Since adjoint flow solvers allow for the computation of sensitivities of global flow parameters under geometric variations in an amount of time which is nearly independent of the number of geometric parameters, automatic shape optimization can be accelerated considerably by the use of an adjoint solver. In this article, a systematic approach for the development of an exact discrete adjoint of a turbomachinery flow solver is described. By using finite differences to differentiate the numerical fluxes, the problems associated with automatic and hand differentiation are circumvented. Moreover, a general treatment of the adjoint numerical boundary conditions is presented. As a result, an exact adjoint boundary condition for the conservative mixing planes is obtained. In combination with nonreflecting boundary conditions the latter are crucial for accurate flow simulations in turbomachinery. The adjoint is validated on the basis of a transonic compressor stage.

In the modern process of the aerodynamic design of multistage compressors and turbines for jet engines as well as for stationary gas turbines, 3D-CFD plays a key role. Before building the first test rig several designs have been investigated using numerical simulations. To understand the characteristics of the individual components it is necessary to simulate their behavior in a multistage simulation and investigate for example, the single stage maps of the compressor in order to understand how the load is divided between the different parts of the compressor during throttling. Increasing computing resources allow ever more details to be incorporated in a 3D simulation. In former times only single blade rows were investigated with a high resolution of the boundary layers, whereas in multistage configurations wall functions were state of the art. Today we are able to apply Low Reynolds resolution even for multistage configurations, so the designer is required to include more and more geometrical details into the simulation. One important such feature is the fillets of rotor and stator blades. Fillets reduce the flow deflection at the endwalls and therefore the loading of the downstream blade rows. This effect is accumulated in a multistage simulation. In this paper a 15-stage compressor with additional inlet and outlet guide vane designed for a stationary gas turbine was investigated with a modern CFD tool by using a real gas approach for two speedlines. Two simulations were done: first a clean configuration with tip and hub clearances but without blade fillets; in the second simulation all rotor blades and the cantilevered stator blades were additionally modeled with fillets. The comparison of the overall global values with measurement data shows a better performance of the simulation with fillets, especially by throttling the compressor. A deeper look into the compressor shows different loads for a considerable number of single stages. The analysis of the steady multistage simulations shows that the numerical stability is reached in different regions of the machine.

A detailed numerical investigation into the influence of the axial gap between the blade rows of a stator/rotor compressor configuration is presented. Unsteady, two-dimensional simulations at both subsonic and transonic operating points have been performed for several axial spacings. From time-averaged data, the influence of the axial gap setting on stage efficiency at the subsonic operating point was found to be opposite to that at the transonic operating point. By examining the passage losses, a correlation between the trends in stage performance and rotor losses as a function of the axial spacing was found. At maximum efficiency, the unsteady flow fields at both operating points show similar vortex patterns. These vortices are rotating clockwise and are located near the suction side of the rotor profile. It was found that these vortices affect the boundary layer behaviour of the rotor and lead to a gain in performance due to a reduction of the rotor losses. This process depends on the operating point and the axial spacing between the rows. Through a detailed analysis of the time-averaged and instantaneous data, the influence of the upstream wake on the stage performance is assessed and discussed in the context of future designs.

The unsteady interaction between blade rows is very important in highly loaded compressors because of its influence on operating performance. One important effect in this context is the impact of a rotor bow shock on the wake of an upstream stator blade. A new transport model is proposed which introduces such deterministic unsteady effects in a steady solution environment. Deterministic stresses are added to the stationary RANS equations by means of an additional source term. The presented approach combines the advantages of time-accurate and stationary simulation procedures, i.e. physical accuracy and computational efficiency. A generic cascade of flat plates and a transonic stator-rotor configuration are investigated numerically using time-accurate methods in order to analyze the wake-shock interactions. The results are compared with steady mixing-plane solutions to point out their shortcomings regarding unsteady effects and to illustrate the demands of a deterministic stress approach. The model is then calibrated for the generic cascade before it is applied to the real three-dimensional compressor stage.