Boiling

• Let's watch water boil....!

  

• It's more interesting than you think! In boiling terminology, this is known as pool boiling.
• This is in contrast to forced boiling, where the boiling fluid is driven through the boiler.

• At first, nothing happens as the liquid and walls are well below the water boiling temperature $T_w\ll T_{boil}$ (the same as the vapour saturation temperature $T_{sat}$).

  

• Heat is transferred by convection but no significant amount of vapour is generated. This is NOT boiling but still classified as Natural Convection.

• After a while the wall rises above the boiling temperature $T_w\gtrsim T_{sat}$, and localised boiling occurs at the surface of the plate.

  

• Small bubbles will form but quickly dissolve or oscillate as they are cooled by the fluid, which is still well below $T_{sat}$.
• This is known as subcooled boiling even though little vapour is produced.

• After a while, the water begins to steam as it reaches the saturation temperature!

  

• Here, there are some bubbles on the surface but they do not detach or grow.
• Water is superheated at the wall and convects to the surface where it evaporates into steam.
• This is the convective region of boiling, and can be treated as Natural Convection.

• 

  As the wall temperature increases further relative to the saturation temperature $T_w\gg T_{sat}$, bubbles grow and detach from the wall.
• This is the critical boiling regime known as nucleate boiling.
• As the bubbles nucleate, grow then detach from the wall, they mix the fluid and greatly increase the heat transfer.
• We must consider nucleate boiling heat transfer coefficients, $h_{nb}$.

• Finally, we have what is called film boiling.
• Here, the bubbles are large enough to merge and completely cover the hot surface.
  Mythbusters video
• This actually insulates the surface, lowering the rate of heat transfer, and is called the Liedenfrost effect.
• You see this when a droplet of water boils on a hot plate, it doesn't instantly boil, but it skips around.
• Or when Mythbusters dip their fingers into molten lead at 450${}^\circ$ C, without burning them.

• Experimental measurements of bulk/boiling generate the following curve
• This is a plot of the log of the heat transfer rate $Q$ versus the log of the wall superheat, $\ln(T_w-T_{sat})$ ).
• Plots of $\ln(h)$ versus $\ln(T_w-T_{sat})$ are common in the literature too, and they are qualitatively identical.
• We can identify many features in this graph…

• The first region of the graph is the convective boiling regime.
• Fluid is superheated at the wall and convects to the surface of the fluid where it evaporates.
• No significant vapour is generated at the wall and we can use Natural Convection to calculate the heat transfer coefficient. \begin{align*} h = C \left(\text{Gr Pr}\right)^n \end{align*}
• This region exists from $T_w=T_{sat}$ until the Onset of Nucleate Boiling (ONB).

• The second region of the graph is the nucleate boiling regime (or “Bubbly Boiling” to the layman).
• Vapour is generated at the wall and the mixing it causes greatly increases the heat transferred.
• This region exists from the Onset of Nucleate Boiling (ONB) until the critical heat flux is reached (CHF).
• This is the region in which industrial boilers typically operate! But they don't operate near the CHF (see Burn-out)!

• The final region of the graph is the film boiling regime (or mythbusters regime).
• Here, the heat flux rapidly drops as the surface bubbles coalesce into a large film, insulating the plate.
• At the Liedenfrost point, film boiling becomes stable (see Burn-out).
• Beyond the Liedenfrost point, the heat transfer increases again as radiation comes into play.

• Why don't we operate industrial boilers near the critical heat flux point?
• Consider an electrical heater which by its nature has a fixed duty $Q_{duty}$ …

• If the heater is in the green or amber regions at steady state, the boiler is stable.
• If fluctuations cause the wall to become hotter …
• … the heat flux will increase above $Q_{duty}$ …
• … and the wall will cool down again back to the steady state.

• If the heater enters the red region, the boiler becomes unstable.
• If we heat up slightly passed the CHF…
• … the heat flux will decrease below $Q_{duty}$ …
• … and the wall will heat up even more!
• If you enter the unstable region from the CHF (heating), the wall temperature will increase uncontrollably.
• If you enter from the Liedenfrost point (cooling) the wall temperature will drop uncontrollably.

• This instability only exists between the CHF and the Liedenfrost point.
• This is why the Liedenfrost point marks the onset of stable film boiling.
• Unfortunately, this point is approaching the melting point of the material the boiler is made out of, and we experience Burn-out if we reach here.
• We will need to use process control (EG3575: Unit Operations) to make sure that our boilers never burn-out.

• The calculation of boiling heat transfer coefficients strongly depends on the surface type, roughness and wettability, as well as the properties of the fluid.
• Enhanced tubes make these predictions even more difficult, as the surface has a complex structure.
• Between cleanings the transfer coefficient also changes significantly.
• For water boiling on copper plates it drops from 8000 W/m${}^2 $ K almost new to 3900 W/m ${}^2 $ K when just cleaned (sandblasted), to 2600 W/m ${}^2 $ K after long use.

• Needless to say, when designing boilers we need experimental data.
• But there are correlations that provide predictions in the absence of this.
• We will present and use the correlations given in Coulson and Richardson Vol. 6.
• First, we have the Forster-Zuber correlation \begin{align*} h_{nb}=0.00122\frac{k_L^{0.79}  C_{p,L}^{0.45}  \rho_L^{0.49}}{\gamma^{0.5} \mu_L^{0.29} h_{fg}^{0.24} \rho_G^{0.24}}\left(T_w - T_{sat}\right)^{0.24}\left(p_w-p_{sat}\right)^{0.75} \end{align*} where $\gamma$ is the surface tension of the liquid, and $h_{fg}$ is the latent heat of vapourisation.
• This correlation requires many fluid properties, such as the surface tension and the temperature and pressure at the hot surface and in the bulk of the saturated fluid.
• If these properties are not available, we must use another correlation…

• In the absence of both experimental data and sufficient fluid data we can use the Mostinski correlation, given by \begin{align*} h_{nb} = 0.104 p_c^{0.69}  q^{0.7} \left[1.8\left(\frac{p}{p_c}\right)^{0.17} +4\left(\frac{p}{p_c}\right)^{1.2} +10\left(\frac{p}{p_c}\right)^{10}\right] \end{align*} where the operating pressure $p$ and the critical pressure $p_c$ are in units of bar.
• Here, we need the critical pressure of the fluid $p_c$. This is a single value for each fluid and does not depend on the temperature/pressure/density, which is readily available in the literature.
• An important thing to note is that the Mostinski correlation is also a function of the heat flux $q\approx h_{nb}\left(T_w-T_{sat}\right)$.
• The estimations of the Forster-Zuber correlation are preferred over the Mostinski correlation, if the data is available.

• When designing a boiler, we must also ensure the boiler is operating well below the Critical Heat Flux.
• We need estimations for this, and Zuber presents a correlation using several fluid properties \begin{align*} q_c=0.149 h_{fg} \rho_G^{0.5}\left(\gamma g  \left(\rho_L-\rho_G\right)\right)^{0.25} \end{align*}
• Again, if there is insufficient experimental data and fluid property data, Mostinski provides a correlation in the critical pressure. \begin{align*} q_c = 3.67\times10^4 p_c\left(\frac{p}{p_c}\right)^{0.35} \left[1-\frac{p}{p_c}\right]^{0.9} \end{align*} where the operating pressure $p$ and the critical pressure $p_c$ are in units of bar.
• Note: These expressions are for the critical heat flux (W/m ${}^2$ )

Learning objectives

• The difference between Subcooled and bulk / saturated boiling.
• The difference between Forced and Pool boiling.
• The bulk / saturated boiling curve, with its three bulk boiling regimes (convective, nucleating and film) and each regimes characteristics.
• When to choose to use the Forster-Zuber or Mostinkski correlation for nucleate boiling.
• How to calculate heat transfer coefficients for forced boiling.