Representative Diameters

Thep and q denote the integral exponents of D in the respective summations, and thereby expHcitiy define the diameter that is being used. and are the number and representative diameter of sampled drops in each size class i For example, the arithmetic mean diameter, is a simple average based on the diameters of all the individual droplets in the spray sample. The volume mean diameter, D q, is the diameter of a droplet whose volume, if multiphed by the total number of droplets, equals the total volume of the sample. The Sauter mean diameter, is the diameter of a droplet whose ratio of volume-to-surface area is equal to that of the entire sample. This diameter is frequendy used because it permits quick estimation of the total Hquid surface area available for a particular industrial process or combustion system. Typical values of pressure swid atomizers range from 50 to 100 p.m. 

Cross-sectional aiea allocated to light phase, sq ft Area of particle projected on plane normal to direction of flow or motion, sq ft Cross-sectional area at top of V essel occupied by continuous hydrocarbon phase, sq ft Actual flow at conditions, cu ft/sec Constant given in table Volume fiaction solids Overall drag coefficient, dimensionless Diameter of vessel, ft See Dp, min Cyclone diameter, ft Cyclone gas exit duct diameter, ft Hy draulic diameter, ft = 4 (flow area for phase in qiiestion/wetted perimeter) also, D in decanter design represents diameter for heavy phase, ft... 

Since the ratio of any two representative diameters is a unique function of q, Rosin-Rammler distribution function can be rewritten as ... 

Before proceeding with description of detonators, and other items used in HE trains of projectiles, we are giving here brief descriptions of "Principal Parts of Projectiles" "Types of Artillery Projectiles and cutaway views of typical projectiles Principal Parts of Artillery Projectiles Body. The main section of the projectile is called the body. Body diameter represents diameter of the projectile between bourrelet and rotating band. To prevent contact with bare lands, body diameter is less than bourrelet or rotating band diameter (See also Ref 44, p B218-R)... 

Figures represent diameter (in inches) of the oil film resulting from the application of one drop of material,... 

For each box, namely for each ejection, the criterion for taking-off is tested. Previously, it is necessary to determine which particle, that is to say, which size range will be tested. The size range of representative diameter Dp of the particle likely to be carried away by the flow is selected randomly from the size distribution. If all the particles of this size range have taken-off, then an other size range is randomly selected. 

Typical visual meteors are associated with particles with representative diameters ranging from 1 mm to 20 cm. ° The size distribution of interplanetary dust, however, peaks at substantially smaller diameters. Meteoroids... 

Keywords Characteristic drop diameter Cumulative volume fraction Discrete probability function (DPF) Drop size distribution Empirical drop size distribution Log-hyperbolic distribution Log-normal distribution Maximum entropy formalism (MEF) Nukiyama-Tanasawa distribution Number distribution function Probability density function (pdf) Representative diameter Root-normal distribution Rosin-Rammler distribution Upper limit distribution Volume distribution... 

Here, cTm is the distribution width, Dmax the maximum diameter, and D a representative diameter. 

This suggests that constraints can be expressed solely in terms of representative diameters, a vast improvement over the source terms appearing in prior formulations, because it is possible to use other means to predict representative diameters. 

Cousin et al. [19] also advocated new approaches for choosing constraints, based on some representative diameter(s) of the resulting distribution. The first approach was to calculate/o(Z)) for an ensemble of spherical drops from one constraint based on some representative drop diameter and normalization ... 

Constraints should be formulated in terms of representative diameters of the distribution. These diameters must be obtained by some other means. 

A single constraint that involves one representative diameter evidently results in unrealistic/o(D). A second constraint (the partition of surface energy, as used by Ahmadi and Sellens [16]) or an a priori probability function (as used by... 

The representative diameters should be some measure of the distribution sought, i.e., the mean, variance, etc. 

It appears that at least two representative diameters or parameters are required as inputs to produce a realistic/q. It is possible to predict one diameter by using a stability analysis for liquid breakup. However, it appears impossible to predict more than one diameter. This seriously hampers the utility of MEF as a method to predict drop size distributions from first principles. 

Inputs that can be computed now One representative diameter (from instability analysis) No experimental PDFs exist N/A... 

Are there predictions that agree with experiments No. Agreement reached only after adjusting source terms or measuring the representative diameter directly No. No experimental PDFs exist Yes. Full numerical simulations produce satisfactory results... 

Irregular particles of practical interest, most often, cannot be uniquely defined. Their sizes are usually defined based on certain reference properties. The choice of any particular diameter for characterization of an irregular particle depends, in many cases, on the intended application. Unfortunately, in most cases, the correct choice of a representative diameter is uncertain. Many diameters have been defined to characterize the irregular particles. The more common ones are summarized below. 

The primary optimization parameter of porous electrodes is the ideal electrochem-ically active surface area per unit volume sa- rough approximation, the value ECSA is proportional to the amount of the electrocatalytically active material Pt, in the case of PEFC electrodes. It is inversely proportional to the feature size d, which could represent diameters of catalyst particles, of pores in a porous catalytic medium, or of rod-like structures (nanotubes or nanorods), onto which a thin film of catalyst is deposited. On the other hand, is also roughly proportional to the energy density... 

For all fluid-dynamic calculations, it is advisable to correct the Sauter diameter by the sphericity yielding the representative diameter based on equivalent specific surface area d. Equation (3.70) assumes a constant sphericity for all size fractions. For pulverized bituminous coal (<100 pm) sphericities between 0.73 and 0.78 are reported while for coarse bituminous coals (4-22.4 mm) somewhat lower values of 0.66-0.71 occur. For lignite fibers (xylite), sphericity may decrease to 0.38 [114,115]. 

If a one-dimensional flow through a packed bed of granular material is assumed (e.g., in moving-bed gasifiers), the pressure drop over a certain bed height Hbed complies to Equation (3.77). It uses the representative diameter based on equivalent specific surface ds, the density of the gas p, the superficial velocity in the bed u, and the dimensionless bed void fraction e for pressure drop calculation (see also Section 3.12.3.2). 

Experiments were carried out for representative diameter rising velocity of bubble was calculated by dividing the vertical displacement of the center of the bubble (y, z) by a predetermined time interval. This velocity became constant (i.e., reached the terminal velocity B,oo) at a location far below the flat plate. Therefore, the bubble collided with the plate at this terminal velocity. For convenience, the size of a stationary bubble or a sessile bubble just beneath the plate was modeled as shown in Fig. 4.42b. 

Representative diameter D is particle s size, and defined as square root of projected area A of a particle. 

Particles having representative diameters D larger than 3 im were selected randomly on the membrane filters. From five to ten views for each of the filter samples were analysed to yield data of about 800 and 100 particles for the dual-pin/disk tests and the ballon-disk test, respectively. 

In Figs. 9(a) to 9(e) are plotted elongation 0, modified roundness vjt , reflectivity R, contrast C and fibre ratio F against representative diameter D, in which data for particles from a number of different sliding... 

Figure 9. Feature parameters for aluminiium wear particles produced in dual-pin/disk experiments (a) elongation, (b) modified roundness, (c) reflectivity, (d) contrast and (e) fibre ratio plotted against representative diameter...

Figure 10. Reflectivity vs. representative diameter for Type 3 particles 2.8 mm/s, 0.48 N after 50 revolutions...

Secondly, rounded shapes of Types 2 and 3 can be distinguished from the above two types using the shape parameters, although there appears to be no parameter to distinguish between these two. In general. Type 3 particles have larger representative diameters D than Type 2. However, both types share the range between 5 and 20 pm. More detailed analysis of shapes or three-dimensional description may be necessary to identify the two types. 

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