Boiling

Boiling is a rapid vaporization of a liquid. It typically takes place when a liquid is heated up to temperatures that exceed the boiling temperature of the liquid. For single-component liquids that are in contact with walls at temperatures that exceed the boiling temperature of the liquid, boiling models simulate the effect of the latent heat of vaporization without simulating vapor.

When a liquid is in contact with a wall that is maintained at temperatures $T_{w a l l}$ above the boiling temperature of the liquid, boiling eventually occurs at that liquid-solid interface. In this case, boiling occurs in three characteristic stages:

Nucleate boiling involves creation and growth of vapor bubbles on a heated surface, which rise from discrete points on a surface. The temperature of the surface is only slightly above the saturation temperature of the liquid. In general, the number of nucleation sites increases with increasing surface temperature. An increased surface roughness can create more nucleation sites, while an exceptionally smooth surface can result in superheating.
Film boiling occurs when the critical heat flux is exceeded and a continuous vapor film covers the heated surface. The vapor layer has a lower thermal conductivity than the liquid so the vapor layer typically insulates the surface.
Transition boiling occurs at surface temperatures between the maximum attainable temperature in nucleate boiling and the minimum attainable temperature in film boiling. It is an intermediate, unstable form of boiling with elements of both types.

There are two distinct choices for modeling boiling in Simcenter STAR-CCM+, namely the Rohsenow and the Transition Boiling models. The former uses the Rohsenow nucleate boiling model applicable for boiling at relatively low solid temperatures. The Transition Boiling model has expressions for nucleate and transition boiling.

Rohsenow Boiling

The empirical correlation that Rohsenow [417] presented is used to calculate the surface heat flux due to boiling:

Figure 1. EQUATION_DISPLAY

q_{b w} = {μ_{l} h}_{l a t} \sqrt{\frac{g (ρ_{l} - ρ_{v})}{σ}} {(\frac{C_{p_{l}} (T_{w} - T_{s a t})}{{C_{q w} h}_{l a t} {P r}_{l}^{n_{p}}})}^{3.03}

(1829)

In this equation, $μ_{l}$ , $h_{l a t}$ , $C_{p_{l}}$ , $ρ_{l}$ , and ${P r}_{l}$ are the dynamic viscosity, latent heat, specific heat, density, and Prandtl number of the liquid phase, $n_{p}$ is the Prandtl number exponent (1.73 by default), $g$ is gravity, and $ρ_{v}$ is the vapor density, $σ$ is the surface tension coefficient at the liquid-vapor interface, $T_{w}$ is the wall temperature, $T_{s a t}$ is the saturation temperature, and $C_{q w}$ is an empirical coefficient varying with the liquid-surface combination.

If the Rohsenow correlation is applied outside its range of applicability (for example, to the film boiling regime), unrealistically high heat fluxes could result. Fluid temperatures can become higher than the near wall temperature. This behavior stems from the fact that the Rohsenow correlation does not depend on the fluid temperature; heat enters the domain irrespective of the fluid temperature.

To prevent this condition, the heat flux that the correlation calculates is multiplied by:

Figure 2. EQUATION_DISPLAY

m a x [0, m i n ((\frac{T_{w} - T}{T w - T_{s a t}}), 1)]

(1830)

where $T$ is the fluid temperature near the heated wall. Thus, if $T < T_{s a t}$ , the Rohsenow correlation is used directly, and if $T > T_{w}$ the boiling heat flux is zero. For fluid temperatures which are between the wall and the saturation temperature, only a fraction of the heat flux predicted by the correlation is used.

Transition Boiling

For the Transition Boiling model, the equations are as follows:

Figure 3. EQUATION_DISPLAY

q_{b o i l i n g} (Δ T) = q_{max} {S ϕ (\frac{Δ T}{Δ T_{1}})}^{K_{1}} 0 \leq Δ T \leq Δ T_{1}

(1831)

Figure 4. EQUATION_DISPLAY

q_{b o i l i n g} (Δ T) = q_{max} S [1 - 4 (1 - ϕ) {(\frac{Δ T - {Δ T}_{max}}{Δ T_{2} - Δ T_{1}})}^{2}] Δ T_{1} \leq Δ T \leq Δ T_{2}

(1832)

Figure 5. EQUATION_DISPLAY

q_{b o i l i n g} (Δ T) = q_{max} {S ϕ (\frac{Δ T}{Δ T_{2}})}^{{- K}_{2}} Δ T_{2} \leq Δ T

(1833)

The first of the above equations simulates nucleate boiling, while the remaining two simulate transition I and transition II boiling. The three regimes are shown graphically in the following figure:

There are five empirical constants in the above model, namely, $K_{1}$ , $K_{2}$ , $Δ T_{1}$ , $Δ T_{2}$ , and $q_{max}$ , all of which are positive. $Δ T_{m a x}$ is $\frac{1}{2} (Δ T_{1} + Δ T_{2})$ .The constant $ϕ$ is set equal to 0.75. Further, $Δ T_{2}$ must be greater than $Δ T_{1}$ . (In the above expressions $K_{2}$ is positive even though it is a negative exponent because the sign is accounted for in the implementation.) The scale factor $S$ in the above expressions is not treated as a sixth constant. It allows you to scale $q_{max}$ up or down for a given boundary. All the constants are likely to be application-specific. Hence, it is recommended that default values for the constants be tuned with credible measurements. The default values are from fits of boiling experiments of Ellion [404] using an apparatus with a particular geometry.

In the Transition Boiling Model, $Δ T_{1}$ and $Δ T_{2}$ are the metrics that switch between the three expressions (or regimes).

The total heat flux at the wall is the sum of the heat fluxes due to boiling, convection, and thermal radiation. In the above equations, $q_{max}$ is the maximum of the boiling heat flux component; it is not the critical heat flux which is a maximum of the total heat flux. The point on the curve corresponding to the minimum of the total heat flux is the Leidenfrost point and it occurs in the Transition II boiling regime. At the Leidenfrost point, vapor completely covers the surface and heat transfer is primarily driven by convection and radiation with a negligible boiling contribution.

If the fluid temperature $T$ is above the saturation temperature $T_{s a t}$ , the boiling heat flux is calculated according to Eqn. (1830).