Optical flow-based velocimetry algorithm for schlieren images of flame plume

Flow velocity measurement methods for weak flame plumes face several challenges due to the complex dynamics involved. Flame plumes, driven by buoyancy forces, are inherently turbulent, with the plume motion accompanied by the entrainment of the surrounding air. The boundary between the plume and the environment continuously evolves in space, making it difficult to capture the plume's true flow characteristics. Past plume velocity measurement methods rely on intrusive methods, using tools such as Pitot tubes, smoke probes, and hot-wire anemometers. These methods disrupt the plume flow field and cannot accurately reflect the undisturbed temporal and spatial characteristics of the entire plume, thereby limiting their applicability for a detailed analysis of weak flame plumes.

To address these challenges, we employed the schlieren imaging technique to visualize flame plumes. This nonintrusive visualization technique allowed the capture of the flow field induced by buoyancy forces at a high resolution. Industrial cameras were used to record the ignition process and flame plume dynamics at varying heights and oil pan diameters. By analyzing the schlieren images, we aimed to overcome the limitations of traditional measurement methods. In this study, we derived a simplified two-dimensional Navier-Stokes equation to develop an optimized optical flow (OF) algorithm tailored for velocity measurements in flow fields. The proposed algorithm was applied to the schlieren images of flame plumes, showing significant improvements over conventional OF methods.

The key advancements of the optimized algorithm are as follows. (1) Enhanced sensitivity and precision: The optimized algorithm produces smoother displacement fields and more uniform vorticity fields. This enables the detection of finer vortex structures that are often overlooked by conventional OF methods. By improving the resolution and accuracy of the calculated flow field, the algorithm provides a more detailed representation of the flame plume's dynamics. (2) Rapid convergence: During the velocity calculation process, the optimized algorithm achieves rapid convergence. The energy residual after the first iteration is reduced to less than 10^-2, and the energy residual in the final OF field remains below 10^-5. This indicates that the proposed algorithm achieves a high accuracy in fewer iterations, making it computationally efficient. (3) Improved robustness in experimental validation: In flame plume velocity measurement experiments, the optimized algorithm demonstrates superior robustness compared with conventional OF methods. A dimensional analysis of the results shows a significant improvement in the fit between the predicted and measured values. Specifically, the coefficient of determination (R²) increases from 0.90 for the conventional OF method to 0.98 for the optimized algorithm. Additionally, the measured results are in close agreement with the Heskestad model results. While conventional OF methods show an average error range of -20%-30% in the plume region, the optimized algorithm reduces this error range to -5%-20%. This reduction highlights the enhanced accuracy and reliability of the optimized algorithm.

Overall, the proposed algorithm provides a more stable, accurate, and efficient approach for measuring the velocity of weak flame plumes. By addressing the limitations of conventional OF measurement techniques and aligning more closely with theoretical prediction models, this study offers a valuable contribution to the flame plume analysis. These findings pave the way for the improved understanding and modeling of fire dynamics, with potential applications in fire safety engineering and combustion research.