Spray droplets Sauter mean diameters

The observed flame features indicated that changing the atomization gas (normal or preheated air) to steam has a dramatic effect on the entire spray characteristics, including the near-nozzle exit region. Results were obtained for the droplet Sauter mean diameter (D32), number density, and velocity as a function of the radial position (from the burner centerline) with steam as the atomization fluid, under burning conditions, and are shown in Figs. 16.3 and 16.4, respectively, at axial positions of z = 10 mm, 20, 30, 40, 50, and 60 mm downstream of the nozzle exit. Results are also included for preheated and normal air at z = 10 and 50 mm to determine the effect of enthalpy associated with the preheated air on fuel atomization in near and far regions of the nozzle exit. Smaller droplet sizes were obtained with steam than with both air cases, near to the nozzle exit at all radial positions see Fig. 16.3. Droplet mean size with steam at z = 10 mm on the central axis of the spray was found to be about 58 /xm as compared to 81 pm with preheated air and 96 pm with normal unheated air. Near the spray boundary the mean droplet sizes were 42, 53, and 73 pm for steam, preheated air, and normal air, respectively. The enthalpy associated with preheated air, therefore, provides smaller droplet sizes as compared to the normal (unheated) air case near the nozzle exit. Smallest droplet mean size (with steam) is attributed to decreased viscosity of the fuel and increased viscosity of the gas. 

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. 

Recently, Razumovskid441 studied the shape of drops, and satellite droplets formed by forced capillary breakup of a liquid jet. On the basis of an instability analysis, Teng et al.[442] derived a simple equation for the prediction of droplet size from the breakup of cylindrical liquid jets at low-velocities. The equation correlates droplet size to a modified Ohnesorge number, and is applicable to both liquid-in-liquid, and liquid-in-gas jets of Newtonian or non-Newtonian fluids. Yamane et al.[439] measured Sauter mean diameter, and air-entrainment characteristics of non-evaporating unsteady dense sprays by means of an image analysis technique which uses an instantaneous shadow picture of the spray and amount of injected fuel. Influences of injection pressure and ambient gas density on the Sauter mean diameter and air entrainment were investigated parametrically. An empirical equation for the Sauter mean diameter was proposed based on a dimensionless analysis of the experimental results. It was indicated that the Sauter mean diameter decreases with an increase in injection pressure and a decrease in ambient gas density. It was also shown that the air-entrainment characteristics can be predicted from the quasi-steady jet theory. 

Whereas few actual values of n for sprays from various fuel injectors are reported, it is usually possible to obtain a fairly reliable estimate of x. This is so because x is uniquely related to various mean droplet diameters solely in terms of n, and data for Sauter mean diameter are rather frequently reported. Sauter mean diameter (SMD) is that diameter representative of the surface area per unit volume which is characteristic of the actual spray. 

The Sauter mean diameters of the spray droplets, D32, both before and after the impingement can be correlated and predicted with Eq. (5.6), which gives reasonable and acceptable fitting of the experimental data. 

According to Assumption (4) above, the specific interface area calculated from the Sauter mean diameter of spray droplets, a, is kept constant. Thus, the integral amount of S02 absorbed within the residence time of the gas and droplets in the effective volume of the reactor, t, can be obtained as... 

Sauter mean diameters of spray droplets with various concentrations of Ca(OH)2 (atomizing... 

The gas-film mass transfer coefficient, kG, was determined based on the Sauter mean diameter of spray droplets. The results show essentially no influence of initial concentration of SOz on kG, suggesting that the process is controlled by diffusion through gas film and that the method proposed for the determination of kG is feasible ... 

Sauter Mean Diameter The diameter of a droplet whose ratio of volume to surface area is equal to that of the complete spray sample. 

The Sauter mean diameter has been found to be the most useful of the above definitions for characterizing the spray produced by a nozzle. It is a good indicator of a spray s performance in complex interactions with a droplet s surface and volume. Applications include spray drying, evaporative cooling, dry scrubbing, gas quenching, and gas absorption (Stavis, 1991). 

The data indicated that droplet-size changes are primarily influenced by injection pressure and orifice size while secondary changes can be attributed to fluid properties, orifice shape, and the nozzle s internal length diameter ratio. This last point was not observed by Dombrowski and Wolfsohn (8) for more conventional swirl spray nozzles. Nevertheless, they present a useful correlation between Sauter mean diameter and operating conditions. 

Sauter mean diameter (D32) is reported frequently for fuel injectors because it is representative of the droplet size that has the same volume/surface area ratio as the whole spray. It is given by ... 

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. 

The mean size of droplet represents a single value that characterizes the whole spray distribution. This value, together with the size distribution, defines the spray characteristics. Many papers have appeared on the subject of drop size prediction. The so-called Sauter mean diameter seems to be the most suitable mean value to characterize the droplet cloud together with the size distribution. This is defined as the ratio of the total droplet volume to the total droplet surface [23] that is. 

The droplet size of a spray is some average droplet size as discussed in Chap. 23. A commonly reported droplet size is the Sauter mean diameter, SMD or D32. Droplet size depends on the type of nozzle, flow rate, feed pressure and spray pattern. 

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... 

To provide clarity when calculating Sauter mean diameter (D32), an example has been provided below. The SMD measurement represents a one number descriptor used to compare different sprays and is considered industry standard for comparing spray quality. Table 15.1 provides a truncated sampling of a hypothetical spray. For this example, whole numbers are used to signify the number of droplets counted for a given diameter measurement. This data can be used to calculate the SMD for the example outlined below. Equations 15.2-15.4 show an example of how to calculate SMD based on the data provided in Table 15.1. 

Figure 9.11 a, b show the numerical and experimental profiles of the Sauter mean diameter and the mean droplet velocity of a PVP-water spray [42] for a mass inflow rate of 120kg/h at 0.12 m downstream the nozzle exit. Similar to the water spray, the typical hollow-cone shape is well predicted by DQMOM. In particular, the agreement with the experimental results is very good in the spray center, but it is somewhat under-predicted towards the periphery of the spray. This may have the same reasons as discussed for the pure water spray. 

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