Development of an experimental technique to investigate droplet cooling phenomena on accident tolerant fuel materials

Development of an experimental technique to investigate

droplet cooling phenomena on accident tolerant fuel

materials

by

Warner McGhee

Submitted to the Department of Nuclear Science and Engineering

in partial fulfillment of the requirements for the degree of

Bachelor of Science in Nuclear Science and Engineering

at the

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

May 2020

c

○ Massachusetts Institute of Technology 2020. All rights reserved.

Author

. . . .

Department

of Nuclear Science and Engineering

May

12, 2020

Certified

by . . . .

Matteo

Bucci

Assistant

Professor of Nuclear Science and Engineering

Thesis

Supervisor

Accepted

by. . . .

Michael

P. Short

Associate

Professor of Nuclear Science and Engineering

Chair,

NSE Committee for Undergraduate Students

Development of an experimental technique to investigate droplet

cooling phenomena on accident tolerant fuel materials

by

Warner McGhee

Submitted to the Department of Nuclear Science and Engineering on May 12, 2020, in partial fulfillment of the

requirements for the degree of

Bachelor of Science in Nuclear Science and Engineering

Abstract

Droplet cooling is used in many heat removal applications, including core spray coolers in boiling water reactors. As new accident tolerant fuels are developed, understanding how they respond to droplet cooling is important to ensuring safe operations. Recent studies have indicated that surfaces engineered with micro- and nanostructures may affect the Lei-denfrost point temperature of water and thus the efficiency of droplet cooling by altering the wettability of the surfaces. In this project, smooth and rough chromium surfaces were subjected to droplet cooling at temperatures ranging from 100 to 400 ∘C, and the surface temperature was measured with a high speed infrared camera while a video camera ob-served the droplet shape and behavior during boiling. While the rough and smooth surfaces performed similarly at temperatures below 200 ∘C, the data indicates that at higher tem-peratures the smooth surface allows for greater heat flux, longer droplet contact time, and more total heat removed. The sparsity of data makes this result very uncertain, especially since it seems to oppose most literature on the topic. The techniques developed for this study are promising for future illumination how surface structure affects droplet cooling. Thesis Supervisor: Matteo Bucci

Acknowledgments

I am grateful for all Professor Bucci did to lead me through this research process. I would also like to thank Artyom Kossolapov, Haeseong Kim, Guanyu Su, and Bert Vandereydt for their mentorship and long hours in the lab with me, and Jared Berezin for his writing guidance. Thank you to Scott Alsid for his constant encouragement and mentorship, and friendship.

Contents

2.4 Thermal conduction and numerical methods . . . 21

3 Experimental procedure 25 3.1 Experiment overview . . . 25

3.2 Preparing quenching surfaces . . . 26

3.3 Heater construction . . . 27

3.4 Experiment setup . . . 30

3.5 Quenching experiments . . . 31

4 Infrared data processing 33 4.1 Non-uniformity correction . . . 33

4.2 Temperature calibration . . . 34

4.3 Noise reduction and partial droplets . . . 35

4.4 3-dimensional conduction . . . 36

5 Results 39 5.1 Comparison of surfaces . . . 39

5.3 Limitations and sources of error . . . 46

List of Figures

1-1 BWR core spray system [1]. . . 16

2-1 A boiling curve depicting the different regimes of droplet boiling and their associated surface temperatures (horizontal axis) and heat transfer rates (vertical axis) [2]. . . 20

2-2 Energy balance for an element in the finite volume analysis (left) and la-beled dimensions of elements and their states(right). . . 22

3-1 Schematic of experiment setup. . . 25

3-2 Layers applied to sapphire substrate to create smooth chromium surface. . . 26

3-3 Layers applied to sapphire substrate to create rough chromium surface. . . . 27

3-4 Samples before and after oxidation. The left sample is roughened and the right is smooth chromium. In each image the left is unoxidized and the right is oxidized. The color change could have affected infrared radiance and surface properties if not controlled. . . 27

3-5 The resistive heating element. Distances are in cm. . . 28

3-6 The resistive heater bolted to the ceramic block and electrical connections to the power supply. . . 28

3-7 Side view of the heater. . . 29

3-8 Top view of the heater. . . 29

3-9 Experiment setup. . . 30

4-1 Non-uniformity correction from a pixel’s counts to its error from the center pixels’ average counts. . . 34 4-2 Uncorrected infrared counts (left) and corrected counts (right). The

non-uniformity correction eliminated effects of optical distortion and reduced noise. . . 34 4-3 The calibration curve from infrared counts to temperature (left) allowed the

surface temperature to be calculated at every frame (right). The axes mark pixels, which are 31.3 µm in length. . . 35 4-4 Space modeled by finite volumes (left) and horizontal meshgrid (right).

White regions are adiabatic boundaries, and the colored region has pre-scribed temperature boundaries. The original viewing area of the infrared camera has the fine resolution of the pixel size, while the buffers have in-creasingly course resolution. . . 36 4-5 Surface temperature (left) and corresponding heat flux (right). . . 37

5-1 The heat removed by the droplet’s first contact (left) was very close for rough and smooth chromium surfaces at low temperatures, but significantly higher for the smooth at high temperatures. The rough and smooth surfaces appear to have similar contact times with the droplet, with an exponential decay that levels off to approximately 0.015 s at high temperatures (right). . 40 5-2 The trends seen in heat removal rate (left) and maximum surface cooling

(right) follow similar trends. In both metrics, the smooth chromium surface outperforms the rough. The maximum surface cooling peaks at a much higher temperature for the rough surface, while the maximum cooling be-gins descending at lower temperatures for the smooth surface. . . 41 5-3 Approximation of surface area wetted by droplet at different temperatures.

The rough surface appears to have been wetted more at low temperatures, while the smooth surface apprears to have been wetted more at high tem-peratures. . . 42 5-4 Droplet behavior at low temperatures is characteristic of nucleate boiling. . 43

5-5 Droplet behavior characteristic of early transition boiling. . . 44 5-6 Droplet behavior beginning to show some characteristics of film boiling. . . 44 5-7 Droplet behavior mostly resembling film boiling. . . 45 5-8 Droplet exhibiting Leidenfrost effect fully. . . 46

List of Tables

2.1 Matrix diagonals for finite volume conduction. At boundaries where ∆x, ∆y, and ∆z may not exist, those values are set to 0. . . 23

Chapter 1

Introduction

Maintaining the balance of heat generation and heat removal is imperative to safety in commercial nuclear power. Among the worst possible accidents is a loss of coolant acci-dent (LOCA), in which all the coolant in the reactor core either leaks out or evaporates, drastically reducing the heat removal rate. As temperatures rise, more severe issues can propagate. In particular, fuel elements can fail through cracking or melting, releasing fis-sion products out of the core. Preventing such accidents is a constant engineering concern and a major focus of nuclear operators [3].

Typically, boiling water reactors (BWRs) use spray coolers on top of the core to remove heat in the case of a LOCA. These sprayers rapidly discharge water as a spray of droplets onto the fuel assemblies from the top of the core, as shown in Figure 1-1. The fuel rods are cooled mostly through evaporative cooling at high temperatures [1]. As new accident tolerant fuel (ATF) coatings are developed, it is important to investigate their performances in droplet cooling conditions to ensure that they have the same, or better performance compared to conventional zircaloy claddings.

Figure 1-1: BWR core spray system [1].

Outside of the nuclear industry, droplet cooling is widely used in steel milling, aero-nautics, and electronics. Understanding the effectiveness of different surfaces for droplet cooling has the potential to greatly improve energy efficiency in these areas [4].

This project aims to develop a rigorous technique for quantifying, comparing, and ana-lyzing droplet cooling performance of different surfaces through infrared thermometry and high-speed video. Previous experiments have studied droplet cooling through more limited metrics, but have not used infrared imaging to analyze the heat flux of droplet cooling on different surfaces through the Leidenfrost point temperature. This data will be useful for understanding why different surface properties lead to different droplet cooling efficiencies. In previous pool boiling and flow boiling studies, infrared thermometry has been used to accurately measure the temperature of boiling surfaces. An IR transparent material such as sapphire was coated with an IR opaque conductive heater, which was in contact with water. Using a DC power supply, the IR opaque coating was heated as an IR camera observed the radiation from the opaque coating. The IR radiation transmitted to the camera lens was calibrated to temperatures, making the boiling process clearly visible and measurable [5]. This experiment modifies these methods for droplet cooling.

A similar process has been used for studying droplet cooling in refrigerant FC-72, which has a significantly lower boiling point than water and very different properties in its vapor phase. That experiment observed how droplet cooling changes with surface

temper-ature, droplet size, and droplet velocity, but did not analyze different surfaces textures [6]. Other droplet cooling studies have observed the effects of surface features, though not with infrared thermometry. Those experiments primarily focused on surface wetting, droplet shape, and identifying the Liedenfrost point temperature without calculating heat flux [7]. This study sheds greater light on the effects of surface roughness by using more com-prehensive measurement techniques that can also be applied to other variables in droplet cooling.

Chapter 2

Background

2.1

Engineered surfaces

Surfaces that improve boiling heat transfer and droplet cooling work by a combination of increasing surface area and wettability. Wettability is an intrinsic property of surface materials and is quantified by the contact angle droplets make with the surface, with smaller contact angles indicating greater wettability. Higher wettability allows for faster droplet evaporation due to greater contact with the heated surface. Surface area can be increased by making surfaces rougher, allowing for a greater heat flux in the time of contact with droplets and thus faster evaporation times [4].

2.2

Leidenfrost effect

At low surface temperatures, droplets wet the surface with a small contact angle and un-dergo nucleate boiling, which allows for high rates of heat transfer. At intermediate tem-peratures, water droplets undergo transition boiling, which is characterized by a violent spray of droplets. At high temperatures, the heat transfer from the hot surface to the water droplets is limited by the Leidenfrost effect. If the boiling surface is hot enough, the water will begin to evaporate prior to making contact with the surface, creating a layer of steam. The rate of convection with steam is much lower than with water, resulting in a much lower rate of heat removal, as seen in Figure 2-1. The Leidenfrost effect can be seen visually by a

large contact angle between the surface and the droplet, no wetting of the surface, and the droplet rebounding from the surface [2].

Figure 2-1: A boiling curve depicting the different regimes of droplet boiling and their associated surface temperatures (horizontal axis) and heat transfer rates (vertical axis) [2].

Recent literature indicates that surface properties related to engineered surfaces affect the Leidenfrost point temperature. However, the researchers have reported inconsistent results with differing conclusions on the degree to which micro- and nanostructures aid droplet cooling. Studies claiming that surface features increase the Leidenfrost point tem-perature theorize that variation in surface height allow some points to protrude high enough to contact the droplet and allow for bubble nucleation. Other studies also claim that poros-ity leading to greater wettabilporos-ity also aids in droplet contact and thus greater heat transfer [4].

2.3

Infrared thermometry

Infrared thermometry uses infrared cameras to infer the temperature of a surface using the relationship between radiation and temperature. Based on the Stefan-Boltzmann law shown in Equation 2.1, the power emitted by a body is proportional to T4and the emissivity of its surface. The Wiens displacement law states that the peak wavelength in thermal emission spectra is proportional to T−1, or that the peak photon energy is proportional to T . Thus, the number of photons emitted by a thermally radiating body is proportional to T3[8].

P= σ εAT4 (2.1)

Accurate infrared thermometry requires external sources of thermal radiation to be min-imized and low infrared absorption in the path from the surface in question to the infrared sensor. Previous studies have used sapphire as a substrate for surfaces to be measured for its low absorption in the infrared range. The surface used to measure temperature must be opaque to infrared light, so the sapphire has been coated with thin layers of metal.

2.4

Thermal conduction and numerical methods

The heat flux through a surface can be found numerically using the finite volume method of solving the 3-dimensional conduction equation. In finite volume analysis, a region of interest is divided into small elements, and conservation law equations are solved to give the state of every element. Most often, these elements are rectangular prisms.

For thermal conduction, the change thermal energy coming into each element must be balanced with the element’s change in internal energy, as shown in Figure 2-2. The variables dx, dy, and dz represent the lengths between edges of the meshgrid, and ∆x, ∆y, and ∆z represent the lengths between the centers of finite volumes.

Figure 2-2: Energy balance for an element in the finite volume analysis (left) and labeled dimensions of elements and their states(right).

The resulting partial differential equation can be solved either implicitly or explicitly. The explicit method, which uses spacial derivatives of the current time step to calculate temperatures at the subsequent time step, is prone to instabilities and requires very small time steps for convergence. The implicit method uses spacial derivatives based on the subsequent time step to simultaneously solve for temperatures through a system of linear equations. The implicit method converges with much larger time steps and is much less prone to instability [9]. The 3-dimensional implicit method is shown in Equation 2.3, with the current state temperature represented by T and the subsequent state temperature represented by T′. ρ cV∂ T ∂ t = ˙ Q_x++ ˙Q_x−+ ˙Q_y++ ˙Q_y−+ ˙Q_z++ ˙Q_z− (2.2) ρ cVT ′_{− T} ∆t = k  T_x+′ − T′ ∆x+ +T ′ x−− T′ ∆x−  dydz+ k _T′ y+− T′ ∆y+ +T ′ y−− T′ ∆y−  dxdz+ k T ′ z+− T′ ∆z+ +T ′ z−− T′ ∆z−  dxdy (2.3)

Equation 2.3 can be put into sparse symmetric matrix form, with only seven diagonals filled. The diagonal elements of the matrix are shown in Table 2.1. Elements at the edges in the volume without all six neighbors had the corresponding diagonal elements set to zero, indicating no heat transfer, or an adiabatic boundary.

Direction Diagonal position Non-boundary value -z −nxny kdxdy/∆z−

-y −n_x kdxdz/∆y−

-x −1 kdydz/∆x−

Self 0 ρ cV /∆t + kdxdy/∆z++ kdxdy/∆z−+ kdxdz/∆y++

kdxdz/∆y−+ kdydz/∆x++ kdydz/∆x−

+x 1 kdydz/∆x+

+y nx kdxdz/∆y+

+z n_xn_y kdxdy/∆z+

Table 2.1: Matrix diagonals for finite volume conduction. At boundaries where ∆x, ∆y, and ∆z may not exist, those values are set to 0.

The system can then be solved with a simple matrix equation. Because the resulting matrix can be too large to invert, iterative solvers are the only practical option for finding T′. A common method for this type of system is preconditioned conjugate gradient [10]. Because the temperature does not change drastically between time steps, T is an effective initial guess for T′. Convergence can be further accelerated by preconditioning the solver with the incomplete Cholesky factorization of the matrix [11].

After the 3-dimensional temperature has been solved for all time steps, heat flux can then be calculated from the temperature gradient across the boundary of interest, as shown in Equation 2.4.

q′′= k∂ T ∂ z = k

Tnz− Tnz−1

Chapter 3

Experimental procedure

3.1

Experiment overview

The general setup of the experiments is show in Figure 3-1. A gold-plated infrared mirror was placed below the heated surface at a 45 degree angle so as to allow an infrared camera to see the bottom of the surface to be tested. A high speed video camera was positioned to be parallel the top of the heated surface. A pipette was positioned 1.0 cm above the top of the heated surface and used to dispense water droplets onto the surface as the cameras recorded.

3.2

Preparing quenching surfaces

To accurately measure the infrared radiation from metal surfaces in boiling experiments, a thin layer of metal must be deposited on a transparent substrate so that the infrared radiation can be observed from behind the substrate without the interference of the water on the surface. Sapphire disks of thickness 2.0 mm and diameter 25 mm were used as the substrate because of sapphire’s low infrared absorption and emission. The disks had to be thick enough to withstand the thermal stresses of the experiment while not absorbing too much infrared radiation in transmission to the camera.

For the smooth chromium surface, 200 nm of chromium was deposited on one side of a sapphire disk by physical vapor deposition (PVD) sputtering. To ensure good adherence to the sapphire, sputtering was performed at a pressure of 1.0 E-6 mmHg. The 200 nm thickness was chosen to ensure complete covering of the sapphire while minimizing any temperature differences across the metal layer. This layering is shown in Figure 3-2. The size of surface features after this process is approximately 10 nm.

Figure 3-2: Layers applied to sapphire substrate to create smooth chromium surface.

For the rough chromium surface, 100 nm of titanium were sputtered onto a sapphire disk, followed by 100 nm of copper. The sapphire disk was then electroplated with 10 µm of additional copper. The copper surface was then gently sanded with 360 grit sandpaper in a single direction until scratches were evenly covering the entire surface. Finally, the sapphire disk was sputtered with 1.0 µm more of chromium. This sequence was used because copper does not readily adhere to sapphire in PVD sputtering, but was the only readily available material for electroplating, which is much more efficient than sputtering for thick layers. This layering is shown in Figure 3-3. The size of surface features after this process is approximately 0.3 to 0.5 µm.

Figure 3-3: Layers applied to sapphire substrate to create rough chromium surface.

Because chromium spontaneously oxidizes in air at high temperatures, the samples were all heated to 400∘C prior to conducting any experiments so that the oxidation would be similar across experiments. The color change caused by this oxidation is shown in Figure 3-4.

Figure 3-4: Samples before and after oxidation. The left sample is roughened and the right is smooth chromium. In each image the left is unoxidized and the right is oxidized. The color change could have affected infrared radiance and surface properties if not controlled.

3.3

Heater construction

The resistive heater used in this experiment was mounted on a heat-resistant ceramic block to protect other components from its high temperatures. This ceramic block had a 1.0 cm hole drilled in its center to allow an infrared camera to see the sapphire disks on the heater. The resistive component, shown in Figure 3-5 was cut from 0.5 mm thick stainless steel. Stainless steel was used tor its resistance to oxidation and high electrical resistivity, and the thickness was chosen to maximize resistance. The inner diameter of the heater’s ring was

14 mm and the outer diameter was 20 mm. This geometry allowed the center of the heated surface to be visible from below while evenly heating it and providing sufficient electrical resistance. The area connected to the center ring of the heater was cut to 6.0 mm to allow for equal resistive heating around the entire circumference.

Figure 3-5: The resistive heating element. Distances are in cm.

The resistive element was bolted to the ceramic block with its ring centered on the hole in the ceramic block, as shown in Figure 3-6. 10 AWG wire was fastened to the surface of the flared ends of the heater for connection to the power supply.

Figure 3-6: The resistive heater bolted to the ceramic block and electrical connections to the power supply.

Two steel bars were used as clamps to hold the sapphire disks to the heater. The surface of the bars in contact with the sapphire was insulated with 1 mm thick Aramid/Buna-N

to prevent thermal losses and to protect the sapphire from scratches. The clamps slid into place on bolts through the ceramic block and were fastened with nuts on springs, allowing a constant pressure to be applied to the sapphire without crushing or straining it.

The sapphire disks were clamped centered on the resistive heating element with their coated faces up. Bare-wire K-type thermocouples were inserted between the insulation on the clamps and the sapphire surface in order to measure the surface temperature for calibration.

Figure 3-7: Side view of the heater.

Figure 3-8: Top view of the heater.

The ceramic block was mounted to a stand that allowed for tilting and sliding in 3 dimensions to aid in camera alignment and focusing.

3.4

Experiment setup

A gold infrared mirror was placed under the heater stand at a 45 degree angle to allow the infrared camera to view the bottom of the sapphire through the hole in the ceramic block. The tilt and position of the heater stand were then adjusted to get the coated surface of the sapphire disk into focus in the viewing window. The infrared camera’s viewing window was 320 by 254 pixels, with the pixel spanning 31.3 µm at the focal point.

A high-speed video camera was mounted opposite the heater from the infrared camera, aligned to view the edge of the sapphire disk when droplets land.

To ensure the correctness of the thermocouple readings, the heater was slowly stepped to the maximum desired temperature using a high-current power supply. At each temper-ature step, the thermocouple readings were compared. A difference of greater than 5.0 Celsius would indicate that at least one of the thermocouples was not well-covered by the insulation. In that case, the heater was cooled back to room temperature and the thermo-couples readjusted before checking for agreement again.

A stand was fitted for a micropipette in order to hold its tip 1.0 cm above the coated sur-face of the sapphire disk. This stand allowed for consistent placement and impact velocity of the water droplets during experiments.

3.5

Quenching experiments

For each temperature to be tested on a surface, the power supply was set to a power expected to give the desired temperature. After setting the power to the heater, its temperature was allowed to reach steady-state for 20 minutes.

7.0 µL of deionized water was drawn into the pipette. This volume was chosen because the droplet radius is only slightly larger than the capillary length for water, but the droplet is large enough to fall from the pipette by gravity. The infrared and high speed video camera were set synchronize at 3000 frames per second, and the lighting was adjusted to ensure the droplet would be visible in the high speed video camera.

The pipette was held in its stand. The cameras were then triggered to record and the droplet released from the pipette, shown in Figure 3-10.

Chapter 4

Infrared data processing

4.1

Non-uniformity correction

Due to the optical distortion from the infrared camera lens and mirror, the relation between surface temperature and measured infrared radiation are not identical across all pixels in the camera. To resolve this discrepancy, the center 3 by 3 pixels in the first five frames in each video prior to droplet contact were averaged as a reference number of counts. Then, the error in each pixel’s counts relative to the reference was fitted with a piecewise cubic Hermite interpolating polynomial (PCHIP). Using this interpolation, a consistent infrared count reading was calculated by adding back the interpolated error at every pixel, shown in Figures 4-1 and 4-2.

Figure 4-1: Non-uniformity correction from a pixel’s counts to its error from the center pixels’ average counts.

Figure 4-2: Uncorrected infrared counts (left) and corrected counts (right). The non-uniformity correction eliminated effects of optical distortion and reduced noise.

4.2

Temperature calibration

A cubic curve was fitted to relate the temperatures measured my the thermocouples to the radiation in the reference pixels. Then, the temperature at each pixel in every video was

calculated by correcting the pixel’s measured radiation to the reference and then calculat-ing the pixel’s temperature from its corrected radiation measurement. The resultcalculat-ing tem-perature profiles, an example shown in Figure 4-3, sometimes contained significant noise depending on the slope of the correction curve.

Based on computational models and experiments performed by Haeseong Kim, the center of the sapphire disk was within 10∘C of the measured thermocouple temperatures in the range tested.

Figure 4-3: The calibration curve from infrared counts to temperature (left) allowed the surface temperature to be calculated at every frame (right). The axes mark pixels, which are 31.3 µm in length.

4.3

Noise reduction and partial droplets

Even after the non-uniformity correction and temperature calibration, some pixels showed significant noise or error. In particular, a near vertical slope in the correction curve for some pixels caused small changes in infrared counts to dramatically change the calculated temperature.

To account for this noise, the surface temperature matrices were filtered first by replac-ing all pixels readreplac-ing values higher or lower than all four of their neighbors to the mean of their neighbors’ temperatures. The resulting temperature matrix was then convoluted with a 3 by 3 Gaussian filter. While some noise remained in the temperature matrices, the temperature images were much sharper and realistic.

Because some droplets did not entirely land in the infrared camera’s viewing area, the temperature matrices for those droplets were reflected about the axis of symmetry of the droplet’s footprint to create a complete view of a droplet.

4.4

3-dimensional conduction

To calculate the heat flux through the surface of the sapphire samples, finite volume analysis was used to solve the 3-dimensional conduction equation. In this computation, only the sapphire in the field of view of the infrared camera was considered, making the volume a rectangular prism. All surfaces of the volume were treated as adiabatic except for the top, coated surface, for which the temperature was determined above. The time step used for these calculates was 1/3000 s, equal to the frame rate of the cameras. The volume under consideration was cut into a 3-dimensional meshgrid with its horizontal dimensions equal to those of the pixels on the infrared camera, shown in Figure 4-4. The horizontal plane was then padded with progressively wider pixels with adiabatic surface boundary conditions to account for possible spreading of thermal energy. The vertical dimension was sliced in thicknesses of half the pixel dimension, or 15.7 µm.

Figure 4-4: Space modeled by finite volumes (left) and horizontal meshgrid (right). White regions are adiabatic boundaries, and the colored region has prescribed temperature bound-aries. The original viewing area of the infrared camera has the fine resolution of the pixel size, while the buffers have increasingly course resolution.

stability and convergence in the 3-dimensional temperature solution and put into matrix form. For the prescribed temperature boundary at the top surface of the meshgrid, an additional term was used for the conduction from the surface to the center of the top layer of the mesh. An example of the resulting surface temperature to heat flux conversion is shown in Figure 4-5.

Chapter 5

Results

5.1

Comparison of surfaces

From the high-speed videos, the time of initial droplet contact was calculated by count-ing the frames between initial droplet contact and either complete evaporation or rebound from the surface. As can be seen in Figure 5-1, the time of droplet contact for the rough and smooth surfaces followed a similar trend of near exponential decay until leveling off at about 0.015 s for temperatures over 300∘C. This data indicates that the onset of the Leiden-frost effect occurs at a similar surface temperature for both rough and smooth chromium surfaces.

The total heat loss in the droplet’s first contact was calculated by integrating the heat flux over the entire viewing window for every frame until the droplet rebounded from the surface or evaporated, as shown in Equation 5.1.

Nf rames

∑

∑

∑

For both surfaces, the maximum heat removal peaks at low temperatures, at which the droplet does not bounce and does not spray smaller water droplets away. At these

temperatures, the time of initial contact lasts until the water droplet fully evaporates. As can be seen in Figure 5-1, the contact time and total heat removal are very closely correlated for both surfaces.

Regardless of initial temperature, the calculated total heat removal never reached the theoretical maximum of 17 J, which accounts for heating the 7.0 µL droplet from 20∘C to 100∘C and the subsequent vaporization. At low temperatures, it was expected that the heat removal would be much closer to this value since the droplet does not bounce. However, this discrepancy is likely due to large amounts of spray from the boiling droplets, seen in Figures 5-5 and 5-6, which caused significant portions of the droplet to absorb heat where it would not be seen by the infrared camera. At lower temperatures, where there was no visible spray, the reason for this discrepancy is less clear, and it is difficult to form a hypothesis with this data. Additionally, some droplets spread partially outside the viewing window, and reflection methods to recover this lost area may not have been completely accurate.

Figure 5-1: The heat removed by the droplet’s first contact (left) was very close for rough and smooth chromium surfaces at low temperatures, but significantly higher for the smooth at high temperatures. The rough and smooth surfaces appear to have similar contact times with the droplet, with an exponential decay that levels off to approximately 0.015 s at high temperatures (right).

first contact with the surface. Much like total heat removal, the rough and smooth surfaces perform similarly at low temperatures, but the smooth surface allows for greater heat trans-fer at higher temperatures. Furthermore, the rough surface has its maximum heat flux around 200∘C, while the smooth surface does not reach its maximum heat flux until about 280∘C.

As shown in Figure 5-2, there is significant noise in the calculated heat loss trends, likely because only one measurement was taken at each temperature. Without more rigor-ous testing with more trials at each temperature, conclusions about the efficacy of rough and smooth chromium surfaces in droplet cooling should be very limited.

Figure 5-2: The trends seen in heat removal rate (left) and maximum surface cooling (right) follow similar trends. In both metrics, the smooth chromium surface outperforms the rough. The maximum surface cooling peaks at a much higher temperature for the rough surface, while the maximum cooling begins descending at lower temperatures for the smooth sur-face.

This pattern seen in heat flux is supported by the pattern seen in temperature. At low initial surface temperatures, the 2 percentile temperature reached is very similar for the rough and smooth surfaces, but over 200 ∘C, the smooth surface reaches a significantly lower minimum temperature than the rough surface, as seen in Figure 5-2.

The area of the surface wetted by the droplet was approximated by counting pixels where the heat flux exceeded 40% of the maximum heat flux achieved. As seen in Figure 5-3, this approximation showed slightly more wetting for the rough surface at low temper-atures but more surface wetting for the smooth surface at high tempertemper-atures. The greater wetting of the rough surface at low temperatures could be a result of capillary effects in the troughs of the scratched surface. At high temperatures, the roughened surface might have caused a greater mean distance from the chromium surface to the droplet, reducing heat flux further from the center of contact below the threshold to be counted.

Figure 5-3: Approximation of surface area wetted by droplet at different temperatures. The rough surface appears to have been wetted more at low temperatures, while the smooth surface apprears to have been wetted more at high temperatures.

5.2

Droplet behavior

Monitoring the minimum surface temperature throughout the initial contact of a droplet provides interesting insight into the boiling and rebound process of the droplet. Regardless of initial surface temperature, most of the surface cooling takes place in the first 0.01 s after contact. As expected, the magnitude of this initial drop in temperature increases with initial surface temperature. Similarly, the heat exchange rate peaks immediately after the droplet makes first contact and increases with surface temperature.

Although the magnitude of temperature drops and heat transfer rates differed for the rough and smooth chromium surfaces, the time-evolution of heat transfer rate and temper-ature were very consistent at the same tempertemper-atures regardless of surface.

At low temperatures in the nucleate boiling regime, as shown in Figure 5-4, the surface temperature immediately rises after the initial droplet contact as the water heats but does not boil. As the droplet boils, the temperature decreases once again. The temperature begins rising again before the droplet fully evaporates. Although the heat transfer rate in the first 0.1 s of droplet contact is over 20 times as large as the rest of the contact time, it accounts for very little of the total heat transfer as the droplet boils.

Figure 5-4: Droplet behavior at low temperatures is characteristic of nucleate boiling.

Around 175 ∘C, in the transition boiling regime, the surface temperature continues to drop directly after the initial droplet contact, but at a slower rate as the droplet boils imme-diately. The temperature begins rising before the droplet has completely boiled or sprayed away, though not as significantly as at lower temperatures. The heat transfer rate during the violent boiling process is much higher than at lower temperatures, but decays very quickly.

Figure 5-5: Droplet behavior characteristic of early transition boiling.

When film boiling begins slightly over 200∘C, the surface reaches its minimum temper-ature immediately at droplet contact. However, the droplet appears to stick to the surface for a short period of time without undergoing any bubble-producing boiling. The tempera-ture rise is faster after the droplet rebounds. The heat transfer to the droplet occurs mostly at the first contact, but continues throughout the droplet’s contact period.

Over 300 ∘C, the droplet no longer sticks to the chromium surface at all. After the droplet makes its initial contact with the surface, it begins rebounding and the surface temperature starts rising. The heat transfer rate spikes very fast and quickly returns to zero. The lingering heat flux long after the droplet has departed is likely due to the numerical approximation for heat flux because as the surface reheats, there is a small thermal gradient in the vertical dimension. As seen in Figure 5-7, the droplet still sprays some.

Figure 5-7: Droplet behavior mostly resembling film boiling.

Near 400∘C, the droplet’s effect on surface temperature is much the same around 300

Figure 5-8: Droplet exhibiting Leidenfrost effect fully.

5.3

Limitations and sources of error

Because only one trial was tested for every temperature step in this experiment, the signif-icance of the data is limited. The data above have many jagged trends with unexplained peaks and dips. Some of the variation observed is likely due to natural variation in the droplet boiling process.

The droplet size and position in the infrared viewing area were not controlled perfectly. Some data was rejected because large portions of the droplet did not leave the pipette tip, causing a smaller droplet to land on the surface. However, other trials may have also had incomplete droplets. Also, the reflection done to reconstruct temperature data from droplets that partially missed the infrared camera view is inherently inaccurate because the water droplets are not perfectly round.

Differences in surface preparation methods may account for some of the measured dif-ferences in the rough and smooth chromium surfaces. The thick electroplated copper layer under the rough chromium surface could have introduced small errors due to its thermal diffusivity. Heat could spread horizontally through the copper before reaching the titanium surface where the infrared emission was measured. Additionally, the copper acts as a heat

sink, delaying any temperature changes from reaching the titanium layer and decreasing their amplitude. Running the heat flux calculations assuming a 10 µm copper layer above the imposed temperature boundary, the resulting heat fluxes were within 2% of the expected values, indicating that the thermal effects of the electroplated copper layer are very small compared to other variations in the data.

Due to changes in internal temperature, the temperature calibration and 3-dimensional conduction model fail to account for the change in radiation coming from the sapphire. The initial calibration points were taken only at static temperatures, where the sapphire was at the same temperature as the chromium surface. However, in transient, the radiation from the sapphire also changes, thus biasing the calibration toward lower temperatures in transient.

Additionally, the surface of the sapphire never was truly isothermal, even at the calibra-tion points, further limiting the accuracy of the calibracalibra-tions. In the horizontal dimensions, the surface temperature varied by as much as 5∘C in steady state. The vertical temperature difference between the bottom near the heater and the top surface was not measured, but was likely within 1∘C with with natural convection of air.

Chapter 6

Conclusions

This study aimed to develop an experimental technique for analyzing the effectiveness of different surfaces for droplet cooling. This knowledge is particularly useful in consider-ing BWR claddconsider-ings that must be able to quickly dissipate heat in case spray coolers are activated in a loss of coolant accident.

The experimental procedure used in this project provided some insight into smooth and rough chromium coatings’ effectiveness at temperatures ranging from 100 ∘C to 400 ∘C, covering nucleate boiling to film boiling regimes. Contrary to what the literature suggests, the data indicated that smooth chromium surfaces may be more effective at transferring heat to water droplets at high temperatures. This difference may be due to greater spreading of the water droplets across the smooth surface compared to a rough surface. The methods developed in this study can be expanded and refined to continue research in the field of droplet quenching.

The reliability and accuracy of this experiment could be greatly improved by repeating trials with the same surface temperature multiple times in order to ensure proper statistics are collected. Some behaviors of boiling water droplets seem to be stochastic, indicating that a range of results could be likely for identical conditions. Additionally, greater controls could be placed on droplet size and landing position. Such controls would prevent more data from being rejected for droplets and eliminate the need to approximate full droplet data from reflections of partial data.

dif-ferences in the rough and smooth chromium surfaces. Although this difference in coating most likely had little effect on the recorded temperatures after calibration, the experiment could have been more tightly controlled by having the same electroplated copper layer under the smooth chromium surface.

Neglecting the change in the sapphire’s infrared emission during transients likely caused some inaccuracies in the results. The Red Lab Group at MIT has developed a method for accounting for this radiation change, which would improve the accuracy of this experi-ments’ results [5].

In addition to these procedural changes, future studies should focus on a wider variety of surface types, including nano-engineered surfaces. Additionally, the effect of droplet size, temperature, and impingement velocity should also be explored. New heater designs should be considered to achieve more uniform temperatures at calibration.

Bibliography

[1] Core Spray System, ch. 10.3. General Electric Systems Technology Manual, General Electric, Sept. 2011.

[2] J. S. Bjørge, M.-M. Metallinou, T. Log, and Øyvind Frette, “Method for measuring cooling efficiency of water droplets impinging onto hot metal discs,” Applied Sci-ences, June 2018.

[3] F. S. Gunnerson and T. R. Yackle, “Quenching and rewetting of nuclear fuel rods,” Nuclear Technology, vol. 54, no. 1, p. 113, 1981.

[4] M. Auliano, Controlling droplet cooling with micro/nano-structured surfaces. PhD dissertation, Norwegian University of Science and Technology, Department of Energy and Process Engineering, Nov. 2018.

[5] M. Bucci, A. Richenderfer, G.-Y. Su, T. McKrell, and J. Buongiorno, “A mechanistic ir calibration technique for boiling heat transfer investigations,” International Journal of Multiphase Flow, vol. 83, pp. 115–127, 2016.

[6] A. Gholijani, C. Schlawitschek, T. Gambaryan-Roisman, and P. Stephan, “Heat trans-fer during drop impingement onto a hot wall: The influence of wall superheat, im-pact velocity, and drop diameter,” International Journal of Heat and Mass Transfer, vol. 153, 2020.

[7] S. H. Kim, Y. Jiang, and H. Kim, “Droplet impact and lfp on wettability and nanos-tructured surface,” Experimental Thermal and Fluid Science, vol. 99, pp. 85–93, July 2018.

[8] “Satellite remote sensing: Thermal radiation.” University of Calfornia, San Diego lecture, SIO 135. Accessed from https://topex.ucsd.edu/rs/Lec06.pdf, 2017.

[9] Q. Wang and K. Wilcox, “Introduction to the finite element methods,” in Computa-tional Methods in Aerospace Engineering, MIT Open Courseware, 2014.

[10] G. Strang, Linear Algebra and Learning from Data, ch. Computations with large matrices, pp. 121–122. Wellesley Cambridge Press, 2019.

[11] I. Arany, “The preconditioned conjugate gradient method with incomplete factoriza-tion precondifactoriza-tioners,” Computers Mathematics with Applicafactoriza-tions, vol. 31, pp. 1–5, Feb. 1996.