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<p>The distribution of local
water vapor in the surrounding air has been shown to be the driving mechanism for
several phase change phenomena during dropwise condensation and condensation frosting. This thesis uses reduced-order modeling approaches,
which account for the effects of the vapor distribution to predict the droplet
growth dynamics during dropwise condensation in systems of many droplets. High-fidelity modeling techniques are used to
further probe and quantify the heat and mass transport mechanisms that govern
the local interactions between a freezing droplet and its surrounding ambient,
including neighboring droplets. The
relative significance of these transport mechanisms in the propagation of frost
are investigated. A reduced-order analytical method is
first developed to calculate the condensation rate of each individual droplet
within a group of droplets on a surface by resolving the vapor concentration
field in the surrounding air. A point sink
superposition method is used to account for the interaction between all droplets
without requiring solution of the diffusion equation for a full
three-dimensional domain. For a
simplified scenario containing two neighboring condensing droplets, the rates
of growth are studied as a function of the inter-droplet distance and the relative
droplet size. Interactions between the
pair of droplets are discussed in terms of changes in the vapor concentration
field in the air domain around the droplets.
For representative systems of condensing droplets on a surface, the total
condensation rates predicted by the reduced-order model match numerical
simulations to within 15%. The results
show that assuming droplets grow as an equivalent film or in a completely
isolated manner can severely overpredict
condensation rates.</p>
<p>The point superposition model is then used to predict the condensation
rates measured during condensation experiments.
The results indicate that it is critical to consider a large number of
interacting droplets to accurately predict the condensation behavior. Even though
the intensity of the interaction between droplets decreases
sharply with their separation distance, droplets located relatively far away from a given droplet must
be considered to accurately predict the condensation rate, due to the large
aggregate effect of all such far away droplets.
By considering an appropriate number of interacting droplets in a
system, the point sink superposition method is able to predict experimental
condensation rates to within 5%. The
model was also capable of predicting the time-varying condensation rates of
individual droplets tracked over time. These
results confirm that diffusion-based models that neglect the interactions of
droplets located far away, or approximate droplet growth as an equivalent film,
overpredict condensation rates.</p>
<p>In dropwise condensation from humid air, a full description
of the interactions between droplets can be determined by solving the vapor
concentration field while neglecting heat transfer across the droplets. In contrast, the latent heat released during
condensation freezing processes cause droplet-to-ambient as well as droplet-to-droplet
interactions via coupled heat and mas transfer processes that are not well
understood, and their relative significance has not been quantified. As a first step in understanding these
mechanisms, high-fidelity modeling of the solidification process, along with
high-resolution infrared (IR) thermography measurements of the surface of a
freezing droplet, are used to quantify the pathways for latent heat dissipation
to the ambient surroundings of a droplet.
The IR measurements are used to show that the crystallization dynamics
are related to the size of the droplet, as the freezing front moves slower in
larger droplets. Numerical simulations
of the solidification process are performed using the IR temperature data at
the contact line of the droplet as a boundary condition. These simulations, which have good agreement
with experimentally measured freezing times, reveal that the heat transferred
to the substrate through the base contact area of the droplet is best described
by a time-dependent temperature boundary condition, contrary to the constant
values of base temperature and rates of heat transfer assumed in previous numerical
simulations reported in the literature.
In further contrast to the highly simplified descriptions of the
interaction between a droplet and its surrounding used in previous models, the
model developed in the current work accounts for heat conduction, convection,
and evaporative cooling at the droplet-air interface. The simulation results indicate that only a
small fraction of heat is lost through the droplet-air interface via conduction
and evaporative cooling. The heat
transfer rate to the substrate of the droplet is shown to be at least one order
of magnitude greater than the heat transferred to the ambient air.</p>
<p>Subsequently, the droplet-to-droplet interactions via heat
and mass exchange between a freezing droplet and a neighboring droplet, for
which asymmetries are observed in the final shape of the frozen droplet, are
investigated. Side-view infrared (IR)
thermography measurements of the surface temperature for a pair of freezing
droplets, along with three-dimensional numerical simulations of the
solidification process, are used to quantify the intensity and nature of these
interactions. Two droplet-to-droplet
interaction mechanisms causing asymmetric freezing are identified: (1)
non-uniform evaporative cooling on the surface of the freezing droplet caused
by vapor starvation in the air between the droplets; and (2) a non-uniform
thermal resistance at the contact area of the freezing droplet caused by the
heat conduction within the neighboring droplet.
The combined experimental and numerical results show that the size of
the freezing droplet relative to its neighbor can significantly impact the
intensity of the interaction between the droplets and, therefore, the degree of
asymmetry. A small droplet freezing in
the presence of a large droplet, which blocks vapor from freely diffusing to
the surface of the small droplet, causes substantial asymmetry in the
solidification process. The droplet-to-droplet
interactions investigated in thesis provide insights into the role of heat
dissipation in the evaporation of neighboring droplets and ice bridging, and
open new avenues for extending this understanding to a system-level description
for the propagation of frost.</p>
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| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/13059029 |
| Date | 16 December 2020 |
| Creators | Julian Castillo (9466352) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY 4.0 |
| Relation | https://figshare.com/articles/thesis/Droplet_Heat_and_Mass_Exchange_with_the_Ambient_During_Dropwise_Condensation_and_Freezing/13059029 |
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