q7

• Chris Nkinthorn, 20190716

Questions

1. Describe the differences, if any, between boiling and evaporation.

   Boiling and evaporation are both processes where a liquid phase's components are transformed into the vapor phase. In starting to ending, the reactants and products are the same. The difference in name comes from the driving forces and their associated boundaries. In boiling, the phase change is driven by solid/liquid boundary because the solid’s temperature is in excess of the liquid saturation temperature. In evaporation, the phase change occurs at the liquid/vapor interface as the liquid’s saturation pressure is in excess of its vapor pressure.

2. Discuss the different types of pool boiling phenomena.

   Pool boiling as analogous to natural convection, as a solid boundary is heated. This leads to buoyant forces as the local density distribution changes. However, as the excess temperature between the fluid and solid is increased, various phenomena not present in purely vapor convection. This is the appearance of vapor as bubbles in the fluid, at nucleation sites, which grow into jets and columns of vapor bubbles. Full film boiling occurs beyond the Leidenfrost point, when the heated surface maintains a continuous vapor barrier, as radiant effects become significant.

3. Describe the different behavior regions associated with pool-boiling in terms of excess temperature.

   Pool boiling is when the liquid boundary condition has a solid interface, which is at a temperature beyond the saturation temperature of the liquid. With increased excess temperature, there is a linear increase in the heat flux through the boundary. An increase in heat flux characterizes the various behavior regions associated with pool boiling: natural convection when the excess temperature is small, followed by nucleation where vapor forms in sites dispersed through the fluid. This increase the effective heat transfer coefficient continues until the burnout point where the applied heat flux equals the critical. Here, where vapor forms faster than the liquid can rewet the surface, radiant effects are help stabilize full film boiling. In total, there are $\text{VI}$ behavior regions.

4. Describe the differences, if any, between burn-out point and Leidenfrost point for pool boiling.

   Both are critical on the effective heat transfer graph that characterizes the boiling curve and both mark a change into the unstable, transitional region of $\text{VI}$. However, the burn out point is a local maxima, whereas the Leidenfrost point is a local minima, as they signal the beginning and end, respectively. The burn out point is where bubbling become such a detriment at removing heat at the surface that material, such as the platinum wire used by Nukiyama, would melt. The Leidenfrost point signals that more heat flux may be added to further increase excess temperature.

5. For pool boiling, which thermo-physical variable needs to be controlled to obtain a continuous curve in the heat flux vs. excess temperature plot.

   The applied heat flux temperature needs to be controlled, so that the material does not melt. The excess temperature then remains, with the power decreasing until the Leidenfrost point, where heat flux can again be increased, as full film boiling occurs. This means in order to obtain a continuous heat flux plot as function of excess temperature, one would increase the heat flux until the temperature reached the burnout point, reduce until the excess temperature reaches the Leidenfrost point, where the applied heat flux can then be increased again.

6. Discuss at which point does nucleate boiling regime starts and ends.

   Nucleation takes over from natural convection, when the excess temperature reaches 5 $^{\circ}\text{C}$, as the heat flux causes vapor to form at nucleation sites dispersed through the fluid. Locally less dense vapor bubbles rise, increasing the effective heat transfer coefficient as buoyant effects support bulk transport mechanisms. Nucleation then ends when radiant heat transport at the surface, beyond Leidenfrost point, causes full film boiling.

7. Describe the reason(s) for lower heat transfer coefficients relative to natural convection when excess temperature exceeds the burn-out point in a heat vs. excess temperature plot.

   The heat transfer coefficient relates the heat flux to the applied temperature temperature difference, do to convective mass transfer. A significant drop in Region $\text{VI}$ where stabilized film boiling occurs, as heat transfer is supplemented by the radiant energy transfer. This is seen when there is a persistent vapor barrier between the solid temperature boundary and the liquid phase.

8. Discuss the relevance of the Clapeyron phase change equation.

   The expression is based on the Maxwell relation from the Helmholtz free function for an ideal gas, where the Helmholtz Function is $A \equiv U - TS$. U is in the internal energy, T is the absolute temperature, and S represents the entropy of the system.

   $$\text{Maxwell Relation: } \left(\frac{\partial p}{\partial T}\right)_{v}=\left(\frac{\partial S}{\partial V}\right)_{T}\\ \text{Clapeyron Equation: } \frac{d p}{d T}=\frac{h_{l}-h_{v}}{T\left(v_{l}-v_{v}\right)}$$

   It allows for the computation of pressure effects on the transitional temperature, as well as the latent heat of vaporization.

9. Discuss the reason(s) for higher heat transfer coefficients for drop condensation relative to film condensation.

   Film condensation is liquid forms generates a contiguous film that is pulled downward by gravity. Drop condensation is the liquid forms droplets that fall downward. Effectively, greater energy being wicked away due to mass transfer from the sweeping motion of the droplets.

10. Discuss the reason(s) why quality is relevant during operation of power plant low pressure turbines.

    Quality is important to the moisture in the vapor and how much is actually vapor. High moisture content associated with low quality vapor leads to steam which will rapidly corrode/degrade metal components. Additionally, low quality is associated with less energy and so less power that expected. This is because reactor expressions, are calculated assuming pure vapor.