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Resolvent Modeling of Turbulent Jets

Citation

Pickering, Ethan (2021) Resolvent Modeling of Turbulent Jets. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/szxb-f168. https://resolver.caltech.edu/CaltechTHESIS:03022021-005902351

Abstract

Optimal control of turbulent flows requires a detailed prediction of the unsteady, three-dimensional turbulent structures that govern quantities of interest like noise, drag, and mixing efficiency. There is a need for physics-based, reduced-order models of turbulent structure for those cases where direct simulation of the flow would be computationally prohibitive. In this thesis, we explore resolvent analysis as a framework for such models. Based on a linearization about the turbulent mean flow field, the resolvent finds optimal (highest gain) forcing functions that give rise, through linear amplification mechanisms, to energetic coherent structures. The forcing functions represent the nonlinear interactions between the coherent structures as well as with background incoherent turbulence. While the high-gain structures capture many characteristics of the observed turbulent coherent structures in both wall-bounded and free-shear flows, closures for the forcing function are required to make these models predictive and thus utilize them for flow control.

In the first part of this thesis, we examine a linear model for the resolvent forcing by adapting the concept of a turbulent (eddy) viscosity from classical Reynolds-Averaged Navier--Stokes (RANS) turbulence modeling. We present a data-driven approach to identify an optimal eddy-viscosity field that best matches the resolvent prediction to the most energetic coherent structure educed via spectral proper orthogonal decomposition (SPOD) of data from high-fidelity simulations. We analyze the specific case of turbulent jets spanning a range of Mach numbers from subsonic to supersonic. We find the optimal eddy-viscosity field to be effective at matching both the shape and energy distribution of structures. More importantly, we find that calibrated eddy-viscosity fields predicted using standard eddy-viscosity models (utilizing only quantities available from RANS) yield results that are close to optimal.

We use the resulting resolvent model together with the high-fidelity data to investigate the full spectrum of amplification mechanisms and coherent structures present in turbulent jets. The addition of a turbulence model provides a clear separation between two established mechanisms in turbulent jets (Kelvin-Helmholtz and Orr) and leads to the identification of a third mechanism known as lift-up. Lift-up becomes the dominant mechanism at low-frequency limits for nonzero azimuthal wavenumbers, generating elongated, streaky structures. We find these streaks to be the most energetic structures in the jet, and that their presence has implications for altering the mean flow and controlling noise.

Finally, we extend resolvent analysis to that of an acoustic analogy that relates the near-field forcing to the far-field acoustics 100 diameters from the nozzle. We again leverage high-fidelity data to produce an ensemble of realizations of the acoustic field and find that only a few resolvent modes are necessary for reconstruction. Ultimately, we find that a resolvent model based solely upon RANS quantities can reconstruct and predict the peak acoustic field at rank-1 to within 2 decibels for both the supersonic and transonic jets.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Resolvent analysis, jets, turbulence, eddy-viscosity, Kelvin-Helmholtz, Orr, lift-up, acoustics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Mechanical Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Colonius, Tim E.
Thesis Committee:
  • Blanquart, Guillaume (chair)
  • McKeon, Beverley J.
  • Dabiri, John O.
  • Colonius, Tim E.
Defense Date:4 February 2021
Non-Caltech Author Email:ethan.pickering (AT) case.edu
Funders:
Funding AgencyGrant Number
National Defense Science and Engineering Graduate (NDSEG) FellowshipUNSPECIFIED
Office of Naval Research (ONR)N00014-16-1-2445
Record Number:CaltechTHESIS:03022021-005902351
Persistent URL:https://resolver.caltech.edu/CaltechTHESIS:03022021-005902351
DOI:10.7907/szxb-f168
Related URLs:
URLURL TypeDescription
https://arxiv.org/pdf/2005.10964.pdfarXivArticle adapted for Chapter 1.
https://doi.org/10.2514/6.2019-2454DOIArticle adapted for Chapter 1.
https://doi.org/10.1017/jfm.2020.301DOIArticle adapted for Chapter 2.
https://doi.org/10.2514/6.2020-0999DOIArticle adapted for Chapter 3.
ORCID:
AuthorORCID
Pickering, Ethan0000-0002-4485-6359
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14097
Collection:CaltechTHESIS
Deposited By: Ethan Pickering
Deposited On:03 Mar 2021 22:19
Last Modified:10 Mar 2021 18:48

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