Linear Modal and Non-Modal Instability Analyses of High-Speed Laminar Separated Flow Over Complex Geometries. Part 1: Algorithmic Developments

Abstract

On the theoretical front, necessary algorithmic developments to address BiGlobal axisymmetric modal and nonmodal instability of supersonic and TriGlobal modal instability of hypersonic flow have been undertaken and first analysis results have been obtained. Work in the completed phase comprised derivation of the direct compressible axisymmetric BiGlobal Linearized Navier-Stokes Equations (LNSE) and the corresponding fully three-dimensional (TriGlobal) LNSE in generalized coordinates, using two alternative but equivalent theoretical approaches employing the transformation Jacobians and the chain rule or metric factors and Christoffel symbols. The corresponding equations have been implemented into the matrix-forming Linear Global analysis for Hypersonic Transition (LiGHT) massively parallel eigenvalue and singular value problem solver. Work in this phase also included computation of steady laminar supersonic axisymmetric base flows on the HCF geometry, as well as fully three-dimensional hypersonic flow over the Oberkampf body, followed by first linear global stability analyses in both conxC;figurations. In the HCF geometry modal and nonmodal analyses have been performed, respectively by solving the eigenvalue and singular value problem on generalized coordinates, while on the Oberkampf body the residuals algorithm was employed to extract the least damped global mode. In both geometries, the intimate connection of instability in the laminar separation zone and that of synchronized oscillations in the shock layer has been documented for the xC;first time. Results have been presented in the 2020 AFOSR Annual Review, the 2020 APS and 2021 AIAA SciTech conferences, as well as the Spring and Autumn meetings of the NATO STO AVT-346 Hypersonic Transition group and published as AIAA conference papers, while preparation of archival journal publications is underway.

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Document Details

Document Type
Technical Report
Publication Date
Dec 15, 2021
Accession Number
AD1161241

Entities

People

  • Vassilios Theofilis

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boundary Layer
  • Boundary Layer Flow
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Equations Of Motion
  • Fluid Dynamics
  • Fluid Flow
  • Fluid Mechanics
  • Hydrodynamics
  • Linear Algebra
  • Mechanical Properties
  • Physics Laboratories
  • Shock Waves
  • Three Dimensional
  • Turbulent Flow
  • Turbulent Mixing

Fields of Study

  • Physics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Fluid Mechanics and Fluid Dynamics.
  • Wave Propagation and Nonlinear Chaotic Dynamics.

Technology Areas

  • Hypersonics
  • Hypersonics - Hypersonic Boundary Layers