A general issue in turbomachinery flow computations is how to capture and resolve two kinds of unsteadiness efficiently and accurately: (a) deterministic disturbances with temporal and spatial periodicities linked to blade count and rotational speed and (b) nondeterministic disturbances including turbulence and self-excited coherent patterns (e.g., vortex shedding, shear layer instabilities, etc.) with temporal and spatial wave lengths unrelated to blade count and rotational speed. In particular, the high cost of large eddy simulations (LES) is further compounded by the need to capture the deterministic unsteadiness of bladerow interactions in computational domains with large number of blade passages. This work addresses this challenge by developing a multiscale solution approach. The framework is based on an ensemble-averaging to split deterministic and nondeterministic disturbances. The two types of disturbances can be solved in suitably selected computational domains and solvers, respectively. The local fine mesh is used for nondeterministic turbulence eddies and vortex shedding, while the global coarse mesh is for deterministic unsteadiness. A key enabler is that the unsteady stress terms (UST) of the nondeterministic disturbances are obtained only in a small set of blade passages and propagated to the whole domain with many more passages by a block spectral mapping. This distinctive multiscale treatment makes it possible to achieve a high-resolution unsteady Reynolds-averaged Navier–Stokes (URANS)/LES solution in a multipassage/whole annulus domain very efficiently. The method description will be followed by test cases demonstrating the validity and potential of the proposed methodology.

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A series of numerical simulations are carried out to analyze a supersonic inlet buzz, which is an unsteady pressure oscillation phenomenon around a supersonic inlet. A simple but efficient geometry, experimentally adopted by Nagashima, is chosen for the analysis of unsteady flow physics. Among the two sets of simulations considered in this study, the effects of various throttling conditions are firstly examined. It is seen that the major physical characteristic of the inlet buzz can be obtained by inviscid computations only and the computed flow patterns inside and around the inlet are qualitatively consistent with the experimental observations. The dominant frequency of the inlet buzz increases as throttle area decreases, and the computed frequency is approximately 60Hz or 15% lower than the experimental data, but interestingly, this gap is constant for all the test cases and shock structures are similar. Secondly, inviscid calculations are performed to examine the effect regarding angle of attack. It is found that patterns of pressure oscillation histories and distortion due to asymmetric (or three-dimensional) shock structures are substantially affected by angle of attack. The dominant frequency of the inlet buzz, however, does not change noticeably even in regards to a wide range of angle of attacks.Key words: supersonic inlet buzz, effect of angle of attack, asymmetric shock structure, distortion This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/bync/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Temporal variation of components' performance is becoming a crucial parameter in turbomachinery design process. The main physical mechanism driving the time-dependent behavior is the unsteady bladerow interaction as stator–rotor relative motion due to rotating frame of reference. However, so far unsteady effects have been ignored in design processes in common engineering practice. In fact, steady approach has been generally employed for computational fluid dynamics (CFD)-based turbomachinery design. Moreover, conventional blade design has been based on single operating point considerations. Taking into account multiple time-dependent phenomena, as the unsteady performance parameters variation, might be beneficial in making a further improvement on component performance. In quantitative terms, first of all it is important to investigate the relative effect of unsteady variation, compared to the standard steady approach, and to create a capability for calculating temporal sensitivity variation, while keeping a reasonable computing cost. This work investigates the unsteady variation of turbomachinery performance on quasi-three-dimensional (3D) geometries: single-stage turbine and single-stage compressor. Steady flow solutions using mixing plane method are compared to the unsteady flow solutions using a direct unsteady calculation, while assessing the introduction of the space–time gradient (STG) method. The results clearly show how the unsteady variation is a non-negligible effect in performance prediction and blade design. Then, a new computational technique to quantify temporal sensitivity variation is introduced, based on the STG method, with an extension to adjoint-based sensitivity analysis. The relation between time and space in multipassage-multirow domain, the fundamental assumption of the STG method, is applied within the adjoint operator formulation, which gives unsteady sensitivity information on a broad range of design parameters, at the cost of a single computation. Finally, the unsteady sensitivities are compared to the ones resulting from steady solution in the two quasi-3D cases. This work introduces a coherent and effective mathematical formulation for accounting deterministic unsteadiness on component design, while reducing computational cost compared to standard unsteady optimization techniques.