On-lattice coalescence and annihilation of immobile reactants in loopless lattices and beyond.
We study the behavior of the chemical reactions A+A-->A+S and A+A-->S+S (where the reactive species A and the inert species S are both assumed to be immobile) embedded on Bethe lattices of arbitrary coordination number z and on a two-dimensional (2D) square lattice. For the Bethe lattice case, exact solutions for the coverage in the A species in terms of the initial condition are obtained. In particular, our results hold for the important case of an infinite one-dimensional (1D) lattice (z=2). The method is based on an expansion in terms of conditional probabilities which exploits a Markovian property of these systems. Along the same lines, an approximate solution for the case of a 2D square lattice is developed. The effect of dilution in a random initial condition is discussed in detail, both for the lattice coverage and for the spatial distribution of reactants.
Exact correlation functions in particle-reaction models with immobile particles
Exact results on particle densities as well as correlators in two models of immobile particles, containing either a single species or else two distinct species, are derived. The models evolve following a descent dynamics through pair annihilation where each particle interacts once at most throughout its entire history. The resulting large number of stationary states leads to a non-vanishing configurational entropy. Our results are established for arbitrary initial conditions and are derived via a generating function method. The single-species model is the dual of the 1D zero-temperature kinetic Ising model with Kimball–Deker–Haake dynamics. In this way, both infinite and semi-infinite chains and also the Bethe lattice can be analysed. The relationship with the random sequential adsorption of dimers and weakly tapped granular materials is discussed.
Turbine blade temperature calculation and life estimation - a sensitivity analysis
Abstract The overall operating cost of the modern gas turbines is greatly influenced by the durability of hot section components operating at high temperatures. In turbine operating conditions, some defects may occur which can decrease hot section life. In the present paper, methods used for calculating blade temperature and life are demonstrated and validated. Using these methods, a set of sensitivity analyses on the parameters affecting temperature and life of a high pressure, high temperature turbine first stage blade is carried out. Investigated uncertainties are: (1) blade coating thickness, (2) coolant inlet pressure and temperature (as a result of secondary air system), and (3) gas turbine load variation. Results show that increasing thermal barrier coating thickness by 3 times, leads to rise in the blade life by 9 times. In addition, considering inlet cooling temperature and pressure, deviation in temperature has greater effect on blade life. One of the interesting points that can be realized from the results is that 300 hours operation at 70% load can be equal to one hour operation at base load.