Droplet temperature

In this equation, is the gas thermal conductivity the Hquid density the Hquid heat capacity T, the gas temperature the initial droplet temperature and the droplet boiling point. 

In subcooled impact, the initial droplet temperature is lower than the saturated temperature of the liquid of the droplet, thus the transient heat transfer inside the droplet needs to be considered. Since the thickness of the vapor layer may be comparable with the mean free path of the gas molecules in the subcooled impact, the kinetic slip treatment of the boundary condition needs to be applied at the liquid-vapor and vapor-solid interface to modify the continuum system. 

During the subcooled droplet impact, the droplet temperature will undergo significant changes due to heat transfer from the hot surface. As the liquid properties such as density p (T), viscosity /q(7), and surface tension a(T) vary with the local temperature T, the local liquid properties can be quantified once the local temperature can be accounted for. The droplet temperature is simulated by the following heat-transfer model and vapor-layer model. Since the liquid temperature changes from its initial temperature (usually room temperature) to the saturated temperature of the liquid during the impact, the linear... 

During the flight of droplets in the spray, the forced convective and radiative heat exchanges with the atomization gas lead to a rapid heat extraction from the droplets. A droplet undergoing cooling and phase change may experience three states (a) fully liquid, (b) semisolid, and (c) fully solid. If the Biot number of a droplet in all three states is smaller than 0.1, the lumped parameter model 1561 can be used for the calculation of droplet temperature. Otherwise, the distributed parameter model 1541 should be used. 

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. 

Figure 5.8. Calculated droplet temperature evolution along the spray centerline (a) and distribution in the radial direction of the spray (b).

Droplet temperature is of interest in practical spray processes since it influences the associated heat and mass transfer, chemical reactions, and phase changes such as evaporation or solidification. Various forms of Rayleigh, Raman and fluorescence spectroscopies have been developed for measurements of droplet temperature and species concentration in sprays.16471 Rainbow refractometry (thermometry), polarization ratioing thermometry, and exciplex method are some examples of the droplet temperature measurement techniques. 

Several theories have been developed to explain the rainbow phenomena, including the Lorenz-Mie theory, Airy s theory, the complex angular momentum theory that provides an approximation to the Lorenz-Mie theory, and the theory based on Huy gen s principle. Among these theories, only the Lorenz-Mie theory provides an exact solution for the scattering of electromagnetic waves by a spherical particle. The implementation of the rainbow thermometry for droplet temperature measurement necessitates two functional relationships. One relates the rainbow angle to the droplet refractive index and size, and the other describes the dependence of the refractive index on temperature of the liquid of interest. The former can be calculated on the basis of the Lorenz-Mie theory, whereas the latter may be either found in reference handbooks/literature or calibrated in laboratory. 

Polarization ratioing thermometry has been proposed as a means of measuring the refractive index of a droplet and relating it to the droplet temperature. However, this approach does not have the... 

Exciplex methodhas also been proposed for droplet temperature measurement. In an oxygen environment, however, the fluorescence from the exciplex is quenched by the oxygen. In addition, fuel droplets may contain aromatic hydrocarbons that can produce fluorescence emissions, masking the fluorescence spectrum of the dopants used for the temperature determination. 

A non-invasive infrared (IK) method has been developed for the measurement of temperatures of small moving fuel droplets in combustion chambers. 7111 The IR system is composed of two coupled off-axis parabolic mirrors and a MCT LWIR detector. The system was used to measure the temperature variations in a chain of monosized droplets generated with equal spacing and diameter (200 pm), moving at a velocity of >5 m/s and evaporating in ambient air. The system was also evaluated for droplet temperature measurements in flames under combustion conditions. 

The solution of Eq. (6.137) must be combined with the nonsteady equations for the diffusion of heat and mass. This system can only be solved numerically and the computing time is substantial. Therefore, a simpler alternative model of droplet heating is adopted [26, 27], In this model, the droplet temperature is assumed to be spatially uniform at Ts and temporally varying. With this assumption Eq. (6.136) becomes... 

Eressure is determined by the water vapor partial pressure, which is carefully ept at saturation with respect to the equilibrium vapor pressure of water at the droplet temperature so that the droplets neither grow nor evaporate. Depending on the temperature of the droplets this sets the minimum pressure at 4 to 20 Torr. The transit time of the droplets through the reaction zone is short, on the order of a few milliseconds, in order to avoid saturation of the trace gas in the liquids. Experimental parameters are computer monitored. The details of the technique and of the experimental procedures are discussed in reference (2). 

In an experiment water droplets were dried over phosphorous pentoxide to give an atmosphere of 0 percent relative humidity. Using Eq. 15.10, determine the droplet temperature if the ambient temperature is 19°C. Compare this value to one found from use of the psychrometric chart in App. F. 

The original equation for the evaporation of a droplet as a function of time was first derived by James Maxwell in 1877. Although his derivation contains a number of simplifying approximations, Maxwell s equation gives reasonable results for fairly large droplets of pure substances. For this equation, it is assumed that the vapor pressure at the droplet temperature is equal to the partial pressure at the surface of the drop, that is, psurfoce = p,(Teurface) = ps. In terms of concentrations of molecules, this means that the vapor concentration at the surface just equals the concentration of saturated vapor, the saturation determined at the droplet temperature. This assumption is valid when the droplet size is not too small compared to the mean free path of the vapor molecules. 

Equation 15.10 is the fundamental psychrometric equation which permits wet-bulb temperatures to be calculated, as pointed out by Davies (1978) and others. Thus a psychrometric chart can be used to estimate steady-state droplet temperature by finding the wet-bulb temperature corresponding to a given ambient temperature and relative humidity. This wet-bulb temperature is the evaporating droplet temperature ... 

As the droplet evaporates, it cools itself. Therefore the saturation vapor pressure p should be determined at the equilibrium droplet temperature, not at the ambient temperature. 

Alternatively, the psychrometric chart in App. F indicates a wet-bulb (droplet) temperature of approximately 13.9°C (57°F). The slight difference between the calculated value and that given in the psychrometric chart is thought to be due to small differences in the values for various parameters in Eq. 15.10, as well as differences in the manner of computing the wet-bulb temperature. 

What would be the drying time for a 10- im water droplet Assume an air temperature of 20°C and a relative humidity of 20 percent. Also take into account the droplet temperature. 

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