Milind A. Bakhle

Time domain flutter analysis of cascades using a full-potential solver

A time domain approach is used to determine the aeroelastic stability of a cascade of blades. The structural model for each blade is a typical section with two degrees of freedom. The aerodynamic model is unsteady, two-dimensional, full-potential flow through the cascade of airfoils. The unsteady equations of motion for the structure and the fluid are integrated simultaneously in time starting with a steady flowfield and a small initial disturbance applied to the airfoils. Each blade is allowed to move independently, and the motion of all blades is analyzed to determine the aeroelastic stability of the cascade

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

Calculation and Correlation of the Unsteady Flowfield in a High Pressure Turbine

Forced vibrations in turbomachinery components can cause blades to crack or fail due to high-cycle fatigue. Such forced response problems will become more pronounced in newer engines with higher pressure ratios and smaller axial gap between blade rows. An accurate numerical prediction of the unsteady aerodynamics phenomena that cause resonant forced vibrations is increasingly important to designers. Validation of the computational fluid dynamics (CFD) codes used to model the unsteady aerodynamic excitations is necessary before these codes can be used with confidence. Recently published benchmark data, including unsteady pressures and vibratory strains, for a high-pressure turbine stage makes such code validation possible. In the present work, a three dimensional, unsteady, multi blade-row, Reynolds-Averaged Navier Stokes code is applied to a turbine stage that was recently tested in a short duration test facility. Two configurations with three operating conditions corresponding to modes 2, 3, and 4 crossings on the Campbell diagram are analyzed. Unsteady pressures on the rotor surface are compared with data.Copyright

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

Unsteady aerodynamics and flutter based on the potential equation

A time-domain three-dimensional full-potential solver is coupled with a linear structural dynamics model to investigate the unsteady aerodynamics and aeroelasticity of propfans. The solver allows calculations in multiple blade passages with independent blade motions. Aeroelastic calculations are performed in both frequency and time domains. Results are presented for two propfan configurations. Good agreement is seen between the full-potential results and results from linear theory since the flow is subsonic and the thickness of the propfan blades is small; the agreement is not as good for the cases in which the angle of attack is high. Some difficulty is encountered due to wave reflections from outer computational boundaries; however, this does not affect the results in the range of frequencies of interest.

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.

Aeroelastic analysis of turbomachinery

Part II of the two‐part paper describes an aeroelastic analysis program and its application for stability computations of turbomachinery blade rows. Unsteady Euler or Navier‐Stokes equations are solved on dynamically deforming, body fitted, and grid to obtain the aeroelastic characteristics. Blade structural response is modeled using a modal representation of the blade and the work‐per‐cycle method is used to evaluate the stability characteristics. Non‐zero inter‐blade phase angle is modeled using phase‐lagged boundary conditions. Results are presented for a flat plate helical fan, a turbine cascade and a high‐speed fan, to highlight the aeroelastic analysis method, and its capability and accuracy. Obtained results showed good correlation with existing experimental, analytical and numerical results. Numerical analysis also showed that given the computational resources available currently, engineering solutions with good accuracy are possible using higher fidelity analyses.

APPLE - An aeroelastic analysis system for turbomachines and propfans

This paper reviews aeroelastic analysis methods for propulsion elements (advanced propellers, compressors and turbines) being developed and used at NASA Lewis Research Center. These aeroelastic models include both structural and aerodynamic components. The structural models include the typical section model, the beam model with and without disk flexibility, and the finite element blade model with plate bending elements. The aerodynamic models are based on the solution of equations ranging from the two-dimensional linear potential equation for a cascade to the three-dimensional Euler equations for multi-blade configurations. Typical results are presented for each aeroelastic model. Suggestions for further research are indicated. All the available aeroelastic models and analysis methods are being incorporated into a unified computer program named APPLE (Aeroelasticity Program for Propulsion at LEwis).