# Turbulent Flow Physics and Control: The Role of Big Data Analyses Tools

## Abstract

We are studying several problems involving turbulence and big data that range from more efficient and lower noise in next generation jet propulsion systems to bio-inspired concepts for energy production. Specific examples include flows over airfoils (flapping and stationary) and other complex bodies such as turrets and high-speed jet flows. These research activities involve the collection of massive amounts of data from multi-scale computer simulations and/or large-scale experiments. Such experiments/simulations routinely produce terabytes of multi-modal data (velocity, pressure, acoustics, etc.) in fractions of a second. Time-resolved particle image velocimetry data, for example, has requirements of 10 kHz or higher sampling rates in time along with spatial resolution requirements over a broad range of spatial scales observed in high Reynolds and Mach number turbulent flows. Common questions that arise include: How do we compare and contrast data that have different levels of *granularity, density (or sparseness), and distribution (e.g. uniform, checkered, lattice, random, etc.)?* Can we combine such fields that span in space and time to develop a holistic systems-level understanding? This is important in linking numerical simulations that apply lenses with varying magnifications to the same system, as well as integrating qualitative and quantitative experimental observations with computer simulations. We will discuss our general efforts to apply big data analyses/modeling tools (the “right filters”) to *identify patterns and predictive models* rather than just a posteriori trends, statistics, and distributions. Our advanced tools include proper orthogonal decomposition, stochastic estimation, optimal inferred decomposition, wavelet analysis, and Lagrangian coherent structure methods which we are using for understanding, modeling, and controlling such flows. In this paper we focus on high Reynolds and Mach number jets, both axisymmetric and more complex. We have also utilized compressive sensing to examine high-dimensional airfoil data but will not discuss those results here and instead refer the reader to other papers in this volume which focus on this approach in some detail.

## Keywords

Particle Imagine Velocimetry Shear Layer Proper Orthogonal Decomposition Oblique Shock Lagrangian Coherent Structure## Notes

### Acknowledgements

The authors would like to acknowledge two funding sources that made this work possible: (1) an SBIR Phase I and II project with Spectral Energies, LLC, and the AFRL turbine engine division under the direction of program manager Dr. Barry V. Kiel, and (2) an AFOSR grant, number FA9550-15-1-0435, under the guidance of program manager Dr. R. Ponnappan.

## References

- 1.N. Aubry, P. Holmes, J.L. Lumley, E. Stone, The dynamics of coherent structures in the wall region of a turbulent boundary layer. J. Fluid Mech.
**192**(1), 115–173 (1988)MathSciNetCrossRefzbMATHGoogle Scholar - 2.Z. Bai, T. Wimalajeewa, Z. Berger, G. Wang, M. Glauser, P.K. Varshney, Low-dimensional approach for reconstruction of airfoil data via compressive sensing. AIAA J.
**53**(4), 920–933 (2014)CrossRefGoogle Scholar - 3.Z.P. Berger, The effects of active flow control on high-speed jet flow physics and noise. Ph.D. thesis, Syracuse University (2014)Google Scholar
- 4.Z. Berger, M. Berry, P. Shea, M. Glauser, N. Jiang, B. Noack, S. Gogineni, E. Kaiser, A. Spohn, Analysis of high speed jet flow physics with time-resolved piv, in
*52nd AIAA Aerospace Sciences Meeting*(1226) (2014)Google Scholar - 5.Z. Berger, P. Shea, M. Berry, B. Noack, S. Gogineni, M. Glauser, Active flow control for high speed jets with large window piv. J. Flow Turbul. Control
**94**(1), 97–123 (2015)CrossRefGoogle Scholar - 6.M.G. Berry, A.S. Magstadt, M.N. Glauser, C.J. Ruscher, S.P. Gogineni, B.V. Kiel, An acoustic investigation of a supersonic, multi-stream jet with aft deck: characterization and acoustically-optimal operating conditions, in
*54*^{th}*AIAA ASM*(AIAA, San Diego, 2016), vol. 2321022Google Scholar - 7.A.V. Cavalieri, G. Daviller, P. Comte, P. Jordan, G. Tadmor, Y. Gervais, Using large eddy simulation to explore sound-source mechanisms in jets. J. Sound Vib.
**330**, 4098–4113 (2011)CrossRefGoogle Scholar - 8.G. Daviller, Étude numérique des effets de température dans les jets simples et coaxiaux. Ph.D. thesis, Institut P’, CNRS - Université de Poitiers (2010)Google Scholar
- 9.W.K. George, Lectures in turbulence for the 21st century. University of Oslo. http://www.uio.no/studier/emner/matnat/math/MEK4300/v13/undervisningsmateriale/tb_16january2013.pdf. Accessed 15 Jan 2016
- 10.M.N. Glauser, Coherent structures in the axisymmetric turbulent jet mixing layer. Ph.D. dissertation, University of Buffalo (1987)CrossRefGoogle Scholar
- 11.M. Glauser, W. George, Orthogonal decomposition of the axisymmetric jet mixing layer including azimuthal dependence, in
*Advances in Turbulence*, ed. by G. Comte-Bellot, J. Mathieu (Springer, Heidelberg, 1987), pp. 357–366CrossRefGoogle Scholar - 12.M. Glauser, X. Zheng, C.R. Doering, The dynamics of organized structures in the axisymmetric jet mixing layer, in
*Turbulence and Coherent Structures*(Springer, Dordrecht, 1991), pp. 253–265zbMATHGoogle Scholar - 13.M.E. Goldstein, Aeroacoustics of turbulent shear flows. Annu. Rev. Fluid Mech.
**16**(1), 263–285 (1984)CrossRefzbMATHGoogle Scholar - 14.M.A Green, C.W. Rowley, G. Haller, Detection of Lagrangian coherent structures in three-dimensional turbulence. J. Fluid Mech.
**572**, 111–120 (2007)Google Scholar - 15.M.A. Green, C.W. Rowley, A.J. Smits, Using hyperbolic Lagrangian coherent structures to investigate vortices in bioinspired fluid flows. Chaos
**20**, 017510 (2010)Google Scholar - 16.M.A. Green, C.W. Rowley, A.J. Smits, The unsteady three-dimensional wake produced by a trapezoidal pitching panel. J. Fluid Mech.
**685**, 117–145 (2011)CrossRefzbMATHGoogle Scholar - 17.A.M. Hall, An experimental investigation of low-dimensional techniques for large scale noise source characterization in a heated jet. Ph.D. dissertation, Syracuse University (2008)Google Scholar
- 18.J.W. Hall, A.M. Hall, J.T. Pinier, N.G. Mark, Cross-spectral analysis of the pressure in a mach 0.85 turbulent jet. AIAA J.
**47**, 54–59 (2009)Google Scholar - 19.Y. Huang, M.A. Green, Detection and tracking of vortex phenomena using Lagrangian coherent structures. Exp. Fluids
**56**(7), 1–12 (2015). doi: 10.1007/s00348-015-2001-z. http://link.springer.com.libezproxy2.syr.edu/article/10.1007/s00348-015-2001-z - 20.P. Kan, J. Lewalle, G. Daviller, Comparison of near-field events and their far-field acoustic signatures in experimental and numerical high speed jets, in
*International Symposium on Turbulence and Shear Flow Phenomena (TSFP-8)*(2013)Google Scholar - 21.P. Kan, J. Lewalle, Z.P. Berger, M. Glauser, The properties and localizations of acoustic sources of high speed jet, in
*53*^{rd}*AIAA ASM*, Kissimmee (2015). AIAA-2015-0737Google Scholar - 22.P. Kan, C.J. Ruscher, J. Lewalle, M.N. Glauser, S. Gogineni, B.V. Kiel, Extracting near-field structures related to noise production in high speed jets, in
*54*^{th}*AIAA ASM*, San Diego (2016). AIAA 2016-0004Google Scholar - 23.J. Lepicovsky, K. AHUJA, W. Brown, R. Burrin, Coherent large-scale structures in high Reynolds number supersonic jets. AIAA J.
**25**(11), 1419–1425 (1987)CrossRefGoogle Scholar - 24.J. Lewalle, K.R. Low, M.N. Glauser, Properties of individual jet noise sources identified from far-field pressure data. Int. J. Aeroacoust.
**5–6**(11), 651–674 (2012)CrossRefGoogle Scholar - 25.J. Lewalle, P. Kan, S. Gogineni, Mach-number dependence of acoustic source properties in high speed jets – Part I: ensemble statistics of acoustically active regions, in
*52nd AIAA Aerospace Sciences Meeting*(1228) (2014)Google Scholar - 26.J. Lewalle, P. Kan, S.P. Gogineni, Mach-number dependence of acoustic source properties in high speed jets–Part I: ensemble statistics of active regions, in
*52nd AIAA ASM*, National Harbor (2014). AIAA-2014-1228Google Scholar - 27.M.J. Lighthill, On sound generated aerodynamically. I. General theory. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci.
**211**(1107), 564–587 (1952)MathSciNetCrossRefzbMATHGoogle Scholar - 28.M.J. Lighthill, On sound generated aerodynamically. II. Turbulence as a source of sound. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci.
**222**(1148), 1–32 (1954)MathSciNetzbMATHGoogle Scholar - 29.K. Low, Z. Berger, S. Kostka, B. El Hadidi, S. Gogineni, M. Glauser, A low-dimensional approach to closed-loop control of a mach 0.6 jet. Exp. Fluids
**54**, 1–17 (2013)Google Scholar - 30.J.L. Lumley, The structure of inhomogeneous turbulent flows, in
*Atmospheric Turbulence and Radio Wave Propagation*, ed. by A.M. Yaglom, V.I. Tatarsky (Nauka, Moscow, 1967), pp. 166–178Google Scholar - 31.A.S. Magstadt, M. Berry, Z. Berger, P. Shea, C.J. Ruscher, S.P. Gogineni, M. Glauser, An investigation of sonic & supersonic axisymmetric jets: correlations between flow physics and far-field noise. J. Flow Turbul. Control (in review, 2016)Google Scholar
- 32.A.S. Magstadt, M.G. Berry, Z.P. Berger, P.R. Shea, M.N. Glauser, C.J. Ruscher, S. Gogineni, An investigation of sonic & supersonic axisymmetric jets: correlations between flow physics and far-field noise, in
*Turbulent Shear Flow Phenomenon 9*(2015)Google Scholar - 33.L. Perret, E. Collin, J. Delville, Polynomial identification of POD based low-order dynamical system. J. Turbul.
**7**, N17 (2006)MathSciNetCrossRefzbMATHGoogle Scholar - 34.J.T. Pinier, Low-dimensional techniques for active control of high-speed jet aeroacoustics. Ph.D. dissertation, Syracuse University (2007)Google Scholar
- 35.J.T. Pinier, M.N. Glauser, Dual-time piv investigation of the sound producing region of the controlled and uncontrolled high-speed jet, in
*Advances in Turbulence XI: Proceeding of the 11th EUROMECH European Turbulence Conference*, vol. 117 (2007), pp. 392–394Google Scholar - 36.A. Powell, On the mechanism of choked jet noise. Proc. Phys. Soc. Sect. B
**66**(12), 1039 (1953)Google Scholar - 37.H.S. Ribner, The generation of sound by turbulent jets, in
*Advances in Applied Mechanics*, vol. 03 (Academic, New York, 1964), pp. 103–182Google Scholar - 38.C. Ruscher, S. Gogineni, K. Viswanath, B. Kiel, M. Berry, A. Magstadt, M. Glauser, Aeroacoustic validation of a simulation for a complex nozzle, in
*51st AIAA/ASME/SAE/ASEE Joint Propulsion Conference*, Orlando (2015)Google Scholar - 39.C.J. Ruscher, A.S. Magstadt, M.G. Berry, M.N. Glauser, P.R. Shea, K. Viswanath, S.P. Gogineni, B.V. Kiel, A.J. Giese, Analysis of a supersonic 3-stream jet flow, Part I: nozzle design, experiments, and simulations. AIAA J. (in review, 2016)Google Scholar
- 40.L. Sirovich, Turbulence and the dynamics of coherent structures, part I: Coherent Structures. Q. Appl. Math.
**45**, 561–571 (1987)MathSciNetzbMATHGoogle Scholar - 41.C.M. Stack, D.V. Gaitonde, L. Agostini, M.G. Berry, A.S. Magstadt, M.N. Glauser, Numerical investigation of a supersonic multistream jet with an aft-deck, in
*AIAA SciTech*(2016). AIAA 2016-2058Google Scholar - 42.C.K. Tam, On the noise of a nearly ideally expanded supersonic jet. J. Fluid Mech.
**51**, 69–95 (1972)CrossRefzbMATHGoogle Scholar - 43.C.K. Tam, Supersonic jet noise. Annu. Rev. Fluid Mech.
**27**, 17–43 (1995)Google Scholar - 44.C.K.W. Tam, Mach wave radiation from high-speed jets. AIAA J.
**47**(10), 2440–2448 (2009)Google Scholar - 45.C.E. Tinney, M.N. Glauser, L.S. Ukeiley, Low-dimensional characteristics of a transonic jet. Part 1. Proper orthogonal decomposition. J. Fluid Mech.
**612**, 107–141 (2008)Google Scholar - 46.C.E. Tinney, L.S. Ukeiley, M.N. Glauser, Low-dimensional characteristics of a transonic jet. Part 2. Estimate and far-field prediction. J. Fluid Mech.
**615**, 53–92 (2008)Google Scholar - 47.L. Ukeiley, L. Cordier, R. Manceau, J. Delville, M. Glauser, J.P. Bonnet, Examination of large-scale structures in a turbulent plane mixing layer. Part 2. Dynamical systems model. J. Fluid Mech.
**441**(1), 67–108 (2001)Google Scholar