Theoretically, the calculation of the flow around a wing, a fuselage or a complete aircraft can be done by solving the Navier-Stokes equations. However, when the Reynolds number is large, as it is the case in aerodynamics, the size of computer which is needed is prohibitive. This is due to the fact that the spectrum of turbulence covers a large range of scales which increases with the Reynolds number. Hence the solution of Navier-Stokes equations is used only for relatively simple flows. We can cite one case where numerical simulations shed light on a problem which experiments were unable to analyse. This is the evolution of turbulence in a flow which is statistically homogeneous and isotropic at an initial time, and which is subjected to the effect of body rotation. The solution of Navier-Stokes equations has shown that the turbulent kinetic energy decreases more slowly in the presence of rotation. Because of a modification in the process of formation of small structures, the energy transfer from the large eddies is less. It follows that the rate of dissipation is less, and the kinetic energy decreases more slowly. Thus, this numerical experiment improved the understanding of turbulence and provided data which have been used to refine turbulence modelling. Indeed, the direct numerical simulations are very useful when simple flows are involved, but they are very far from being able to calculate the flow around an aircraft. Even if it is possible to perform such calculations in the future, it must be recalled that the design of a wing or of an aircraft requires a very large number of runs.
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