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Droplets size calculation

Pawlowski [432] derived a simulation model for calculating droplet size distributions upon dispersion in the I/L system and tested it on equilibrium distributions [55, 244] and on the time sequence of distributions in the case of suppressed coalescence [392]. In total 6 material systems with 34 distributions in 7 test arrangements were taken into consideration. The volume fraction of the dispersed phase was ipy = 0.001 to 0.20. [Pg.268]

Equation (1.7a) and (1.17b). The calculated droplet sizes were correlated with oil viscosity, and the following equations resulted ... [Pg.68]

The charge on a droplet surface produces a repulsive barrier to coalescence into the London-van der Waals primary attractive minimum (see Section VI-4). If the droplet size is appropriate, a secondary minimum exists outside the repulsive barrier as illustrated by DLVO calculations shown in Fig. XIV-6 (see also Refs. 36-38). Here the influence of pH on the repulsive barrier between n-hexadecane drops is shown in Fig. XIV-6a, while the secondary minimum is enlarged in Fig. XIV-6b [39]. The inset to the figures contains t,. the coalescence time. Emulsion particles may flocculate into the secondary minimum without further coalescence. [Pg.508]

Figure Bl.14.13. Derivation of the droplet size distribution in a cream layer of a decane/water emulsion from PGSE data. The inset shows the signal attenuation as a fiinction of the gradient strength for diflfiision weighting recorded at each position (top trace = bottom of cream). A Stokes-based velocity model (solid lines) was fitted to the experimental data (solid circles). The curious horizontal trace in the centre of the plot is due to partial volume filling at the water/cream interface. The droplet size distribution of the emulsion was calculated as a fiinction of height from these NMR data. The most intense narrowest distribution occurs at the base of the cream and the curves proceed logically up tlirough the cream in steps of 0.041 cm. It is concluded from these data that the biggest droplets are found at the top and the smallest at the bottom of tlie cream. Figure Bl.14.13. Derivation of the droplet size distribution in a cream layer of a decane/water emulsion from PGSE data. The inset shows the signal attenuation as a fiinction of the gradient strength for diflfiision weighting recorded at each position (top trace = bottom of cream). A Stokes-based velocity model (solid lines) was fitted to the experimental data (solid circles). The curious horizontal trace in the centre of the plot is due to partial volume filling at the water/cream interface. The droplet size distribution of the emulsion was calculated as a fiinction of height from these NMR data. The most intense narrowest distribution occurs at the base of the cream and the curves proceed logically up tlirough the cream in steps of 0.041 cm. It is concluded from these data that the biggest droplets are found at the top and the smallest at the bottom of tlie cream.
Atomization. Droplet heatup and evaporation calculations can be done for any droplet size, but are most often carried out to reflect the behavior of a mean-sized droplet. The finer the droplet, the less time required for the various steps in the destmction of the waste. [Pg.57]

Droplet trajectories for limiting cases can be calculated by combining the equations of motion with the droplet evaporation rate equation to assess the likelihood that drops exit or hit the wall before evaporating. It is best to consider upper bound droplet sizes in addition to the mean size in these calculations. If desired, an instantaneous value for the evaporation rate constant may also be used based on an instantaneous Reynolds number calculated not from the terminal velocity but at a resultant velocity. In this case, equation 37 is substituted for equation 32 ... [Pg.57]

After breakup, droplets continue to interact with the surrounding environment before reaching thein final destination. In theory (24), each droplet group produced during primary breakup can be traced by using a Lagrangian calculation procedure. Droplet size and velocity can be deterrnined as a function of spatial locations. [Pg.330]

However, any average drop size is fictitious, and none is completely satisfactory. For example, there is no way in which the high surface and transfer coefficients in small drops can be made avail le to the larger drops. Hence, a process calculation based on a given droplet size describes only what happens to that size and gives at best an approximation to the total mass. [Pg.1409]

Equation 10.7 is used to calculate the settling velocity with an assumed droplet size of 150 pm, which is well below the droplet sizes normally found in decanter feeds. If the calculated settling velocity is greater than 4 x 10-3 m/s, then a figure of 4 x 10 3 m/s is used. [Pg.442]

In order to characterize quantitatively the polydisperse morphology, the shape and the size distribution functions are constructed. The size distribution function gives the probability to find a droplet of a given area (or volume), while the shape distribution function specified the probability to find a droplet of given compactness. The separation of the disconnected objects has to be performed in order to collect the data for such statistics. It is sometimes convenient to use the quantity v1/3 = [Kiropiet/ ]1 3 as a dimensionless measure of the droplet size. Each droplet itself can be further analyzed by calculating the mass center and principal inertia momenta from the scalar field distribution inside the droplet [110]. These data describe the droplet anisotropy. [Pg.228]

The recommended method is from Guidelines for Pressure Relief and Effluent Handling Systems (AIChE-CCPS, 1998). It is an improvement over the method presented in the 7th edition of this Handbook. The procedure involves calculating a terminal velocity for a selected droplet size, then providing enough residence time in the vapor space to allow the droplets to fall from the top of the vessel to the level of liquid collected. Also, the vapor velocity in the separator must not exceed the value above which liquid may Be entrained from the liquid surface in the separator. The tank is treated as a simple horizontal cylinder, neglecting the volume of liquid in the heads. [Pg.88]

MMD/SMD that may be 1.1, 1.2 or 1.5J2491 Thus, once the SMD is calculated, the entire droplet size distribution after primary breakup can be determined. [Pg.162]

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 ... [Pg.248]

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... [Pg.249]

The substantial effect of secondary breakup of droplets on the final droplet size distributions in sprays has been reported by many researchers, particularly for overheated hydrocarbon fuel sprays. 557 A quantitative analysis of the secondary breakup process must deal with the aerodynamic effects caused by the flow around each individual, moving droplet, introducing additional difficulty in theoretical treatment. Aslanov and Shamshev 557 presented an elementary mathematical model of this highly transient phenomenon, formulated on the basis of the theory of hydrodynamic instability on the droplet-gas interface. The model and approach may be used to make estimations of the range of droplet sizes and to calculate droplet breakup in high-speed flows behind shock waves, characteristic of detonation spray processes. [Pg.330]

The solution of the gas flow and temperature fields in the nearnozzle region (as described in the previous subsection), along with process parameters, thermophysical properties, and atomizer geometry parameters, were used as inputs for this liquid metal breakup model to calculate the liquid film and sheet characteristics, primary and secondary breakup, as well as droplet dynamics and cooling. The trajectories and temperatures of droplets were calculated until the onset of secondary breakup, the onset of solidification, or the attainment of the computational domain boundary. This procedure was repeated for all droplet size classes. Finally, the droplets were numerically sieved and the droplet size distribution was determined. [Pg.363]

Droplet collision is a phenomenon inherent in the dense region of a spray. Droplet collisions may lead to local agglomeration that affects the droplet size distribution. There have been considerable efforts in modeling droplet-droplet collisions and coalescence,12291 but the models are still not generally applicable. 1576] Moreover, the calculations in the dense region of a metal spray is much more complicated than in a diesel spray because the physical phenomena and mechanisms in the dense region are not well understood. [Pg.364]

For agiven system of metal/alloy and atomization gas, the 2-D velocity distributions of the gas and droplets in the spray can be then calculated using the above-described models, once the initial droplet sizes and velocities are known from the modeling of the atomization stage, as described in the previous subsection. With the uncoupled solution of the gas velocity field in the spray, the simplified Thomas 2-D nonlinear differential equations for droplet trajectories may be solved simultaneously using a 4th-orderRunge-Kutta algorithm, as detailed in Refs. 154 and 156. [Pg.371]

With the above-described heat transfer model and rapid solidification kinetic model, along with the related process parameters and thermophysical properties of atomization gases (Tables 2.6 and 2.7) and metals/alloys (Tables 2.8,2.9,2.10 and 2.11), the 2-D distributions of transient droplet temperatures, cooling rates, achievable undercoolings, and solid fractions in the spray can be calculated, once the initial droplet sizes, temperatures, and velocities are established by the modeling of the atomization stage, as discussed in the previous subsection. For the implementation of the heat transfer model and the rapid solidification kinetic model, finite difference methods or finite element methods may be used. To characterize the entire size distribution of droplets, some specific droplet sizes (forexample,.D0 16,Z>05, andZ)0 84) are to be considered in the calculations of the 2-D motion, cooling and solidification histories. [Pg.374]

The phase-Doppler method is capable of accurately measuring particle size distribution and velocity J655] The most recent models ofphase-Doppler particle analyzer (PDPA) can generate data of droplet size and velocity simultaneously as a function of time, from that droplet drag can be calculated and clustering phenomenon can... [Pg.431]

Once no has been determined, the hold-up for any particular set of flowrates may be calculated from equation 13.42, the mean droplet size from equation 13.43, and the specific area from equation 13.44. [Pg.757]

In order to obtain the solution desired, a value of Ts is assumed, the vapor pressure of A is determined from tables, and mAs is calculated from Eq. (6.98). This value of mAs and the assumed value of Ts are inserted in Eq. (6.97). If this equation is satisfied, the correct Ts is chosen. If not, one must reiterate. When the correct value of Ts and mAs are found, BT or BM are determined for the given initial conditions Tx or mAco. For fuel combustion problems, mAcc is usually zero however, for evaporation, say of water, there is humidity in the atmosphere and this humidity must be represented as mAco. Once BT and BM are determined, the mass evaporation rate is determined from Eq. (6.87) for a fixed droplet size. It is, of course, much preferable to know the evaporation coefficient (5 from which the total evaporation time can be determined. Once B is known, the evaporation coefficient can be determined readily, as will be shown later. [Pg.346]


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Droplet size

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