The turbulence models review for aerodynamic, thermal and structural problems in jet engine turbines

Abstract

In the processes of their processing to obtain finished products, the internal structure and the properties of various scale levels of the material that depend on it change significantly, the prediction of which using empirical methods is extremely costly. For this reason, the development of processing technologies is unthinkable without mathematical models, the central element of which is constitutive relations. A promising approach for constructing the latter is the physical approach, which makes it possible to describe the evolution of the internal structure at various scale levels. As a rule, such models of materials are multilevel and represent a whole class of constitutive models. Of particular interest are elastoplastic models, since they allow calculations with sufficiently large time steps. Most models of this type are based on the Taylor - Bishop - Hill model. Models of this type have a drawback: uncertainty in the choice of a set of active slip systems. This uncertainty is due to the fact that the dislocation shear rates along slip systems are determined from a system of equations, the dimension of which may exceed the dimension of the space of independent variables being sought. In this paper, we study the influence of a random choice of sets of active slip systems in elastoplastic models of the Taylor - Bishop - Hill type on the results of mod-eling the elastoplastic deformation of polycrystals with a face-centered cubic lat-tice. The deviation in the simulation results was considered for a random choice of sets of active slip systems. For this purpose, special metrics were introduced to show the effect of uncertainty on the macrolevel stress tensor and misorientation angles between crystallites. It is shown that with increasing strains, a random choice of sets of active slip systems leads to an almost monotonous increase in differences in the calculation of the macrolevel stress tensor and misorientation angles between grains. This fact means that the problem of uncertainty in the choice of active slip systems inherent in these models affects the simulation re-sults. The indicated discrepancy between the simulation results evidences the need to develop an algorithm to eliminate the noted uncertainty, which is the sub-ject of the forthcoming publication of the authors.