Uncertainty quantification in relation to crud behaviour in a PWR

• Provides a new one-dimensional model to describe crud behaviour.
• Develops an exact two-dimensional model based on the chimney model.
• Assesses effect of uncertainty in data of crud properties.
• Obtains effective thermal conductivity and crud-clad interface temperature.
• Gives table of sensitivities so that the influence of data can be assessed.

Studies of crud behaviour in PWRs based upon the chimney model have been made by a number of authors. The chimney model is not exact but it appears to give a very reasonable physical description of crud formation and effect. A serious drawback of the model is, however, the uncertainty in the values of the data used. Essentially every parameter involved, both geometric and physical, has large variations and it is the purpose of this paper to assess the influence of these variations, i.e. uncertainties, on the important output parameters, e.g. the effective thermal conductivity and the clad–crud interface temperature.In order to effect such a study we need a relatively simple, yet physically realistic, model of the crud. To this end, analytic two-dimensional solutions have been obtained for the temperature, fluid velocity and solute concentrations. Due to their complexity, however, these solutions are not ideal for uncertainty quantification studies and so we also develop an approximate, one-dimensional model which, by comparison with the two-dimensional model, is shown to be an accurate description of the processes occurring. This one-dimensional model is then used in the uncertainty quantification using simulation methods and direct quadrature. The uncertainty is introduced by means of random variables and certain prescribed probability distribution functions for the input data. The outcome is a set of probability distributions for the effective thermal conductivity and the clad–crud temperature together with mean values and standard deviations. From these calculations we are able to demonstrate which parameters have the most influence and hence which should be given the most attention.