Unsteady Flow Field Projection and Compressive Sensing by Model Order Reduction

In nuclear reactors, enhancing safety via active monitoring of conditions and automation of routine aspects of plant operation require sensors to be integrated into the nuclear reactor system. Incorporating sensors that are compatible with advanced reactor environments can increases capital cost significantly. Additionally, many locations in the system that contain valuable data are wholly inaccessible to current sensor technology. Model order reduction allows critical information about sensor placement and experiment design to be distilled from fully resolved fluid mechanics simulation results. In many cases, sensed information in conjunction with reduced order models can also be used to regenerate full field variables. Previous work has demonstrated projection of sensed pressure data from one spatial domain to another via proper orthogonal decomposition (POD). In this work, the POD inferencing method is extended to the modeling and compressive sensing of temperature, a scalar field variable, and the modeling of pressure from sensed temperature data.

The method is applied to the problem of flow over a cylinder with heat generation at the cylinder boundary with Pr>>1, Pr\~1, and Pr<<1. The model is trained on pressure and temperature data from simulations. Field reconstructions are then generated using data from selected sensors and the POD model. Finally, the reconstruction performance is evaluated and presented as a function of Prandtl number, sensor count, and mode count. The predicted trend of increasing reconstruction accuracy with decreasing Prandtl number is confirmed and a Prandtl number/sensor count reconstruction performance matrix is presented. In order to examine the efficacy of this algorithm in transfer learning from one scalar field to another scalar field, temperature data sensors are used to predict pressure field information.

Three empirical sensor location selection techniques are developed and compared: mode-based, random sampling, and boundary-layer based. The random sampling yielded the highest accuracy but required significant computational resources. The mode-based approach, despite its lower accuracy, is used in the analysis of the POD ROM for its explainability and compatibility with existing studies.

It is shown that the lower Prandtl number flows require fewer sensors and modes for accurate temperature reconstruction, with models utilizing more modes generally outperforming those with fewer as expected. Notably, reconstruction accuracy for temperature and pressure was comparable in high Prandtl number fluids, but in moderate and low Prandtl number fluids, increased thermal diffusion led to smoother temperature gradients and enhanced reconstruction performance with fewer modes.

This study extends prior work by applying POD ROM techniques to the sparse sensing of temperature. It considers the effect of varying thermal diffusivity between materials and develops trends in accuracy between them. Furthermore, it introduces cross-scalar projection to this technique as a form virtual sensing. Additionally, the question of sensor placement is addressed in greater detail than in prior literature and alternative methods are evaluated. This study confirms the potential of POD ROMs for cross-scalar data projection and presents novel sensor selection techniques while providing insights into optimal conditions for their application.