Chapter 2: Hydrodynamics and Turbulence Analysis 2.1 Selection of the k-omega SST Model To accurately simulate the behavior of a high-density liquid metal (13,546 \text{ kg/m}^3) at extreme angular velocities of 600 \text{ rad/s}, the k-omega SST (Shear Stress Transport) model was selected. This model is superior for the ULA-10 project because: Near-wall Accuracy: It effectively captures the flow behavior near the walls of the toroidal chamber, where viscous effects are dominant. Flow Separation: It provides superior prediction of flow separation in the asymmetric "thrust pockets" (35^{\circ}-45^{\circ}). Stability: It ensures computational stability in regions with high pressure gradients, which is essential for verifying the axial thrust F_z. 2.2 Managing Viscous Losses and Secondary Flows One of the primary challenges in closed-loop inertial systems is the dissipation of energy through turbulence. 3D Stability Analysis: Our ongoing 3D simulations are designed to detect and mitigate secondary flows that could potentially neutralize the primary thrust vector. Fluid-Structure Interaction (FSI): The ULA-10 framework accounts for the extreme mechanical stress placed on the composite housing by the rotating mercury/galinstan mass. 2.3 Simulation Environment: OpenFOAM All R&D milestones are validated within the OpenFOAM environment. This allows for: Scalability: Benchmarking the thrust output as the mass density and chamber dimensions are increased. Validation: Transitioning from confirmed 2D vector data to full-scale 3D performance metrics.
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