An Analysis of the Melt Casting of Metallic Fuel Pins

Transcription

1 An Analysis of the Melt Casting of Metallic Fuel Pins Xiaolong Wu, Randy Clarksean, Yitung Chen, Darrell Pepper Department of Mechanical Engineering University of Nevada, Las Vegas and Mitchell K. Meyer Nuclear Technology Division Argonne National Laboratory, Idaho Falls, ID Abstract A model is developed and analyses are conducted to analyze the casting of metallic fuels pins. The important physics of the model includes the flow of the melt into the mold, the heat transfer into the mold, the amount of preheating in the mold, and the rate of heat transfer from the melt to the mold. This paper discusses and presents preliminary modeling results for the casting of long, slender fuel rods. Parametric modeling results are presented and discussed. Background The United States is embarking on a national program to develop accelerator transmutation of high-level radioactive waste (ATW) as part of the Advanced Accelerator Applications (AAA) project at its national laboratories. Through the AAA Program, the U.S. joins international efforts to evaluate the potential of partitioning and transmutation along with advanced nuclear fuel cycles. Transmutation means nuclear transformation that changes the contents of the nucleus (protons and/or neutrons). The research and development efforts will consider a coupled accelerator and sub-critical multiplying assembly, explore the transmutation of waste from used nuclear fuel, testing of advanced nuclear fuels, and the production of isotopes that may be required for national security and commercial applications. The AAA program has listed several critical issues in fuel requirements: cladding integrity, fission product retention, and dimensional, chemical, and metallurgical stability during irradiation under both normal and off-normal conditions. One of the potential fuel types is a metallic fuel, which is being developed by Argonne National Laboratory. An important aspect of this program is the development of a casting process by which volatile actinide elements (i.e., americium) can be easily incorporated into metallic fuel pins. The process relies on a traditional casting process using induction heating and quartz glass rods as molds. This process works well for the fabrication of metal fuel pins traditionally composed of alloys of uranium and plutonium, but does not work well when highly volatile actinides are included in the melt. Previous experience with this process indicates that there is the potential for large losses of americium. The present process relies on a vacuum casting procedure that is briefly overviewed here. The process relies on the use of quartz glass molds: straw-like tubes with one end closed. Quartz glass is used because it will not soften or distort when filled with molten metallic fuel. The feed-stock, which consists of the end pieces chopped from previously cast fuel slugs, leftover fragments from previous casting, rejected slugs, and fresh feedstock (including actinides, Americium, Plutonium and Zirconium), is loaded into the crucible. The feed-stock is inductively heated until it is melted. The mold pallet, which contains the quartz molds, is then positioned above the crucible. When the proper temperature is reached, the system is evacuated by a vacuum pump. The molds are then submerged into the melt, the unit is pressurized, and the molten fuel is injected into the evacuated molds. The casting process takes less than a second. Once filled, the molds are withdrawn from the remaining melt and cooled - producing about a hundred metallic fuel pins - all in one operation. The americium loss most likely occurs both during the extended time period required to superheat the alloy melt as well as when the chamber must be evacuated. The low vapor-pressure actinides, particularly americium, are susceptible to rapid vaporization and transport throughout the casting furnaces, resulting in only a fraction of the charge being incorporated into the fuel pins as desired. This is undesirable both from a materials accountability standpoint as well as from the failure to achieve the objectives of including these actinides in the fuel for transmutation. Americium volatility during fabrication and irradiation, and actinide compatibility with cladding are also very important fuel issues. The present investigation supports the design and analysis of the melt casting of metallic fuel pins incorporating volatile actinides. The present paper briefly outlines the casting furnace system design, presents the proposed fuel pin casting model, and presents preliminary modeling results for the casting of long slender fuel pins. Description of Furnace Design Figure 1 shows a schematic of the proposed furnace design to cast metallic fuel pins that contain americium. The system consists of an induction skull melter, a crucible cover, chill molds, and resistance heaters to control the preheating of the

2 molds. The crucible cover was selected to aid in controlling the transport of americium from the melt. Chill molds were selected over continuous casting to insure proper geometric control, and the resistance heaters were added to insure that preheating of the molds could be controlled to insure the melt will flow into the mold. Several basic phenomenon exist in the proposed furnace and need to be analyzed. These phenomenon include Transport of americium from the melt into the upper regions of the crucible region, Impact of induction heating on the flow and heating of the melt material, and The flow of melt into the chill molds. The present paper addresses this last phenomenon, the flow and heat transfer associated with the melt entering the chill molds. The important physics of this process includes Heat transfer from the melt into the mold, Mold size, shape and material, Preheating of the molds, Mechanism to force the flow into the molds (pressure injection vs. gravity), and Phase change characteristics of the melt. "Cover" Coils "Chill Mold" Resistance Heaters Coolant Flow Figure 1 - Schematic of proposed induction skull melting furnace for the casting of high americium content fuels. Numerical Model The important physics of the mold filling process can be assessed through the analysis of a simplified geometry. Figure 3 shows a schematic of the model, which includes the melt and the mold. The problem can further be simplified through the use of an axisymmetric model. This model will capture all of the significant physics of the problem. r Inlet Flow Mold z Outlet Figure 2 - Schematic of fuel rod casting model. The important physics of the problem include the heat transfer into the mold, cooling and solidification rate of the melt, thermal mass of the mold, and the necessary forces to cause the melt to flow into the mold. All of these phenomenon can be captured by an axisymmetric model. The problem will be analyzed numerically through the use of the commercial finite element package FIDAP. This package is a general-purpose heat transfer and fluid mechanics code. The governing equations for the transient analyses of the melting of the phase change material included the Navier-Stokes (momentum) equations, the continuity equation, and the energy equation. These equations are shown in tensor notation below. u 2 ρ + ρ ( u ) u = p+ µ u t u = 0 T 2 ρcp ρcpu T k T t + = The viscosity is modeled with a temperature dependence to allow for the change from a flow to a no-flow state. The viscosity of the melt is modeled as a fluid, while the viscosity of the solid material is set to a large value to prevent flow from occurring in the solidified material. Future analyses will take phase change into consideration. At the interface between the solid and the liquid the conditions of equal temperatures between the interfaces and the heat transfer between the phases includes the latent heat release. These two relationships are shown below in equation form.

3 Tl = Ts Tl Ts kl ks = ρslu* n* n* The condition of a no-slip velocity within the liquid phase is also imposed. Phase change was modeled through the use of the slope method within FIDAP. In general, the slope method uses the slope of the enthalpy-temperature curve to define a specific heat of the material of interest. The enthalpy of a material that changes phase at a temperature T m, is defined as where T H ( T) = ( C ( T) + Lη ( T T )) dt Tref p 1 if ( T Tm ) 0 η( T Tm ) = 0 if ( T Tm ) < 0 An equivalent specific heat can be defined as the derivative of the enthalpy function which gives dh Ceqiv = = Cp( T) + Lδ ( T Tm ) dt where, δ(t-t m ) is the Dirac delta function. For pure liquids, phase change occurs at a constant temperature. To approximate this process numerically, the slope method requires the definition of a finite temperature difference over which the phase change occurs. Without defining a small temperature difference, the specific heat determined from the enthalpy-temperature curve is infinite. To numerically implement the relationship shown above for the finite element technique, the following modification is made C C T L T T T * eqiv = p( ) + δ ( m, ) where δ * (T-T m, T) has a large but finite value over the temperature range (T m - T/2) to (T m - T/2) and is zero outside this range. The use of this artificial specific heat allows for the correct amount of energy removal to occur from an element before it is considered to be a solid. Physically, the total energy transfer required for phase change is correct. m ρ T t 2 Cp = k T At the interface between the solid (metal) and the adjacent PCM the conditions of energy conservation is required. The interface temperature does not have to match identically because a convective heat transfer relationship is used to model the interface between the melt and the mold. This technique is commonly used in casting analyses. k mt T n mt Tl = kl n The Volume of Fluid (VOF) approach was used to model the flow of the melt into the fuel rod region. Complete details of this technique can be found in the FIDAP User s Manual. The preliminary results presented here did not consider phase change, but this portion of the model is included for completeness. Preliminary Modeling Results Preliminary modeling efforts centered around model development and the analysis of the impact of mold preheating on heat transfer into the mold. Results from three runs are discussed below. The conditions for each model included: Melt temperature of o C. Average fill velocity of 0.1 or 1.0 m/sec. Mold thermal properties assumed to be copper or quartz. Pin diameter of m. Mold outside diameter of m. Mold length of 0.50 m. Properties of melt assumed to be dependent on plutonium, americium, and zirconium. Heat transfer coefficient between the melt and the mold assumed to be 2,000 or 5,000 W/m 2 K as noted. Initial mold temperatures were varied ( o C, o C, or 400 o C). Figures 4 through 7 below show radial temperature profiles of the melt just behind the melt front as it advances into the mold. This region would be the melt region that would solidify most rapidly. The axial location for each of the temperature profiles is approximately located at the product of the velocity (1.6 m/sec) times the time. Conduction within the solid (mold) required the solution of the conduction equation, which is shown below.

4 secs 3.4 secs 0.25 secs Radius Locations (m) Figure 3 - Comparison of mold materials: Quartz (symbols) and Copper (lines). Model conditions are heat transfer coefficient = 5,000 W/m 2 K, mold temperature = o C, velocity = 0.1 m/sec Figure 5 Temperature profiles at the interface of the COPPER mold as the melt flows into the system. Model conditions are heat transfer coefficient = 5,000 W/m 2 K, mold temperature = o C, velocity = 0.1 m/sec secs 0.25 secs 1.40 secs 2.70 secs 3.45 secs Temperature (oc) Radial Location (m) Figure 6 - Temperature profiles at the interface of the QUARTZ mold as the melt flows into the system. Model conditions are heat transfer coefficient = 5,000 W/m 2 K, mold temperature = o C, velocity = 0.1 m/sec. Figure 4 - Comparison of mold materials: Quartz (symbols) and Copper (lines). Model conditions are heat transfer coefficient = 2,000 W/m 2 K, mold temperature = 400 o C, velocity = 0.1 m/sec. Figure 7 shows temperature profiles along the mold-melt interface as the flow enters the mold. The small bump on each of the profiles is the direct result of the initial conditions. To start the simulation, a small region of the mold is considered filled (0.020 m of the m length). This fluid is at an initial condition of o C. The fluid has already filled a portion of the mold without undergoing any cooling due to the mold. This fluid does not undergo that initial rapid cooling that any subsequent fluid entering the computational domain experiences. This temperature result is not significantly smeared out as time advances because of the low conductivity of the melt (6 W/m K).

5 Effectively, one can ignore this portion of the curve when interpreting the numerical results secs secs secs secs secs Figure 7 - Temperature profile of melt near the mold surface as the flow enters the mold. The "bump" on each curve is a result of the initial conditions for a small region of fluid filling the mold prior to the start of the flow Initial Conditions oc 900 oc 600 oc Figure 8 - Temperature profiles of melt material near the mold interface at 0.30 seconds. Lower to upper curves represent mold temperatures of 600 o C, o C, and o C. 2, Initial Conditions 10,000 20, h = 20,000 W/m K 700 h = 10,000 W/m K 600 h = 2000 W/m K Figure 9 - Examination on the impact of assumed heat transfer coefficient on the cooling of the melt. Mold temperature = 600 o C. It is not surprising that the mold temperature greatly impacts the cooling rate of the melt as it flows into the mold. In addition, the estimated heat transfer coefficient between the melt and the mold also greatly impacts the cooling rate of the melt as it enters the mold. These preliminary modeling results clearly indicate the need for good estimates of heat transfer between the mold and the melt, a thorough understanding of the preheating of the mold, and thermal mass of the mold necessary produce a fuel pin of the desired length. Future work will include a study of literature related steel processing to better understand the heat transfer between the melt and the mold. In addition, analyses will be conducted to determine the proper thermal mass of the mold. Summary A research effort is being undertaken at UNLV, with the assistance of ANL, to develop a casting furnace to cast fuel pins containing low vapor pressure materials (americium). The proposed concept is an induction skull melter, which includes a lid on the crucible region, chill molds, and resistance heaters to preheat the molds. To aid in the development of this concept, several computational models have been developed. One of these models, the analysis of the flow and solidification into the chill molds is presented and discussed here. The preliminary modeling results indicate that this phenomenon can be modeled, but that it is important to properly model the heat transfer rate between the melt and the mold. Future work will include analyses to assess the importance of the mold thermal mass and a better assessment of the heat transfer coefficient between the melt and mold. Acknowledgements

6 This research work is funded by the Advanced Accelerator Applications-University Participation Program (AAA-UPP) (U.S. Department of Energy Grant No. DE-FG AL67358). IEEE Transactions on Magnetics Vol. 30, No. 5, pp References: 1. C.L. Trybus, J.E. Sanecki and S.P. Henslee (1993), Casting of metallic fuel containing minor actinide additions, J. of Nuclear materials 204, pp F.L. Oetting, M.H. Rand and R.J. (1976) The Chemical Thermodynamics of Actinides Elements and Compounds (Part1: The actinides elements), International Atomic Energy Agency, Vienna 3. Hidekazu Kurimoto, Harendra Hath Mondal, and Toshiya Morisue (1996), Analysis of Velocity and Temperature Fields of Molten Metal in DC Electric Arc Furnace, J. of Chemical Engineering of Japan, Vol. 29, No.1, pp Joseph J. Katz, Glenn T. Seaborg and Lester R. Morss, The Chemistry of the Actinide Elements, second edition, volume 2 5. J. Szekely, J. Mckelliget, and M. Choudhary (1983), Heat-transfer Fluid Flow and Bath Circulation in Electric-arc Furnaces and DC Plasma Furnaces, Ironmaking and Steelmaking, Vol. 10, No. 4, pp M. Ushio, J. Szekely, and C. W. Chang (1981), Mathematical Modeling of Flow Field and Heat Transfer in High-current arc Discharge, Ironmaking and Steelmaking, No. 6, pp Randy Clarksean and Charles Solbrig, A Simplified Thermal Analysis of an Inductively Heated Casting Furnace, 1995 ASME International Congress and Exposition San Francisco, California, Nov , 1995 ASME Heat Transfer Division, Vol , pp P.G. Breig and S. W. Scott (1989), Induction Skull Melting of Titanium Aluminides, Materials & Manufacturing Processes, Vol. 4(1), pp R. Kageyama and J.W. Evans (Aug. 1998), A Mathematical Model for the Dynamic Behavior of Melts Subjected to Electromagnetic Forces: Part 1. Model Development and Comparison of Predictions with Published Experimental Results, Metallurgical and Materials Transactions B, Vol. 29B, pp Seaborg, G. T., Katz, J. J., and Manning, W. M. (eds) (1949) The Transuranium Elements: Research Paper, Natl Nucl. En. Ser., Div. IV, 14B, McGraw-Hill, New York 11. V. Bojarevics, K. Pericleous, and M. Cross (Feb. 2000), Modeling the Dynamics of Magnetic Semilevitation Melting, Metallurgical and Materials Transactions B, vol. 31B, pp Vlatko Cingoski and Hideo Yamashita (Sep. 1994), Analysis of Induction Skull Melting Furnace by Edge Finite Element Methods Excited from Voltage Source,