An attempt to generate high-Reynolds-number homogeneous turbulence using disturbances of a small number of frequencies

Abstract

This paper deals with the influence of the number and combination of frequency components in an input signal on the spatial evolution of turbulence using a multi-fan type wind tunnel, where 99 fans were driven to generate turbulence. In order to understand the elementary process of the evolution, we compose the input signal of a small number of frequencies (i.e. one or two). The input frequencies are defined as integer multiples of f₀, the reciprocal of a basic input data period. In the single-frequency case, the evolution of the spectrum of the streamwise velocity fluctuations shows that the peaks associated with the input frequency and its harmonics remain over the tunnel length. In the two-frequency case, f₁ and f₂ (f₁ = n₁ f₀ and f₂ = n₂ f₀;n₁ < n₂), where n₁ and n₂ are integers, the generated turbulence characteristics depend on the relation between n₁ and n₂. When n₁ and n₂ are not coprime, dominant spectral peaks associated with f₁ and f₂ remain over the tunnel length as in the single-frequency case. However, when n₁ and n₂ are coprime (i.e., the only common positive factor of the two number is one), the spectral shape becomes broader as the turbulence convects downstream, with the peaks gradually merging into the background turbulence and also identified is a scaling region, known as the inertial subrange. Thus, we select this way as a driving mode. The evolutions of the turbulence characteristics including turbulence Reynolds number, intensity, homogeneity, and isotropy are examined. In the downstream region for X/M_D ≥ 46.5, the evolutions are in good agreement with those of the forty-frequency case obtained in a previous study, although the development of turbulence is much slower for the two frequency case than for the forty-frequency case.