Search

The accurate prediction of rotating stall inception is critical for determining the stable operating regime of a compressor. Among the two widely accepted pathways to stall, namely, modal and spike, the former is plausibly believed to originate from a global linear instability, and experiments have partially confirmed it. As for the latter, recent computational and experimental findings have shown it to exhibit itself as a rapidly amplified flow perturbation. However, rigorous analysis has yet to be performed to prove that this is due to global linear instability. In this work, an eigenanalysis approach is used to investigate the rotating stall inception of a transonic annular cascade. Steady analyses were performed to compute the performance characteristics at a given rotational speed. A numerical stall boundary was first estimated based on the residual convergence behavior of the steady solver. Eigenanalyses were then performed for flow solutions at a few near-stall points to determine their global linear stability. Once the relevant unstable modes were identified according to the signs of real parts of eigenvalues, they were examined in detail to understand the flow destabilizing mechanism. Furthermore, time-accurate unsteady simulations were performed to verify the obtained eigenvalues and eigenvectors. The eigenanalysis results reveal that at the rotating stall inception condition, multiple unstable modes appear almost simultaneously with a leading mode that grows most rapidly. In addition, it was found that the unstable modes are continuous in their nodal diameters, and are members of a particular family of modes typical of a dynamic system with cyclic symmetries. This is the first time such an interesting structure of the unstable modes is found numerically, which to some extent explains the rich and complex results constantly observed from experiments but have never been consistently explained. The verified eigenanalysis method can be used to predict the onset of a rotating stall with a CPU time cost orders of magnitude lower than time-accurate simulations, thus making compressor stall onset prediction based on the global linear instability approach feasible in engineering practice. [ABSTRACT FROM AUTHOR]

Nonlinear, time-linearized and adjoint Reynolds-averaged Navier-Stokes (RANS) computational fluid dynamics (CFD) solvers are widely used to assess and improve the aerodynamic and aeroelastic performance of aircrafts and turbomachines. While RANS CFD solver technologies are relatively mature for applications at design conditions where the flow is benign, their use in off-design conditions, featuring flow instabilities, such as separations and shock wave/boundary layer interactions, still faces many challenges, with tight residual convergence being a major difficulty. To cope with this, several solver stabilization techniques have been proposed. However, a systematic and comparative study of these techniques has not been reported, to some extent hindering the wide deployment of these methods for industrial applications. In this paper, we critically review the existing methods for solver convergence stabilization, with the main purpose of explaining the rationale behind the algorithms and providing a systematic view of the seemingly different methods. Specifically, mathematical formulations and implementation details of these methods, example applications, and the pros and cons of the methods are discussed in detail, along with suggestions for further improvements. This review is expected to give CFD method developers an overview of the various solution stabilization methods and application engineers an idea how to choose a suitable method for their respective applications. [ABSTRACT FROM AUTHOR]

Precise and inexpensive uncertainty quantification (UQ) is crucial for robust optimization of compressor blades and to control manufacturing tolerances. This study looks into the suitability of MC−adj−nonlinear, a nonlinear adjoint-based approach, to precisely and rapidly assess the performance discrepancies of a transonic compressor blade section, arising from geometric alterations, and building upon previous research. In order to assess the practicality and illustrate the benefits of the adjoint-based nonlinear approach, its proficiency and precision are gauged against two other methodologies, the adjoint-based linear approach (MC−adj−linear) and the high-fidelity nonlinear Computational Fluid Dynamics (MC−CFD) method. The MC−adj−nonlinear methodology exhibits impressive generalization capabilities. The MC−adj−nonlinear method offers a great balance between precision and time efficiency, since it is more precise than the MC−adj−linear method in both design and near-stall conditions, yet requires approximately a thirtieth of the time of the MC−CFD method. Finally, the MC−adj−nonlinear method was utilized to conduct fast UQ analyses of the section at four distinct speeds to quantify the performance uncertainty for the compressor map. It is found that aerodynamic performance is more sensitive to geometric deviations at high speeds than at low speeds. The impact of the geometric deviations is generally detrimental to the mean efficiency. [ABSTRACT FROM AUTHOR]

Steady computational fluid dynamics solvers based on the Reynolds-averaged Navier-Stokes equations are the primary workhorses for turbomachinery aerodynamic analysis due to their good engineering accuracy at a low computational cost. However, even state-of-the-art steady solvers suffer from convergence slowdown or failure when applied to challenging off-design conditions. This severely limits the reliable nonlinear and linearized turbomachinery aerodynamic analysis over a wide operating range. To alleviate the convergence difficulties, a nonlinear flow solver using the Newton-Krylov method is developed. This is the first time the Newton-Krylov algorithm is used for achieving robust analysis of turbomachinery aerodynamics in the open literature. The proposed solution algorithm features 1) the exact Jacobian matrix forming, 2) straightforward parallelization, and 3) a reliable globalization strategy; and it aims to achieve fast machine-zero convergence. The solver accuracy is validated using four test cases: an airfoil, a linear turbine cascade, a centrifugal compressor, and an axial compressor. Machine-zero convergence is achieved for all cases over a wide range of operating conditions without manual intervention. The method shows great potential for enabling an automated and reliable whole-map turbomachinery aerodynamic analysis, and it paves the way for a robust and efficient linearized aerodynamic analysis, such as adjoint, time-linearized, and eigenvalue analyses. [ABSTRACT FROM AUTHOR]

SUMMARY One of the major challenges of shape optimisation in practical industrial cases is to generically parametrise the wide range of complex shapes. A novel approach is presented, which takes CAD descriptions as input and produces the optimal shape in CAD form using the control points of the Non-Uniform Rational B-Splines (NURBS) boundary representation as design variables. An implementation of the NURBS equations in source allows to include the CAD-based shape deformation inside the design loop and evaluate its sensitivities efficiently and robustly. In order to maintain or establish the required level of geometric continuity across patch interfaces, geometric constraints are imposed on the control point displacements. The paper discusses the discrete adjoint flow solver used and the computation of the complete sensitivities of the design loop by differentiating all components using automatic differentiation tools. The resulting rich but smooth deformation space is demonstrated on the optimisation of a vehicle climate duct. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]