George L. Stefko

Cascade flutter analysis with transient response aerodynamics

Abstract Two methods for calculating linear frequency domain unsteady aerodynamic coefficients from a time-marching full-potential cascade solver are developed and verified. In the first method, the influence coefficient method, solutions to elemental problems are superposed to obtain the solutions for a cascade in which all blades are vibrating with a constant interblade phase angle. The elemental problem consists of a single blade in the cascade oscillating while the other blades remain stationary. In the second method, the pulse response method, the response to the transient motion of a blade is used to calculate influence coefficients. This is done by calculating the Fourier transforms of the blade motion and the response. Both methods are validated by comparison with the harmonic oscillation method, in which all the airfoils are oscillated, and are found to give accurate results. The aerodynamic coefficients obtained from these methods are used for frequency domain flutter calculations involving a typical section blade structural model. Flutter calculations are performed for two examples over a range of subsonic Mach numbers using both flat plates and actual airfoils.

Development of an Aeroelastic Code Based on an Euler / Navier-Stokes Aerodynamic Solver

This paper describes the development of an aeroelastic code (TURBO-AE) based on an Euler / Navier-Stokes unsteady aerodynamic analysis. A brief review of the relevant research in the area of propulsion aeroelasticity is presented. The paper briefly describes the original Euler / Navier-Stokes code (TURBO) and then details the development of the aeroelastic extenstons. The aeroelastic formulation is described. The modeling of the dynamics of the blade using a modal approach is detailed, along with the grid deformation approach used to model the elastic deformation of the blade. The work-per-cycle approach used to evaluate aeroelastic stability is described. Representative results used to verify the code are presented. At the present stage of development, the aeroelastic code is limited to in-phase blade motions. The paper concludes with an evaluation of the development thus far, and some plans for further development and validation of the TURBO-AE code.Copyright

A 3D EULER / NAVIER-STOKES AEROELASTIC CODE FOR PROPULSION APPLICATIONS

This paper describes the development and verification of an aeroelastic code (TURBO-AE) based on an Euler / Navier-Stokes unsteady aerodynamic code (TURBO). The aeroelastic formulation is described. The modeling of the dynamics of the blade using a modal method is detailed, along with the grid deformation procedure used to model the elastic deformation of the blade. The work-per-cycle method used to evaluate aeroelastic stability is described. Representative results are presented for a helical fan test configuration used to verify the code. Results included are for both zero and non-zero interblade phase angles. Excellent agreement with linear theory is seen in all cases. Some representative results are also presented for a realistic compressor configuration. The paper concludes with an evaluation of the development thus far, and some plans for further development and validation of the TURBO-AE code.

Flutter Analysis of a Transonic Fan

This paper describes the calculation of flutter stability characteristics for a transonic forward swept fan configuration using a viscous aeroelastic analysis program. Unsteady Navier-Stokes equations are solved on a dynamically deforming, body fitted, grid to obtain the aeroelastic characteristics using the energy exchange method. The non-zero inter-blade phase angle is modeled using phase-lagged boundary conditions. Results obtained show good correlation with measurements. It is found that the location of shock and variation of shock strength strongly influenced stability. Also, outboard stations primarily contributed to stability characteristics. Results demonstrate that changes in blade shape impact the calculated aerodynamic damping, indicating importance of using accurate blade operating shape under centrifugal and steady aerodynamic loading for flutter prediction. It was found that the calculated aerodynamic damping was relatively insensitive to variation in natural frequency.Copyright

Application of Time-Shifted Boundary Conditions to a 3D Euler/Navier-Stokes Aeroelastic Code

In the present work the unsteady aerodynamic characteristics of harmonically oscillating fan blades are investigated by applying a time-shifted boundary condition at the periodic boundaries. The direct-store method is used to implement the time-shifted boundary condition in a time-marching Euler/Navier-Stokes solver. Inviscid flow calculations for a flat plate helical fan, in a single-blade passage domain, are used to verify the analysis. The results obtained show good correlation with other published results as well as with the same solver using multiple blade passages stacked together. Significant savings in computer time is realized, especially for smaller phase angles.Copyright

Aeroelastic analysis of turbomachinery: Part I – phase lagged boundary condition methods

In this two‐part paper, aeroelastic analysis of turbomachinery blade rows and phase‐lagged boundary conditions used for analysis are described. Part I of the paper describes a study of phase‐lagged boundary condition methods used for non‐zero interblade phase angle analysis. The merits of time‐shifted (direct‐store), Fourier decomposition and multiple passage methods are compared. These methods are implemented in a time marching Euler/Navier‐Stokes solver and are applied to a fan for subsonic and supersonic inflow and to a turbine geometry with supersonic exit flow. Results showed good comparisons with published results and measured data. The time‐shifted and Fourier decomposition methods compared favorably in computational costs with respect to multiple passage analysis despite a slower rate of convergence. The Fourier‐decomposition method was found to be better suited for workstation environment as it required significantly less storage, although at the expense of slightly higher computational cost. The time‐shifted method was found to be better suited for computers where fast input‐output devices are available.

Cyclic Symmetry Finite Element Forced Response Analysis of a Distortion Tolerant Fan with Boundary Layer Ingestion

Accurate prediction of the blade vibration stress is required to determine overall durability of fan blade design under Boundary Layer Ingestion (BLI) distorted flow environments. Traditional single blade modeling technique is incapable of representing accurate modeling for the entire rotor blade system subject to complex dynamic loading behaviors and vibrations in distorted flow conditions. A particular objective of our work was to develop a high-fidelity full-rotor aeromechanics analysis capability for a system subjected to a distorted inlet flow by applying cyclic symmetry finite element modeling methodology. This reduction modeling method allows computationally very efficient analysis using a small periodic section of the full rotor blade system. Experimental testing by the use of the 8-foot by 6-foot Supersonic Wind Tunnel Test facility at NASA Glenn Research Center was also carried out for the system designated as the Boundary Layer Ingesting Inlet/Distortion-Tolerant Fan (BLIDTF) technology development. The results obtained from the present numerical modeling technique were evaluated with those of the wind tunnel experimental test, toward establishing a computationally efficient aeromechanics analysis modeling tool facilitating for analyses of the full rotor blade systems subjected to a distorted inlet flow conditions. Fairly good correlations were achieved hence our computational modeling techniques were fully demonstrated. The analysis result showed that the safety margin requirement set in the BLIDTF fan blade design provided a sufficient margin with respect to the operating speed range.

Aeromechanics Analysis of a Distortion-Tolerant Fan with Boundary Layer Ingestion

A propulsion system with Boundary Layer Ingestion (BLI) has the potential to significantly reduce aircraft engine fuel burn. But a critical challenge is to design a fan that can operate continuously with a persistent BLI distortion without aeromechanical failure – flutter or high cycle fatigue due to forced response. High-fidelity computational aeromechanics analysis can be very valuable to support the design of a fan that has satisfactory aeromechanic characteristics and good aerodynamic performance and operability. Detailed aeromechanics analyses together with careful monitoring of the test article is necessary to avoid unexpected problems or failures during testing. In the present work, an aeromechanics analysis based on a three-dimensional, time-accurate, Reynolds-averaged Navier Stokes computational fluid dynamics code is used to study the performance and aeromechanical characteristics of the fan in both circumferentially-uniform and circumferentially-varying distorted flows. Pre-test aeromechanics analyses are used to prepare for the wind tunnel test and comparisons are made with measured blade vibration data after the test. The analysis shows that the fan has low levels of aerodynamic damping at various operating conditions examined. In the test, the fan remained free of flutter except at one near-stall operating condition. Analysis could not be performed at this low mass flow rate operating condition since it fell beyond the limit of numerical stability of the analysis code. The measured resonant forced response at a specific low-response crossing indicated that the analysis under-predicted this response and work is in progress to understand possible sources of differences and to analyze other larger resonant responses. Follow-on work is also planned with a coupled inlet-fan aeromechanics analysis that will more accurately represent the interactions between the fan and BLI distortion.

Phase-Lagged Boundary Condition Methods for Aeroelastic Analysis of Turbomachines: A Comparative Study

In the present work a comparative study of phase-lagged boundary condition methods is carried out. The relative merits and advantages of time-shifted and the Fourier decomposition methods are compared. Both methods are implemented in a time marching Euler/Navier-Stokes solver and are applied to a flat plate helical fan with harmonically oscillating blades to perform the study. Results were obtained for subsonic as well as supersonic inflows. Results for subsonic inflow showed good comparisons with published results and between the two methods along with comparable computational costs. For the supersonic inflow, despite the presence of shocks at the periodic boundary results from both the methods compared well, however, Fourier decomposition method was computationally more expensive. For linear flowfield Fourier decomposition method is best suited, especially for work-station environment. The time-shifted method is better suited for CRAY category of computers where fast input-output devices are available.Copyright

Aeroelastic calculations based on three-dimensional Euler analysis

This paper presents representative results from an aeroelastic code (TURBO-AE) based on an Euler/Navier-Stokes unsteady aerodynamic code (TURBO). Unsteady pressure, lift, and moment distributions are presented for a helical fan test configuration which is used to verify the code by comparison to two-dimensional linear potential (flat plate) theory. The results are for pitching and plunging motions over a range of phase angles, Good agreement with linear theory is seen for all phase angles except those near acoustic resonances. The agreement is better for pitching motions than for plunging motions. The reason for this difference is not understood at present. Numerical checks have been performed to ensure that solutions are independent of time step, converged to periodicity, and linearly dependent on amplitude of blade motion. The paper concludes with an evaluation of the current state of development of the TURBO-AE code and presents some plans for further development and validation of the TURBO-AE code.