The Cooling Effects of Varying Water Droplet Volume and Surface
Contact Angle with a Metal Surface in a Steady State, High
Temperature Air Flow
by
Matthew James Noll
An Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
Master of Engineering
Major Subject: Mechanical Engineering
Approved:
_________________________________________
Dr. Noberto Lemcoff, Project Adviser
_________________________________________
Dr. Ernesto Gutierrez-Miravete,Co-Adviser
Rensselaer Polytechnic Institute
Hartford, Connecticut
March, 2015
(For Graduation August 2015)
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© Copyright 2015
by
Matthew Noll
All Rights Reserved
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CONTENTS
Copyright ........................................................................................................................... ii
LIST OF FIGURES .......................................................................................................... iv
1. INTRODUCTION/BACKGROUND .......................................................................... 1
1.1
PREVIOUS WORK ........................................................................................... 2
1.2
PROBLEM DESCRIPTION .............................................................................. 3
2. THEORY/METHODOLOGY ..................................................................................... 4
2.1
PHYSICAL MODEL ......................................................................................... 4
2.2
ASSUMPTIONS ................................................................................................ 4
2.3
MATHEMATICAL MODEL ............................................................................ 5
2.3.1
HEAT TRANSFER ................................................................................ 5
3. PRELINARY RESULTS............................................................................................. 6
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LIST OF FIGURES
Figure 1: Conical Spray Nozzles and Their Applications ................................................. 1
Figure 2: Model of Analysis Performed by This Paper ..................................................... 3
Figure 3: Surface Plot of Water Vapor Concentration ...................................................... 4
Figure 4: Latent and Sensible Heat Exchange at a Gas-Liquid Interface .......................... 5
Figure 5: Velocity Field for Walls with No Slip ............................................................... 6
Figure 6: Close Up of Wall Effect ..................................................................................... 6
Figure 7: Velocity Profile for This Analysis ..................................................................... 7
Figure 8: Velocity Vectors in Velocity Field .................................................................... 7
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1. INTRODUCTION/BACKGROUND
Systems for the removal of exhaust gases from process such as stationary power
generation, or vehicle propulsion are subjected to high temperature gas flows. Maintaining
the integrity of the materials and components of the exhaust systems with components and
cooling methods which are affordable and effective can be a very difficult task. Typically,
if the materials of the components in the system are not rated for the high temperature of
the exhaust gases a spray system is utilized to cool the material and lengthen the functional
life of the material.
Figure 1: Conical Spray Nozzles and Their Applications
Spray systems can vary greatly by using different fluids to provide the cooling, injecting
the fluid ad different pressures into the exhaust gas flow, and by using different nozzles to
disperse the cooling fluid into the system. The fluid sprayed into the system can vary
depending on the environment that the system is located in, or by the exposure limitations
of the materials used in the exhaust system. Depending on the available components for
the system the pressure of the spray can vary, which affects the last variable that can dictate
the spray method that is ideal for the exhaust system. Once a droplet of fluid interacts with
a surface in the exhaust flow, the droplet surface tension can be manipulated with added
surfactants in order to change the contact angle with the surface.
Cooling fluids such as ethanol are used for transportation systems, but require a reservoir
of fluid which must be replenished. For stationary systems, such as power generation,
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system locations are often chosen so that spray fluids, such as fresh water, are available
relatively nearby. Sources of water are typically rivers or lakes, but can also be salt water
sources.
Operating system pressures are determined either by the capability of the component
creating the pressure, for example a water pump, or by the material used in the piping for
the delivery of the spraying fluid to the exhaust flow. If the system is capable of delivering
the spraying fluid at a high enough pressure, an atomizing system can be used. This creates
droplets on the nanometer scale to decrease the time required to evaporate, which is ideal
for a system that depends on evaporative cooling. However, a system may be limited in
pressure or not have a fluid capable of being atomized, so other spraying nozzles are used
which create larger diameter droplets.
This project studies the cooling effects of a single droplet in an exhaust system that has
fresh water available but is unable to atomize the cooling spray, limiting how small the
diameter of the water droplets are able to be produced. The volume of the droplet as well
as the contact angle that the droplet makes with the surface will be changed independently,
to study their individual effects to the heat transfer from the surface.
1.1 PREVIOUS WORK
Evaporative cooling occurs when a gas flows over a liquid causing evaporation that occurs
from the liquid surface. The energy that is dissipated by the phase change of this
evaporation is taken from the internal energy of the liquid in the gas flow. The loss of this
internal energy cools the liquid, and if the liquid is on a metal surface also subjected to the
gas flow, will then draw energy from it and cool the metal surface.
Evaporative cooling is a subject that has been studied for cooling electronics, high
temperature gas flows, as well as metal slabs. A large number of these studies are centered
on sprays that are atomized due to the droplets’ ability to remove large amounts of heat at
fast rates. This is attributed to the small diameter of the droplets’, allowing them to
evaporate quickly.
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1.2
PROBLEM DESCRIPTION
Based on the amount of research that focuses on systems with atomized droplets, it was
determined that systems with relatively large diameter (≥1mm) droplets in a hot exhaust
flows have a need to be further analyzed. This paper compares the cooling effects of
changing the volume and contact surface angle of a large droplet on a metal surface heated
by a hot exhaust gas flow. This paper does not study the components required to produce
the varying size of the droplets, or the composition of the surfactants needed to alter the
contact angle that the droplet makes with the metal surface.
Figure 2: Model of Analysis Performed by This Paper
In this model, the high temperature exhaust gas is flowing over the droplet which has
collected on the steel surface.
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2. THEORY/METHODOLOGY
2.1 PHYSICAL MODEL
This paper begins the analysis with a droplet modeled as half of a circle, above a
rectangular plate in a rectangular region of hot exhaust flow. The circle with a radius of
0.5 mm can be seen in Figure 3, which shows the concentration of the water vapor in the
gas flow, 0.1 m by 0.1 m. The beginning surface contact angle is 90° since the droplet is
assumed to be exactly ½ of a circle.
Figure 3: Surface Plot of Water Vapor Concentration
2.2 ASSUMPTIONS

Heat and mass transfer processes are in steady state.

The properties of the water are assumed to be constant.

The analysis of this paper assumes that the droplet is of a constant volume and
surface area; therefore, the heat transfer is modeled as a snapshot in time compared
to a constantly changing droplet that is evaporating in the hot exhaust flow.

The walls are assumed to have no friction (modeled as slip) so that there are no
velocity profiles for the upper or lower walls. See Figure 7.
These assumptions were used to create the model in COMSOL.
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2.3 MATHEMATICAL MODEL
2.3.1
HEAT TRANSFER
Evaporative cooling occurs when a gas flows over a liquid, evaporating the liquid. The
energy associated with the phase change of evaporation is the latent heat of vaporization
of the liquid. The process is shown in Figure 5.
𝑞"𝑐𝑜𝑛𝑣 + 𝑞"𝑎𝑑𝑑 = 𝑞"𝑒𝑣𝑎𝑝
Figure 4: Latent and Sensible Heat Exchange at a Gas-Liquid Interface
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3. PRELINARY RESULTS
When a droplet having a radius of 0.5mm on a flat surface was modeled in a hot flow,
Figure 5, It was noticed that the upper and lower walls were affecting the velocity fields,
Figure 6. In Figures 5 and 6, both walls were modeled as “no slip”, which disrupted the
velocity field surface plot.
Figure 5: Velocity Field for Walls with No Slip
Figure 6: Close Up of Wall Effect
The same model was run again with a “no-slip” condition on both of the walls, and the
velocity field in Figure 7 was the result. Figure 8 shows velocity vectors in the velocity
field over the droplet.
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Figure 7: Velocity Profile for This Analysis
Figure 8: Velocity Vectors in Velocity Field
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