Distributions of Wall Heat Flux and Wall Shear Stress and their Interrelation During Head-on Quenching of Premixed Flames within Turbulent Boundary Layers

The statistical behaviours of wall heat flux and wall shear stress and their interdependence during unsteady head-on quenching of statistically planar turbulent premixed flames within turbulent boundary layers due to heat loss through the cold wall have been analysed using three-dimensional Direct Numerical Simulation data with friction Reynolds numbers of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>R</mml:mi> <mml:msub><mml:mi>e</mml:mi> <mml:mi>τ</mml:mi></mml:msub> <mml:mo>=</mml:mo> <mml:mn>110</mml:mn></mml:mrow> </mml:math> and 180. In both cases, the mean wall shear stress decreases during flame-wall interaction, whereas the mean wall heat flux magnitude increases with time as the flame approaches the wall and eventually assumes a maximum value before decreasing with the progress of flame quenching. The integral length scales of wall heat flux in both streamwise and spanwise directions have been found to grow with time after the maximum mean heat flux magnitude is obtained for the two <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>R</mml:mi> <mml:msub><mml:mi>e</mml:mi> <mml:mi>τ</mml:mi></mml:msub> </mml:mrow> </mml:math> cases considered. However, the integral length scale of wall shear stress in the streamwise direction grows but the integral length scale of wall shear stress in the spanwise direction decreases with time after the maximum mean heat flux magnitude is reached. Moreover, the correlation coefficient between the wall heat flux magnitude and wall shear stress becomes increasingly negative while the mean wall heat flux increases with time, but this negative correlation weakens with the progress of flame quenching. The first few (i.e., most energetic) Proper Orthogonal Decomposition (POD) modes of wall shear stress and the wall heat flux magnitude have been found to capture the qualitative nature of the correlation between these quantities and their spatial variations. It is found that tens of most energetic POD modes are needed to capture the mean and variances of wall heat flux and wall shear stress. The number of most energetic modes, which contribute significantly to the statistics of both wall heat flux and wall shear stress, decreases with decreasing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>R</mml:mi> <mml:msub><mml:mi>e</mml:mi> <mml:mi>τ</mml:mi></mml:msub> </mml:mrow> </mml:math> and also with the progress of flame quenching due to the weakening of turbulence effects.