Theoretical and experimental investigations on aero-optical effect at the second stage of the compressible mixing layer

Convective speed of a vortex structure in mixing layer is an important physical quantity for correcting aero-optics caused by the flowfield as a beam passes; however, knowledge about the dynamic characteristics of convective speed of a vortex structure in mixing layer is limited because the convective speed calculated from isentropic model, which is widely used at present, is a constant. Based on the large eddy simulation and ray tracing method, the optical path length (OPL) profile over the mixing layer flowfield as beams pass through the flowfield is calculated and compared with the instantaneous vorticity contours at the same time instant. The analysis of the relationship between the local minimum of OPL in the OPL profile and the position of vortex core shows that the point of the local minimum of OPL just corresponds to the center of the vortex core. Based on this corresponding relation, the position extraction of vortex core, which is a quantitative method of calculating the instantaneous convective speed of a vortex structures in mixing layer, is proposed and validated with the data obtained from direct geometry measurement. Using this quantitative method, the instantaneous convective speeds of vortex structures with different sizes, two vortexes in the process of vortex pairing and merging, and vortex structures in the strongly compressive flowfield are calculated quantitatively and analyzed. Our quantitative results clearly present the characteristics of convective speed of vortex structures in mixing layer as follows. 1) The instantaneous convective velocity of a single vortex structure in the mixing layer flowfield varies with time, that is the fluctuation characteristics, and the fluctuation amplitude also varies with the size of a vortex structure and the compressibility of the flowfield. Specifically, the amplitude is proportional to the size of a vortex and the compressibility of the flowfield. 2) In the process of vortex pairing and merging, the variation ranges of instantaneous convective speeds of the two vortex structures are large. Specifically, the maximum value of instantaneous convective speed is close to the speed of the high-speed layer and the minimum value of instantaneous convective speed is close to the speed of the low-speed layer, and the profile of instantaneous convective speed of each vortex structure in this process approximately shows a shape of sinusoidal curve. 3) The mean value of instantaneous convective speed of a vortex structure in mixing layer is not consistent with the theoretical convective speed of vortex structure, which is calculated from the isentropic model, and the deviation between instantaneous convective speed and theoretical convective speed varies with the size of a vortex structure and the compressibility of the flowfield. In addition, the physical reasons for explaining the characteristics of instantaneous convective speed of the vortex structures in mixing layer are also presented.

Characteristics of convective speeds of vortex structures in mixing layer

Guo¹,

Li²,

Zhang³

et al. 2016

Evolution mechanism of vortices in a supersonic mixing layer controlled by the pulsed forcing

Guo¹,

Hong²,

Zhang³

et al. 2017

Pulsed actuation is one of the most fundamental control types to study regularity of flow structures in supersonic mixing layers, which helps to predict the aero-optical effects caused by the supersonic mixing layer where the different-sized vortices dominate the flow field. However, the knowledge about the evolution mechanism of vortices in the supersonic mixing layer which is controlled by the pulsed forcing is limited. Based on the large eddy simulation (LES), the visualized flow field of a supersonic mixing layer controlled by the pulsed forcing is presented and the unique growth mechanism of the vortices in such a case is revealed clearly. The method of position extraction of the vortex core in the supersonic mixing layer, which is a quantitative technique to obtain the instantaneous location of a vortex in flow field, is employed to calculate the dynamic characteristics (e.g., instantaneous convective speed and size) of the vortices quantitatively. The pulsed forcings of different frequencies are imposed on the same supersonic mixing layer respectively, and the instantaneous convective speed and size of the vortices for each pulse frequency considered in this study are then computed. By comparing the dynamic characteristics of the vortices between cases, the evolution mechanism of the vortices in the supersonic mixing layer controlled by the pulsed forcing is revealed.as follows. 1) Growth of the vortices in the supersonic mixing layer controlled by the pulsed forcing no longer depends on the pairing nor merging between adjacent vortices, which is just the growth mechanism of vortices in a free supersonic mixing layer. Actually, the size of a vortex in the controlled supersonic mixing layer is dominated by the imposed pulse frequency, so the size of each vortex in such a flow field is approximately identical. 2) The number of vortices in the controlled supersonic mixing layer is proportional to the pulse frequency, whereas the size of vortex is inversely proportional to the pulse frequency. That is, the higher the pulse frequency, the bigger the number of vortices in the controlled flow field is and the smaller the size of every vortex. 3) The average convective speed of vortices in the controlled supersonic mixing layer gradually decreases with pulse frequency increasing because the pulsed forcing essentially drags on the movement of vortices in flow field. Finally, an equation which describes the quantitative relationship between the dynamic characteristics of a vortex and the pulsed forcing frequency is derived, that is, the product of the average convective speed of vortices in the controlled supersonic mixing layer and the imposed pulse period is approximately equal to the mean diameter of vortices in the flow field.

Density distribution characteristics of fluid inside vortex in supersonic mixing layer

Guo¹,

Zhu²,

Xing³

2020

Based on the large eddy simulation, the boundary of a vortex and the coordinates of its core are both obtained by using the Lagrangian coherent structure method and the location extraction method of the vortex core, and thus the method of representing fluid density inside a vortex is proposed. The density distribution characteristics of fluid inside the vortex in a supersonic mixing layer are revealed by analyzing the changes in density of the fluid inside a vortex under different conditions (e.g. spatial size of the vortex, compressibility of the supersonic mixing layer, and merging process of the two paired vortices) as follows. For the weak and medium compressive supersonic mixing layers, the density distribution of the fluid inside a vortex is symmetrical about both the flow direction (x-axis) and longitudinal direction (y-axis), the fluid density at the vortex core is lowest while it is highest at the vortex boundary, and fluid density increases monotonically and nearly uniformly along the ray connecting the vortex core and the vortex boundary. For the strongly compressible supersonic mixing layer, however, the density distribution of the fluid inside the vortex is no longer symmetrical about any flow direction and moreover it shows the fluctuation characteristics of fluid density distribution. With the increase of the spatial size of a vortex and the compressibility of a supersonic mixing layer, the fluid density at the vortex core decreases (the maximum reduction is about 31%–56%) while it changes about 6%–27% at the vortex boundary. In the merging process of two adjacent vortices, the variation of fluid density in the two vortices is slight, which shows that the merging process is probably of a peer-to-peer combination of fluid inside the two adjacent vortices. Considering the practical engineering applications, the density distribution characteristics of fluid inside the vortex in the supersonic mixing layer with different inflow densities of its upper and lower layers are also investigated, and the results show that the density distribution of the fluid inside a vortex is symmetrical about the longitudinal direction (y-axis), but not the flow direction (x-axis). It is also found that the density distribution near the vortex boundary is determined by the inflow density there, so a good strategy of reducing the aero-optical effects caused by the supersonic mixing layer is that the difference in density between the upper and lower layers should be as small as possible.