Photographic Study of Nucleate Boiling On the Surface of a Heated Rod

Transcription

1 Photographic Study of Nucleate Boiling On the Surface of a Heated Rod Lionel Nelson Lobo A thesis submitted in conformity with the requirements for the degree of Master of Engineering Graduate Department of Mechanical and Industrial Engineering University of Toronto Copyright by Lionel Nelson Lobo 2010

2 Acknowledgements Special thanks to Professor Nasser Ashgriz for his help and continuous support on this project. I would also like to thanks Farhan Sultan, Reza Karami and Amireza Amighi for their contributions. Their knowledge in machining, thermodynamics and fluid mechanics helped contribute to the success of this project. Finally, I would like to acknowledge the huge contributions made by Nadim Vira, my colleague at the University of Toronto. His unconditional support was crucial to the completion of this project. Page 2 of 29

3 Abstract The two phase liquid-vapour flow in a CANDU reactor core is an important part of the nuclear power generation process. In order to improve the safety and economics of a CANDU reactor, it is essential to understand the mechanisms governing this flow and the mechanism governing the formation of vapour bubbles at the Critical Heat Flux. While prior research exists about nucleation and heat transfer at normally achievable temperatures and pressures, not enough is known about nucleation at nuclear conditions. This project is the first step towards developing effective heat transfer models at nuclear conditions and is intended to demonstrate the feasibility of such an analysis. The setup used for this study was developed using dimensions from existing nuclear fuel rod systems in order to simulate a single fuel rod immersed in a horizontal liquid flow. Inlet water pressure and flow rate can be varied in this setup and the effects of these variations on nucleation can be observed photographically. Due to time constraints a complete analysis of pressure and flow rate effects was not completed, however detailed recommendations on how to proceed with such an analysis has been presented. A significant setback faced during this project was related to the design and installation of the glass windows. To determine the thickness of these windows and maximum allowable torque, a detailed analysis was performed in SolidWorks and Cosmos and the results have been presented in this report. Page 3 of 29

4 Table of Contents Acknowledgements...2 Abstract Introduction Literature Review Subcooled Boiling Nucleation Nucleate Boiling Relations Bubble Diameter Bubble Velocity Bubble Departure Frequency Experimental Setup Tank Sub-Assembly The Nucleation Chamber Results and Discussion General Observations Bubble Departure Diameter Bubble Velocity Bubble Frequency Future Recommendations Conclusion References...29 Page 4 of 29

5 List of Symbols or Abbreviations A A 1F A 2F c C PL d d W E f F g G H LG H L0 h Q Unsupported Area Wall fraction cooled by single phase convection Wall fraction cooled by quenching Crack depth Specific heat capacity of the liquid Bubble diameter Bubble departure diameter on the wall Young s modulus Bubble departure frequency Safety factor Acceleration due to gravity Gibbs free energy Evaporation enthalpy convective heat transfer coefficient Quenching heat transfer coefficient. m L Mass flow rate of water (kg/s) m W M n N a Evaporation rate Modulus of rupture Polytropic exponent Active nucleation site density Page 5 of 29

6 Nu P Pr Q F Q Q Q E Nusselt number Pressure Prandtl number Heat flux due to single phase turbulent convection Heat flux due to single phase turbulent quenching Heat flux due to single phase turbulent evaporation " qw Wall heat flux (W/m 2 ) S f T T L T L,in T LW T sat Fracture stress Glass thickness Local liquid temperature Bulk temperature of inlet water Liquid characteristic near wall temperature Saturation temperature T sub, LW Change in liquid characteristic near wall temperature t W Waiting time between the bubble departure and the appearance of a next bubble at the same nucleation site T w Wall temperature T W,ONB Wall temperature at which onset of nucleate boiling occurs u W Friction velocity Z ONB Location of ONB point θ ρ G, ρ V Contact angle Vapour density Page 6 of 29

7 ρ L Δρ σ γ Liquid density ρ L -ρ G Interfacial tension Surface energy µ l Liquid viscosity Page 7 of 29

8 1.0 Introduction Fuel rods in nuclear power plants must be cooled at all times to ensure safe operation. To do this, the surface of these rods are constantly surrounded by a layer of fast moving pressurized water, which while acting as a coolant is also responsible for acting as an agent of energy transfer. The presence of liquid coolant ensures that power generated by the reactor does not exceed a critical level. Above this level the coolant surrounding the fuel rods start to dry out causing nucleation and appearance of bubbles. If this condition is sustained, the lack of a satisfactory heat transfer mechanism can cause the fuel rods to overheat, leading to reactor meltdown. A number of studies have been conducted on nucleation at normally achievable temperatures and pressures however, not enough is known about the characteristics of these bubbles at nuclear conditions to accurately predict their effect on the heat transfer process. As a result design methods must be conservative. An accurate prediction of these characteristics could lead to the development of better heat transfer models leading to savings in materials and energy by removing unpredictability in design. The objective of this research project is to study the characteristics of the bubbles formed due to nucleation on the surface of a heated fuel rod. This was done by designing a scaled model of a nuclear fuel channel and observing the thermal and physical characteristics of the rod-liquid interface. The results obtained by studying characteristics such as bubble Page 8 of 29

9 frequency, bubble diameter and initial bubble velocity can be used in future studies on more complex models and at higher temperatures and pressures. Page 9 of 29

10 2.0 Literature Review 2.1 Subcooled Boiling Subcooled flow boiling is an efficient heat transfer mechanism which occurs in many industrial applications, including nuclear reactor cores. The term subcooled means that saturation temperature is exceeded only at a heated surface while the bulk of the liquid is at a temperature below its saturation point. This type of boiling is observed at fuel rod and coolant interface where the heat flux supplied by the fuel rod surface is too high to be transferred to the flow of the coolant by a single phase convective conductive mechanism. At this point steam bubbles are generated at the heated surface through the onset of nucleate boiling. These bubbles grow and leave the wall at a critical size which is determined by surface tension, flow regime of the surrounding fluid and heat transfer from the heated surface. Heat transfer from the wall is now not only being carried out by turbulent convection of liquid, but also by transient conduction due to the departing bubbles and by evaporation. The movement of steam bubbles through the subcooled liquid result in the release of latent heat from the bubbles when they condense. An accurate model for the distribution of wall heat flux can now only be calculated by taking into account nucleation site density, size of the departing bubbles, their detachment frequency, and time taken for next bubble to form at the same site (or frequency of bubble formation). Page 10 of 29

11 2.2 Nucleation The formation of bubbles can be attributed to a process called nucleation, which is the onset of a phase transition in a small region. Nucleation sites are normally present on the outer surface of the heated tube which is in contact with water. Formation of these sites can be attributed to imperfections in the heated tube and presence of suspended particles and minute bubbles in the cooling water. This is called heterogeneous nucleation. Nucleation without preferential nucleation sites, which is rare, is called homogeneous nucleation. The figure below shows the different stages of bubble growth and development. The cavity or imperfection represents a nucleation site. In Stage I, the Waiting Period, vapour trapped in this cavity receives energy from the hot surface causing it to grow. In Stage II, the Growth Period, the bubble reaches the mouth of the cavity and keeps increasing its volume while decreasing its radius. The final stage, the Departure (or Collapse) Period, is reached when the radius of the bubble is equal to the radius of the cavity. Beyond this point, bubble growth depends on the degree of superheating of the liquid. Above a certain level of superheating, bubbles gain enough energy to leave the surface and travel to the bulk. Page 11 of 29

12 Figure 1: Stages of Bubble Formation 1 Heterogeneous nucleation can also be explained by free energy changes between liquid and gas phases. Energy is gained due to the creation of a new volume and lost due to creation of a new interface. When the overall change in free energy is negative, nucleation is favoured G r Gv 4 r 3 The first term shows the energy gained by creating a new volume and the second term shows energy loss due to surface tension of the new interface. 2.3 Nucleate Boiling Relations The onset of nucleate boiling (ONB) process is similar to heterogeneous nucleation on wall crevices and occurs when bubbles forming on crevices survive. Temperature at which onset of nucleate boiling occurs can be predicted using the correlation developed by Bergles and Rohsenhow (1964): Page 12 of 29

13 Figure 2: Nucleate Boiling 2 T W sat ONB " n q w T P T W,ONB is the wall temperature at which onset of nucleate boiling occurs, in W/m 2, P is the system pressure and T sat is saturation temperature. " qw is wall heat flux The location of the point of ONB can be determined from the following energy balance:. " L PL L, ONB L, in w ONB m C T T Dq Z 3. m is mass flow rate of water (kg/s), C PL is specific heat at constant pressure, T L,in is the bulk L temperature of inlet water, Z ONB is the location of ONB point Bubble Diameter If interactions from adjacent bubbles and lateral motion of the liquid are ignored, bubble diameter can be estimated by equating force balance between buoyancy and surface tension 1 : Page 13 of 29

14 3 D D l v 3 g D 3 l v g This simplified model is not completely accurate for the following reasons: At higher heat fluxes, the number of nucleation sites increases. This increases the probability of a single bubble growing from adjacent cavities. Bubble departure diameter is significantly affected by lateral motion of liquid which increases at higher heat fluxes. A number of correlations have been developed to increase the accuracy of predicting bubble departure diameter. Most of these models are either highly simplified with a limited range of validity or highly complicated and requiring an iterative procedure. The models described below are intended for nucleate pool boiling without flowing water. Adding the flow rate component is expected to lead to a deviation from these formulas: Fritz Model Extensive research determined Fritz model to be one of the most reliable model available for predicting bubble diameter for pool boiling of pure liquids. D g 2 l v Fritz 4 Page 14 of 29

15 θ = contact angle (due to the complexity involved in determining contact angle, Fritz recommends using an average value of 45 ) σ = interfacial tension (N/m) C g = acceleration due to gravity (m/s 2 ) ρ l ρ v = Density of liquid density of vapor = = kg/m 3 Stephan Ja D , Ar g Pr l v Stephan 5 This is a modified version of the Fritz model which includes dimensionless Prandtl (Pr), Jacob (Ja) and Archimedes (Ar) numbers and is considered slightly more accurate than the Fritz model. The drawback is that this model requires an iterative procedure. Cole 2 D 0.04Ja g l v Cole 6 Cole proposed a modification of contact angle theories by including the effect of system pressure through a modified Jacob number, Ja. Page 15 of 29

16 Van Stralen et al l Ja D Van Stralen et al. 7 g 3Ja The Van Stralen model predicts the nucleate boiling phenomenon by taking into account the mechanisms governing bubble growth. All the above models except Fritz contain the Jacob number which is a dimensionless quantity which is a function of surface temperature and is generally unknown for a system. For the purpose of this project the theoretical value of bubble diameter will be obtained using Fritz model and these values will be compared with the experimentally obtained readings to determine if a curve fit is possible. Due to the high complexity of contact angle measurements an average value of 45 will be used in this project as recommended by Fritz Bubble Velocity After a bubble is formed on the heater surface, it rapidly accelerates to its terminal velocity V t which is determined by the cumulative effects of the buoyant rising force and the downward drag force. For very small, spherical bubbles, Stokes law can be used to obtain a theoretical estimate for V t as it takes both of these effects into account. According to this law, the terminal velocity in the vertical direction is given by: 2 gd Vt 18 l Page 16 of 29

17 g = acceleration due to gravity, d = bubble diameter, Δρ = difference in density between liquid and gas and µ l = liquid viscosity This law only applies to small bubbles with an immobile surface. An extension of this law with a mobile surface was developed by Hadamard-Rybcszynski. This relation is only applicable to spherical bubbles: V t 2 g(1 ) 0_ Clean 2 3 r (2 3 ) _ Dirty The trajectory of a bubble rising in a fluid is also greatly affected by temperature. A change in temperature leads to a change in fluid viscosity and density and as a result bubbles rise faster with increasing temperature Bubble Departure Frequency Bubble departure frequency can be estimated as the terminal rise velocity over the bubble departure diameter (Cole, 1960): f 4 g( L G) 3d W L Where L and G are liquid and vapour densities respectively This relation was developed using a system consisting of an electric heater suspended in a pool of water at its saturation temperature. Page 17 of 29

18 3.0 Experimental Setup The setup consists of 2 main sub-assemblies; the tank and the nucleation chamber as shown in the schematic below: Figure 3: Schematics of the Entire Set-Up 3.1 Tank Sub-Assembly The function of the 30 gallon steel tank is to provide a study supply of heated water to the nucleation chamber. The tank is covered by a layer of insulation to help keep water temperature constant during testing when the heater has been turned off. Attached to the tank is a pump, pressure gauge, heater and data acquisition system. These devices help control the pressure and temperature of the water in the tank. Release and relief valves are Page 18 of 29

19 attached to the set-up to ensure that pressure in the tank is always at an acceptable level. The setup contains two inlet valves; the water inlet valve is attached to a small pipe that allowed the user to estimate the level of the water in the tank. The compressed air inlet valve is attached to the top of the tank and receives compressed air from the building main line as shown in the figure below. The outlet is attached to a stainless steel tube covered by insulation. Settings on the data acquisition system can be modified to obtain the desired inlet water temperature. Compressed air pressure can be set using the gauge attached to the main line. Figure 4: The Tank Assembly Page 19 of 29

20 3.2 The Nucleation Chamber The function of this sub-assembly is to create conditions favourable for the study of nucleation. This section consists of a combination of measurement instruments, an aluminum chamber with glass windows and a cartridge heater to simulate the nuclear fuel rod, as shown below. Figure 5: Solid Model of Chamber Assembly Page 20 of 29

21 Figure 6: Actual Chamber Assembly The surface finish of the cartridge heater is an important parameter that affects the location and rate of nucleation. As mentioned in section 2.2, imperfections on heated surfaces produce favourable nucleation sites. Optimal nucleation conditions were produced by polishing the heater surface and adding a few strategically placed scratches in order to create nucleation sites. The 3 thermocouples installed on the upper side of the chamber are intended to keep track of water temperature at different points along the chamber. When installing these thermocouples, it is important to ensure that the bulb tips do not touch the heater surface as this produces skewed temperature readings (see figure below). Temperature measurements were also recorded by a thermocouple placed in the inlet water pipe and a K-type thermocouple placed near the heater resistance element. A pressure gauge attached to the section of the pipe in front of the chamber measured pressure of inlet water and a flow meter is used to monitor the flow rate of inlet water. Page 21 of 29

22 Figure 7: Installing the Thermocouple Glass windows are present on 2 sides of this assembly in order to allow enough light enter the chamber while filming the nucleation process. These windows are sandwiched between 2 layers of gasket and are attached to the main chamber by 2 flanges. A torque of 20ft-lb was applied to each bolt on the flange to prevent water leakage when running the experiment. Page 22 of 29

23 4.0 Results and Discussion Information about bubble departure diameter, bubble departure velocity and bubble frequency was to be obtained by analyzing the images taken by the Photron Fastcam camera. Due to time constraints on the project only one measurement was obtained and therefore the following sections will contain information about the observations from this set of images and the recommended approach for collecting and analyzing further data. 4.1 General Observations Polishing the heater and adding scratches on the surface helps induce nucleation by creating nucleation sites. The rate of nucleation and number of nucleation sites was observed to increase with an increase in temperature of the inlet water and decreases in system pressure and flow rate. 4.2 Bubble Departure Diameter Observations: The development and evolution of bubbles was observed by comparing data at consecutive time points. It was clear that average bubble diameter increased as it moved away from the heater and into the bulk. The increase in bubble diameter can be explained by the fact that super saturation, which is the driving force for mass transfer, decreases as distance from Page 23 of 29

24 the heater increases. It was also observed that the size of bubbles decreased with increase in pressure and increase in flow rate if all other conditions were kept constant. Recommended Approach: Extensive research indicated that Fritz model is one of the most reliable for predicting bubble diameter for pool boiling of pure liquids. The shape and form of the theoretical pressure versus bubble diameter curve obtained from this model would be compared to the graph obtained from actual measurements to determine if a new relation can be obtained by finding a correction factor that accurately fits the theoretical curve to the actual curve. A graph depicting effects of flow rate on diameter would also be added. D g 2 l v Fritz Model 4.3 Bubble Velocity Observation: Bubbles were found to move in both vertical and horizontal directions when they detached from the heater surface. Liquid flow rate and system pressure were the most important parameters for determining bubble velocity, which was observed to increase with decrease in pressure and flow rate. Page 24 of 29

25 Recommended Approach: Stokes law is recommended for obtaining the theoretical curve and a comparison should be made with the actual curve to determine if it can be fitted by adding a correction factor. Graph of flow rate versus bubble velocity would also be added. V t 2 gd 18 l Stokes Law 4.4 Bubble Frequency Observations: A set of images was obtained at the following conditions: Inlet water temperature: 93 C Water flow rate: 0.6 gallons per minute Chamber pressure: 15psi Camera frame rate: 1000 frames per second Frequency was determined by measuring the time lapse between the moment a bubble broke from the heater surface at a specific location to the moment the next bubble formed at the same location broke from the surface. The table below lists the number of frames between consecutive bubbles. The average number of frames between consecutive bubbles was calculated to be Since each frame lasts second, the average time between bubbles is second and frequency is bubbles per second. Similar readings Page 25 of 29

26 could be taken by varying pressure and flow rate and graphs of these variables versus bubble frequency could be obtained Table 1: Number of frames between the appearances of consecutive bubbles at a single location Figure 8: Sample image used for calculating bubble frequency Page 26 of 29

27 5.0 Future Recommendations Throughout the life of this project there have been continuous modifications and improvements made to the design and testing procedure. Although these changes have been useful a set of recommendations to further improve the functionality of the set-up will be discussed in this chapter. The tank currently being used is made of steel and is highly susceptible to corrosion. A stainless steel tank would help feed uncontaminated water into the nucleation chamber allowing for cleaner images. The chamber itself is made entirely of aluminium which is not the best material to use to support a glass window as it can bend easily if uneven torque is applied to the bolts holding the setup together. Stainless steel would significantly reduce this bending. If a redesign of the chamber is possible, larger windows would be beneficial as it would allow more light to pass through, leading to better visibility. Quartz of thickness ¾ has been used for the windows. Further research into another type of glass called sapphire glass might produce a stronger, but more expensive alternative to Quartz. A stage that allows small and accurate displacements of the camera along the x, y and z axis would greatly help locating and focusing on nucleation zones making it easier to obtain accurate measurements. Finally, better lighting sources that have adjustable intensity and dispersion levels would help produce clear, well lit images. Page 27 of 29

28 6.0 Conclusion An experimental set-up was created to mimic a nuclear fuel channel for the purpose of studying the following characteristics of nucleation: bubble departure diameter, bubble departure velocity and bubble frequency. Due to constraints in the design, useful images were difficult to obtain. The small window size placed serious limitations on the variability in camera and lighting angles making it hard to capture images that could be used for diameter and velocity measurements. A single frequency measurement was obtained at a pressure of 15psi and flow rate of 0.6 gallons per minute. Further frequency studies can be carried out by varying chamber pressure and inlet water flow rate to obtain relationships between frequency and pressure and frequency and flow rate. It is highly recommended to change the material used to build the chamber from aluminium to stainless steel as aluminium is more prone to warping when subject to high torque leading to uneven forces being applied to the glass window. Page 28 of 29

29 7.0 References [1] Seyed Ali Alavi Fazel and Seyed Baher Shafaee, Bubble Dynamics for Nucleate Pool Boiling of Electrolyte Solutions, 2010 [2] Office National d'études et de Recherches Aérospatiales, Nucleate Boiling, March 17, [Online]. Available: [3] S. MostafaGhiaasiaan, Two Phase Flow, Boiling and Condensation in Conventional and Miniature Systems, 2008 [4] Fritz, W., Berechunung des maximal volumens von Dampfblasen, Phys. Z., 36, pp , 1935 [5] Stephan, K., Saturated Pool Boiling and Subcooled Flow Boiling of Mixtures, Ph.D. thesis, University of Auckland, New Zealand, 1992 [6] Cole, R., Bubble Frequencies and Departure Volumes at Sub atmospheric Pressures, AIChE J., 13, pp , 1967 [7] Van Stralen, S. J. D., and Zijl, W., Fundamental Developments in Bubble Dynamics, Proceedings of the Sixth International Heat Transfer Conference, Toronto, Vol. 6, pp , 1978 Page 29 of 29