2d Natural Convection and Radiation Heat Transfer Simulations of a Pwr Fuel Assembly within a Constant Temperature Support Structure

Two-dimensional simulations of steady natural convection and radiation heat transfer for a 14x14 pressurized water reactor (PWR) spent nuclear fuel assembly within a square basket tube of a typical transport package were conducted using a commercial computational fluid dynamics package. The assembly is composed of 176 heat generating fuel rods and 5 larger guide tubes. The maximum cladding temperature was determined for a range of assembly heat generation rates and uniform basket wall temperatures, with both helium and nitrogen backfill gases. The results are compared with those from earlier simulations of a 7x7 boiling water reactor (BWR). Natural convection/radiation simulations exhibited measurably lower cladding temperatures only when nitrogen is the backfill gas and the wall temperature is below 100°C. The reduction in temperature is larger for the PWR assembly than it was for the BWR. For nitrogen backfill, a ten percent increase in the cladding emissivity (whose value is not well characterized) causes a 4.7% reduction in the maximum cladding to wall temperature difference in the PWR, compared to 4.3% in the BWR at a basket wall temperature of 400°C. Helium backfill exhibits reductions of 2.8% and 3.1% for PWR and BWR respectively. Simulations were performed in which each guide tube was replaced with four heat generating fuel rods, to give a homogeneous array. They show that the maximum cladding to wall temperature difference versus total heat generation within the assembly is not sensitive to this geometric variation. INTRODUCTION Spent nuclear fuel (SNF) assemblies are placed in packages for transport away from reactor sites [1,2]. These 1 packages consist of a cylindrical container in which multiple assemblies are placed horizontally. Each assembly is placed within an individual cell of the basket support structure, and the containment region is typically evacuated and backfilled with a non-oxidizing gas of high thermal conductivity. A spent nuclear fuel (SNF) assembly is a square array of spent fuel rods. The heat generated by the rods elevates the assembly and package temperatures above their surroundings. The number assemblies and the heat generation rate that a package can transport are limited by maximum allowable cladding temperatures. In order to be licensed a package must maintain rod cladding temperatures below a limit value of 400°C [3]. The heat transfer within the backfilled region exhibits transport by means of convection and radiation from the rods to the basket structure and through the backfill gas. It is not clear how sensitive the temperature distributions within an assembly are with respect to the surface emissivity, which is not well characterized. Some authors have reported values of emissivity from 0.4 [4] to 0.8 [5]. Also, radiation and natural convection within the assembly may not be accurately represented by a simple conduction smeared model. Some studies have neglected natural convection [5,6,7] while others consider it a significant transport mechanism [8,9,10,11]. Previous numerical studies of the heat transfer in SNF assemblies have been conducted using a variety of computational methods in order to obtain the internal temperatures within the fuel/backfill gas region. However, these studies are limited in assembly types and the numerical models employ simplifications in geometry and assembly components. Bahney and Lotz [6] studied steady conduction and 1 Copyright © #### by ASME Copyright © 2006 by ASME gap radiation for assemblies within transport basket cells. They constructed six models of BWR and three models of PWR geometries within constant temperature basket cells. They also considered natural convection transport negligible. Bahney and Lotz [6] ran simulation for a range of assembly heat generation rates of 100 W to 1000 W to model different fuel burn-ups and cooling times. They also varied basket wall temperatures from 25°C to 400°C to model cells at the center of different sized packages with different total heat generation rates. All of Bahney and Lotz [6] simulations were run on one-quarter models with helium, nitrogen and argon backfill gas at atmospheric pressures. Their simulation results were used to develop temperature dependent effective thermal conductivity correlations for each of the assembly geometries. These can be used to predict the maximum cladding temperature near the package center, where the basket cell wall temperature is nearly uniform. Their study is the source of information used in the current work. However, Bahney and Lotz [6] do not explicitly describe the criteria used to demonstrate grid independence, or describe the symmetry conditions used to simulate full assembly cross sections using quarter models. Also, they do not compare results with experimental data. The current study is focused on developing a temperature prediction model that will incorporate the wide variety of characteristics of SNF assemblies. These include geometric variations, such as array size and enclosure dimensions, as well as material properties, such as surface emissivity of backfill gas composition. Initial simulations were conducted using a twodimensional numerical model of a General Electric 7x7 BWR assembly [11]. The goal of the work was to quantify the relative effects of conduction, radiation and natural convection in this mixed mode heat transfer environment. Steady state computational fluid dynamics (CFD) calculations of the model were conducted for natural convection and gap radiation with uniform basket wall temperatures. The model considered a specific BWR geometry with 49 heat generating pins in a square array surrounded by a channel. Simulations were run for the same heat generation rates and basket wall temperatures for helium and nitrogen backfill gases. Conduction/radiation results were compared to those from Bahney and Lotz [6] and showed consistently higher maximum cladding to wall temperature differences. It is not clear which factors cause this difference. Araya and Greiner [11] modeled the full assembly cross-section and therefore did not need the symmetric boundary conditions required by Bahney and Lotz’ [6] one-quarter model. Moreover, grid independence was explicitly demonstrated by Araya and Greiner [11]. To further the characterization of the 7x7 BWR study natural convection was added and showed significant effects only in nitrogen backfill at lower basket wall temperatures. Simulations were also run to quantify the effect of surface emissivity in the radiation calculations. Results showed a variation in the values of rod surface emissivities has measurable effects on maximum cladding temperatures [11]. At the present, there are no experimentally benchmarked models that can be applied to the full range of conditions that may describe different SNF assembly types. Therefore, there is uncertainty in the temperature predictions 2 that a package designer or analyst may use to predict thermal behavior [5]. This means that designers have to lower heat generation limits to make sure that the allowable cladding temperature is not exceeded. To do this they must lower the number or heat generation rate of assemblies within each package. The objective of this work is to characterize the heat transfer of a 14x14 PWR assembly. This report shows results from two-dimensional steady CFD simulations of the 14x14 PWR. The simulations are conducted for the same heat generation rates and uniform wall temperatures as those used by Bahney and Lotz [6]. The influence of natural convection and the variation of cladding emissivity on the resulting temperatures are studied and compared to previous simulation results with the 7x7 BWR [11]. PWR fuel assemblies consist of a square array of heated rods. However, some PWR contain a number of unheated guide tubes. We wish to determine how this type of geometric variation affects the maximum cladding to wall temperature difference versus total heat generation within the assembly volume. NOMENCLATURE PWR Pressurized Water Reactor BWR Boiling Water Reactor SNF Spent Nuclear Fuel T Local temperature [oC] Tw Basket wall temperature [oC] TC,R Temperature results for conduction/radiation [°C] TNC,R Temperature results for natural convection/radiation [°C] Tc,max Maximum cladding temperature [oC] ∆T Tc-max–Tw; Maximum cladding to wall temperature difference [oC] Q Total assembly heat load [W]