Dendrite primary spacing selection simulation by the cellular automaton model

A cellular automaton model was developed to simulate the primary spacing selection of dendritic array during directional solidification. A simplified growth kinetics was adopted, which could relax the computing complexity, and a strict method to determine the stable state of the system was proposed. Based on two types of primary spacing adjustment mechanisms in the simulation, branching-instability and submerging-instability, in order to determine the allowable range of primary spacing of dendritic arrays for given growth conditions, two different methods of tests were adopted, in one way the seed number was fixed with a step-varying pulling velocity, and in another way the pulling velocity was constant with different seed numbers. The simulated results show that the allowable range is independent from test methods. The upper limit, λ_max, and the lower limit, λ_min, of the allowable range as the function of pulling velocity, v_p, can be generally expressed as the power function of the pulling velocity. During the simulation of the succinonitrite (SCN)-2.5% ethanol dendrite growth, the parameters of the power function are in good agreement with experiments, which was better than the agreement of Hunt-Lu model and the experiments. The simulated lower limit was better agreement with the experiments' lower limit than the Hunt-Lu model.