Rosin-Rammler relation

Size Distribution Relationships. Different models have been used to describe the size distribution of particles experiencing single and multiple fractures. A model based on fracture at the site of the weakest link and a distribution of weakest links in the system gave results that could be described as well by the Rosin-Rammler relation (56). The latter is based on the concept that fracture takes place at pre-existing flaws that are distributed randomly throughout the particle. 

Milling of coal or coke produces a powder called pulverized fuel which contains particles of a wide range of sizes. As we saw in Chapter 3, the distance at which a particle in a particle-laden jet will travel in a combustion chamber plays a role in the damping of the jet s turbulent energy. Therefore theoretical analysis of combustion must take the particle size distribution of the fuel into account. Pulverized fuel fineness is therefore an important parameter in the modeling of coal combustion. An analytical expression of particle size distribution that has found a wide application for expressing the fineness of pulverized fuel is the Rosin-Rammler relation. The relationship is given by (Field et al., 1964)... 

Cylinder radius or kiln internal radius, (m, ft), or Specific gas constant (kJ/kg K), Resistance to heat flow, also Rosin-Rammler relation Reynolds Number (-)... 

To characterize a droplet size distribution, at least two parameters are typically necessary, i.e., a representative droplet diameter, (for example, mean droplet size) and a measure of droplet size range (for example, standard deviation or q). Many representative droplet diameters have been used in specifying distribution functions. The definitions of these diameters and the relevant relationships are summarized in Table 4.2. These relationships are derived on the basis of the Rosin-Rammler distribution function (Eq. 14), and the diameters are uniquely related to each other via the distribution parameter q in the Rosin-Rammler distribution function. Lefebvre 1 calculated the values of these diameters for q ranging from 1.2 to 4.0. The calculated results showed that Dpeak is always larger than SMD, and SMD is between 80% and 84% of Dpeak for many droplet generation processes for which 2left-hand side of Dpeak. The ratio MMD/SMD is... 

Related Calculations. Sometimes the Rosin-Rammler equation is used to represent the size distribution graphically. The dashed line on Fig. 13.1 corresponds to the Rossin-Rammler equation in the form y = 100 — lOOexp [—(x/A)b], where, in this case, A = 1558 and b = 1.135. 

Knudsen s model led to the prediction that, if linear kinetics were followed, the age at which 50% of the cement has hydrated is proportional to the fineness constant (or xj in the Rosin/Rammler distribution (equation 4.1) for parabolic kinetics, it predicted that this age is proportional to (K40). Evidence was presented in support of this conclusion for cements considered to follow linear kinetics. The theory did not predict any relation to the breadth of the particle size distribution, which is represented by the slope of the Rosin-Rammler curve. 

Measurements have been made of the combustion characteristics of an air blast kerosene spray flame and of droplet sizes within the spray boundary of isothermal sprays. Specific techniques were used to measure velocity, temperature, concentration, and droplet size. Velocities measured by laser anemometer in spray flames in some areas are 400% higher than those in isothermal sprays. Temperature profiles are similar to those of gaseous diffusion flames. Gas analyses indicate the formation of intermediate reactants, e.g., CO and Hg, in the cracking process. Rosin-Rammler mean size and size distribution of droplets in isothermal sprays are related to atomizer efficiency and subsequent secondary atomizer/vaporization effects. 

The Rosin-Rammler distribution is used to represent sprays from nozzles. It is anpirical and relates the volume percentage oversize Vq to droplet diameter D. The mathematical form is as follows [23] ... 

Rosin-Rammler Equation. An equation relating to fine grinding for most powders that have been prepared by grinding, the relationship between R, the residue remaining on any particular sieve, and the grain-size in microns (x) is exponential ... 

Because of such factors as wave formation, jet turbulence, and secondary breakup, the drops formed are not of uniform size. Various ways of describing the distribution, including the methods of Rosin and Rammler (R9) and of Nukiyama and Tanasawa (N3), are discussed by Mugele and Evans (M7). A completely theoretical prediction of the drop-size distribution resulting from the complex phenomena discussed has not yet been obtained. However, for simple jets issuing in still air, the following approximate relation has been suggested (P3) ... 

---