A SCOPING CFD EVALUATION OF RIA CONSEQUENCES

by

W.W. Yuen and T.G. Theofanous

Introduction

We were asked by Dave Diamond (BNL) to examine pressure pulses potentially generated by fine scale fragmentation of fuel in the core of a nuclear reactor undergoing a postulated RIA. The core region involved was given as ~ 0.9 m, near the core exit, of 20 central fuel assemblies. The amount of fuel fragmented was initially specified as an outside rim region of the fuel pellet 0.1 mm thick. Later on, Ralph Meyer (NRC) requested a calculation involving a much more significant fraction of the pellet, perhaps even 100%. Meanwhile, on our own initiative, we had carried out calculations for a 50% fraction. Since these results are indicative, in the interest of time we go forward with this report. A 100% fragmentation case can be added later, if desirable.
 
 

Specification of the Calculations

Calculations were carried out with an adapted version of the ESPROSE.m code. The code is a multidimensional, multiphase dynamics code, originally developed for the calculation of energetics in steam explosions (Theofanous et al., DOE/ID-10503). The key characteristics of the calculation are as follows.
 

  1. Overall Geometry. The reactor pressure vessel is simplified as an upright cylinder, full of water at 553 K and 150 bar pressure. The dimension and the positioning of the core are shown in Figure 1. The same figure also shows the region of the core assumed to be disrupted. The calculations are carried out in 2D, with axial symmetry. The node size was 10 x 10 cm. A check made with 5 x 5 cm nodalization showed that the accuracy is sufficient for this scoping study.

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    Figure 1. The geometry considered. The fuel/coolant ratio in the core is taken as 1:1. (The "dark" area represents the disrupted region.)

     

     

  3. Fragmentation Assumptions. As noted above, two cases were considered. The "rim-only" case amounts to a dispersed fuel fraction at only 2.4%. The other case is for a 50% dispersal. In both cases the particles are assumed to be small enough so as to thermally equilibrate with the coolant in 1 ms. All the coolant inside the disrupted region is taken to participate in this thermal equilibration process. In ESPROSE.m formulation, this coolant plus the fragmented fuel make up the microinteractions "fluid" or "m-fluid". This is specified by the entrainment factor based on the quantities involved, and it turns out to be 42 and 2 for the 2.4% and the 50% cases respectively. To simulate the gradual 1 ms mixing time, we take the fragmented fuel quantity to evolve, linearly, over the time of 1 ms. The fuel is taken to be at 773 K.
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  5. Other Modelling Features. The m-fluid can expand in whichever direction, upward/sideways, as dictated by the momentum equation. Its thermodynamic state is dictated by the equation of state, and correctly crosses the supercritical region. The fuel in the non-disturbed region of the core is assumed incompressible, and free to move (radially only) under the action of pressure and drag forces in the coolant, limited only by its own inertia. The radial-axial unisotropy of the fuel rods array is taken into account by assuming that the axial drag is zero (the vertical fuel velocity is reset to zero in each time step), while the actual drag, or some multiple of it (specified as 10 x normal; this is not a very significant factor on the results), is used in radial direction. In this way, by plotting the fuel displacement along a vertical, we can see the potential bending of a fuel rod at any particular radial position and time. The treatment of fuel motion, or resistance thereof, could be changed, to account for end-supports and clad bending. For now, this treatment can be considered conservative. The outer walls of the cylinder are taken to be rigid. Other refinement could be made as well to account for upper and lower core support structures, upper internal structures (currently approximated by a uniformly distributed solid fraction of 50%) and "venting" through the hot legs, if necessary. We don’t think these are very important for the main behaviors of interest, however.

 

 

Results and Discussion

The results of main interest are pressure wave dynamics, coolant and fuel motions, and fuel displacements. The cases considered are denoted by the main parameter, which is the fraction of fuel fragmented. Thus we have Run 2% and Run 50%.

Sample evolutions of radial pressure distributions on a horizontal chord going through the center of the disrupted region are shown in Figures 2a and 2b. For complete animations, click here  P2% P50%. The key difference is that Run 2% remains (the mixing region) in single phase, so the pressure actually undershoots as a result of the outwards imparted motion, while Run 50% goes two-phase, which sustains the pressure at the saturation level (determined by the amount of thermal energy in the fragmented fuel). We note that the pressure gradients are very significant in magnitude, and highly transient.

Sample evolutions of radial coolant and fuel velocities can be seen in Figures 3a and 3b. We can readily see that fuel motions in Run 2% are very slow and of very limited duration, while for Run 50%, they are quite substantial. Fuel displacements for various radial positions and times for Run 50% are shown in Figure 4. It is obvious from these that the 50% case could lead to rather significant distortion of the core rod geometry and hence, potentially, a significant impact on control rod operation.
 

 

Concluding Remarks

As expected, the consequences of RIA on core geometry depend on the amount of fuel assumed to have been dispersed. The 2% case seems to be rather inconsequential, while the 50% case could be very severe. Potential "relief" of this severity could be found by relaxing any of the following conservative assumptions (they are listed in perceived order of priority).

  1. Less fraction of fuel dispersed.
  2. Reduced thermal energy of dispersed fuel (radial non-uniformity in pellet energy deposition during RIA).
  3. Increasing time constants for fuel dispersal, and thermal equilibration time.
  4. Accounting for structural resistances to fuel motion, such as rod-end and grid supports, rod bending.

On the other hand, it may be of interest to examine the structural integrity of the core barrel and core supports (at both ends) under the action of pressure waves.