Modern CFD flow solvers can be readily used to obtain time-averaged results on industrial size turbomachinery flow problem at low computational cost and overall effort. On the other hand, time-accurate computations are still expensive and require substantial resources in CPU and computer memory. However, numerical techniques such as phase shift and time inclining method can be used to reduce overall computational cost and memory requirements. The unsteady effects of moving wakes, tip vortices and upstream propagation of shock waves in the front stages of multi-stage compressors are crucial to determine the stability and efficiency of gas turbines at part-load conditions. Accurate predictions of efficiency and aerodynamic stability of turbomachinery stages with strong blade row interaction based on transient CFD simulations are therefore of increasing importance today. The T106D turbine profile is under investigation as well as the transonic compressor test rig at Purdue. The main objective of this paper is to contribute to the understanding of unsteady flow phenomena that can lead to the next generation design of turbomachinery blading. Transient results obtained from simulations utilizing shape correction (phase shift) and time inclining methods in an implicit pressure-based solver, are compared with those of a full transient model in terms of computational cost and accuracy.

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Computational predictions of the transient flow in turbine blade rows are considered. Adjacent blade rows typically contain unequal numbers of blades and vanes, requiring a computation over multiple passages per row to permit application of simple periodic boundary conditions. For typical geometries, use of conventional solution methods requires computation over all or a significant portion of the wheel to ensure a time accurate solution. The computational load is significantly reduced by methods which enable a one or two-passage solution to accurately model the full wheel (or part wheel, if applicable) solution. In this work, three methods are used: Profile Transformation, Fourier Transformation and Time Transformation. This paper will concentrate on the evaluation of these methods on two turbine geometries. The first test case is a frozen gust analysis for a high pressure transonic turbine; the geometry includes hub and casing cavities together with a complex tip. The second test case is a low pressure turbine stage run over a range of operating points. Comparisons between the various methods and the equivalent part wheel periodic solution are made to demonstrate the accuracy and computational efficiency of the transformation methods.

Unsteady computations are necessary if blade row interactions effects are relevant, for example for detailed optimization of a compressor at off-design conditions towards the aerodynamic stability limit, or for structural mechanical tuning of the blades. Modeling time accurate transient multistage flow is expensive both in terms of computer time and memory. Recently the implicit time-resolved Time Transformation method (based on Giles’ time inclining) has been shown to be computationally efficient and a good alternative for modeling transient flow in a single stage (one pitch ratio) turbomachinery configuration. A further advantage of this time resolved method is its ability to capture not only blade passing frequencies but also self-excited frequencies such as in wakes and tip vortex shedding. In this work, an extension of the Time Transformation method (TT) to multistage modeling has been employed to assess the method’s ability in predicting modern multistage compressor performance speedline curve, as well as its ability in capturing dominant machine frequencies. The multistage TT method is verified on a two and a half stage modified Hannover compressor, followed by an industrial validation on a Siemens Energy half scale six stage axial compressor based on the last stages of the Siemens Platform Compressor (PCO). Reference transient solutions on reduced portions of the compressor and/or modified blade count solutions are obtained and compared directly to single passage multistage Time Transformation predictions for the Hannover compressor. The method is then applied directly to the full six stage Siemens compressor employing the true blade counts for all six stages. The first goal of this work is to investigate the ability and accuracy of the multistage TT method to capture all relevant blades passing frequencies, including the impact of different degrees of pitch change between components. The second goal of this work is to explore how best to apply the method for the prediction of a compressor map, up to the surge line. Solutions are compared to experimental test rig data. Physical explanations of the key flow features observed in the experiment, as well as of the differences between the predictions and experimental data, are given.

The natural convection at low and moderate Rayleigh numbers (Ra) incylindrical horizontal annuli with imposed temperatures in both surfaces isnumerically studied. This flow inside concentric cylinders classic configuration has a wide range of practical and technological applications, which justifies its growing studies efforts. In this work, the governing equations are discretized by the volume finite technique over a staggered grid, with second-order accuracy in space and time. The flow pattern is presented by several Rayleigh numbers, with an analysis of the heat transfer coefficient and flow properties. Furthermore, a three-dimensional field is shown at a moderate Ra number. The results showed a good agreement with the experimental data.