Numerical study on the Welander oscillatory natural circulation problem using high-order numerical methods

- The Welander problem was investigated using high-order numerical methods.
- High-order numerical methods reduced numerical diffusion significantly for stability analysis.
- High-order numerical methods were proved to be promising for natural circulation analysis.

In this paper, high-order numerical methods are investigated in a system analysis-like code. The classical Welander oscillatory natural circulation problem, which resembles a simplified example for many types of natural circulation loops widely seen in nuclear reactor systems, was chosen to illustrate the applicability of such methods in system analysis codes, and to demonstrate the advantages of such methods over the low-order methods widely used in existing system analysis codes. As originally studied by Welander, the fluid motion in a differentially heated fluid loop can exhibit stable, weakly unstable, and strongly unstable modes. A theoretical stability map has also been originally derived from the stability analysis. Numerical results obtained in this paper show very good agreement with Welander's theoretical derivations. For stable cases, numerical results from both the high-order and low-order numerical methods agree well with the non-dimensional flow rate that were analytically derived. The high-order numerical methods give much less numerical errors compared to those using low-order numerical methods. For stability analysis, the high-order numerical methods perfectly predicted the stability map even with coarse mesh and large time step, while the low-order numerical methods failed to do so unless very fine mesh and time step are used. The result obtained in this paper is a strong evidence for the benefits of using high-order numerical methods over the low-order ones, when they are applied to simulate natural circulation phenomenon that has already gained increasing interests in many existing and advanced nuclear reactor designs.