## 1 Introduction
Because there is an exponential correlation between the NO\({}_{\rm x}\) emissions and local combustion temperature, the local temperature peaks and NO\({}_{\rm x}\) emissions could be reduced through decreasing the burning zone equivalence ratio (below stoichiometric values). There are several low emission combustion technologies, such as lean prevaporized premixed (LPP) combustion [19; 20; 21], rich quench lean (RQL) combustion [22; 23; 24; 25; 26], and lean direct injection (LDI) combustion [27]. Compared with traditional designs, the LDI combustion concept has received considerable attention as an extremely promising technology that utilizes rapid mixing of fuel-air to produce lean combustible mixtures, as well as reduce NO\({}_{\rm x}\) emissions from the gas turbine engine. LPP combustion technologies could reduce the NO\({}_{\rm x}\) emission from gas turbine engines, but there are some shortcomings of autoignition and flashback problems for LPP combustor, so that the ignition delay times of the kerosene fuels is shorter when the kerosene is at high pressure and in high temperature conditions [28]. Using multiple smaller assemblies to produce an injector/swirler assembly, rapid mixing could be achieved. Then, multiple small burning zones would be produced. To promote reduced NO\({}_{\rm x}\) formation, a rapid mixing process, a uniform fuel air mixture, and a short residence time in high temperature zones, are generally best [29]. The evolution of LDI technologies for combustor design was summarized by the authors of [30; 31]. To define and refine the next-generation and look for a tool to provide guidance, the combustion characteristics in multi-lean direct injection combustors were investigated with the National Combustion Code (NCC). The different vane angles swirlers were used to form a 3 \(\times\) 3 element array LDI combustor. Using experimental data, the predictions of CO emission index, NOx emissions index and lean blowout were verified for two different geometry configurations [32]. To gather experience for the next-generation LDI-2, the non-reacting and reacting flow computation method was used to simulate the LDI-2 combustor, which consists of thirteen-element injectors. The NCC includes an approach of spray-modeling, mesh-refinement, kinetics-modeling and ignition. The emissions predictions of E\({}_{\text{NOX}}\), the emission index of CO (EI\({}_{\text{CO}}\)) and the unburned hydrocarbon (UHC) were evaluated for LDI-2 [33]. A parameterized model of swirl-venturi LDI was used to explore a design method [34]. The Reynolds-averaged Navier-Stokes equation for steady-state reacting computations was used to simulate the 20 three-element LDI combustor. The 18-step Jet-A reduced reaction mechanism was used to directly solve the species concentrations of combustion in the LDI combustor. The axial flow field would be vulnerable to the geometric perturbations. The turbulent kinetic energy, axial velocity, fuel distribution, static temperature and species mass fractions were analyzed. At inlet temperatures between 835 and 865 K and inlet pressure of 1034 kPa, the emission of 9-point swirl-venturi LDI (SV-LDI) was measured [35]. The two swirler blade angles were 45\({}^{\circ}\) and 60\({}^{\circ}\), respectively. The NOx emissions of LDI with 45\({}^{\circ}\) swirler was lower than that of the LDI with 60\({}^{\circ}\) swirler. The swirling flow field characteristics of the multipoint LDI combustor with nine fuel injectors were also investigated [36]. Using an injector, an axial swirler and a convergent-divergent venturi, the fuel/air rapid mixing and a recirculation zone for a stabilized flame were achieved. The vane angle of each swirler was 60\({}^{\circ}\) and the swirl number was 1.0. The transient swirling flow field structure, the component of velocity and Reynolds stresses were measured by a 3D Particle Image Velocimetry (PIV) system. If the recessed center swirler arrays of LDI combustor are different, the flow structures are significantly different.