No abstract

Exact budget equations are derived for the coherent and stochastic contributions to the second-order structure function tensor. They extend the anisotropic generalised Kolmogorov equations (AGKE) by considering the coherent and stochastic parts of the Reynolds stress tensor, and are useful for the statistical description of turbulent flows with periodic or quasi-periodic features, like, for example, the alternate shedding after a bluff body. While the original AGKE describe production, transport, inter-component redistribution and dissipation of the Reynolds stresses in the combined space of scales and positions, the new equations, called $\varphi$ AGKE, contain the phase $\varphi$ as an additional independent variable, and describe the interplay among the mean, coherent and stochastic fields at the various phases. The newly derived $\varphi$ AGKE are then applied to a case where an exactly periodic external forcing drives the flow: a turbulent plane channel flow modified by harmonic spanwise oscillations of the wall to reduce drag. The phase-by-phase action of the oscillating transversal Stokes layer generated by the forcing on the near-wall turbulent structures is observed, and a detailed description of the scale-space interaction among mean, coherent and stochastic fields is provided thanks to the $\varphi$ AGKE.

A multi-objective continuous adjoint strategy based on the superposition of boundary functions for topology optimization of problems where the heat transfer must be enhanced and the dissipated mechanical power controlled at the same time, has been here implemented in a finite volume (FV), incompressible, steady flow solver supporting a dynamic adaptive mesh refinement (AMR) strategy. The solver models the transition from fluid to solid by a porosity field, that appears in the form of penalization in the momentum equation; the material distribution is optimized by the method of moving asymptotes (MMA).AMR is based on a hierarchical nonconforming h-refinement strategy and is applied together with a flux correction to enforce conservation across topology changes. It is shown that a proper choice of the refinement criterium favors a mesh-independent solution. Finally, a Pareto front built from the components of the objective function is used to find the best combination of the weights in the optimization cycle. Numerical experiments on two-and three-dimensional test cases, including the aero-thermal optimization of a simplified layout of a cooling system, have been used to validate the implemented methodology.

Exact budget equations are derived for the coherent and stochastic contributions to the second-order structure function tensor. They extend the anisotropic generalised Kolmogorov equations (AGKE) by considering the coherent and stochastic parts of the Reynolds stress tensor, and are useful for the statistical description of turbulent flows with periodic or quasiperiodic features, like e.g. the alternate shedding after a bluff body. While the original AGKE describe production, transport, inter-component redistribution and dissipation of the Reynolds stresses in the combined space of scales and positions, the new equations, called AGKE, contain the phase as an additional independent variable, and describe the interplay among the mean, coherent and stochastic fields at the various phases. The newly derived AGKE are then applied to a case where an exactly periodic external forcing drives the flow: a turbulent plane channel flow modified by harmonic spanwise oscillations of the wall to reduce drag. The phase-by-phase action of the oscillating transversal Stokes layer generated by the forcing on the near-wall turbulent structures is observed, and a detailed description of the scale-space interaction among mean, coherent and stochastic fields is provided thanks to the AGKE.