Two-dimensional isotropic turbulent inflow conditions for vortex particle method

The unsteady loading on an airfoil due to the inflow turbulence is the primary source of broadband noise in turbomachinery, which makes the modeling of the inflow conditions a crucial task. This Rapid Communication presents an advanced method to model isotropic turbulent inflow conditions for a two-dimensional vortex particle method. The method relies on the classical view of turbulence as a superposition of random vortices convected with the mean flow. The fluctuating velocity is formulated using the scalar potential given by a convolution product which furnishes a solenoidal velocity field. The system is then optimized stochastically to create a realistic turbulence field based on a target energy spectra using an evolutionary optimization algorithm.

Figure 1

Distributions of the vortices are indicated by disks with area proportional to the vortex intensity; red symbols indicate negative (clockwise flow) and green symbols indicate positive (counterclockwise flow) circulation, respectively.

Figure 2

Three-dimensional view of a Gaussian shape vortex by plotting the magnitude of the (a) $u_1$, (b) $u_2$, and (c) u velocity as the $z$ axis.

Figure 3

Scheme of the usage of the genetic algorithm (GA) to optimize the statistics of the newly generated turbulence spectrum to the target one.

Figure 4

(a) Longitudinal, (b) transverse von Kármán energy spectra of two-dimensional turbulence with $u_{\text{rms}}/u_{\infty }=0.02$ and $\mathrm{\Lambda }=0.04$;—, von Kármán spectrum; - - -, numerical spectra; and (c)—, analytical von Kármán spectrum; - - -, numerical spectra; and experimental spectrum represented by gray dots.

Figure 5

Contour plot of vorticity field in two dimensions for three random iterations on a grid with spatial resolution of $100\times 100$ divisions on the vortex window.