Dana A. Gottfried

Turbomachine Blade Row Interaction Predictions with a Three-Dimensional Finite Element Method

High-cycle fatigue (HCF) is a key issue for the advancement of gas-turbine performance and endurance. Models simulating the cyclic aerodynamic forces experienced by gas-turbine vanes are necessary to make quantitative predictions of HCF during design. Although such models exist, there is an urgent need to compare them with benchmark data to assess their accuracy and reliability. In this study, TAM-ALE3D is utilized to simulate the inlet guide vane (IGV) and rotor blade rows in the Purdue Transonic Compressor at both part-speed and design-speed conditions. Of particular interest is the unsteady flow in the IGV row generated by the part-speed potential field and the design-speed shock system generated by the downstream rotor. To assess the accuracy of the TAM-ALE3D predictions, the 90% span instantaneous IGV vane-to-vane flowfield and vane surface pressures are correlated with appropriate state-of-the-art data.

Aerodynamic damping predictions in turbomachines using a coupled fluid-structure model

Flow-induced vibration of turbomachine blade rows is a coupled fluid-structure problem. Thus, rather than separate fluid and structural models, a coupled interacting fluid-structures analysis is needed. This need is addressed by extending the finite element code ALE3D that solves the three-dimensional Euler equations to model the unsteady aerodynamics of turbomachine blade rows. The same finite element model is applied to both the blading and the fluid, which results in consistency between the fluid and structure. Such a coupled interacting fluid-structure analysis enables the aerodynamic damping of multiple vibration modes to be predicted from two time-domain simulations: one with the blading in a vacuum and one with the blading in flow. This novel approach to predict aerodynamic damping is demonstrated by the consideration of a modern transonic compressor blade row. The blading is first impulsed in its first bending and first torsion modes in a vacuum. It is then immersed in the design-point flowfield and impulsed in its first bending and first torsion modes again. Signal processing tools applied to the predicted blade response time history extract the difference in the decay rate of both modes.

Development and Application of an Arbitrary Lagrangian Eulerian Solver for Turbomachinery Aeromechanics

This paper describes the development and application of turbomachinery aeromechanics arbitrary Lagrangian Eulerian 3-D, an arbitrary Lagrangian Eulerian finite-element-coupled fluid―structure interaction solver, to axial and radial flow turbomachinery aeromechanics issues. The incorporation of turbomachinery-specific algorithms enables the analysis of crack generation in the inlet guide vanes of a modern transonic compressor due to resonant vibrations generated by the potential/shock field of the downstream rotor. The capability to model turbulent wake forcing functions makes possible predictions of the resonant vibratory stress resulting from the subsonic rotor wakes interacting with the downstream stators. The modification of outflow boundary conditions to model incoming acoustic waves allows the unsteady aerodynamic response of a high-speed centrifugal compressor impeller to the potential field/shock excitation generated by the downstream radial-vaned diffuser to be simulated. Finally, the impeller blade aerodynamic damping is calculated to quantify the effect of blade-motion-induced aerodynamics at the exducer. The results make a case that, with increasing computing capacity, coupled fluid―structure interaction methods can become the approach of choice for high cycle fatigue design predictions.

Resonant Response of Mistuned Bladed Disks Including Aerodynamic Damping Effects

A mathematical model is developed to investigate the effects of aerodynamic damping on the maximum amplification factor of mistuned bladed disks. LINSUB, an inviscid linearized unsteady aerodynamic damping code, provides aerodynamic damping influence coefficients that are incorporated into a partial-mistuning model that takes advantage of mode localization. This mistuning analysis is then used to demonstrate the effects of aerodynamic damping on the maximum amplification factor of mistuned bladed disks. The relative importance of aerodynamic effects is determined by a comparison of aerodynamic damping and structural damping factors. It is shown that neglecting unsteady aerodynamics may result in the predicted optimal mistuning pattern not being optimum in the actual operating environment wherein unsteady aerodynamic effects are present.

IMPELLER BLADE UNSTEADY AERODYNAMIC RESPONSE TO VANED DIFFUSER POTENTIAL FIELDS

To predict the unsteady aerodynamic response of centrifugal compressor impeller blades to the potential field generated by the downstream vaned diffuser, a small perturbation model is developed that considers the number of impeller blades and diffuser vanes, the impeller blade backsweep angle, the impeller rotational speed, and the mass flow rate. The unsteady flow is analyzed in the impeller exit region and the vaneless diffuser space between the impeller and the diffuser leading edge radius, where the unsteady flow generated by the diffuser vane potential field is most significant. The unsteady flow perturbations are superimposed on an irrotational two-dimensional steady flow model, resulting in an analysis that is consistent with the small perturbation velocity potential equation. This model is then applied to a representative modern high speed impeller-vaned diffuser configuration.

Passive Detuning for HCF Reduction

Geometric detuning effects are considered in this study of flow induced vibrations of the I nlet Guide Vane (IGV) row of the Purdue Transonic Compressor. The TAM -ALE3D fluid -structure interaction finite element code is used for the analysis, with the IGV and rotor rows modeled. The downstream rotor operating subsonically excites a trailing edge flapping mode in the IGVs. Two detuning strategies are evaluated: (1) decreasing the rotor -generated forcing function to the upstream IGVs, accomplished by detuning the rotor by unequal blade tangential spacing and (2) altering the IGV -rotor unsteady a erodynamic interactions, accomplished by detuning the IGVs by unequal tangential spacing. Evaluation of these strategies is quantified by the IGV unsteady aerodynamic modal force and internal IGV stresses. The unequal rotor blade row spacing produced li ttle change in the IGV stresses, while the unequal IGV row spacing was much more effective, reducing unsteady IGV stresses by a factor of six. Nomenclature

Development and Application of an ALE Solver for Turbomachinery Aeromechanics

High Cycle Fatigue (HCF) is a key issue in the development and endurance of gas turbine engines that results from the flow-induced vibratory response of turbomachine blading to unsteady aerodynamic excitations. This paper describes the development and application of TAM-ALE3D, an Arbitrary Lagrangian Eulerian (ALE) finite element coupled fluid- structure interaction solver, to axial and radial flow turbomachinery aeromechanics issues. The incorporation of turbomachinery-specific algorithms enables the analysis of crack generation in the Inlet Guide Vanes (IGVs) of a modern transonic compressor due to resonant vibrations generated by the potential/shock field of the downstream rotor. The capability to model turbulent wake forcing functions makes possible predictions of the resonant vibratory stress resulting from the subsonic rotor wakes interacting with the downstream stators. The modification of outflow boundary conditions to model incoming acoustic waves allows the unsteady aerodynamic response of a high-speed centrifugal compressor impeller to the potential/shock excitation generated by the downstream radial- vaned diffuser to be simulated. Finally, the impeller blade aerodynamic damping is calculated to quantify the effect of blade-motion induced aerodynamics at the exducer.

UNSTEADY CASCADE AERODYNAMICS IN THE TIME DOMAIN

A linearized unsteady incompressible aerodynamic model for airfoil cascades is developed that is not restricted to harmonic motion at a constant interblade phase angle. This is accomplished by starting with the unsteady aerodynamic coefe cients generated by LINSUB, a semianalyticunsteady cascadeaerodynamics codethat assumes linearity in both space and time. An inverse Fourier transform is then performed to predict the unsteady aerodynamic forces on the airfoils due to an impulsive acceleration. This result, termed the cascade indicial function, is then convolved with the arbitrary motion of the blades to obtain the unsteady aerodynamic forces on the airfoils in the time domain. The aerodynamic damping predicted by the time domain model is shown to compare well to LINSUB results when the interblade phase angle is constant. Results demonstrating the ability of the model to handle arbitrary airfoil motion are also presented. Nomenclature

Off -Design Rotor -IGV Interactions in a Transonic Axial Flow Compressor - A Numerical Investigation

High cycle fatigue (HCF) i s a key issue for the advancement of gas turbine performance and endurance. TAM -ALE3D, a model that simulates cyclic aerodynamic forces and internal blading stresses, is evaluated at off -design conditions where aerodynamically induced cyclic stresses can be especially large, with this evaluation directed toward TAM -ALE3Ds aerodynamic prediction capability. Specifically, TAM -ALE3D simulates the inlet guide vane (IGV) and rotor flow field in the Purdue Transonic Compressor at an off -design operating condit ion where the IGV reset angle causes the rotor to just be on the verge of becoming transonic and the IGV exit metal angle is nearly aligned with the detached rotor shocks. To assess the accuracy of the TAM -ALE3D predictions, the 90% span instantaneous IGV vane -to - vane flow field and vane surface pressures are correlated with recently obtained experimental data at this off -design condition. TAM -ALE3D does well in predicting general features of this off -design flow, however quantitative comparison with the data reveals several deficiencies.