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Flow Control pp 79-109 | Cite as

Quasi-Analytical Shape Modification for Neighboring Steady-State Euler Solutions

  • J. S. Brock
  • W. F. Ng
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 68)

Abstract

Aerodynamic inverse design methods which are governing equation consistent are generally limited to the Full Potential equations. Consistent design methods use identical governing equations for all fluid dynamic segments of the algorithm, including shape modification. This ensures that all relevant physical information is included within each design estimate, and therefore, a minimum number of analysis/design iterations are required. This report presents a new, and consistent, shape modification method for future use within a direct-iterative inverse design algorithm. The method is simple, being developed from a truncated quasi-analytical Taylor’s series expansion of the global governing equations. The method is general, since it may use either the Euler or Navier-Stokes equations, any combination of numerical techniques, and any number of spatial dimensions. The proposed method also includes a unique iterative algorithm, and new geometry/grid constraints, to solve the over-determined design problem. An upwind, cell-centered, finite-volume formulation of the two-dimensional Euler equations is used within the present effort. The method is evaluated within a symmetric channel where the design variable is a mid-channel ramp angle which is nominally θ = 5°. Tests were conducted for three target ramp angle perturbations, Δθ = 2%, 10%, and 40%, and three inlet Mach numbers, M = 0.30, 0.85, and 2.00. For a single design estimate, using design-like test conditions, the new method is demonstrated to accurately predict geometry shape changes. This includes the transonic test case with an extreme 40% design variable perturbation where the target geometry was predicted with 95% accuracy.

Keywords

Computational Fluid Dynamics AIAA Paper Normal Matrix Jacobian Matrice Shape Modification 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 1995

Authors and Affiliations

  • J. S. Brock
    • 1
  • W. F. Ng
    • 1
  1. 1.Mechanical Engineering DepartmentVirginia Polytechnic Institute and State UniversityBlacksburgUSA

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