dR(k) 3m(k) . = 2 dt 4 R(k) l in Visual Studio .NET Creation Code 39 in Visual Studio .NET dR(k) 3m(k) . = 2 dt 4 R(k) l

dR(k) 3m(k) . = 2 dt 4 R(k) l Using Barcode printer for VS .NET Control to generate, create Code 3/9 image in .NET applications. barcode A liquid-phas .NET framework Code39 e heat diffusion equation can be selected from the choices considered in s 2 and 3. The method for proper transformation of the source and sink terms from the Lagrangian grid to the Eulerian grid and vice versa is discussed in Section 8.

2. Aggarwal et al. (1984) used a system of equations equivalent to the preceding equations to evaluate spray vaporization models in situations without chemical reaction.

They concluded that signi cant differences can result from the different droplet-heating and -vaporization models that they studied [types (ii), (iii), and (v)]. In high-temperature environments, the spatial variation, as well as the temporal variation, of the temperature within the droplet should be resolved. When spatial variation of the liquid temperature is important, the internal circulation will have an effect; therefore it should be considered for accuracy.

Aggarwal et al. did show that signi cant variations in composition and temperature could occur on the scale of the spacing between neighboring droplets. For example, see Fig.

9.7, in which mass fraction versus axial position at certain instances of time are plotted. These microscale variations were later shown to be important.

Aggarwal and Sirignano (1985a) considered an initially monodisperse fuel air spray in contact with a hot wall at one end; this wall was suf ciently hot to serve as an ignition source. The air and the droplets initially were not in motion; only the expanding hot gases cause a relative motion and drag force on the droplets. On account of the low-speed motion, internal circulation is not considered to be important, and the droplet-heating and -vaporization model is spherically symmetric.

The parameters varied in this study included initial droplet size, hot-wall temperature, equivalence ratio, fuel type (volatility), and the distance from the hot wall to the nearest droplet. As expected, increases in the hot-wall temperature resulted in a decrease for the heating time required before ignition (ignition delay). An increase in the fuel volatility also resulted in a decrease for ignition delay and for the accumulated energy required for ignition to occur (ignition energy).

Volatility in uence was. Spray Applications Figure 9.7. F Code 3/9 for Visual Studio .

NET uel-vapor mass fraction versus distance at 16 ms for different liquid-phase models. (Aggarwal et al., 1984, with permission of AIAA Journal.

). especially pr onounced for larger initial droplet sizes. Equivalence ratio also had an in uence; too little fuel vapor or too much fuel vapor could inhibit ignition. The effects of the droplet-heating and -vaporization model choice was shown to be signi cant for less-volatile fuels or for larger initial droplet sizes.

A comparison was made between nite-conductivity and in nite-conductivity models here. The differences were much less important for volatile fuels or small initial droplet size. The in nite-conductivity model overpredicts ignition delay and ignition energy for the same reasons that it underpredicts vaporization rate during the early lifetime (see 2).

For example, a hexane droplet with a 52.5- m initial radius has a 2% difference in the ignition-delay prediction between the two models, but a hexane droplet with a 105- m radius shows a 35% disagreement. One interesting result is that a strong dependence on the distance between the nearest droplet and the ignition source exists for the ignition delay and for the ignition energy (Fig.

9.8). Note that an optimal distance occurs whereby delay and energy are minimized.

This implies that, in a practical spray, in which distance to the ignition source is not controlled precisely or known, we should not expect a reproducible ignition delay or ignition energy. It is a statistical quality, and a range of variation will occur. Another interesting result is that, for a xed equivalence ratio and a xed distance from the ignition source, the dependence of ignition delay and ignition energy on the initial droplet radius is not monotonic.

In particular, minimum ignition delay and energy occur for a nite droplet size rather than at the premixed limit (zero initial droplet radius). This optimal initial droplet size increases as xed volatility increases..

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