Graham Ashcroft

Time-Linearized and Time-Accurate 3D RANS Methods for Aeroelastic Analysis in Turbomachinery

Graham Ashcroft Institute of Propulsion Technology, German Aerospace Center (DLR), Linder HA¶he, 51147 Cologne, Germany A computational method for performing aeroelastic analysis using either a time-linearized or an unsteady time-accurate solver for the compressible Reynolds averaged Navier--Stokes (RANS) equations is described. The time-linearized solver employs the assumption of small time-harmonic perturbations and is implemented via finite differences of the nonlinear flux routines of the time-accurate solver. The resulting linear system is solved using a parallelized generalized minimal residual (GMRES) method with block-local preconditioning. The time accurate solver uses a dual time stepping algorithm for the solution of the unsteady RANS equations on a periodically moving computational grid. For either solver, and both flutter and forced response problems, a mapping algorithm has been developed to map structural eigenmodes, obtained from finite element structural analysis, from the surface mesh of the finite element structural solver to the surface mesh of the finite volume flow solver. Using the surface displacement data an elliptic mesh deformation algorithm, based on linear elasticity theory, is then used to compute the grid deformation vector field. The developed methods are validated first using standard configuration 10. Finally, for an ultra-high bypass ratio fan, the results of the time-linearized and the unsteady module are compared. The gain in prediction time using the linearized methods is highlighted.

A Harmonic Balance Technique for Multistage Turbomachinery Applications

This article describes a nonlinear frequency domain method for the simulation of unsteady blade row interaction problems across several blade rows in turbomachinery. The capability to efficiently simulate such interactions is crucial for the improvement of the prediction of blade vibrations, tonal noise, and the impact of unsteadiness on aerodynamic performance.The simulation technique presented here is based on the harmonic balance approach and has been integrated into an existing flow solver. A nontrivial issue in the application of harmonic balance methods to turbomachinery flows is the fact that various fundamental frequencies may occur simultaneously in one relative system, each one being due to the interaction of two blade rows. It is shown that, considering the disturbances corresponding to different fundamental frequencies as mutually uncoupled, one can develop an unsteady simulation method which from a practial view point turns out to be highly attractive. On the one hand, it is possible to take into account arbitrarily many nonlinear interaction terms. On the other, the computational efficiency can be increased considerably once it is known that the nonlinear coupling between certain subsets of the harmonics plays only a minor role.To validate the method and demonstrate its accuracy and efficiency a multistage compressor configuration is simulated using both the method described in this article and a conventional time-domain solver.Copyright

CFD/CAA Coupling Applied to the DLR UHBR-Fan: Comparison to Experimental Data

A CFD-CAA hybrid method for fan noise prediction is presented and compared to experimental data. The study shows a very good agreement between numerical simulations and experimental measurements regarding the level of the rotor-stator interaction tones generated by a Ultra-High Bypass Ratio Fan designed by DLR. The comparison is done at a single approach condition for which the blade passing frequency (BPF 1) is cut-off. For the BPF 2, the sound pressure level measured in the inlet is in agreement within 1 or 2 dB with the experimental results. The agreement in terms of radial mode amplitudes is also very satisfying. The discrepancies are slightly higher for the BPF 3 and 4. Nevertheless the trends of the results, for instance the fact that the tone is higher at BPF 4 than BPF 3, are all well predicted. Most of the discrepancies are of the order of the amplitude variations measured between the two investigated experimental runs. The boundary layer influence on the sound propagation is shown to increase with the frequency as stated in literature. Some numerical results from the bypass duct are also presented.

Numerical Modelling of Wake-Jet Interaction with Application to Active Noise Control in Turbomachinery

Recent experimental work conducted at the German Aerospace Center (DLR) in cooperation with the Technical University of Berlin (TUB) has demonstrated the feasibility of using artificially induced aerodynamic noise sources to generate the secondary (anti-phase) sound field for the active control of tonal noise in axial turbomachinery. One strategy to realize this approach is to disturb the primary flow in the blade tip regions using high-speed air jets located in the casing wall. In the present study the noise generation mechanisms in such a configuration are investigated. Time-accurate numerical simulations using a short-time Reynolds Averaged Navier-Stokes flow solver are performed for a low-speed high-pressure axial fan with and without air injection. To mitigate spurious reflections along external domain boundaries, time-accurate implicit non-reflecting boundary conditions are developed and described in detail. A single jet per blade passage, located aft of the rotor trailing edge, is considered with a prescribed constant mass flow rate for the active control of the dominant plane wave at the blade passing frequency. The analysis focuses on the three-dimensional interaction between the jet and the rotor flow field. The jet flow field is characterized by the formation of a pair of counter-rotating vortices that persist far downstream of the injection nozzle. For the configurations investigated potential flow field interaction eects are shown to play a decisive role in the noise generation process.

Advanced Numerical Methods for the Prediction of Tonal Noise in Turbomachinery—Part II: Time-Linearized Methods

This is the second part of a series of two papers on unsteady computational fluid dynamics (CFD) methods for the numerical simulation of aerodynamic noise generation and propagation. It focuses on the application of linearized RANS methods to turbomachinery noise problems. The convective and viscous fluxes of an existing URANS solver are linearized and the resulting unsteady linear equations are transferred into the frequency domain, thereby simplifying the solution problem from unsteady time-integration to a complex linear system. The linear system is solved using a parallel, preconditioned general minimized residual (GMRES) method with restarts. In order to prescribe disturbances due to rotor stator interaction, a so-called gust boundary condition is implemented. Using this inhomogeneous boundary condition, one can compute the generation of the acoustic modes and their near field propagation. The application of the time-linearized methods to a modern high-bypass ratio fan is investigated. The tonal fan noise predicted by the time-linearized solver is compared to numerical results presented in the first part and to measurements.

A Computational Investigation of Broadband Noise Generation in a Low-speed Axial Fan

The generation of broadband noise in a lab-scale, low-speed axial fan is investigated computationally. The time-dependent aerodynamic and acoustic fields are computed directly by numerically solving the unsteady compressible Navier-Stokes equations. Through the application of both the Detached Eddy Simulation (DES) and the Large Eddy Simulation (LES) approaches, the larger scale turbulent eddies in the wakes of the rotor- and stator-blades, and the tip-flow regions of the rotors, are resolved directly in the numerical simulations. Alongside assessing the applicability of the applied methods to the modeling of broadband noise sources in turbomachinery, the broadband noise generation processes are investigated, and the results are compared with available hot-wire and surface-pressure data.

Nonreflecting Boundary Conditions for Aeroelastic Analysis in Time and Frequency Domain 3D RANS Solvers

This paper describes the implementation of a set of nonreflecting boundary conditions of increasing approximation quality for time-accurate and time-linearized 3D RANS solvers in the time and frequency domain. The implementations are based on the computation of eigenfunctions, either analytically or numerically, of the linearized Euler or Navier-Stokes equations for increasingly complex background flows. This results in a hierarchy of nonreflecting boundary conditions based on 1D characteristics, 2D circumferential mode decomposition, and 3D circumferential and radial mode decomposition, including viscous effects in the latter, for the frequency domain solver. By applying a Fourier transform in time at the boundaries the frequency domain implementations can be employed in the time domain solver as well. The limitations of each approximation are discussed and it is shown that increasing the precision of the boundary treatment the nonreflecting property of the boundary conditions is preserved for more complex flows without incurring an excessive increase in computing time.Results of a flutter analysis of a low pressure turbine blade obtained by time and frequency domain simulations are validated against each other and against reference results obtained with a 3D Euler frequency domain solver. The comparison of the results for different boundary conditions reveals the importance of using high quality boundary conditions.Copyright

Advanced Numerical Methods for the Prediction of Tonal Noise in Turbomachinery—Part I: Implicit Runge–Kutta Schemes

This is the first part of a series of two papers on unsteady CFD methods for the numerical simulation of aerodynamic noise generation and propagation. In this part, the stability, accuracy and efficiency of implicit Runge-Kutta schemes for the temporal integration of the compressible Navier-Stokes equations are investigated in the context of a CFD code for turbomachinery applications. Using two model academic problems, the properties of two Explicit first stage, Singly Diagonal Implicit Runge-Kutta (ESDIRK) schemes of second- and third-order accuracy are quantified and compared with more conventional second-order multi-step methods. Finally, to assess the ESDIRK schemes in the context of an industrially relevant configuration, the schemes are applied to predict the tonal noise generation and transmission in a modern high bypass ratio fan stage and comparisons with the corresponding experimental data are provided.

Simulations of Unsteady Blade Row Interactions Using Linear and Non-Linear Frequency Domain Methods

This paper compares various approaches to simulate unsteady blade row interactions in turbomachinery. Unsteady simulations of turbomachinery flows have gained importance over the last years since increasing computing power allows the user to consider 3D unsteady flows for industrially relevant configurations. Furthermore, for turbomachinery flows, the last two decades have seen considerable efforts in developing adequate CFD methods which exploit the rotational symmetries of blade rows and are therefore up to several orders of magnitude more efficient than the standard unsteady approach for full wheel configurations.This paper focusses on the harmonic balance method which has been developed recently by the authors. The system of equations as well as the iterative solver are formulated in the frequency domain.The aim of this paper is to compare the harmonic balance method with the time-linearized as well as the non-linear unsteady approach. For the latter the unsteady flow fields in a fan stage are compared to reference results obtained with a highly resolved unsteady simulation. Moreover the amplitudes of the acoustic modes which are due to the rotor stator interaction are compared to measurement data available for this fan stage.The harmonic balance results for different sets of harmonics in the blade rows are used to explain the minor discrepancies between the time-linearized and unsteady results published by the authors in previous publications. The results show that the differences are primarily due to the neglection of the two-way coupling in the time-linearized simulations.Copyright

A Comparative Study of Gradient Reconstruction Methods for Unstructured Meshes with Application to Turbomachinery Flows

The accuracy of second-order upwind spatial discretization schemes on unstructured meshes depends strongly on the accuracy of the calculated spatial gradients. In this work the Green-Gauss and least-squares methods for the calculation of spatial gradients have been implemented in a hybrid CFD solver for turbomachinery flows and analysed in the context of both academic and industrially relevant test cases. Alongside the stability and accuracy characteristics of the methods, the issues of computational overhead and implementation complexity are discussed in detail.