Relative importance of initial conditions on outflows from multiple fans

Generation of homogeneous isotropic turbulence was attempted using an innovative “multifan wind tunnel” with 99 fans installed. The driving method used is based on a principle that the shear layers generated between outflows from the adjacent ducts lead to turbulent flow downstream. First, a signal composed of two frequency components is set, and then it is fed to all the fans for three kinds of arrangements of phases. Here, parameter $N$ is introduced as the number of phases used for the 99 fans, which represents a variety of emanated shear layers. Furthermore, $S$ is introduced as a measure of shear magnitude at the inlet of the test section. Relative importance of the initial conditions ($N$ and $S$) in the development of turbulence was investigated. To estimate the contribution from naturally induced turbulence, we numerically decomposed the resulting velocity fluctuations into the periodic and nonperiodic component. Energy spectra for three values of $N$ were calculated using nonperiodic data. The inertial subrange of a gradient of $-5/3$ widens with increasing $N$. The value $S$ is the largest for $N=2$, but the turbulence intensity of the nonperiodic component is the largest for $N=99$. Hence, it might be suggested that the shear magnitude at the inlet of the test section is not as important as the variety of shear layers for effective generation of high-Reynolds-number turbulence.

Figure 1

Experimental setup. (a) A perspective view of the test section and the coordinate system of the multifan type wind tunnel (MFWT). (b) Side view and driving mechanism of the MFWT.

Figure 2

Arrangement of $n$ and the coordinate axes. (a) $N=2$, (b) $N=5$, (c) $N=99$.

Figure 3

Sketch of the mechanism of generating unsteady shears. Assume two signals shifted by ${\psi }_n$ are fed to two fans, named Fan1 and Fan2. At a time $t$, a difference in velocity occurs. This difference leads to a difference between blowing velocities $u_1$ and $u_2$, thereby causing a shear layer.

Figure 4

Indices assigned to each fan. The region surrounded by a red line shows the range used for estimating $S_c$. Here, $S_c$ is introduced to confirm whether the local shear magnitude around the central duct is close to the average shear magnitude. The indices correspond to $(i,j)$ of Eqs. (A1) and (A2) in the Appendix.

Figure 5

Spatial variations of average velocity $U$. (a) Vertical variations. (b) Streamwise variations.

Figure 6

(a) Comparison of the time traces of velocity fluctuations $u$(black) at $X/M_D=60.5$ and $Y/M_Y=Z/M_Z=0$ with the input signal $u_{\text{in}}$(red). (b) Cross-correlation coefficient of the input signal and the turbulent velocity at $X/M_D=60.5$. As the input signal is shifted in phase, the correlation coefficient reaches a maximum [indicated by the arrow in Fig. 6], when the signal is fixed and displayed in the Fig. 6.

Figure 7

Streamwise development of anisotropy.

Figure 8

Comparison of power spectra of the streamwise velocity fluctuation at $X/M_D=60.5$. (a) $N=2$, (b) $N=5$, (c) $N=99$. The black line is from the raw data, and the red line is obtained by removing the peaks.

Figure 9

Typical example of decomposition of $u$ into $u_{\theta }$ and $u_s$. A time trace $u$ is taken from data for $N=2$ at $X/M_D=4.6$. An extracted component $u_s$ seems to fluctuate about a level of $u=0\mathrm{m}/\mathrm{s}$.

Figure 10

Characteristics of $u_s^{\prime }$. (a) Streamwise variation of intensity. (b) Streamwise variation of isotropy.

Figure 11

Streamwise variation of the Taylor-microscale Reynolds number ${\text{Re}}_{\lambda s}$.

Figure 12

Comparison of energy spectra at $X/M_D=60.5$. Nonperiodic data $u_s$ are used in the analysis.

Figure 13

Streamwise variation of ${u_{\theta }^{\prime }}^2$ and $q^2$. The difference between $q^2$ and $u_{\theta }^{\prime 2}$ is nearly equal to the total energy of nonperiodic components, i.e., $u_s^{\prime 2}+v^{\prime 2}+w^{\prime 2}$.

Figure 14

Partition of turbulent energy. Hatched region, ${u_{\theta }^{\prime }}^2$; cross-hatched, ${u_s^{\prime }}^2$; white, $v^{\prime 2}$ and $w^{\prime 2}$; green, $2\langle u_{\theta }{u}_s\rangle$.