Mean droplet diameter arithmetic

Plotting droplet size data on an arithmetic-probability graph paper will generate a straight line if the data follow normal distribution. Thus, the mean droplet diameter and standard deviation can be determined from such a plot. 

In many applications, a mean droplet size is a factor of foremost concern. Mean droplet size can be taken as a measure of the quality of an atomization process. It is also convenient to use only mean droplet size in calculations involving discrete droplets such as multiphase flow and mass transfer processes. Various definitions of mean droplet size have been employed in different applications, as summarized in Table 4.1. The concept and notation of mean droplet diameter have been generalized and standardized by Mugele and Evans.[423] The arithmetic, surface, and volume mean droplet diameter (D10, D2o, and D30) are some most common mean droplet diameters ... 

This corresponds to the ratio of arithmetic mean volume and arithmetic mean droplet surface and comprises the droplet size distribution of the investigated emulsions. For a theoretical monomodal size distribution [36] the Sauter diameter is approx, two times higher than the arithmetic diameter, because the influence of larger but less numerous droplets is more pronounced. 

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. 

Arithmetic Mean Diameter The average diameter of all the droplets in the spray sample. 

Note d 2 the Sauter mean diameter defined as the arithmetic mean of several measurements of the Sauter diameter SD (SD = 6 V/A with V the volume and A the surface area of the particle), d, the volume median diameter, which refers to the midpoint droplet size (mean), where half of the volume of spray is in droplets smaller and half of the volume is in droplets larger than the mean, p, p, and a, respectively the density, the viscosity, and the surface tension of liquid, D, the diameter of the disk, Q, the flow rate, and o> the angular speed of the disk. 

There are multiple spray measurements used to quantify an injectors spray quality. Some of these measurements include DIO (arithmetic mean), D32 (Sauter mean diameter), D31 (evaporative mean diameter), DvO.9, and droplet distribution curve. Figure 15.9 provides a description and equation used to calculate SMD, DIO, and D31. Figure 15.10 shows a typical droplet distribution curve with an overlay to show the DvO.9 calculation. The DvO.9 value represents the point where... 

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