To examine the aeroacoustic response of the downstream blade row of a rotor/stator pair, the turbulent flowfield between the two components must be accurately represented. To that end, a recent experimental study sought to examine this complex flowfield, establishing a causal relationship between the flowfield influences and their relative contributions to the total turbulence. Although these influences and their relative impact might depend on specific geometry, two will play a dominant role in almost every rotor/stator application: wake turbulence from the upstream blade row (the topic of Part 1) and turbulence ingested by the system and modified by the upstream blade row (the topic of Part 2). The extensive scope of decomposing these influences necessitates their discussion in separate publications. Part 1 begins with an overview as to the relevence and utility of separating these influences, providing motivation for the study. The paper then examines the contribution of the broadband and tonal contributions associated with wake turbulence. A model is proposed that infers broadband turbulence levels from a single, appropriately chosen length scale. This length scale is determined through reconstruction of the temporal mean wake profile shape utilizing the tonal component of the ensemble-averaged, measured wake spectra. Results show that simple models can be used effectively to isolate the wake turbulence contribution, forwarding the concept of a globally applicable theory for use in modeling efforts involving similar flowfields. Part 2 (the topic of this paper) examines turbulence ingested by the system and modified by the upstream upstream blade row. A theoretical model is adapted to predict the level of ingested turbulence suppression using easily quantified geometric arguments. With an appropriate choice of coordinate system, this model accurately predicts broadband suppression of ingested turbulence, showing that simple models can be used to isolate contributions and forwarding the concept of a globally applicable theory for extracting such information from other similar flowfields.

Expressions to describe the correlation length scales of turbulent inflow to an aerodynamic body are derived as functions of the classic integral length scale and anisotropy correction factors. These one-point parameters are significantly easier to determine experimentally than traditional correlation-scale measurement techniques, which involve multiple probes at multiple locations. As such correlation scales are necessary to properly estimate the aeroacoustic response of the body, such a technique could have substantial benefit in a wide variety of applications. The approach is applied to a recent experimental study examining the response of a stator downstream of a propeller that is itself ingesting broadband turbulence. Results suggest that the derived. expressions not only accurately represent correlation length scales, but also enable the accurate prediction of the acoustic output of the stator.

Results are presented of an experimental investigation into the aeroacoustic response characteristics of rotor turbulence ingestion. To fully characterize the rotor response, both the ingested velocity field and the resulting far-field sound were measured. The results are presented of a detailed velocity characterization, which was performed upstream of the rotor. The velocity measurements included an evaluation of the streamwise development of turbulence characteristics downstream of the grid, a high-resolution mapping of the spatial distribution of the mean velocity and rms turbulence fluctuations in the rotor inlet plane, and the development of a semi-empirical, functional representation of the three-dimensional wave number spectral density of the ingested turbulence. These data comprise a comprehensive empirical velocity model that was developed for specific application to rotor turbulence ingestion noise.

This is the second of two papers that discuss an experimental investigation of the aeroacoustic response characteristics of a 10-bladed rotor to grid-generated turbulence. To characterize empirically the rotor response, both the ingested velocity field and resulting far-field sound were measured. In part 1, an empirical velocity characterization of the grid- generated turbulence field was presented. This characterization culminated in a semi-empirical model of the ingested small-scale turbulence field and a modal decomposition of the circumferentially varying mean velocity field in the rotor inlet plane. This detailed velocity model is now used to investigate the aeroacoustic response of a 10-bladed rotor ingesting the grid-generated turbulence field. In particular, the semi-empirical turbulence model is used, in conjunction with theoretical spectral analysis techniques, to predict the far-field sound generated by the 10-bladed rotor. These predictions are compared to corresponding measured data to assess the fidelity of the spectral analysis methods and the semi-empirical turbulence model. Finally, the measured 10-bladed acoustic response is compared to the corresponding response of a 4-bladed rotor ingesting the same grid-generated turbulence field. These comparisons demonstrate the effect of geometry on the rotor acroacoustic sensitivity to both large-scale, spatial mean velocity modes and small-scale turbulence.

Data analysis techniques were previously developed for rotating machinery that predicted the far-field radiation, inferred inflow characteristics, and defined the near-field/far-field acoustic Green's function based on measurements of the pressure near field (Minniti, R. J., Blake, W. K., and Mueller, T. J., Inferring Propeller Inflow and Radiation from Near-Field Response, Part 1: Analytic Development, AIAA Journal, Vol. 39, No. 6, 2000, pp. 1030-1036). The techniques are applied to a free-running propeller in subsonic flow. As a first case, the propeller ingesting large-scale, mean-flow distortions as would be present downstream of stators or inlet guide vanes was considered. This simplified case allowed qualitative analysis in the time domain and complimenting quantitative analysis in the frequency domain. In addition, the case acted as a calibrating configuration to map the frequency response of the individual blades to the incoming flow by varying the number of distortions present and the rotational speed of the propeller. Based on the results of the first case, the analysis was extended to the propeller ingesting grid-generated turbulence. Because of the complex nature of the flow, all analysis was completed in the frequency domain. By the use of the techniques in Inferring Propeller Inflow and Radiation from Near-Field Response, Part 1: Analytic Development, an estimate of the blade summation gain was used to complete the direct solution of the aeroacoustic problem and predict the acoustic far field from a measurement of the ingested flow. Additionally, the inflow character was inferred from the near-field measurements.

In general, the physics of the relationship between the pressure field surrounding a rotating propeller in subsonic flow and the flow characteristics is understood. However, quantification of this relationship in a way that allows engineering analysis of propeller noise is limited by complete definition of the inflow distortions. Therefore, a way of inferring this relationship and the distortion characteristics unobtrusively and in situ has been developed. The technique is based on the assumption that measurements of the unsteady pressure on the blades are available. From the pressures, the technique predicts the radiated acoustic far field, infers incoming flow characteristics, and defines Green's function between the near and far pressure fields. The analysis combines theoretical and empirical treatments of pressure data to infer the acoustic quantities. Thus, the turbulence ingestion problem is approached in a practical manner without the need for many of the simplifying assumptions required by purely theoretical means. The technique is developed for use on experimental data. The technique is subsequently applied to a propeller operating downstream of large-scale, mean-flow distortions, and ingesting broadband turbulence (Minniti, R. J., Blake, W. K., and Mueller, T. J., Inferring Propeller Inflow and Radiation from Near-Field Response, Part 2: Empirical Application, AIAA Journal, Vol. 39, No. 6, 2001, pp. 1037-1046).

AIChE JournalVolume 11, Issue 5 p. 951-954 Communication to the Editor Heat transfer to coils in propeller-agitated vessels A. H. P. Skelland, A. H. P. Skelland University of Notre Dame, Notre Dame, Indiana, and Illinois Institute of Technology, Chicago, IllinoisSearch for more papers by this authorW. K. Blake, W. K. Blake University of Notre Dame, Notre Dame, Indiana, and Illinois Institute of Technology, Chicago, IllinoisSearch for more papers by this authorJ. W. Dabrowski, J. W. Dabrowski University of Notre Dame, Notre Dame, Indiana, and Illinois Institute of Technology, Chicago, IllinoisSearch for more papers by this authorJ. A. Ulrich, J. A. Ulrich University of Notre Dame, Notre Dame, Indiana, and Illinois Institute of Technology, Chicago, IllinoisSearch for more papers by this authorT. F. Mach, T. F. Mach University of Notre Dame, Notre Dame, Indiana, and Illinois Institute of Technology, Chicago, IllinoisSearch for more papers by this author A. H. P. Skelland, A. H. P. Skelland University of Notre Dame, Notre Dame, Indiana, and Illinois Institute of Technology, Chicago, IllinoisSearch for more papers by this authorW. K. Blake, W. K. Blake University of Notre Dame, Notre Dame, Indiana, and Illinois Institute of Technology, Chicago, IllinoisSearch for more papers by this authorJ. W. Dabrowski, J. W. Dabrowski University of Notre Dame, Notre Dame, Indiana, and Illinois Institute of Technology, Chicago, IllinoisSearch for more papers by this authorJ. A. Ulrich, J. A. Ulrich University of Notre Dame, Notre Dame, Indiana, and Illinois Institute of Technology, Chicago, IllinoisSearch for more papers by this authorT. F. Mach, T. F. Mach University of Notre Dame, Notre Dame, Indiana, and Illinois Institute of Technology, Chicago, IllinoisSearch for more papers by this author First published: September 1965 https://doi.org/10.1002/aic.690110541Citations: 11AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Literature Cited 1 Ackley, E. J., Chem. Eng., 67, 133–140 (Aug. 22, 1960). 2 Brown, R. W., R. Scott, and C. Toyne, Trans. Inst. Chem. Engrs. (London), 25, 181 (1947). 3 Chapman, F. S., and F. A. Holland, Chem. Eng., 156 (Jan. 18, 1965). 4 Chilton, T. H., T. B. Drew, and R. H. Jebens, Ind. Eng. Chem., 36, 510 (1944). 5 Coulson, J. M., and J. F. Richardson, “ Chemical Engineering,” Vol. 1, 1 ed., p. 201, Pergamon Press, London, England (1956). 6 Cummings, C. H., and A. S. West, Ind. Eng. Chem., 42, 2303–2313 (1950). 7 Malina, J. A., and E. M. Sparrow, Chem. Eng. Sci., 19, 957–958 (1964). 8 Maxwell, J. B., “ Data Book on Hydrocarbons,” Van Nostrand (1957). 9 McCabe, W. L., and J. C. Smith, “ Unit Operations of Chemical Engineering,” p. 494, McGraw-Hill, New York (1956). 10 McCabe, W. L., and J. C. Smith, “ Unit Operations of Chemical Engineering,” p. 436. 11 Oldshue, J. Y., and A. I. Gretton, Chem. Eng. Progr., 50, 615–621 (1954). 12 Pratt, N. H., Trans. Inst. Chem. Engrs. (London), 25, 163 (1947). 13 Sieder, E. N., and G. E. Tate, Ind. Eng. Chem., 28, 1429 (1936). 14 Strek, F., Intern. Chem. Eng., 3, No. 4, 533 (1963). Citing Literature Volume11, Issue5September 1965Pages 951-954 ReferencesRelatedInformation