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Fluids 2016, 1(4), 42; doi:10.3390/fluids1040042

Reynolds Stresses and Hemolysis in Turbulent Flow Examined by Threshold Analysis

1
School of Chemical, Biological, and Materials Engineering, University of Oklahoma, Norman, OK 73019, USA
2
School of Chemical, Biological, and Materials Engineering; Institute for Biomedical Engineering, Science and Technology, University of Oklahoma, Norman, OK 73019, USA
*
Author to whom correspondence should be addressed.
Academic Editors: Mehrdad Massoudi and Wei-Tao Wu
Received: 6 September 2016 / Revised: 25 November 2016 / Accepted: 13 December 2016 / Published: 21 December 2016
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Abstract

Use of laminar flow-derived power law models to predict hemolysis with turbulence remains problematical. Flows in a Couette viscometer and a capillary tube have been simulated to investigate various combinations of Reynolds and/or viscous stresses power law models for hemolysis prediction. A finite volume-based computational method provided Reynolds and viscous stresses so that the effects of area-averaged and time-averaged Reynolds stresses, as well as total, viscous, and wall shear on hemolysis prediction could be assessed. The flow computations were conducted by using Reynolds-Averaged Navier-Stokes models of turbulence (k-ε and k-ω SST) to simulate four different experimental conditions in a capillary tube and seven experimental conditions in a Couette viscometer taken from the literature. Power law models were compared by calculating standard errors between measured hemolysis values and those derived from power law models with data from the simulations. In addition, suitability of Reynolds and viscous stresses was studied by threshold analysis. Results showed there was no evidence of a threshold value for hemolysis in terms of Reynolds and viscous stresses. Therefore, Reynolds and viscous stresses are not good predictors of hemolysis. Of power law models, the Zhang power law model (Artificial Organs, 2011, 35, 1180–1186) gives the lowest error overall for the hemolysis index and Reynolds stress (0.05570), while Giersiepen’s model (The International journal of Artificial Organs, 1990, 13, 300–306) yields the highest (6.6658), and intermediate errors are found through use of Heuser’s (Biorheology, 1980, 17, 17–24) model (0.3861) and Fraser’s (Journal of Biomechanical Engineering, 2012, 134, 081002) model (0.3947). View Full-Text
Keywords: computational fluid dynamics; red blood cell trauma; turbulence; Reynolds stress; viscous stress; power law model; erythrocyte; prosthetic heart devices computational fluid dynamics; red blood cell trauma; turbulence; Reynolds stress; viscous stress; power law model; erythrocyte; prosthetic heart devices
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MDPI and ACS Style

Ozturk, M.; O’Rear, E.A.; Papavassiliou, D.V. Reynolds Stresses and Hemolysis in Turbulent Flow Examined by Threshold Analysis. Fluids 2016, 1, 42.

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