Traditional supersonic flameholders, such as cavities and struts, face severe thermal protection problems. Recently, some scholars have investigated methods for plasma supersonic flameholding in scramjet combustors without flameholders. However, the main flame remains concentrated near the boundary layer, which leads to the same thermal protection problem. Laser-induced plasma (LIP) presents many potential benefits over conventional plasma generation methods, such as non-intrusion of the flow field and availability of easily changing energy deposition locations. Thus, the use of LIP is a novel solution for the study of plasma flameholding methods under supersonic conditions. Research on the evolution characteristics of a multi-point LIP in quiescent air is the basis for studying and optimizing its supersonic ignition and flameholding effects. Owing to the limitations of measurement techniques and equipment in experimental research, it is challenging to obtain sufficient information of the flow field after applying multi-point LIP in quiescent air. Numerical simulation has become an important approach for studying LIP in quiescent air. Therefore, the instantaneous energy deposition model was used in this study to numerically investigate the evolution characteristics of multi-point LIP in quiescent air.

Although plasma is the fourth state of a substance, it can be considered as a Newtonian fluid in numerical simulations. In this study, high-temperature and high-pressure effects of LIP were mainly studied so that the Navier-Stokes (N-S) equations could be used to describe its control equations. The study was based on an improved instantaneous energy deposition model proposed by Dors, who simplified the region after LIP in air at the laser focus into regions of high-temperature and high-pressure gas in the experiment. Dors assumed that after the LIP in quiescent air at the laser focus, the temperature was exponentially distributed in the laser direction and normally distributed in the direction perpendicular to the laser direction. The pressure distribution can be defined using the ideal gas state equation. In this study, the laser wavelength was set to 532 nm, pulse width was set to 10 ns, static temperature was set to 291 K, and static pressure was set to 100 kPa. The size of the calculation domain was 20 mm×20 mm×10 mm. The grid independence was verified by comparing the pressure distribution at y=0 at 10 μs. Subsequently, the reliability of the model was verified by comparing it with the experimental schlieren diagram.

The shock wave and plasma kernel are generated by multi-point LIP in quiescent air at the laser focus, and the plasma kernel completely fuses at 10 μs (Fig. 4). Although the shock wave shapes vary in different laser focal layouts, the development trend and time for complete fusion remain similar. The average temperature and volume of the plasma kernels vary with different focal layouts. However, they are approximately inversely proportional to each other within 5-30 μs (Figs. 9 and 11). The time for complete fusion of the plasma kernel is shorter when the distance between adjacent focal spots (D_s) is 2 mm. However, the plasma kernel cannot fuse when D_s=4 mm (Fig. 14). D_s significantly influences the ignition and flameholding characteristics of the multi-point LIP. A D_s of 3 mm is more conducive to the ignition and pursuit of the previous flame kernel in a supersonic flow (Fig. 15).

In this study, an improved instantaneous energy deposition model based on the model proposed by Dors was used to numerically simulate the evolution characteristics of a multi-point LIP in quiescent air. From the results of the multi-point LIP with the linear focal configuration when D_s=2 mm, we confirm that a shock wave is generated by the multi-point LIP, and the shock wave pressure remains stable during the propagation stage. The fusion of the plasma kernel can reduce energy dissipation when its size increases, which is beneficial to the survival and pursuit of the previous flame kernel in a supersonic flow. In addition, the shock wave generated by the LIP can deflect the supersonic flow, which can build a low-speed region behind the shock wave. By comparing the average temperature, volume, specific surface area, and pressure at the characteristic position of the plasma kernel, we determine that the evolution characteristics of the multi-point LIP are mainly affected by D_s. When D_s is extremely small, the advantages of multiple points cannot be fully utilized. When D_s is extremely large, the plasma kernel cannot fuse. Under such conditions, D_s should be set to approximately 3 mm to achieve better survival ability and pursue the previous flame kernel in supersonic flow for the initial flame kernel generated by the multi-point LIP.