The flow of a power-law fluid in the near-wake of a flat plate. Zhou, M.; Ladeinde, F.; and Bluestein, D. Physics of Fluids, 18:088102-088105, 2006.
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The analysis of the near-wake flow downstream of a flat plate is reported in this paper for the case of a non-Newtonian (power-law) constitutive model. To our knowledge, the present paper is the first to address this problem, as previous work on near-wakes has been limited to the use of a Newtonian model. The motivation for this work comes from the biomedical engineering problem of blood flow around the bileaflet of a mechanical heart valve. In the present paper, the series method has been used to calculate the flow near the centerline of the wake, while an asymptotic method has been used for larger distances from the centerline. The effects of power-law inlet conditions on the wake flow are reported for various values of the power-law index nn, within the range 0.7≤n≤1.3. The present analysis has been successfully validated by comparing the results for n=1 to the near-wake results by Goldstein [Proc. Cambridge Philos. Soc.26, 1 (1930)]. We generalized the equations for arbitrary values of nn, without any special considerations for n=1. Therefore, the accurate results observed for n=1 validate our procedure as a whole. The first major finding is that a fluid with smaller nn develops faster downstream, such that decreasing nn leads to monotonically increasing velocities compared to fluids with large nn values. Another finding is that the non-Newtonian effects become more significant as the downstream distance increases. Finally, these effects tend to be more pronounced in the vicinity of the wake centerline compared to larger y locations.
@article{z62,
 author = {Zhou, M. and Ladeinde, F. and Bluestein, D.},
 year = {2006},
 title = {The flow of a power-law fluid in the near-wake of a flat plate},
 journal = {Physics of Fluids},
 volume = {18},
 issue = {8},
 pages = {088102-088105},
 url_Paper={/labs/dbluestein/PDF/Zhou_2006_power_law_fluid_flat_plate.pdf},
 url_Link = {https://doi.org/10.1063/1.2338825},
 abstract = {The analysis of the near-wake flow downstream of a flat plate is reported in this paper for the case of a non-Newtonian (power-law) constitutive model. To our knowledge, the present paper is the first to address this problem, as previous work on near-wakes has been limited to the use of a Newtonian model. The motivation for this work comes from the biomedical engineering problem of blood flow around the bileaflet of a mechanical heart valve. In the present paper, the series method has been used to calculate the flow near the centerline of the wake, while an asymptotic method has been used for larger distances from the centerline. The effects of power-law inlet conditions on the wake flow are reported for various values of the power-law index nn, within the range 0.7≤n≤1.3. The present analysis has been successfully validated by comparing the results for n=1 to the near-wake results by Goldstein [Proc. Cambridge Philos. Soc.26, 1 (1930)]. We generalized the equations for arbitrary values of nn, without any special considerations for n=1. Therefore, the accurate results observed for n=1 validate our procedure as a whole. The first major finding is that a fluid with smaller nn develops faster downstream, such that decreasing nn leads to monotonically increasing velocities compared to fluids with large nn values. Another finding is that the non-Newtonian effects become more significant as the downstream distance increases. Finally, these effects tend to be more pronounced in the vicinity of the wake centerline compared to larger y locations.},
 type = {1. Peer-Reviewed Journal Papers}
}
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