Sensitivity and Uncertainty Analysis of Coupled Reactor Physics Problems: Method Development for Multi-Physics in Reactors

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This thesis presents novel adjoint and spectral methods for the sensitivity and uncertainty (S&U) analysis of multi-physics problems encountered in the field of reactor physics. The first part focuses on the steady state of reactors and extends the adjoint sensitivity analysis methods well established for pure neutron transport problems to coupled criticality calculations, where feedbacks are present between neutronics and other phenomena (e.g. thermalhydraulics or fission product poisoning). The second part presents novel spectral techniques, namely grid and basis adaptive Polynomial Chaos (PC) methods for the S&U analysis of generic problems, together with a large scale application of the developed Fully Adaptive Non-Intrusive Spectral Projection (FANISP) algorithm for the sensitivity and uncertainty analysis of a transient. Following a short introduction in Chapter 1 to some of the most frequently used S&U analysis techniques Chapter 2 presents the theory for the adjoint based sensitivity analysis of coupled criticality problems. This enables the computation of first order changes in responses of interest due to variations of both neutronic input parameters (such as cross sections) and those describing augmenting phenomena (e.g. thermal-hydraulics). The chapter also presents a very efficient procedure for calculating the necessary neutronics and augmenting adjoint functions that relies on using Krylov algorithms together with the individual neutron transport and augmenting codes to perform the required matrix-vector multiplications and inversions during preconditioning. As a proof of principle study a one-dimensional slab model is investigated, where two-group diffusion theory is coupled with heat-conduction and xenon-poisoning. In Chapter 3 the larger scale applicability of the coupled adjoint theory is studied. A deeper look into the exact form of the adjoint operators reveals that for the most common cases of coupling neutron transport to thermal-hydraulics and fission product poisoning the effects of the operators can easily be calculated by routines present in the adjoint capable neutron transport and augmenting codes. This enables their reuse with little code modifications, therefore the main challenge lies in the coupling scheme rather than in dedicated code development (once both codes are already suited for solving the individual adjoint problems). As a more realistic application the S&U analysis of a coupled model of an infinite array of fuel pins was performed employing a purpose made thermal-hydraulics code and a general purpose discrete ordinates neutron transport solver. The results confirmed that the preconditioned Krylov algorithm provides excellent performance in calculating the necessary adjoint functions and these properly provide the first order changes of responses of interest due to perturbations in any of the system input parameters. In Chapter 4 the development of novel adaptive Polynomial Chaos techniques is detailed aimed at the S&U analysis of generic problems. Two types of adaptivity is discussed: adaptive sparse grid algorithms relying on Gerstner’s original technique for calculating multidimensional integrals and adaptive PC basis set construction for building up the Polynomial Chaos Expansion (PCE) of responses in an efficient way. The details of the implementation of the developed methods in the FANISP algorithm are also presented and three demonstrational problems are studied. They all focus on specific merits of the adaptive algorithms and confirm that they are significantly more effective than traditional spectral techniques as well as brute force Monte Carlo methods. As a truly large scale, realistic application of the FANISP algorithm the sensitivity and uncertainty analysis of an Unprotected Loss Of Flow transient in the GFR2400 Gas Cooled Fast Reactor is performed in Chapter 5. For dealing with the 42 considered uncertain input parameters two further cost reduction techniques are discussed based on a reduction of dimensionality and an adaptive increase of the global polynomial order. It is shown that due to the non-intrusive nature of the developed PC methods they are easy to apply and can be far more efficient in determining sensitivities, uncertainties and even full probability density functions than standard techniques. The most important merit of the chapter is that it greatly expands the usefulness of PC methods to problems with up to 40-50 input parameters, providing a lot of new opportunities for application. In conclusion, the work presented in this thesis provides attractive methods for the sensitivity and uncertainty analysis of the two most common types of multi-physics calculations in the nuclear field, namely determining the coupled steady state and the transient behaviour of reactors. The practical applicability of both the developed coupled adjoint method and the FANISP algorithm was demonstrated, which serves as a strong basis for future use. Since adjoint methods are uniquely capable of taking into account all input parameters at once, whereas PC techniques can deal with nonlinearities, their combined use has even higher potentials. As a closure several possible future research topics are highlighted among the recommendations.