Averaging for High Fidelity Modeling—Toward Large Eddy Simulations in Multi-Passage Multi-Row Configurations

Abstract

Abstract A major challenge in high-fidelity turbomachinery flow computations is the need for high resolution in a very large domain of multiple blade-passages and multiple blade rows. Scale-resolving turbulent solutions are prohibitively costly. The question is, what will it take to get high-fidelity solutions if we are only after time-mean flows for aerothermal performance? A novel two-scale approach is adopted to address the issue by coupling between a local fine-mesh domain in a single-passage and a global coarse-mesh multi-passage domain. This is achieved by harnessing the extra product terms generated when averaging a nonlinear process in time, as well as in space. As such a space-time averaging is purposely applied in either a direct mode or an inverse one in the two domains respectively. The source terms in a compact form (one scalar for one equation) are conveniently obtained to enable the interaction between the single-passage fine-mesh and the multi-passage coarse-mesh solutions. The converged solution for this two-scale coupled system should meet two seemingly conflicting requirements: an otherwise poorly conditioned local fine-mesh domain is now subject to a right environment/flow conditions, and an otherwise poorly resolved global coarse-mesh domain is now effectively subject to high resolution. In this paper, the concepts, the formulations of the framework methodology, and the implementation methods will be described. The validity and feasibility of the approach for efficient scale-resolving high- fidelity turbomachinery flow simulations will be illustrated by several computational examples of practical interest.