Gaseous detonation propagation through a bifurcated tube was numerically investigated. A 2^nd additive semi-implicit Runge-Kutta method and a 5^th order WENO scheme were used to solve two-dimensional reactive Euler equations. A detailed chemical reaction model was utilized to describe the heat release of detonation. The contours of density, pressure, temperature, species OH mass fraction, the computed cellular pattern and the traveling speed of detonation were obtained. The results show that, influenced by the rarefaction waves from the left sharp comer, the reaction zone is separated from the leading shock. Then, the detonation is degenerated into the deflagration. The winkled reaction front can be clearly identified in numerical schlieren and temperature contours. Re-initiation is induced by the leading shock reflection on the right wall in the vertical branch. Mach reflection of disturbed detonation occurs in both vertical and horizontal branches. The boundary between regions of uniform and larger cells is not a straight line; it doesn't exactly start at the left sharp comer and is usually upstream of the left sharp comer. The triple-point trajectory characterizing Mach reflection locates downstream of the right comer in the horizontal branch. Complex structures of vortices, the unreacted region, and shock-vortex interaction are observed in flow field around the left comer. Vortices accelerate reaction rates of the unreacted region. The reflected shock interacts with vortices and breaks them into pieces. Reflected shock also accelerates the consumption of the unreacted region and then an embedded jet is produced. The evolution of detonation wave and computed cellular pattern are qualitatively consistent with those from experiments.

The key step for reliability assessment with small sampling is to take advantage of the subjective information and the test data of input parameters. Subjective inference could just offer the reliability some incomplete information which can be generally assumed to exist in the form of either a prior mean or a prior credibility interval. To the trials with the outcomes of either survival-failure or normal distributed parameters, efficient approaches are developed to determine the conjugate prior distributions from the subjective information according to the principle of maximum entropy. The test data of input parameters are also transformed as the prior information of the output parameters according to statistics theory. Bayes theorem is used to synthesize the different informations and numerical examples are presented to illustrate the impact of non-experimental information on the reliability posterior, the needed test number and the reliability assessment.