ANSYS FLUENT 12.0 Theory Guide - 15.4.3 Droplet Boiling (Law 3)

15.4.3 Droplet Boiling (Law 3)

Law 3 is applied to predict the convective boiling of a discrete phase droplet when the temperature of the droplet has reached the boiling temperature, $T_{\rm bp}$ , and while the mass of the droplet exceeds the nonvolatile fraction, ( $1 - f_{v,0}$ ):

$T_p \geq T_{\rm bp}$

(15.4-18)

and

$m_p > (1 - f_{v,0}) m_{p,0}$

(15.4-19)

When the droplet temperature reaches the boiling point, a boiling rate equation is applied [ 173]:

$\frac{d (d_p)}{dt} = \frac{4 k_{\infty}}{\rho_p c_{p,\infty... ...\frac{c_{p,\infty} (T_{\infty} - T_p) }{ h_{\rm fg} } \right ]$

(15.4-20)

where	$c_{p,\infty}$	=	heat capacity of the gas (J/kg-K)
	$\rho_p$	=	droplet density (kg/m )
	$k_{\infty}$	=	thermal conductivity of the gas (W/m-K)

Equation 15.4-20 was derived assuming steady flow at constant pressure. Note that the model requires $T_{\infty} > T_{{\rm bp}}$ in order for boiling to occur and that the droplet remains at fixed temperature ( $T_{{\rm bp}}$ ) throughout the boiling law.

When radiation heat transfer is active, ANSYS FLUENT uses a slight modification of Equation 15.4-20, derived by starting from Equation 15.4-17 and assuming that the droplet temperature is constant. This yields

$- \frac{d m_p}{dt} h_{\rm fg} = h A_p (T_{\infty} - T_p) + A_p \epsilon_p \sigma ({\theta_R}^4 - {T_p}^4)$

(15.4-21)

$-\frac{d (d_p)}{dt} = \frac{2}{\rho_{p} h_{\rm fg} } \left[ ... ...p}) + \epsilon_{p} \sigma (\theta_{R}^{4} - T_{p}^{4}) \right]$

(15.4-22)

Using Equation 15.4-9 for the Nusselt number correlation and replacing the Prandtl number term with an empirical constant, Equation 15.4-22 becomes

$-\frac{d (d_p)}{dt} = \frac{2}{\rho_{p} h_{\rm fg} } \left[ ... ...p}) + \epsilon_{p} \sigma (\theta_{R}^{4} - T_{p}^{4}) \right]$

(15.4-23)

In the absence of radiation, this result matches that of Equation 15.4-20 in the limit that the argument of the logarithm is close to unity. ANSYS FLUENT uses Equation 15.4-23 when radiation is active in your model and Equation 15.4-20 when radiation is not active. Radiation heat transfer to the particle is included only if you have enabled the P-1 or discrete ordinates radiation model and you have activated radiation heat transfer to particles using the Particle Radiation Interaction option in the Discrete Phase Model dialog box.

The droplet is assumed to stay at constant temperature while the boiling rate is applied. Once the boiling law is entered it is applied for the duration of the particle trajectory. The energy required for vaporization appears as a (negative) source term in the energy equation for the gas phase. The evaporated liquid enters the gas phase as species , as defined by your input for the destination species (see this section in the separate User's Guide).

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