14.7.6. Semi-Mechanistic Boiling Model

The study of heat transfer in boiling is important in many industrial sectors such as nuclear and automotive industries. Several boiling models have been proposed for heat transfer predictions in high-pressure applications in the nuclear industry. However, for low pressure automotive systems, high-pressure boiling models, which are based on specific experimental correlations, may be unreliable and numerically unstable.

To model sub-cooled nucleate boiling at low pressure, bulk evaporation/condensation phenomena is generally combined with the heat transfer augmentation at the wall due to boiling. In Ansys Fluent, the Lee model is used to capture the phase change process both near the wall and in the bulk domain. The heat transfer augmentation at wall is modeled by empirical correlations by Chen [133].

Figure 14.14: The Boiling Curve

Chen [104] proposed the flow boiling correlation for vertical tubes where the effective wall heat flux is expressed as the weighted sum of the nucleate boiling heat flux and the force convective heat flux. Chen's correlation is based on the following assumptions:

Vapor formed by the evaporation process increases the liquid velocity, and, therefore, the convective heat transfer contribution is augmented relative to that of a single-phase liquid flow.
The convection partially suppresses the nucleation of boiling sites and, therefore, reduces the contribution of nucleate boiling.

The effective wall heat flux as proposed by Chen is expressed as:

(14–626)

where
	= forced convective augmentation factor
	and = heat flux multipliers for the single phase and nucleate boiling, respectively
	= single phase heat flux
	= nucleate boiling heat flux
	= nucleate boiling suppression factor

Kutateladze [329] proposed a modified form of effective heat flux using the asymptotic power law, which is expressed as:

(14–627)

where is the power law superposition constant. Setting to 1 results in a linear superposition of the single phase and the nucleate boiling heat flux, as proposed by Chen. Kutateladze proposed an asymptotic method with = 2. With the increase in the value of , the effective heat flux tends to become larger than the single phase heat flux and nucleate boiling heat flux.

The single phase heat flux in Equation 14–626 is given by:

(14–628)

where

The nucleate boiling heat flux in Equation 14–626 is given by:

(14–629)

where

In the above equations,

	and = heat transfer coefficients for the single phase and nucleate boiling, respectively
	= wall temperature
	= boundary cell temperature
	= saturation temperature

The effective single phase heat transfer coefficient is calculated as:

(14–630)

where and are single phase heat transfer coefficients for liquid and vapor, respectively, and is the wetting fraction (fraction of wall wetted by liquid).

The nucleate boiling heat transfer coefficient is calculated using the Foster and Zuber correlation:

(14–631)

where
	= thermal conductivity of liquid
	= specific heat of liquid
	= density of liquid
	= viscosity of liquid
	= density of vapor
	= surface tension coefficient
	= latent heat
	and = saturation pressures corresponding to wall temperature and saturation temperature, respectively

The forced convective augmentation factor is proposed by Chen in the form of [319]:

(14–632)

where the Martinelli parameter is used to account for the two-phase effect on convection and is defined as follows:

(14–633)

(14–634)

where is the vapor quality (mass fraction).

The nucleate boiling suppression factor is given by:

(14–635)

where is the suppression factor due to forced convection, and is the suppression factor due to subcooled effects. According to a proposal by Steiner et al. [633], is calculated as: