Aeronautical engineering

The students willing to attend the Turbulence course already posses a background concerning fluid motion and the basic mathematical models, the Navier-Stokes equations, say, used for its description, as acquired from previous courses. However, practically all the flows which are relevant for Aeronautical and Aerospace design applications in Aerodynamics, Fluid Dynamics and Gas Dynamics are incredibly more complex than the elementary solutions known to Batchelor students. Hence, all the background knowledge acquired by the student on fluid motion, although valuable for the foundations, is scarcely relevant for addressing the physical phenomena targeted by aerodynamic design and optimization, say. The student is left in the the same conditions of nineteen century scholars, who knew the mathematical model - the correct one, by the way — but ware unable to extract from it any valuable predictive information (just to cite known example, one may think of the wall known D’Alembert paradox or to the poor correspondence between the Poiseuille solution and the actual flow found in irrigation channels, not to talk of boundary layers). Indeed, still today we sometimes colloquially, though improperly, refer to a fluid undergoing turbulent flow as a turbulent fluid, a remnant of the historical gap between understanding of fluid motion and actual experience. In fact, in all cases of practical relevance, with the exception of microfluidic and nanofluidic ones, are turbulent (e.g., the flow in a room where we perceive still air is a stets of turbulent motion. Where it not, we would perceive smells by molecular diffusion, on a time scale of hours, as compared by the actual turbulent diffusion, on the time scale of seconds). The crucial point is that turbulence is the only fundamental problem of classical physics left unsolved after the scientific revolution of the early twentieth century. In this general context, the basic objective of the course is ferrying the student from basic understanding toward the more advanced and complete knowledge needed for actual use in aerodynamic design. In view of this, the student needs to gain a clear comprehension of the fundamental dynamics operating in free (jets, say) and wall bounded flows (e.g. boundary layers). Turbulence is a stochastic process governed by deterministic equations. In order to be able to dealt with turbulence we need the specialized language of stochastic processes applied to the Navier-Stokes equations, fro sure the most complex and difficult system of partial differential equations of wide interest for engineering applications. First aim of the course is setting up the appropriate mathematical language for describing turbulent fields. Suitable tools in the context of probability and statistics will be explained to allow the student mastering the most appropriate description of stochastic fields governed by deterministic and stochastic equations. Students will familiarize with the notion of stochastic process and the basic tools for its statistical analysis. Once the language is understood and mastered, the course will provide the students with tools for understanding and computing the most common turbulent flows, such as wall bounded (e.g. boundary layers) and free flows (such as free jets). Time will be dedicated also to figure out the universal mechanisms underpinning fully developed turbulence, namely the homogeneous, isotropic turbulence paradigm. This part of the course will lead the student to a complete and clear understanding of fundamental turbulent processes, such as turbulent transport, which implies increased mixing efficiency and heat transfer, and the magnified skin friction brought about by turbulence, which is crucial in aerodynamics. Further step is to bring the student to master current and advanced predictive and semi-predictive models of most common use in the aeronautical and aerospace design. In order to achieve this result, the modern techniques for the numerical simulation of turbulent flows, ranging from direct numerical simulation (DNS), Reynolds averaged equations (RANS) and large eddy simulation (LES). Beside providing simulation and analysis skills to be used in aerodynamical and fluid dynamical design, the purpose here is to enable the student to discriminate between the different approaches to select the most appropriate one to solve the specific problem at hand. In many cases it may be crucial to be able to understand how turbulence develops in a given flow geometry. For this reason flow stability and the different routes of laminar-turbulence transition are crucial topics the gain familiarity with. Additionally, students will be exposed to complementary aspects such as noise generation by turbulence. In conclusion, the overall, global objective of the course is to move the student from her/his basic school level knowledge to advanced and operative understanding of fluid motion in realistic contexts.