We have proposed a new compressive combustion principle leading to the auto-ignition of fuel by focusing compression due to the collision of the pulsed supermulti-jets. This principle has the potential of nearly-complete air insulation due to encasing burned gas around the center of the combustion chamber and a high compression ratio around the chamber center while suppressing vibration and noise levels. We have developed the first prototype engine having a very small combustion chamber of a diameter of 18 mm and also 14 side passages for the supermulti-jets colliding at the chamber center. Combustion experimental results indicating air insulation effect and high thrust over 100 N were obtained as basic data for various types of applications, including automobiles and aerospace usage such as for rockets. However, it was found that higher compression due to more jets is necessary to get stabler combustion. Therefore, by using a metal 3D printer, we have developed the second engine with 24 side passages of gas jets colliding, while performing direct injection of liquid fuel at injection pressure over 5 MPa into the combustion chamber. In our previous report, the experiment without combustion and its computational simulation show that the second engine enables a higher compression ratio than that of the first prototype engine. In this research, we conduct fundamental combustion experiments using the second engine with a direct injection system, purposing to achieve stable multi-cycle combustion with auto-ignition of the fuel by focusing compression due to the collision of supermulti-jets. As a result, a stabler occurrence of combustion is confirmed for the second engine. Experimental data of wall pressure obtained also indicate that auto-ignition occurs due to collision of the supermulti-jets while showing a possibility of higher thrust over 300 N. Furthermore, we qualitatively perform computations of reacting flows for the second engine, while showing liquid fuel spray atomized strongly by the gas jets.