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Application of the Two-Dimensional Navier-Stokes Equations to Steam Cooling in Asymmetrically Heated Channels

L. W. Ward

Nuclear Technology

Volume 131 / Number 1 / July 2000 / Pages 69-81


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A model was developed to compute the two-dimensional velocity profiles in hot fuel channels of a pressurized water reactor core following a small-break loss-of-coolant accident (SBLOCA). Following an SBLOCA, the transient two-phase level in the core recedes below the top of the core, exposing the core to steam cooling and heatup of the fuel. To compute the velocity distributions, the Navier-Stokes equations were solved in vorticity form using an explicit upwind finite difference numerical scheme. The model was applied to the well-known lid-driven cavity problem and the data in the literature for vertically heated channels. Comparison of the model to the data in the literature provided validation of the approach.

Application of the model to the conditions at the time of the peak clad temperature during core uncovery for a typical limiting small cold-leg break in a pressurized water reactor further revealed that the hot-channel steam flow can vary dramatically at the hot spot due to the severe distortion in the axial steam flow that is characteristic of asymmetrically heated channels. The results of the evaluation support the need for a thorough technical basis for the steam flow rates that are typically assumed to cool the hot rods in many commercial fuel rod heatup codes. These codes typically assume a constant mass flow along the axis of the fuel rod to compute the cladding temperature response. Mixed convection is shown to reduce the channel average velocity along the axis of the fuel rod by as much as 15%. The reductions in channel velocity will produce an attendant increase in the peak clad temperature achieved during an SBLOCA. The results of this study suggest that for the steam velocities used to cool hot rods during an SBLOCA, one needs to consider the mixed-convection behavior that can affect the convective heat transfer in the upper portions of exposed nuclear fuel bundles.

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