Counteracting ring formation in rotary kilns The authors study a model which accounts for the production of cement in a rotary kiln. During this production process, rings may occur which may lead to shutdowns of the production in severe cases. The model starts with the Navier-Stokes equations which describe the conservation of the overall mass, of the concentration of the $N$ species which are involved, of the momentum and of the energy. The authors here quote these equations from the books of {it F. A. Williams} [Combustion theory. 2nd ed. New York: Westview Press (1994)] and of {it K. K. Kuo} [Principles of combustion. 2nd ed. Chichester: Wiley (1999; Zbl 1050.80503)]. They then introduce the Reynolds averaged Navier-Stokes equations rewriting the above conservation laws. They also introduce a turbulence model based on Boussinesq’s assumption, leading to a so-called realizable $k$-$varepsilon$ model. The main part of the paper presents a numerical resolution of this model based on the finite volume technique and implemented in the software { t STAR-CCM}$^{+}$. The authors describe the cases of standard and modified operating conditions, considering the ratio between air and fuel. They prove that when this ratio increases from 9 to 12 the peaks in radiative heat transfer which creates the rings reduce in the zones of ring formation. Many figures illustrate the properties of the solution.