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RESEARCH PAPERS

Assessing Convergence in Predictions of Periodic-Unsteady Flowfields

[+] Author and Article Information
J. P. Clark

Turbine Branch, Turbine Engine Division, Propulsion Directorate,  Air Force Research Laboratory, Building 18, Room 136D, 1950 5th Street, WPAFB, OH 45433john.clark@pr.wpafb.af.mil

E. A. Grover

Turbine Aerodynamics,  United Technologies Pratt & Whitney, 400 Main Street, M∕S 169-29, East Hartford, CT 06108eric.grover@pw.utc.com

J. Turbomach 129(4), 740-749 (Aug 09, 2006) (10 pages) doi:10.1115/1.2720504 History: Received July 18, 2006; Revised August 09, 2006

Predictions of time-resolved flowfields are now commonplace within the gas-turbine industry, and the results of such simulations are often used to make design decisions during the development of new products. Hence it is necessary for design engineers to have a robust method to determine the level of convergence in design predictions. Here we report on a method developed to determine the level of convergence in a predicted flowfield that is characterized by periodic unsteadiness. The method relies on fundamental concepts from digital signal processing including the discrete Fourier transform, cross correlation, and Parseval’s theorem. Often in predictions of vane–blade interaction in turbomachines, the period of the unsteady fluctuations is expected. In this method, the development of time-mean quantities, Fourier components (both magnitude and phase), cross correlations, and integrated signal power are tracked at locations of interest from one period to the next as the solution progresses. Each of these separate quantities yields some relative measure of convergence that is subsequently processed to form a fuzzy set. Thus the overall level of convergence in the solution is given by the intersection of these sets. Examples of the application of this technique to several predictions of unsteady flows from two separate solvers are given. These include a prediction of hot-streak migration as well as more typical cases. It is shown that the method yields a robust determination of convergence. Also, the results of the technique can guide further analysis and∕or post-processing of the flowfield. Finally, the method is useful for the detection of inherent unsteadiness in the flowfield, and as such it can be used to prevent design escapes.

Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Instantaneous static pressure on the no-slip surfaces of the HIT turbine rig simulation (HPT1)

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Figure 2

An example of signal-analysis techniques used in the current method for HPT1: (a) time mean; (b) DFT magnitudes; (c) phase angles; (d) cross-correlation coefficients; and (e) power-spectral densities

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Figure 3

Convergence behavior of the flowfield at the location of interest given in Fig. 1 for HPT1

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Figure 4

Convergence levels for blade force components as a function of periodic cycle for HPT2

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Figure 5

Convergence of flow rates, total pressures, and total temperatures at the blade interrow boundaries for HPT2

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Figure 6

Convergence levels for blade force components as a function of periodic cycle for HPT3

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Figure 7

Plots of time-resolved blade axial force and fuzzy-set membership grades as functions of the periodic cycle (HPT3)

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Figure 8

The results of a PSD analysis performed on cycle seven of the axial force signal for the blade of HPT3. Power contributions from unexpected frequencies are apparent.

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Figure 9

Normalized flow rate into the blade row versus periodic cycle number and the results of a PSD analysis of the signal (HPT3)

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Figure 10

Normalized flow rate out of the blade row versus periodic cycle number and the results of a PSD analysis of the signal (HPT3)

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Figure 11

Contours of DFT magnitude at 168E calculated from time-resolved entropy rise (J∕kg∕K) at midspan through the blade passage (HPT3)

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Figure 12

Contours of DFT magnitude at 168E calculated from time-resolved static pressure (kPa) at midspan through the blade passage (HPT3)

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Figure 13

Instantaneous total temperatures through HPT4 for the hot-streak simulation

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Figure 14

Convergence levels for the blade flowfield variables considering the 8E and 24E frequencies associated with the hot-streak inlet profile (HPT4)

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Figure 15

Normalized total pressure upstream of the blade row versus cycle number and a PSD analysis of the signal (HPT4)

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Figure 16

Plots of time-resolved blade tangential force and fuzzy-set membership grades as functions of the periodic cycle (HPT4)

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