Effect of Low Temporal Resolution on the Uncertainty of Resolving Flame Speed of Moving Flames

Abstract

This paper analyzes the effect of low temporal resolution on the accuracy of determining the local flame speed for experimental measurements and simulations. Flame speed measurement of moving flames requires the evaluation of a temporal derivative of flame front motion. Measurements have limited temporal resolution, which can lead to a bias error in the calculation of flame speed. The error associated with the temporal resolution was derived in the leading order effect on sampling time. In order to demonstrate the error term, we employed numerical examples. Artificial flame solutions are generated by solving the G-equation with prescribed flow fields and fine spatial/temporal resolutions. By varying the sampling time step, we demonstrated the error can lead to negative values of the measured flame speed. Furthermore, when coarse sampling time steps are used, the calculated flame speed also exhibits a spurious curvature dependency. Lastly, the associated error can be estimated by spatial gradients of the flame front for convection dominated flows.