Analytical Stability Analogue for a Single-Phase Natural-Circulation Loop

Numerical solutions for transient fluid flow in nuclear systems often suffer from the effects of numerical diffusion and damping making the assessment of system stability rather difficult. Efforts for coping with this problem include research and development of algorithms with improved fidelity for stability calculations as they apply to particular problems. Benchmarking exercises in comparison with specially designed experiments are necessary to verify algorithmic fidelity and guide the development and adjustments of the algorithms. In this paper, an analytical approach is introduced where a simple model—an analogue—is constructed such that the basic instability mechanisms are represented in a form that lends itself to analytical solutions that are free from the diffusion and damping problems that plague finite volume algorithms. Direct conclusions can be made regarding the stability of a system in the case where the analogue closely resembles the system under study. However, when the system is too complex for direct assessment, the stability fidelity of numerical solutions can be assessed by comparing the numerical solution for the simple system with the analytical solution and using the comparison to quantify any damping effects and justify the application of the numerical method to the complex representation of the real system under study. The theoretical analysis is supported by reference to recent test data in the NuScale Integral System Test (NIST) facility representing a scaled-down NuScale module.