Capturing accelerating flames in 3D: dual-view reconstruction methodology of flame morphology

Abstract A methodology for 3D flame surface reconstruction during flame acceleration (FA) in unobstructed channels is proposed. Experimental images obtained with a two-directional schlieren visualization setup in a 10 mm $$\times ~10$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>×</mml:mo> <mml:mspace/> <mml:mn>10</mml:mn> </mml:mrow> </mml:math> mm squared channel, 1 m length, are used to this end. This setup allows visualizing simultaneously the flame morphology in the two orthogonal directions of the channel during the entire FA process. The reconstruction methodology initially takes the simultaneous images to generate a 3D point cloud volume, where the points from its front and rear surfaces are extracted. Subsequently, these points are linearly interpolated to obtain an intermediate solution, which corresponds to the reconstructed surface. To maximize the overlap between the intermediate surface and the views of the original images, a nonlinear optimization series is solved using a genetic algorithm with random continuous mutations and uniform crossover. The methodology was tested with different analytical flame surfaces to evaluate its performance, obtaining errors $$&lt; 3.2 \%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>&lt;</mml:mo> <mml:mn>3.2</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> . Furthermore, the reconstruction of the experimental flame images observed during the early stages of FA for a $$2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> $$\hbox {H}_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>H</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> </mml:math> + $$\hbox {O}_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>O</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> </mml:math> + $$\hbox {N}_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>N</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> </mml:math> mixture was performed, making it possible to correlate the experimentally estimated flame surface area with its velocity.