Dirk Nürnberger

The Discrete Adjoint of a Turbomachinery RANS Solver

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.Copyright

A Numerical Study on the Influence of Vane-Blade Spacing on a Compressor Stage at Sub- and Transonic Operating Conditions

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.Copyright

Numerical investigation of unsteady transitional flows in turbomachinery components based on a RANS approach

This paper presents results of the numerical simulation of periodically unsteady flows with focus on turbomachinery applications. The unsteady CFD solver used for the simulations is based on the Reynolds averaged Navier–Stokes equations. The numerical scheme applies an extended version of the Spalart–Allmaras one-equation turbulence model coupled with a transition correlation. The first example of validation consists of boundary layer flow with separation bubble on a flat plate, both under steady and periodically unsteady main flow conditions. The investigation includes a variation of the major parameters Strouhal number, amplitude, and Reynolds number. The second, more complex test case consists of the flow through a cascade of turbine blades which is influenced by wakes periodically passing over the cascade. The computations were carried out for two different blade loadings. The results of the numerical simulations are discussed and compared with experimental data in detail. Special emphasis is given to the investigation of boundary layers with regard to transition, separation and reattachment under the influence of main flow unsteadiness.

Appropriate Turbulence Modelling for Turbomachinery Flows using a Two-Equation Turbulence Model

The simulation quality of numerical flow simulations depends on the choice of physical modelling as well as an appropriate numerical treatment. In this study, a standard two-equation turbulence model has been extended for compressible, rotational flow as it occurs in turbomachinery and subsequently applied to different turbomachinery relevant flows of varying complexity. A number of different numerical schemes has been employed to evaluate their impact on the solution.

Evaluation of the Principle of Aerodynamic Superposition in Forced Response Calculations

The validity of the principle of superposition for forced response analysis is evaluated by its application to a research propfan stage. The counter-rotating propfan features transonic flow conditions and aerodynamic interaction between the blade rows. The computed unsteady aerodynamics are verified by compar- ison with rig measurements. A forced response analysis based on the principle of superposition is conducted, similar to the current practice in turbomachinery design. For reference, a fully coupled simulation of the propfan forced response is undertaken. This simulation does not rely on the principle of superposition, and the model can also resolve non-linear interaction effects beyond the valid- ity of the linear superposition principle. The comparison shows a full validity of the superposition principle for the present case: Computed blade vibration amplitudes, as well as the unsteady aerodynamics inside the blade passages, are correct, even in quantitative terms. This supports the application of the superpo- sition principle for forced response analysis within the industrial design process.