Resolvent Analysis of Shock Buffet on Infinite Wings



He, Wei ORCID: 0000-0002-2633-6114 and Timme, Sebastian ORCID: 0000-0002-2409-1686
(2020) Resolvent Analysis of Shock Buffet on Infinite Wings. In: AIAA AVIATION 2020 FORUM, Virtual Event.

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Abstract

Resolvent analysis to identify the unsteady aerodynamic response to harmonic forcing (interpreted as higher-order non-linear terms in the governing equations or external) is presented for three-dimensional infinite straight and swept wings without assumptions on spatial spanwise homogeneity (so-called triglobal). This work continues the recent triglobal modal stability analysis by He and Timme [1] and expands upon the elucidation of shock-buffet flow physics presented earlier in Sartor et al. [2] for two-dimensional aerofoil flow. The flow conditions are a freestream Mach number of 0.73 with a reference chord Reynolds number of 3.2 × 106 and angles of attack describing pre-and post-onset shock-buffet conditions. The infinite wing is modelled as a rectangular geometry with a chosen aspect ratio of 3 and spanwise periodic boundary condition imposed. The base flow is solved in the framework of steady Reynolds-averaged Navier–Stokes equations with a closure using the negative Spalart–Allmaras turbulence model and assumed to be spanwise parallel both for the infinite straight and swept wings. The novel algorithm, following the work by Gómez et al. [3], without the need to evaluate the resolvent operator explicitly enables the efficient computation of optimal forcing and response modes together with the amplification gain at arbitrary frequencies. At the flow conditions investigated, a high amplification is found at a low Strouhal number of St ≈ 0.06 to 0.07 coinciding with the well-known two-dimensional aerofoil shock-buffet mode, both on straight and swept wings. Spanwise-periodic resolvent modes are observed at St< 0.03 for the straight wing and St = 0.1 to 1 for the swept wing. These results for the spanwise-periodic modes are consistent with recent global stability studies on infinite wings. For yet higher Strouhal numbers, specifically St = 1 to 5, another mode, resembling a Kelvin–Helmholtz shear-layer instability, is observed. The results suggest, particularly for the subcritical flow, that resolvent analysis is a powerful tool to detect modes of an imminent instability early when global stability analysis would fail.

Item Type: Conference or Workshop Item (Unspecified)
Depositing User: Symplectic Admin
Date Deposited: 19 May 2020 09:09
Last Modified: 18 Jan 2023 23:51
DOI: 10.2514/6.2020-2727
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3087879