Using numerical simulation in the ProCAST program complex, the conditions of the solidification of heat-resistant nickel alloy in curvilinear channels of a ceramic mold have been investigated. It has been shown that, in practically important cases, the vector of the temperature gradient is oriented along the axis of the curvilinear channel. In a spiral crystal selector, a cyclic change in the preferred direction of growth occurs because of the cyclic change in the direction of the vector of the temperature gradient. The fact that the vector of the temperature gradient is almost always directed along the axis of the curvilinear channel makes it possible to govern the orientation of the vector of the temperature gradient in space and, therefore, to obtain a grain with the preferred crystallographic orientation. Based on the results of this investigation, a method of the grain selection with a desired azimuthal orientation is proposed.