ISSN:
1573-2703
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Technology
Notes:
Abstract The stability of a local laminar shear flow and its transition into turbulent flow is considered as a local phenomenon. This transition may remain local, in which case the flow field is partially laminar and partially turbulent, or it may spread and make the whole field turbulent. One of the applications of this analysis is the prediction of local heat-convection rates, which are enhanced by local turbulence. Another application is in heart-lung blood pumps, where excessive shear rates are detrimental to red blood cells. The analysis is Lagrangian, which concentrates on the stability of a fluid particle in maintaining its position in a laminar shear flow. This stability is shown to depend on the magnitude of a non-dimensional parameter, namely the local Reynolds numberRe L =ha 2/v whereh is the local shear rate,a is the particle radius andv is the fluid's kinematic viscosity. It is shown that when, locally,Re L 〉 530, the flow is, locally, unstable. The application of this criterion is simple and direct, and in certain cases it can be shown that the resulting unstable flow is indeed turbulent. Because the analysis relies on an experimental coefficient which has been obtained for a rigid sphere, rather than for a fluid particle, the criterion is introduced at this stage as a conjecture. Several examples are presented which demonstrate the criterion's ability to yield correct predictions for instability.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00129901
Permalink