Brian A. Freno

A Reduced-Order Model for Turbomachinery Flows Using Proper Orthogonal Decomposition

This paper presents the development of a reduced-order model based on the proper orthogonal decomposition (POD) method. The POD method has been developed to predict turbomachinery flows modeled by the Reynolds-averaged Navier–Stokes equations. The purpose of using a POD-based reduced-order model is to decrease the computational cost of turbomachinery flows. The POD model has been tested for two configurations: a canonical channel with a bump case and the transonic NASA Rotor 67 case. The Rotor 67 case has been simulated at design wheel speed and at three off-design conditions: 70, 80, and 90% of the wheel speed. The results of the POD-based reduced-order model where in excellent agreement with the full-order model results. The computational time of the reduced-order model was approximately one order of magnitude smaller than that of the full-order model.Copyright

Proper Orthogonal Decomposition Applied to the Reynolds-Averaged Navier--Stokes Equations

Despite continuous advances in computational power, the scope of highdelity computational uid dynamic results remains limited for applications requiring numerous repetitions. Examples of such applications include parametric studies and design iterations. This limited scope is particularly evident in computational aeroelasticity, for which the costs associated with unsteadiness of the ow and temporal variation of the mesh for higherdelity uid models can be a burden computationally. Through reduced-order modeling, the governing partial di erential equations of motion are reduced to ordinary di erential equations through temporal{spatial separation. Reduced-order models have become an increasingly popular method in uid and solid mechanics. For uid mechanics, proper orthogonal decomposition can be used to develop a reduced-order model wherein the optimal set of spatial basis functions is computed from the ow snapshots collected from a full-order model, permitting subsequent simulations to determine the time-dependent coe cients that weight the basis functions. In this paper, proper orthogonal decomposition is discussed and applied to the Reynolds-averaged Navier{Stokes equations, and results are shown for ow through a channel. The results from subsonic and transonic ow regimes are presented and the full-order model is compared with reduced-order models using basis functions generated through proper orthogonal decomposition of the full-order model and through interpolation.

The Role of Structural Nonlinearities in Wind Turbine Blade Aeroelastic Analysis

The large aspect ratio of wind turbine blades introduces a significant susceptibility to aeroelastic phenomena. Aeroelastic analysis of airplane wings is traditionally concerned with small deformations associated with torsional motion and planar bending. On the other hand, wind turbine blades are subjected to large nonplanar, coupled deformations, introducing additional complications. Finite element analysis provides an effective and generalized method to model these structures; however, it is computationally expensive. The large aspect ratio of these blades is exploitable as these potential aeroelastically unstable structures can be modeled as nonlinear nonuniform cantilevered beams, drastically reducing computational time. In this paper, a previously developed nonlinear beam model is discussed. To illustrate the significance of retaining structural nonlinearities, the beam model is run both independently and tightly coupled with an in-house flow solver based on the Reynolds-averaged Navier-Stokes equations with a mesh deformation algorithm based on a spring analogy.