Optimal and Model Predictive Control of Single Phase Natural Circulation in a Rectangular Closed Loop

Pipeline systems are essential across various industries for transporting fluids over various ranges of distances. A notable application is natural circulation through thermo-syphoning, driven by temperature-induced density variations that generate fluid flow in closed loops. This passive mechanism is widely employed in sectors such as process engineering, oil and gas, geothermal energy, solar water heaters and fertilizers etc. Natural circulation loops eliminate the need for mechanical pumps, reducing both energy consumption and maintenance costs. This study investigates thermo-syphoning in a rectangular closed-loop system and develops an optimal control strategies like Linear Quadratic Control (LQR) and Model Predictive Control (MPC) to ensure stable and efficient heat removal while explicitly addressing physical constraints. The results demonstrate that MPC improves system stability and reduces energy usage through optimized control actions. Compared to the LQR and unconstrained MPC, MPC with active constraints effectively manages input limitations, ensuring safer and more practical operation. With its predictive capability and adaptability, the proposed MPC framework offers a robust, scalable solution for real-time industrial applications, supporting the development of sustainable and adaptive natural circulation pipeline systems.