This paper considers the issues of numerical modeling of nonstationary spatial gas dynamics in the pre-nozzle volume of the combustion chamber of a power plant with a cylindrical slot channel at the power plant of the mass supply surface. The numerical simulation for spatial objects is based on the solution conjugate problem of heat exchange by the control volume method in the open integrated platform for numerical simulation of continuum mechanics problems (openFoam). The calculation results for gas-dynamic and thermal processes in the power plant with a four-nozzle cover are presented. The analysis of gas-dynamic parameters and thermal flows near the nozzle cover, depending on the canal geometry, is given. The topological features of the flow structure and thermophysical parameters near the nozzle cap were studied. For the first time, the transformation of topological features of the flow structure in the pre-nozzle volume at changes in the mass channel’s geometry is revealed, described, and analyzed. The dependence of the Nusselt number in the central point of stagnation on the time of the power plants operation is revealed.