A rescaled matrix-valued dissipation is reformulated for the Roe scheme in low Mach-number flow regions from a well known family of local low-speed preconditioners popularized by Turkel.The rescaling is obtained by suppressing the iterative preconditioning and by deriving explicitly the full set of eigenspaces of the Roe-Turkel matrix dissipation. This formulation preserves the time consistency and does not require to reformulate the boundary conditions based on the characteristic theory. The dissipation matrix achieves by construction the proper scaling in low-speed flow regions and returns the original Roe scheme at the sonic line. We find that all eigenvalues are nonnegative in the subsonic regime. By removing the iterative preconditioning, it becomes necessary to formulate a stringent stability condition to the explicit scheme in the low-speed flow regions based on the spectral radius of the rescaled matrix dissipation. This formulation also raises a two-timescale problem for the acoustic waves, which is circumvented for a steady-state iterative procedure by the development of a robust implicit characteristic matrix time-stepping scheme. The behaviour of the modified eigenvalues in the incompressible limit and at the sonic line also suggest applying the entropy correction carefully for complex non-linear flows.
The present paper provides an overview of technological evolutions aimed at improving the aerodynamic performance of Snecma’s High Pressure Compressors. Several concepts were investigated under its CREATE compressor research program, involving an extensive simulation effort. An overview of the computational approaches involved in the evaluation and selection of innovative and most promising concepts will be given in the paper. The main topics dealt with are:
1) Aeromechanical optimization of airfoils and flow path:
In recent years, great efforts have been made to improve the aerodynamic design of airfoils. Among them, optimization methods have been progressively implemented in the design process with an increased complexity logic. The latest methods used at Snecma involve multi-objective, multi-parameters aeromechanical optimization including mean camber line, stacking axis, flow path contouring and more. This work is illustrated by two practical examples.
2) Vortex generators:
In order to control the flow, vortex generators can be forecasted as a promising step forward. The goal is to create exogenous vorticity that will counter-balance the endogenous vorticity. Thus they appear as a tool to reduce losses and improve stability in highly loaded turbomachinery devices such as modern high pressure compressors. This section of the paper will give an overview of the dedicated numerical simulations completed.
3) Clocking:
Numerous studies are related to the benefit drawn from turbine clocking on turbomachinery performance. However, fewer examples of successful compressor clocking exist. The recent capability of computational fluid dynamics tools to reduce the computational effort necessary to investigate such an issue (by the use of harmonic balance methodology) gives the opportunity for a renewed evaluation.
4) Optimization of shroud leakage flow with main flow:
A strong interaction exists with the secondary flows originated in the inner flow path cavities. Coupled main flow path and cavities aerodynamic simulations were conducted to improve the relevance of the computations and understand the mechanisms involved.
5) Tandem bladings and splitters in axial rotors:
The last aspect of the study was focused on dual blading concepts. After a brief review of the literature, some simulations were carried out to explore the relevance of such concepts from the viewpoint of modern high pressure compressors performance improvement.
The flow within turbomachines is intrinsically complex and involves boundary layer transition, separation and vortices such as the tip leakage vortex and wakes. In a low-pressure turbine, as the Reynolds number can be small, the flow over the suction side is likely to separate leading to the formation of a laminar (or transitional) separation bubble. This flow mechanism can be predicted using Large-Eddy Simulation. However the computation is still very expensive in a design framework. Thus, Reynolds-Averaged Navier-Stokes (RANS) method is used in the present investigation to simulate the flow over the low-pressure turbine airfoil T106C. The laminar-turbulent transition is modeled with the γ-Rθt~ model of Menter and Langtry. Following the work of Minot et al. in which the CFD setup was deeply investigated, the present study aims at evaluating the sensitivity to uncertainties relative to experimental values (freestream turbulence, Reynolds number, incidence flow angle and exit isentropic Mach number) and at improving this model regarding the calibration of several functions using optimization process. The uncertainty study highlights the parameters which mainly influence the isentropic Mach number and loss distributions. The new calibration of the Menter-Langtry model improves significantly the flow prediction over the suction side, except for the open bubble configuration.
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