The paper presents results of the incorporation of the harmonic nonlinear method into an existing turbomachinery Navier-Stokes code. This approach, introduced by He and Ning in 1998, can be considered as a bridge between classical steady state and full unsteady calculations, providing an approximate unsteady solution at affordable calculation costs. The unsteady flow perturbation is Fourier decomposed in time, and by a casting in the frequency domain transport equations are obtained for each time frequency. The user controls the accuracy of the unsteady solution through the order of the Fourier series. Alongside the solving of the time-averaged flow steady-state equations, each frequency requires the solving of two additional sets of conservation equations (for the real and imaginary parts of each harmonic). The method is made nonlinear by the injection of the so-called deterministic stresses, resulting from all the solved frequencies, into the time-averaged flow solver. Because of the transposition to the frequency domain, only one blade channel is required like a steady flow simulation. The presented method also features a new improved treatment that enhances the flow continuity across the rotor/stator interface by a reconstruction of the harmonics and the time-averaged flow on both sides of the interface. A non-reflective treatment is applied as well at each interface. Validation for analytical and turbomachinery test cases are presented. In particular, results are compared between the harmonic method, steady-state mixing plane and full unsteady calculations. The comparison with the reference full unsteady calculation provides a quantitative indication of the accuracy of the approach, as well as the significant gain in CPU time, whereas the comparison with classical quasi-steady state solutions indicates the gain of accuracy. A multistage compressor flow is also presented to show the capabilities of the method.

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The nonlinear harmonic method (NLH) and its extension to the modeling of the clocking effects can simulate the unsteady flows in multistage machines at drastically reduced CPU costs. The blade row interactions that are reproduced are those between adjacent rotors and stators and also between successive rotors or successive stators. At an additional level of complexity, it appears that in stator1 / rotor / stator2 configurations the amplitude of the perturbation associated with a blade passing frequency (BPF) in a row is not only created by the adjacent row but is also modified in space by the interaction of the periodic disturbances coming from the other two rows. For instance, the spatial modes of the periodic disturbance in stator2 are provoked not only by the interaction with the adjacent rotor but also by an additional interaction with the periodic flow coming from stator1. The present paper introduces a method that enables the identification of these modes for a general configuration row1 / row2 / row3. Any row can be a stator or a rotor and the time-varying disturbances are not only produced by the interaction with the adjacent row but also with the other rows. In particular, this is validated and illustrated for the calculation of the unsteady effects provoked in contra-rotating open rotors (CROR) by the engine pylon. Results are also shown for stator/rotor/stator configurations that shows the effects of clocking on the time harmonics.

Pursuing higher levels of efficiency in turbomachines requires the capability to reproduce a fuller extent of the blade row interactions. This is especially true for the clocking phenomena, whose influence on the efficiency can be important. For instance, the efficiency variation over a set of relative positions between two successive stators could reach 1 to 2% in high pressure turbines (Huber et al, 1996, Haldeman et al, 2004). The simulation of these complex effects still relies on time-dependent methods for the reproduction of the unsteadiness and its impact onto the time-mean flow. The nonlinear harmonic method and its extension to clocking effects, as introduced by He (1998), and He and Chen (2002), can simulate the whole unsteady flow at considerably reduced CPU costs. The treatment is very powerful since it can predict the performances of a multirow component for all the clocking positions. This is done by means of harmonics that describe a spatial phase shift of the flow in a rotor or stator, due respectively to a co-rotating rotor or stator. The present paper applies this approach for the simulation of the clocking effects. This is handled by a full connection treatment, which was shown (Vilmin et al, 2006) to give a significant improvement over the mixing-plane method in the time-averaged flow estimations of the full unsteady flow across the rotor/stator interface. In a first part of the paper, implementation issues of the treatment are presented. In particular, consideration is made of the importance of the clocking effects related to the ratios between the blade numbers. In a second part, a validation pseudo-2D multirow test case is presented that demonstrate the capabilities of the method. The third part deals with the simulation of the clocking effect on the performance of a 1.5 stage turbine. CPU and cost are presented, that show the considerable efficiency of the extended harmonic method.

Enhancing the representation of turbulence processes is a critical issue for CFD codes devoted to turbomachinery industry. Though more complex methods are available, Reynolds-Averaged Navier-Stokes models are widely used in the daily design process. Therefore, there is a constant need for improving eddy-viscosity based turbulence models. The present work aims at investigating the capabilities of the v2-f turbulence model for turbomachinery applications. Three types of flow features that are of importance for such applications are investigated in details: heat transfer, secondary flows, and laminar to turbulent transition. From a series of test cases, it appears that the v2-f turbulence model is specially adapted for heat transfer applications and shows potentialities in predicting laminar to turbulent transition.