Thrust Vectoring Control of Supersonic Flow Through an Orifice Injector

Traditional mechanical control systems in thrust vectoring are efficient in rocket thrust guidance but their costs and their weights are excessive. The fluidic injection in the nozzle divergent constitutes an alternative procedure to achieve the goal. In this paper, we present a 3D analytical model for fluidic injection in a supersonic nozzle integrating an orifice. The fluidic vectoring uses a sonic secondary injection in the divergent. As a result, the flow and interaction between the main and secondary jet has built in order to express the pressure fields from which the forces and thrust vectoring are deduced. Under various separation criteria, the present analytical model results are compared with the existing numerical and experimental data from the literature. Keywords—Flow separation, Fluidic thrust vectoring, Nozzle, Secondary jet, Shock wave. NOMENCLATURE NPR Nozzle pressure ratio (0i Pa ). SPR Secondary pressure ratio (0j P0i ). P0i Chamber stagnation pressure. P0j Second injection pressure. Pa Ambient pressure. Pp Plateau pressure. P Isentropic pressure. Pb The pressure at the hyperbolic surface. Cd Discharge Coefficient. δ Deviation angle. Fx,y Force components in x and y direction. Fj Second injection reactive force. Fc Primary flow reactive force (Dynalpy flux). x Nozzle axis with coordinate beginning at the nozzle throat. xt Divergent length of the nozzle. xm x-coordinate of the secondary injection port. xd x-coordinate of the end of the secondary injection port. xe x-coordinate of the end of the nozzle. Ac Surface of the throat of the nozzle. Ajc Surface of the orifice. Ae Surface of the nozzle at the exit. fm Mass-flow ratio. α Divergent conical half-angle. r Radius of the nozzle at x. rc Throat radius. ψ Angular coordinate. xs x-coordinate of the separation point. I. Mnafeg is with the LIM Laboratory, Polytechnic School of Tunisia, BP743, 2078 La Marsa, Tunisia. [email protected] A. Abichou is with the LIM Laboratory, Polytechnic School of Tunisia, BP743, 2078 La Marsa, Tunisia. [email protected] L. Beji is with the IBISC-EA4526 Laboratory, University of Evry, 40 rue du Pelvoux, 91020 Evry, France. [email protected] Δ Standoff distance. Ls Curvature radius. ψMax Maximum angle to the hyperbolic curve. ψ0 Maximum angle to the boundary of the orifice. γ Heat capacity ration of the primary flow. γj Heat capacity ration of the secondary flow. M Mach number.