Reynolds number classification

For steady injection of a liquid through a single nozzle with circular orifice into a quiescent gas (air), the mechanisms of jet breakup are typically classified into four primary regimes (Fig. 3 2)[4°][41][22°][227] according to the relative importance of inertial, surface tension, viscous, and aerodynamic forces. The most commonly quoted criteria for the classification are perhaps those proposed by Ohnesorge)40] Each regime is characterized by the magnitudes of the Reynolds number ReL and a dimensionless number Z ... 

Although the Jet number is used for the classification, it should be noted that the intrinsic characters of a liquid flow depend on the Reynolds number. By combining the Jet number with the Reynolds number and introducing a correction factor for viscosity, the modes and configurations of liquid jet breakup can be clearly defined and described.[41]... 

Perhaps the simplest classification of flow regimes is on the basis of the superficial Reynolds number of each phase. Such a Reynolds number is expressed on the basis of the tube diameter (or an apparent hydraulic radius for noncircular channels), the gas or liquid superficial mass-velocity, and the gas or liquid viscosity. At least four types of flow are then possible, namely liquid in apparent viscous or turbulent flow combined with gas in apparent viscous or turbulent flow. The critical Reynolds number would seem to be a rather uncertain quantity with this definition. In usage, a value of 2000 has been suggested (L6) and widely adopted for this purpose. Other workers (N4, S5) have found that superficial liquid Reynolds numbers of 8000 are required to give turbulent behavior in horizontal or vertical bubble, plug, slug or froth flow. Therefore, although this classification based on superficial Reynolds number is widely used... 

The classification of flames depends on the mixture characteristics of the fuel and oxidizer, and on the interaction between the flow properties and the chemistry. This classification is done by means of dimensionless quantities, namely, the mrbulent Reynolds number, the turbulent Damkohler number, and the turbulent Karlovitz number, respectively defined by... 

However, this classification originally was introduced for jet breakups and not for drop-on-demand breakups with short pressure pulses. Since the Weber number can be written using the Reynolds number and the Ohnesorge number... 

Sedimentation is another classical particle classification and sizing method for liquid-bom particles. Sedimentation methods are based on the rate of settling of particles in a liquid at rest under a gravitational or centrifugal field. The relationship between settling velocity and particle size is reduced to the Stokes equation at low Reynolds numbers ... 

Perhaps a more useful means of quantifying structural data is to use a similarity measurement. These are reviewed by Ludwig and Reynolds (1988) and form the basis of multivariate clustering and ordination. Similarity measures can compare the presence of species in two sites or compare a site to a predetermined set of species derived from historical data or as an artificial set comprised of measurement endpoints from the problem formulation of an ecological risk assessment. The simplest similarity measures are binary in nature, but others can accommodate the number of individuals in each set. Related to similarity measurements are distance metrics. Distance measurements, such as Euclidean distance, have the drawbacks of being sensitive to outliers, scale, transformations, and magnitudes. Distance measures form the basis of many classification and clustering techniques. 

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