Numerical simulation of transverse jet flow field under supersonic inflow

Transverse jet flow field under supersonic inflow is simulated numerically for studying the characteristic of fuel transverse jet and fuel mixing in scramjet combustion chamber. Comparison is performed between simulated results and the results of references and experiments. Results indicate that the CFD code in this paper is applicable for simulation of transverse jut flow field under supersonic inflow, but in order to providing more effective numerical predictive method, CFD code should be modified through increasing mesh density and adding LES module.


Introduction
With the development of aerospace technology, higher flight velocity is purchased by people, so the study of scramjet is becoming one of the key problems in the research field of hypersonic vehicle. Compared with other ramjet engines, problems exist in the mixing of air and fuel in scramjet: (1) When the inflow velocity achieved supersonic speed, residence time of fuel in the combustor is ms, and the mixing efficiency of fuel and air descends rapidly with the increasing of Mach number [1] . (2) In supersonic air flow, compression and stability of the mixed layer informed by mixing of fuel and air are very strong. At the same main inflow and density ratio, diffusion coefficient of compressible mixed layer is 1/3 of incompressible one [2] . (3) Because the energy density of H 2 is very low, hydrocarbon fuel should be used for realization of high specific impulse propulsion [3] .
Experimental method is usually used in the study on mixing of fuel and air of supersonic vehicle. However, for the limitation of costs, etc., superiority of numerical simulation becomes more and more outstanding gradually. Koji [4] compared the reliability of tetrahedron mesh, optimized mesh and structured mesh with CFD software. Separated shear layer can be captured distinctly through using optimized mesh and structured mesh. For the capture of shocks, optimized mesh is more adaptive. Xiao [5] computed the transverse jet flow field under supersonic inflow with SST turbulent model, and N-S equations are solved with AUSMPW scheme. He [6] added the component transport equations into the controlling equations, selected standard k-2 model as the turbulent model, then computed 2-D transverse side jet flow field under supersonic inflow. Sparkman [7] optimized the fuel array spray design of scramjet with JET-PEN analysis software based on former experimental data.
In summary, as favorable supplement of experiments, study of numerical predictive method is very necessary, so as to provide references for engineering. Based on the needs, aimed at the problem of fuel jet and supersonic mixing in the combustor, transverse jet flow field under supersonic inflow is simulated numerically. In the further study, the method will be modified, and provide references for experiments.

Computational method and conditions
Computational zone and boundary conditions are shown in Figure 1. The number of mesh is 900, 000. Left edge is supersonic inflow, right edge is outflow, continuous line is no-slip solid surface, and imaginary line is symmetry boundary condition. The Mach number of inflow is 2.5, static pressure is 5.810 4 Pa, and static temperature is 130K. The diameter of jet is 2mm, total pressure of is 1Mpa, and total temperature is 300K.

Comparison of references
Simulated conditions of this paper and Cranfield University [9] are shown in Table 1. Mach number contours of both are shown in Figure 4 and Figure 5. It should be noticed that the simulated conditions is the same with that of experiments.   [9]  shock, Mach disc and separated region can be observed in Figure 4, but the bow shock is not simulated ideally, and large scale eddies configuration is not shown. The reason is that the mesh is rare, especially the mesh far from the wall. There is no LES turbulent model in the program, too. Bow shock, Mach disc,  shock and separated region are all be shown in Figure 5. Although LES is adopted, large scale eddies is not simulated.

Comparison of experiments
Simulated result and schlieren photos of the flow field are shown in Figure 6. Figure 6 (a) is integral result of the density along z axis. Figure 6 Figure 6) it can be observed that the simulated results agree well with that of experiments if the oblique shock induced by the rough upper wall is neglected. Mach disc, barred shock, bow shock, trigeminal shock and reflected shock can all be shown clearly. Compared with colored schlieren, information is less in monochrome schlieren, and the sensitivity is lower. Even so, if the cutting edge is deep enough, that is, the sensitivity of monochrome schlieren is high enough, barred shock and rear mixing zone can both be observed. Otherwise, distinction between bow shock and mixing layer boundary can be seen obviously through monochrome schlieren, while through the colored schlieren with high sensitivity, it is not easy to be districted. Photos taken by long time exposure can display wave configuration. Exposure time of several ns is suitable for the display of turbulence, especially the disordered situation of turbulence can be observed through colored schlieren.

Conclusion
From the comparison of research results, references and experiments, barred shock and Mach disc can be simulated, while  shock and back flow zone in transverse jet can be computed, too, which indicates that the computational method and scheme is suitable for research of this kind of problem. However, the deficiency is that detailed vortexes are not be displayed. The main reasons are: (1) the number of mesh is few; (2) there is no LES module in CFD code; (3) affection on transverse jet of boundary layer development is not considered. In the further study, modification should be made aimed at the above problems, so more accurate numerical predictive method would be provided.