Turbulence generated by an array of opposed piston-driven synthetic jet actuators

Abstract

This paper investigates turbulence generated by an array of opposed piston-driven synthetic jet actuators in a closed chamber. Each actuator intermittently generates supersonic jets with four orifice holes, and the interaction of 32 supersonic jets produces turbulence. Velocity measurement is conducted with particle image velocimetry using oil mist as the tracer particles, which are internally generated by the synthetic jet actuators. The turbulence with a small mean velocity is generated at the central region of the chamber, where the root-mean-square (rms) velocity fluctuations are also almost uniform in space. The rms velocity fluctuations around the chamber center are about 1.2 times larger in the jet direction than in other directions. The strongly intermittent nature of supersonic synthetic jets causes large-scale intermittency of turbulence. The turbulent Reynolds number and turbulent Mach number reach $O(10^3)$ and $O(10^{-2})$, respectively, at the chamber center. Although the turbulent Mach number at the chamber center is not large, the generation process of turbulence due to the supersonic jets is strongly influenced by compressibility. Therefore, density variations exist in turbulence, where the shadowgraph image exhibits the brightness distribution with a characteristic length scale related to the Kolmogorov scale. The shape of longitudinal velocity auto-correlation functions and the relation between the turbulent Reynolds number and velocity derivative flatness agree well with previous studies on incompressible turbulence.

Graphical abstract

Appendix: Effects of spatial resolution

The PIV measurement conducted in this study has a spatial resolution of $10\eta$-$20\eta$. The effects of the unresolved velocity fluctuations on velocity statistics are assessed with direct numerical simulation (DNS) of incompressible turbulence. Here, we use the DNS database of a temporally evolving turbulent planar jet with the jet Reynolds number of 40,000 (Watanabe et al. 2019). An energy spectrum of streamwise velocity fluctuations $E_u(k_x)$ is calculated on the jet centerline, where $k_x$ is the streamwise wavenumber. We define the cutoff wavenumber as $k_C=2\pi /C\eta _0$ with a parameter C and the Kolmogorov scale $\eta _0$. Here, $\eta _0$ is calculated with the turbulent kinetic energy dissipation rate $\varepsilon =2\nu \overline{S_{ij}S_{ij}}$, where $S_{ij}$ is the rate-of-strain tensor. Streamwise velocity variance at the scales greater than $C\eta _0$ is evaluated as $\overline{{u'}^2}(C)=\int _0^{k_C}E_u(k_x)dk_x$. Similarly, the variance of $\partial u /\partial x$ at scales greater than $C\eta _0$ is given by $\overline{(\partial u' /\partial x)^2}(C)=\int _0^{k_C}k_x^2E_u(k_x)dk_x$. Then, the turbulent Reynolds number $Re_\lambda (C)$ and Kolmogorov scale $\eta (C)$ of the filtered velocity are calculated with $\overline{{u'}^2}(C)$ and $\overline{(\partial u' /\partial x)^2}(C)$:

$$\begin{aligned} Re_\lambda (C)=\frac{\overline{{u'}^2}}{\nu \sqrt{\overline{(\partial u' /\partial x)^2}}}, ~~ \eta (C)=\left( \frac{\nu ^2}{15\overline{(\partial u' /\partial x)^2}}\right) ^{1/4}. \end{aligned}$$

(6)

Figure 17 shows the cutoff-length dependence of $\overline{{u'}^2}(C)$, $Re_\lambda (C)$, and $\eta (C)$ normalized by their values for $C=1$. As C increases, the range of the unresolved scale becomes wider. Because velocity fluctuations are dominated by large-scale turbulent motions, $\overline{{u'}^2}(C)/\overline{{u'}^2}(1)$ stays 1 even for $C=30$. $Re_\lambda (C)$ and $\eta (C)$ increase with C. However, $Re_\lambda (C)/Re_\lambda (1)$ and $\eta (C)/\eta (1)$ are less than 1.3 even at $C=30$. Thus, the present PIV measurement with the spatial resolution of 10–$20\eta$ is still useful for the approximate estimation of turbulent Reynolds number and Kolmogorov scale.