Reynolds number effect on jet control and its scaling

This work aims to investigate experimentally the effect of Reynolds number \textit{Re} on the mixing effectiveness of a turbulent jet manipulated using a single unsteady radial minijet. A novel artificial intelligence (AI) control system has been developed to manipulate the turbulent jet. The \textit{Re }examined is 8000-50000 based on the time-averaged jet exit velocity $\overline {U_{j} } $ \begin{figure}[htbp] \centerline{\includegraphics[width=0.13in,height=0.19in]{030820201.eps}} \label{fig1} \end{figure} and the nozzle exit diameter $D$. The control parameters include the mass flow rate ratio $C_{m}$ of the minijet to main jet, the frequency ratio $f_{e}$/$f_{\mathrm{0}}$ of the minijet excitation frequency $f_{e}$ to the preferred-mode frequency $f_{\mathrm{0\thinspace }}$of main jet, the duty cycle $\alpha ,$ and the diameter ratio $d$/$D$ of the minijet to the main jet. Jet mixing is quantified using $K_{e}$/$K_{\mathrm{0}}$, where $K $is the decay rate of the jet centreline mean velocity, and subscripts $e$ and 0 denote the manipulated and unforced jets, respectively. Empirical scaling analysis of the AI-obtained experimental data reveals that the relationship $K_{e} = g_{\mathrm{1}}$ ($C_{m}$, $f_{e}$/$f_{\mathrm{0}}$, $\alpha $, $d$/\textit{D, Re, K}$_{\mathrm{0}})$ may be reduced to $K_{e}$/$K_{\mathrm{0}} \quad = \quad g_{\mathrm{2}}$ \begin{figure}[htbp] \centerline{\includegraphics[width=0.19in,height=0.17in]{030820202.eps}} \label{fig2} \end{figure} $(\zeta ),$ where $\zeta \quad = \quad \frac{\sqrt {MR} }{\alpha }\left( {\frac{d}{D}} \right)^{n}\frac{1}{Re}\left( {\frac{f_{e} }{f_{0} }} \right)^{m}$ ($n$ and $m$ are power indices) \begin{figure}[htbp] \centerline{\includegraphics[width=1.04in,height=0.28in]{030820203.eps}} \label{fig3} \end{figure} ,$\sqrt {MR} \equiv C_{m} \frac{D}{d}$ \begin{figure}[htbp] \centerline{\includegraphics[width=0.71in,height=0.23in]{030820204.eps}} \label{fig4} \end{figure} and $g_{\mathrm{2}}$ is approximately a linear function. The scaling law is discussed, along with the physical meanings of the dimensionless parameters $K_{e}$/$K_{0}$, $\zeta $, $\frac{\sqrt {MR} }{\alpha }\left( {\frac{d}{D}} \right)^{n}\frac{1}{Re}$ \begin{figure}[htbp] \centerline{\includegraphics[width=0.69in,height=0.27in]{030820205.eps}} \label{fig5} \end{figure} and $\left( {\frac{f_{e} }{f_{0} }} \right)^{m}$ \begin{figure}[htbp] \centerline{\includegraphics[width=0.33in,height=0.28in]{030820206.eps}} \label{fig6} \end{figure} .