## 4 Results
\begin{table}
\begin{tabular}{c c c c c} \hline
**Description** & **Definition** & **Non-Dimensional Value** & **Dimensional Value** & **Normalizing Value** \\ \hline Freestream Max number & M\({}_{\infty}\) & 2.0; 1.5 & & \\ \hline Freestream pressure & \(p_{\infty}\) & 0.2 & 26.5 kPa & \(p_{n}=132.5\) kPa \\ \hline Ratio of specific heats & \(\gamma\) & 1.4 & & \\ \hline Maximal radius of AD body & \(R\) & 0.8 & 6.4 m & \(l_{n}=8\) m \\ \hline Length of the AD body & \(L\) & 10.0 & 80 m & \(l_{n}=8\) m \\ \hline The half-width of the layers in & \(r_{s}\) & 0.04 & 0.32 m & \(l_{n}=8\) m \\ considered TSSs & \(N\) & 7.5 & & \\ \hline Rarefaction parameter in the layer & \(j\) in different TSSs & \(\alpha_{j}\) & 0.25 & \\ \hline \end{tabular}
\end{table} 
Table 3: Characteristics of the flow and the AD model used in the calculations. M\({}_{\infty}\) = 2 for \(\alpha_{j}\) = 0.25 under the action of the TSSs with 7.5 layers (of the greatest effect). The effect in the reduction of the drag force \(F\) is 20.7% at M\({}_{\infty}\) = 2 and 19.0% at M\({}_{\infty}\) = 1.5. Figure 13: Cont. Figure 15 shows a comparison of the NFPS \(\Delta p/p_{\infty}\) at \(r=16.8\) in the case of the absence of TSS (blue) and in the presence of TSS with \(\alpha_{j}=0.25\), \(N=7.5\) (orange). For this flow geometry, the NFPS is considered for \(t=40\). One can see that the action of TSS does not increase the amplitude of the BSW in the NFPS in spite of the presence of the effect of drag reduction. The reason for this is that the TSS impact on the BSW is concentrated in the area closest to the body. Using the Formulas (20) and (25) from [5], it is possible to evaluate the effective power \(P\) required for the creation of the considered stratified energy sources. Taken into account that the half-width of the layers in considered TSSs \(r_{s}=10t_{r}\) and the coordinates of the centers of layers \(r_{c}\) in these simulations can be calculated as \(r_{c}=30(N-0.5)t_{r}\), the effective power \(P\) can be evaluated as follows:  
\[P=\pi/4\frac{\gamma}{\gamma-1}\beta u_{\infty}p_{\infty}r_{s}^{ 2}/4\big{(}1-\alpha_{j}\big{)}+4\pi(N-0.5)\frac{\gamma}{\gamma-1}\beta u_{ \infty}p_{\infty}r_{c}r_{s}\big{(}1-\alpha_{j}\big{)}\] \[=\pi\frac{\gamma}{\gamma-1}\beta M_{\infty}c_{\infty}p_{\infty} 100h_{r}^{2}\big{(}1-\alpha_{j}\big{)}\big{(}1/16+12(N-0.5)^{2}\big{)},\]  
Figure 14: Dynamics of the drag force for TSS with \(N=7.5\), \(\alpha_{j}=0.25\) in comparison with the undisturbed flow case: (**a**) \(\text{M}_{\infty}=2\); (**b**) \(\text{M}_{\infty}=1.5\). Figure 13: Impact of TSS on the flow past the body: dynamics of the density fields, \(\text{M}_{\infty}=2\), without energy source—_blue_, with TSS, \(\alpha_{j}=0.25\); \(N=7.5\)—_rad_; (**a**) \(t=9.0\); (**b**) \(t=20.0\); (**c**) \(t=40.0\); (**d**) interaction of TSS with the BSW (increased). The distance between isochores is 0.05; (**e**) with TSS, \(t=20.0\), colors and isochores. where a constant \(\beta=0.1\)[5]. The values of the effective power for the parameters of the simulations from Sections 4.2 and 4.3, \(\alpha_{j}=0.25\), \(N=7.5\) using the obtained expression for \(P\) are 591.27 MW for M\({}_{\infty}=1.5\) and 788.37 MW for M\({}_{\infty}=2\), which are large and likely impractical. Nevertheless, we examine the maximal possible effect from the considered TSS to evaluate the perceived level in decibels (PLdB) impact on the ground during the implementation of the flow control using TSS.