Reference : Investigation et modélisation des tensions circonférentielles en simulation méridienne
Dissertations and theses : Master of advanced studies dissertation
Engineering, computing & technology : Aerospace & aeronautics engineering
Investigation et modélisation des tensions circonférentielles en simulation méridienne
[en] Investigation and modeling of the circumferential stresses in throughflow simulation
Thomas, Jean-Philippe mailto [Université de Liège - ULg > Département d'aérospatiale et mécanique > Turbomachines et propulsion aérospatiale >]
Léonard, Olivier mailto
Essers, Jean-André mailto
Delhez, Eric mailto
Simon, Jean-François
[en] Harmonic Method ; Throughflow simulation ; Circumferential stresses
[en] The computation time and the extraction of useful information remain severe drawbacks to systematic use of modern 3D Navier-Stokes codes in a design procedure of multistage turbomachines. That explains why throughflow simulation is still widely used at industrial scale. The main limitation of throughflow is however the need for empirical models to reproduce blade-flow interactions and major 3D flow features. As an alternative, Adamczyk (1984) proposed three averaging operators (ensemble, time and passage) that lead to the average-passage model, linking the unsteady turbulent flow field to a steady flow field in a typical blade passage. This model involves additional terms that respectively bring back the mean effect of turbulence, deterministic unsteadiness and aperiodicity on the mean periodic flow. These terms need to be modelled; it is the closure problem. Harmonic closure, which consists in solving a linearized perturbation system in the frequency domain, revealed to be an efficient method to approximate deterministic stresses (He and Ning, 1998, Stridh, 2005, Vilmin, 2006). A fourth averaging can be performed, a circumferential averaging, giving rise to the throughflow model. Additional terms appear: the so-called circumferential stresses. It has been proven that these terms play an important role in the description of the flow (Jennions, 1986, Perrin, 1995), being at least as considerable as deterministic stresses. Introducing these terms in a throughflow simulation allows to reproduce the averaged 3D steady flow field (Simon, 2007). The purpose of this work is to investigate how far empiricism could be reduced by using the averaged-passage equations of Adamczyk, combined with a harmonic closure strategy. To that aim, in the first part of the work, results of a computation performed with a steady three-dimensional Navier-Stokes code are used to calculate the circumferential stresses. The importance of the latter to bring back the mean eff ect of circumferential non-uniformities, linked to 3D phenomena, is illustrated by injecting them into a throughfow simulation. Then the ability of truncated Fourier series to reproduce the flow and its level of non-uniformity in the core flow and near the hub and shroud walls is detailed. It is finally shown that the harmonic approximated stresses can lead to a good reproduction of local 3D flow features in throughflow simulation and to a better accuracy. In the second part of this work it is proposed to adapt the "Nonlinear Harmonic" method to the throughflow model, where the main non-linear system would be the common throughflow equations and the auxiliary systems would give access to a mean high order information; the circumferential stresses. On the way to the adaptation of this technique to the throughflow model, the work shows that a reformulation of the effect of the blades is needed. The latter cannot appear anymore as numerical local explicit impermeability conditions that could not be supported by Fourier series, needing a continuous circumferential evolution of the flow. To get rid of this issue, the blade effect is replaced by a smooth force field as in the "Immersed Boundary Method" of Peskin. A simple example of an inviscid flow around a cylinder illustrates the preceding developments, coupling the "Nonlinear Harmonic Method" to the "Immersed Boundary Method" in a throughflow model, to bring back the mean e ffect of the circumferential non uniformities into the meridional flow.
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