Benchmark Natural Convection/radiation Simulations within an Enclosed Array of Horizontal Heated Rods

Experiments performed by others measured the temperature of an 8x8 array of horizontal heated rods in air within a constant temperature enclosure. That apparatus was a scaled-down model of a spent boiling water reactor fuel assembly in a transport package. In the current work, threedimensional computational fluid dynamics simulations of natural convection and radiation heat transfer within this domain were conducted to determine appropriate boundary conditions and benchmark the results. Initial simulations employed nearly equal specified temperatures on the walls and endplates, and insulated rod ends. They accurately reproduced the shapes of the temperature profiles in the midplane between the rod ends, but over-predicted the temperature level at the highest heat load. Simulations that included conduction within the endplates and convection from their outside surfaces more accurately modeled heat losses. They brought the midplane temperatures at the highest heat load to the measured data once an appropriate convection coefficient was determined. The simulation technique will be used to design future experiments that model heat transfer from spent fuel assemblies to highlynon-isothermal support structures. INTRODUCTION Spent nuclear fuel is transported away from power reactors in thick walled rail and truck casks [1,2]. They are placed in the containment region at the center of the cask where they are supported horizontally within square cross section tubes of a basket structure. Before transport, the containment region is evacuated and backfilled with a non-oxidizing gas. Heat generated by the fuel (and solar heating) make the package hotter than its surroundings. Package manufacturers must demonstrate that the zircaloy cladding that contains the spent fuel pellets does not exceed 400°C during normal transport [3]. This generally limits the number and heat generation rate of the fuel assemblies that can be transported in a package. The heat transfer processes within the fuel assembly/backfill gas region have not been fully characterized. This contributes uncertainty to the prediction of both the maximum cladding temperature for a given fuel heat load, and the maximum fuel heat load so that the maximum cladding temperature does not exceed its allowed limit. Package designers address this uncertainty by reducing the number and/or heat generation rate of assembles that may be loaded in casks to assure that the cladding temperature limit is not exceeded. However, under-loading casks increases the number of shipments and the associated risk to the public. Accurate models for predicting fuel cladding temperatures therefore have potential public safety consequences. Federal regulations require that package temperatures be determined for a normal hot day environment temperature of 38°C [4]. The temperature difference between the hottest fuel cladding (near the package center) and the environment may be divided into three components. These components are the temperature differences in (a) the environment ∆TE (between the 38°C environment and package surface), (b) the package ∆TP (between the package surface and hottest basket wall near the package center), and (c) the center fuel assembly ∆TF (between the hottest basket surface and the hottest cladding). All three components increase with the fuel heat generation rate. Natural convection heat transfer correlations and package surface emissivities are used to determine the environment temperature difference ∆TE. Finite element models of loaded packages are typically employed to predict the package and fuel assembly temperatures, including ∆TP and ∆TF. In these calculations, the multiple fuel assemblies are typically replaced by solids with an effective thermal 1 Copyright © #### by ASME 1 Copyright © 2006 by ASME conductivity [2]. These solid models are used because it is computationally intensive to directly model the natural convection fluid motion and heat transfer as well as the thermal radiation within the fuel assembly/backfill gas regions. The temperature dependent effective thermal conductivity must be determined based on analysis of fuel assembly/backfill gas transport. Bahney and Lotz [5] performed two-dimensional finite element simulations of conduction and radiation heat transfer within fuel assembly/backfill gas regions. Several boiling water reactor (BWR) and pressurized water reactor (PWR) fuel assembly configurations were accurately represented, including unheated instrument sheath and guide thimble tubes, and external channels. The maximum cladding temperature was determined as functions of assembly heat generation rate and basket wall temperature. These simulations employed a uniform wall temperature to model basket cells near the package center, where the hottest fuel cladding resides. Effective thermal conductivity models of these regions were developed based on the simulations. These models are intended for use within finite element package models to calculate the center fuel assembly temperature difference. The results were not compared to experimental data and mesh independence was not explicitly demonstrated. Manteufel and Todreas [6] developed an analytical model for one-dimensional conduction and radiation within a rectangular array of heated fuel rods immersed in stagnant gas. They used this model to calculate an effective thermal conductivity for the region within the fuel assembly, and a conductance model for the thin band between the assembly envelope and the basket walls. This model neglects possible effects of two-dimensional heat transfer at the corners, and the unheated components (instrument sheath and guide thimble tubes and external channels). Simulations of experiments performed by other investigators were performed using this thermal conductivity model. These simulations consistently over-predict the measured maximum cladding temperature. This is conservative with regard to calculations used to transport packages. Araya and Greiner [7] performed two-dimensional computational fluid dynamics (CFD) simulations of natural convection and radiation heat transfer for a 7x7 BWR fuel assembly within a uniform temperature basket cell. The maximum cladding temperature was determined for both helium and nitrogen backfill gases as functions of fuel assembly heat generation rate, basket wall temperature, and cladding emissivity. Simulations were also performed with conduction/radiation only across the gas (no fluid motion) to determine the conditions that cause natural convection to enhance heat transfer relative to conduction. The 7x7 simulations [7] showed that fluid motion (natural convection) does not measurably reduce the maximum cladding temperature compared to stagnant gas when helium is the backfill gas (due to its high thermal conductivity), or when the basket wall temperature is 400°C (due to significant radiation effects). However, natural convection effects were important for lower wall temperatures when nitrogen was the backfill gas. A 10% increase in cladding emissivity reduces the maximum cladding to wall temperature difference by 4.3% when nitrogen is the backfill gas and the basket temperature is 400°C. For helium or lower basket temperatures, the effect is smaller. These results were not benchmarked against experimental data [7]. Greiner et al. [8] used fuel assembly/backfill gas effective thermal conductivity models developed by other investigators [2,5,6,9,10] to calculate the temperatures within a rail package designed to transport 21 PWR fuel assembles under normal hot day conditions. Package temperatures were presented for a range of fuel heat generation rates, which were uniform in all 21 assemblies. Different conductivity models were applied to determine their effect on the results. For the large rail package the magnitude of the package temperature difference ∆TP was even more sensitive to the fuel assembly/backfill gas effective thermal conductivity model than the center fuel assembly difference ∆TF. This is because the package temperature difference is affected by the thermal resistance of the periphery fuel assembly/backfill gas regions. There is a larger total thickness to the fuel assembly/backfill region in the package periphery than in the center fuel assembly. The simulations also show that the temperature profiles along the walls of the periphery basket cells are highly non-uniform. A shortcoming of using thermal conductivity models to simulate heat transfer within fuel assembly/backfill gas regions is that they approximate heat flux at a location based on the temperature and its spatial gradient at that location. This is not universally appropriate when natural convection and/or thermal radiation effects are significant. For example, natural convection heat transfer is affected by the local fluid velocity, which depends on temperatures at other locations. Moreover, the radiant heat flux at a location is affected by temperatures at a distance from that location. As a result, it is not currently known if the effective thermal conductivity model developed by Bahney and Lotz [5] for central basket cells (where the wall temperature is essentially uniform) can be used to accurately model heat transfer in periphery cells with non-uniform temperature profiles. To our knowledge, no studies have quantified the effect of non-uniform basket wall temperature profiles on fuel assembly/backfill gas heat transfer. These results motivate the development and experimental benchmark of fuel assembly/backfill gas heat transfer models for non-uniform basket wall temperature profiles. An initial task for this work is to benchmark computational fluid dynamics simulations using data from a relevant flow configuration. In the current work, threedimensional simulations are performed of an experiment performed by Lovett [11]. In that experiment, a horizontal 8x8 array of heated rods is contained within a nearly uniform temperature aluminum enclosure. This facility is a scaled down model of a boiling water reactor spent fuel assembly in a transport basket. The rod temperatures are determined for a range of rod heat generation rates. Since the experiment was performed by another investigator, we do not know all the details of the test facility, thermal boundary conditions, or the experimental method. The current multi-mode heat transfer simulation results are compared to the experimental data for the following purposes: (a) to develop methods to compare simulation results with measured data and use them to assess the computational methods, (b) determine appropriate boundary conditions and material properties (that are not reported by Lovett [11]) that bring the simulation results as close as possible to the data, and 2 Copyright © #### by ASME 2 Copyright © 2006 by ASME (c) gain information that may be useful to us in developing our own experiments. Simulations for non-uniform wall temperature configurations will be performed after we have developed confidence in uniform wall temperature calculations. NOMENCLATURE T Local temperature [oC] Tw Enclosure outer wall temperature [oC] Tmax Maximum rod temperature [oC] ∆T Tmax–Tw; Maximum rod to wall temperature difference [oC] Q Total assembly heat load [W] ∆TE Difference between package surface and environment temperatures [oC] ∆TP Difference between maximum basket wall and package surface temperatures [oC] ∆TF Difference between maximum cladding and maximum basket wall temperatures [oC] d Rod outer diameter [mm] p Center-to-center pitch [mm] E Enclosure inner dimension [in] w distance from wall to nearest rod [mm] H Rod Length [in] ε Surface emissivity Q total heat generation rate [W] q Volumetric heat generation rate [W/m] Lh heated length of rod A Cross sectional area of the MgO core on the rod, πdc /4 [m] dc Diameter of the MgO core N Order of the heater rod array TB Bottom enclosure wall temperature [oC] TT Top enclosure wall temperature [oC] TR Right enclosure wall temperature [oC] TL Left enclosure wall temperature [oC] TA Average enclosure wall temperature [oC] ∆TA,C Average rod to bottom wall temperature difference for each column of rods [oC] S∆T,C Standard deviation of the rod to bottom wall temperature difference by columns [oC] ∆TA Average rod to bottom wall temperature difference for entire array [oC] S∆T Standard deviation of the rod to bottom wall temperature difference for entire array [oC] LOVETT [1991] EXPERIMENT Figure 1 shows a cross section through the experimental apparatus used by Lovett [11]. It consisted of an 8x8 array of heated rods within a 2.54 cm (1 inch) thick aluminum enclosure. One column of Table 1 reports the rod diameter d, rod center-to-center pitch p, enclosure inner dimension E, and distance between the wall and nearest rod center, w. The rod length in the direction normal to the page H is also included. Another column shows the corresponding dimensions of a General Electric (GE) 8x8 BWR assembly in a typical transport basket cell [5]. This table shows that the experimental apparatus is a scaled down version of the BWR 3 assembly, and that the ratios p/d, w/d and E/d were essentially preserved. These experiments were chosen to benchmark our simulations for two reasons. The first is that the geometry closely resembles a BWR assembly in a transport package. The second is that a fairly complete presentation of experimental methods, facility, measurement results and errors are given. The heater rods are supported at their ends by holes in 0.81 mm (0.032 inch) thick carbon steel plates that are fastened to the aluminum enclosure. The rods are Watlow Firerod cartridge heaters. They are composed of a compressed powder magnesium oxide (MgO, thermal conductivity 2.07 W/mK [12,13]) core that is encapsulated within a copper sheath of 1.2 mm thickness. Heat is generated by passing current through a coiled wire within the MgO. Heat is generated uniformly along the length of each rod except for two 12.7 mm (0.5 inch) long regions at each end that do not generate heat. Each heater rod was equipped with an internal k-type thermocouple at its radial and axial center. Additional surface thermocouples were installed near the ends of four rods. The Figure 1 Schematic of the experimental 8x8 heater array within an aluminum enclosure [Lovett, 1991]. y Copper Sheath MgO Core E