.8%, p < 0.001). Doppler ultrasound (DUS) was used to measure velocity profiles for blood and Newtonian samples at different flow rates to produce Reynolds numbers (Re) ranging from 1000 to 3300 (based on viscosity at SR = 1000 s−1). Two mathematically defined methods, based on the velocity profile shape change and turbulent kinetic energy (TKE), were used to detect TT. Results show similar parabolic velocity profiles for both blood and the Newtonian fluid for Re < 2200. However, differences were observed between blood and Newtonian fluid velocity profiles for larger Re. The Newtonian fluid had blunt-like velocity profiles starting at Re = 2403 ± 8 which indicated transition. In contrast, blood did not show this velocity profile change until Re = 2871 ± 104. The Newtonian fluid had large velocity fluctuations (root mean square (RMS) > 20%) with a maximum TKE near the pipe center at Re = 2316 ± 34 which indicated transition. In contrast, blood results showed the maximum TKE at Re = 2806 ± 109. Overall, the critical Re was delayed by ∼20% (p < 0.001) for blood compared to the Newtonian fluid. Thus, a Newtonian assumption for blood at flow conditions near transition could lead to large errors in velocity prediction for steady flow in a straight pipe. However, these results are specific to this pipe diameter and not generalizable since SR is highly dependent on pipe diameter. Further research is necessary to understand this relation in different pipe sizes, more complex geometries, and under pulsatile flow conditions.

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Figures

Grahic Jump Location
Fig. 2

Measured rheology of blood and WG at measured SR from 1 to 1500 s−1. WG rheology showed a Newtonian behavior with a viscosity of 3.65, 4.3, and 3.98 cP for samples 1, 2, and 3, respectively, for SRs > 10 s−1. Blood viscosity at high SR (1000 s−1), was 2.76, 2.76, 3.34, 3.28, 3.54, and 3.42 cP, for samples 1, 2, 3, 4, 5, and 6, respectively. Mean and SEM of the six blood samples and the three individual samples of WG are shown in the inset.

Grahic Jump Location
Fig. 3

Representative micrographs of blood before (left) and after (right) experiment. Images show that erythrocytes retain their physiological toroid morphology before and after the velocity experiment. Cell fragments are not visible, indicating that cells were not mechanically or osmotically lysed during the experiment. No large change in the number of cells was observed, also indicating that cells were not lysed. Additionally, large three-dimensional amorphous clusters of cells linked by dense fibrous masses were not observed, indicating that the blood did not clot during the velocity experiments.

Grahic Jump Location
Fig. 4

Nondimensional unsteady velocity traces measured by DUS at pipe centerline for blood sample 6, first run (A) and WG sample 1, first run (B). Velocity traces from the different flow rates are shown separated on the vertical axis using a consistent shift of 0.5. WG and blood Re are similar at the same flow rate since viscosity was measured to be 3.65 and 3.42 cP at SR = 1000 s−1 for WG and blood, respectively. High frequency velocity fluctuations are visible at Re = 2560 for WG and Re = 2983 for blood indicating TT occurs at a lower Re for a Newtonian fluid than for blood.

Grahic Jump Location
Fig. 5

Velocity profiles measured by DUS for the first runs of six different blood samples (top two rows) and three different WG samples (bottom row), shown as the mean velocity over 3 s normalized by the average velocity over the pipe cross-sectional area for each Re. Error bars show TKE (×10). Multiple Re are shown separated on the horizontal-axis using a shift of 0.5. Results show the change in velocity profile (parabolic to blunt) and increased TKE at a lower Re for WG compared to blood. Data shown are for the first runs of each fluid; similar results were obtained for subsequent runs. A dashed line extends from the wall to the nearest radial measurement location. Note, Re is different for all lines and indicated at the end of each line.

Grahic Jump Location
Fig. 6

PSIL and PSIT quantify velocity profile shape differences for each Re and are defined as the RMS of the difference from a laminar, parabolic-like shape (profile at Re = 1000) for PSIL and a near turbulent, blunt-like shape (profile at Re = 3300) for PSIT. Dot, cross and plus markers represent runs 1, 2 and 3, respectively, for PSIL. Circle, square and diamond markers represent runs 1, 2 and 3, respectively, for PSIT. Arrows indicate line intersection points, Recr,PSI, for run 1.

Grahic Jump Location
Fig. 7

Distribution of TKEmean for seven points near the center (−1.8 to + 1.8 mm) normalized by the area-averaged velocity as a function of Re. The Re at peak TKEmean provided an estimate of when transition occurs, Recr,TKE. Circle, square and diamond markers represent runs 1, 2, and 3, respectively. Arrows indicate points of maximum TKEmean, Recr,TKE, for run 1.

Grahic Jump Location
Fig. 8

Mean Recr over all samples (six for blood and three for WG) for the PSI method when computed based on the viscosity values measured at each SR. The error bars represent the SEM of the sample mean Recr,PSI. The Recr,TKE values, not shown here, were consistently slightly smaller than the Recr,PSI values (2% for blood and 4% for WG).

Grahic Jump Location
Fig. 1

Experimental setup for blood flow DUS studies. Schematic depicts the flow system with the location of pump, cooling systems, turbulator, test section, DUS probe with linear stage, entrance pipe, flow meter probe, heater, and temperature thermistor.

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