Reduced Order Modeling for Stratified Flows

Overview

This project extends the reduced-order modeling framework to incorporate buoyancy effects using the Boussinesq approximation to model thermally stratified environmental flows. The framework is evaluated on a 2D buoyancy-driven heated cavity at Rayleigh numbers of (Ra = 1.89 \times 10^5) and (Ra = 1.50 \times 10^9). The research further applies this methodology to atmospheric boundary layers (ABL) interacting with wind turbines under stable, neutral, and unstable thermal stratification conditions.

Results

• At a moderate (Ra = 1.89 \times 10^5), 15 modes accurately reconstruct the steady-state thermal and hydrodynamic structures of the heated cavity.

• For the highly turbulent (Ra = 1.50 \times 10^9) case, the flow demands 200 modes to represent the broadband energy distribution of the unsteady thermal plumes, though the VMS stabilization maintains numerical stability.

• In wind turbine applications, the ROM captures the suppressed vertical mixing of a stable ABL and the enhanced convective mixing of an unstable ABL, accurately preserving wake deficits and thermal profiles with 20 modes.

• Limitations & Future Work: High Rayleigh number flows require a large number of modes due to rapidly evolving small-scale vortex structures, which limits computational efficiency. Future directions include developing closure models for truncated modal dynamics, adaptive basis enrichment, and incorporating real-world atmospheric inflow models.

Visualizations