A computational method tailored for the simulation of fluidic thrust-vectoring systems is employed to investigate the dynamic response of a dual-throat nozzle in open-and closed-loop control. Thrust vectoring in fixed, symmetric nozzles is obtained by secondary flow injections that cause local flow separations, asymmetric pressure distributions, and, as a consequence, the vectoring of primary jet flow. The computational technique is based on a well-assessed mathematical model for the compressible unsteady Reynolds-averaged Navier-Stokes equations. A minimal control system governs the unsteady blowing. Nozzle performances and thrust-vector angles have been computed for a wide range of nozzle pressure ratios and secondary flow injection rates. The numerical results are compared with the experimental data available in the open literature. Several computations of the open-loop dynamics of the nozzle under different forcing have been performed to investigate the system response in terms of thrust-vectoring effectiveness and controllability. These computations have been used to extract autoregressive exogenous models of the nozzle dynamics. The effects of including the actuator dynamics are also discussed. Simple strategies of closed-loop control of the nozzle system by proportional-integrative-derivative regulators are investigated numerically. The closed-loop model predictive control of the system, based on the autoregressive exogenous models, is addressed.

An adjoint optimization method, based on the solution of an inverse flow problem, is proposed. Given a certain performance functional, it is necessary to find its extremum with respect to a flow variable distribution on the domain boundary, for example, pressure. The adjoint formulation delivers the functional gradient with respect to such a flow variable distribution, and a descent method can be used for optimization. The flow constraints are easily imposed in the parameterization of the distributed control, and therefore those problems with several strict constraints on the flow solution can be solved very efficiently. Conversely, the geometric constraints are imposed either by additional partial differential equations, or by penalization. By adequately constraining the geometric solution, the classical limitations of the inverse problem design can be overcome. Several examples pertaining to internal flows are given.

A time-marching throughflow method for the off-design performance analysis of axial compressors is described. The method is based on the Euler equations, and a new inviscid blade force model is proposed in order to achieve desired flow deflection. The flow discontinuity problems at the leading and trailing edges are tackled by automatic correction of blade mean surface using cubic spline interpolation. Empirical loss models have been integrated into the throughflow model in order to simulate the viscous force effects in the real three-dimensional flow. Two test cases have been presented to validate the throughflow model, including the transonic fan rotor – NASA Rotor 67 working at a near-peak-efficiency point and a 1.5-stage high-speed axial compressor with inlet guide vane operating at 68% nominal speed. Reasonable flow parameters distributions have been obtained in the Rotor 67 fan calculating results, and accurate overall performance characteristics have also been predicted at the strong off-design condition for the 1.5-stage axial compressor. The CPU time of both cases cost less than one minute at one operating point. The results indicate that the developed time-marching throughflow model is effective and efficient in the turbomachinery performance analysis.

Robust and flexible numerical methodologies for the imposition of boundary conditions are required to formulate well-posed problems. A boundary condition should be nonreflecting, to avoid spurious perturbations that can provocate unsteadiness or instabilities. The reflectiveness of various boundary conditions is analyzed in the context of the Godunov methods. A nonlinear, isentropic wave propagation model is used to investigate the reflection mechanism on the flowfield borders, and a parameter τ is defined to give a measure of the boundary reflectiveness. A new set of boundary conditions, in which τ = 0, that is, totally nonreflecting, is then proposed. The approach has been integrated in an aerodynamic design procedure using a distributed boundary control.

Point vortex model for asymmetric inviscid wakes past bluff bodies / Alan Elcrat; Michele Ferlauto; Luca Zannetti.-In: FLUID DYNAMICS RESEARCH.