Unsteady separation processes at large finite, Reynolds number, Re, are considered,
as well as the possible relation to existing descriptions of boundary-layer separation
in the limit Re → ∞. The model problem is a fundamental vortex-driven three-dimensional flow,
believed to be relevant to bursting near the wall in a turbulent
boundary layer. Bursting is known to be associated with streamwise vortex motion,
but the vortex/wall interactions that drive the near-wall flow toward breakdown have
not yet been fully identified. Here, a simulation of symmetric counter-rotating vortices
is used to assess the influence of sustained pumping action on the development of a
viscous wall layer. The calculated solutions describe a three-dimensional flow at finite
Re that is independent of the streamwise coordinate and consists of a crossflow plane
motion, with a developing streamwise flow. The unsteady problem is constructed to
mimic a typical cycle in turbulent wall layers and numerical solutions are obtained
over a range of Re. Recirculating eddies develop rapidly in the near-wall flow, but
these eddies are eventually bisected by alleyways which open up from the external
flow region to the wall. At sufficiently high Re, an oscillation was found to develop in
the streamwise vorticity field near the alleyways with a concurrent evolution of a local
spiky behaviour in the wall shear. Above a critical value of Re, the oscillation grows
rapidly in amplitude and eventually penetrates the external flow field, suggesting
the onset of an unstable wall-layer breakdown. Local zones of severely retarded
streamwise velocity are computed which are reminiscent of the low-speed streaks
commonly observed in turbulent boundary layers. A number of other features also
bear a resemblance to observed coherent structure in the turbulent wall layer.
Water hammer transients in a pipe line with an entrapped air pocket are analyzed with three one-dimensional models of varying complexity. The most simple model neglects the influence of gas-liquid interface movement on wave propagation through the liquid region and assumes uniform compression of the entrapped noncondensable gas. In the most complex model, the full two-region wave propagation problem is solved for adjoining gas and liquid regions with time varying domains. An intermediate model which allows for time variation of the liquid domain, but assumes uniform gas compression, is also considered. Calculations are carried out for a wide range of initial system pressure ranging from 0.101 MPa (14.7 psia) to 6.89 MPa (1000 psia). A step increase in pressure equal to 5 times the initial system pressure is imposed at the pipe inlet and the pressure response of the system is investigated. Results show that time variation of the liquid domain and nonuniform gas compression can be neglected for initial air volumes comprising 5% or less of the initial pipe volume. The uniform compression model with time-varying liquid domain captures all of the essential features predicted by the full two-region model for the entire range of pressure and initial gas volume considered in the study, and it is the recommended model for analysis of waterhammer in pipe lines with entrapped air.
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