THE OPTIMUM EXPERIMENTAL-DESIGN FOR RECONSTRUCTION OF FLAME-FRONT PROPAGATION IN A LONG PIPE

By using spline polynomials with free nodal points, the propagation of a flame front and its velocity in a long pipe is reconstructed from i ncomplete and only relative data produced by optical sensors. The prop osed method of reconstruction is illustrated by processing of results obtained for a stoichiometric hydrogen-air mixture (1 bar, ambient tem perature) ignited by a single hot wire in a smooth-walled detonation t ube (diameter D = 110 mm; length 21 m). The optimum nodal points of th e splines (15D, 85D and 100D) divide the piping into four physically d ifferent parts. A stationary detonation velocity 2028 +/- 7 m s(-1) fr om position 100D and a maximum velocity about 2590 m s(-1) at 85D are observed. (A neglect of the predetonation excess velocity provides onl y a misleading mean detonation speed 2098 +/- 9 m s(-1) from 67D.) Usi ng the theory of experimental design, the minimum number (11) and opti mum positions of monitoring sensors within the characteristic regions of the whole pipe are calculated. With respect to the complexity of th e deflagration-to-detonation transition, also the optimum distribution of 16 sensors is discussed.