## 1 Introduction
[PERSON] and [PERSON] [19] experimentally researched the engine power of a DI diesel engine with toroidal and shallow depth re-entrant piston bowls fueled with biodiesel. The authors reported that the re-entrant piston bowl improved the fuel/air mixing quality, resulting in a performance improvement. [PERSON] et al. [26] investigated the performance and fuel/air mixing quality for three various piston bowl geometries for a four-stroke diesel engine. Their optimized piston bowl had a positive influence on fluid flow turbulence, fuel/air mixing quality, diffusion combustion phase, fuel oil consumption, smoke, and NOx emissions. [PERSON] et al. [27] studied the impact of re-entrant piston bowl geometry on a diesel engine and found out that the higher re-entrant piston bowl produced better TKE and swirl while reducing NOx and soot emissions simultaneously. [PERSON] and [PERSON] [28] numerically investigated the effects of piston bowl geometries on a turbocharged diesel engine, and they concluded that enhancement in in-cylinder turbulence has a positive influence on fuel oil consumption, soot, and NOx emissions. [PERSON] et al. [29] studied the performance and emissions of a diesel engine with various piston bowl designs. They reported that increasing the toroidal radius led to better combustion efficiency while reducing soot emissions. The re-entrant piston bowl was more suitable for DI diesel engines due to it producing a higher in-cylinder pressure and lower soot formation, which is the same as reported in [30]. [PERSON] et al. [30] also studied the effect of piston bowl design on the combustion process of a diesel engine. They concluded that the re-entrant piston bowl was suitable for swirl generation and TKE intensification around the top dead center (TDC). [PERSON] et al. [17] conducted an experimental analysis on the combined effects of fuel injection timing and piston bowl geometry on the performance of a diesel engine fueled with biodiesel. The research reported that a re-entrant piston bowl could improve engine performance but increase NOx emission. [PERSON] et al. [31] researched the effects of piston bowl geometry on the in-cylinder flow behavior and performance of the engine and reported that the piston bowl must be fully optimized to achieve the optimum performance. [PERSON] et al. [32] numerically investigated the effect of piston bowl geometry on the mixing, combustion, and emissions of a diesel engine and concluded that improving the piston bowl design could form stronger squish flow. This helped to increase air-fuel mixing quality. [PERSON] et al. [33] studied the effects of piston bowl geometry on in-cylinder combustion and engine performance of a gasoline DI compression ignition engine. The study concluded that, to improve engine efficiency and decrease emissions simultaneously, the piston bowl geometry and injection strategy should be co-optimized. [PERSON] et al. [34] investigated the effects of the piston bowl geometry, exhaust gas recirculation (EGR) ratio, and fuel injection timing on the engine performance of a 4-stroke diesel engine in 2022. They concluded that the combination of an optimized piston bowl design, correct fuel injection timing, and appropriate EGR ratio helped to increase engine performance while reducing exhaust gas emissions of the engine. [PERSON] et al. [35] investigated the combined effects of the injector spray angle and combustion chamber geometry on combustion performance at a full load of a diesel engine using a genetic algorithm. They concluded that the optimization of both the injector spray angle and piston bowl geometry improved the air-fuel mixing quality and thus the combustion process of the engine. This helped to increase engine power while reducing soot unburnt hydrocarbon (HC), and carbon monoxide (CO) emissions. [PERSON] et al. [36] performed a survey on the combustion chamber modification to improve engine performance while reducing emissions from diesel engines in 2021.