Variation of the statistical properties of an incompressible velocity, passive vector and passive scalar in isotropic turbulence was studied using direct numerical simulation. The structure functions of the gradients, and the moments of the dissipation rates, began to increase at about
R
λ
∼
2
from the Gaussian state and grew rapidly at
R
λ
>
20
in the turbulent state. A contour map of the probability density functions (PDFs) indicated that PDF expansion of the gradients of the passive vector and passive scalar begins at around
R
λ
≈
4
, whereas that of the longitudinal velocity gradient PDF is more gradual. The left tails of the dissipation rate PDF were found to follow a power law with an exponent of 3/2 for the incompressible velocity and passive vector dissipation rates, and 1/2 for the scalar dissipation rate and the enstrophy; they remained constant for all Reynolds numbers, indicating the universality of the left tail. The analytical PDFs of the dissipation rates and enstrophy of the Gaussian state were obtained and found to be the Gamma distribution. It was shown that the number of terms contributing to the dissipation rates and the enstrophy determines the decay rates of the two PDFs for low to moderate amplitudes.
This article is part of the theme issue ‘Scaling the turbulence edifice (part 1)’.
A fast static aeroelastic analysis method, coupling with the modal method and Kriging surrogate model, is proposed in this paper. The deflection of the wing is described by the modal method, and the Kriging surrogate model is utilized to model the generalized forces under different deformations, angles of attack, and Mach numbers in order to replace the CFD solver. We analyzed the static aeroelasticity of HIRENASD wing in transonic flow field by coupling with the generalized force model by the static equilibrium equation. The results were compared with those of the experimental data and the references, and the comparison shows that the method is useful for the small deflections. After enough training cases are finished, the high-accuracy aerodynamic force coefficients and wing deflection will be obtained rapidly, which will only take several seconds. This method is more time saving than the CFD/CSD method, when it comes to a large quantity of the static aeroelastic analyses. Hence, it has good perspective for engineering applications during the aircraft design period.
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