PSE-based sensitivity analysis of turbulent and supersonic single stream jet

Abstract

Reducing noise emission from jet is a major topics of aeroacoustics. Recently, it has been shown that the large coherent structures of a turbulent single-stream jet, which are parts of the noise generation mechanisms, can be interpreted as instability of the mean turbulent flow, especially in the region of the potential core. Reducing noise will be probably only achieved with some new control strategy on the underlying physics of the acoustic wave generation. The present work deals with the last investigations associated to the sensitivity analysis of the single and dual-stream jet instability to any local forcing. Sensitivity is a first step of any aeroacoustic or flow control approach and it is performed by the Parabolized Stability Equations and their adjoint counter part. Validation is first made on a simple semi-analytical supersonic jet. Then sensitivity functions to a source of momentum, mass or energy forcing are given in a supersonic single (M = 1.15) and dualstream jets (Mp = 0.89 and Ms = 1.20). The base-flow is obtained from accurate Large Eddy Simulations and included some shock cells. Highest sensitivities are found inside the shear layer close to the external boundary of the potential core and close to the jet inlet, similar to the previous results found in incompressible single stream jet. The growth rate and wave number of the Kelvin-Helmhotz instability and the acoustic (pressure) perturbation are strongly influenced by the shock cell positions.

A Parabolised Stability Equation based Broadband Shock-Associated Noise Model

“…Due to the slow-varying assumption of the base flow in the PSE formulation, we decided not to use a base flow with shocks but rather the ideally-expanded jet with the same perfectly-expanded jet velocity M j . While this is consistent with the methodology of previous BBSAN studies [42], it is not possible to study the effects that the shock cells might have on the instability waves [49]. The two-point behaviour of the wavepacket is also probed from the azimuthally decomposed velocity field of the jet, allowing the CSD to be computed to recover the MSC.…”

Wavepacket modelling of broadband shock-associated noise in supersonic jets

“…While there is evidence to suggest that wavepacket dynamics are not affected by weak shocks (Edgington-Mitchell et al 2019), it remains unknown whether this extends to highly underexpanded jets, such as that studied here. Despite PSE having been attempted on a shock-containing base flow (Ansaldi et al 2016), that approach is not pursued here, due to the breakdown of the slowly diverging mean flow assumption in the vicinity of the shocks.…”

Optimal ‘quiet’ inlet perturbation using adjoint-based PSE in supersonic jets

“…f . And the body forcing term f here aims to verify our APSE code with Ansaldi (2016). In the optimal control theory, all the derivatives except the gradient of the control parameters must vanish.…”

“…The LPSE code is validated according to section 2.2 in Ansaldi (2016). The mean flow is an incompressible axisymmetric jet flow, with Ma j =0.01 (Yen andMessersmith 1998, Piot et al 2006), given by:…”

“…As the simplification of adjoint Navier-Stokes equations, the adjoint PSE (APSE), firstly proposed by Herbert and Lin (1993), mainly benefiting from PSE assumptions and its low computational cost, has been successfully applied in sensitivity and receptivity analysis (Airiau 2000, Collis and Dobrinsky 2000, Pralits et al 2000, and determining the optimal distribution suction for the delay of transition in boundary layers (Walther et al 2001, Pralits et al 2002, Airiau et al 2003. In Ansaldi and Airiau (2015), Ansaldi et al (2016), an APSE-based sensitivity analysis is carried out in jet instabilities by introducing a body-force term in the right-hand side of PSE, which provides a feasible way in sensitivity analysis and noise control based on the PSE and APSE models. In present work, this APSE-based algorithm is extended to the optimization problem associated with the energy amplification control of instability waves and noise suppression.…”