Operating Reynolds Number Research Articles

An approach to turbulent incompressible separation under adverse pressure gradients

A separation criterion is developed, relating the maximum pressure-recovery ratio at separation to the skin-friction coefficient at the start of the adverse gradient. This criterion shows very good agreement with six experimental points. A method of computing the skin friction is also given, and it has been applied to three experimental runs; the agreement is good in two cases and poor in the third. The present theory indicates that separation will move upstream with increasing Reynolds number, therefore affecting the scaling procedures from model test to prototypes. The theory also indicates that inviscid pressure profiles must be considered in relation to the desired operational Reynolds number, since the effective pressure gradients and the pressure-recovery ratios will change. The theory is based on the assumptions of dissipative-region similarity under any pressure gradient and of a constant total-head line at a fixed distance from the wall under adverse pressure gradients.

Stable-flow free boundary migration and fractionation of cell mixtures: II. Laminar flow and density gradient stability

In addition to: (1) hydrodynamic feedback (Paper I), † † For convenience the cross references among this group of closely related papers will be written in this simplified style. Paper III will appear in a future number of the Journal. the stable-flow free boundary (STAFLO) solution to flow stability depends upon, (2) a special kind of laminar flow, and (3) density gradient stability. With the maximum operating Reynolds number of approximately 17, there appears ample safety margin in STAFLO experiments before onset of turbulence. Laminar flow demonstrated under the demanding conditions of initial set-up further supports this idea. Steady state STAFLO flow is seen to be a kind of vertical plug flow. Comparison with the velocity relations of ordinary laminar flow illustrates the manner in which the feedback principle overrides these usual relations. Equations for gravitational density gradient stability, previously developed primarily for batch type columns, are a useful starting point for treating this subject in STAFLO experiments. With flow rate as an additional variable, certain limitations inherent in stability requirements of static gradient-columns, e.g. in solution composition, sample capacity, heat dissipation, are removed. Almost arbitrary combinations of steady state density gradients with gradients of composition, conductivity, pH, etc., can be established in STAFLO experiments without the usual gradient mixing devices. A kind of experimental cell behaviour called “clump sedimentation”, related to density gradient instability, is discussed in terms of weak intercellular interactions. Since complete analysis of density gradient stability during migrations must await advances in basic theory of multiple transport processes in solution, the importance of the experimental approach is emphasized.

Models Primarily Dependent on the Reynolds Number

Design, construction, and operation of models of closed-conduit fluid systems, and interpretation of test data; viscous and inertia forces in flowing fluids of such models, and hence Reynolds number, are predominant factors; general rules for model size, construction, instrumentation, operating Reynolds number ranges, and data analysis are given.

Models Primarily Dependent on the Reynolds Number

Design, construction, and operation of models of closed-conduit fluid systems, and interpretation of test data; viscous and inertia forces in flowing fluids of such models, and hence Reynolds number, are predominant factors; general rules for model size, construction, instrumentation, operating Reynolds number ranges, and data analysis are given.