Real-Time Estimation in a Turbulent Jet Using Multiple-Input-Multiple-Output Transfer Functions

Igor Maia (1) , Peter Jordan (2) , Eduardo Martini (3) , André Cavalieri (3) , Aaron Towne (4) , Lutz Lesshafft (5) , Oliver Schmidt (6)

1 PPrime [Poitiers] - Institut Pprime [UPR 3346]
2 2AT - Acoustique, Aérodynamique, Turbulence [Institut Pprime]
3 ITA - Instituto Tecnológico de Aeronáutica [São José dos Campos]
4 CTR - Center for Turbulence Research [Stanford]
5 LadHyX - Laboratoire d'hydrodynamique
6 IFW Dresden - Leibniz Institute for Solid State and Materials Research

In this work we investigate the use of multiple-input, multiple-output (MIMO) transfer functions obtained empirically from a large-eddy simulation of a turbulent jet to improve estimates of the space-time evolution of flow disturbances by single-input-single-output (SISO) transfer functions used in previous studies. The choice of sensor placement has been made based on results of linear stability analysis from the literature. The results have shown that MIMO transfer functions are capable of improving predictions of SISO transfer functions concerning both single-and two-point statistics. It has also been observed that MIMO estimates have good accuracy even for large separation distances between input and output and that the number of sensors necessary to converge the estimates depends strongly on Strouhal number. I. Nomenclature y = Input measurement z = Output measurement H 1 = Transfer function corresponding to H 1 estimator S zy = Cross-spectral density matrix between inputs and outputs S yy = Cross-spectral density matrix between input measurements h 1 = Time-domain transfer function γ 2 = Two-point coherence c = Speed of sound St = Strouhal number p = Fluctuating pressure u = Fluctuating streamwise velocity u r = Fluctuating radial velocity II. Introduction Input-output analysis has been increasingly used in control of fluid systems, because it provides a framework in which to associate control design and reduced-order models, notably the ones based on hydrodynamic stability theory[1]. In this framework the frequency response of the system to given excitations is described by means of transfer functions, and this information is used to feed actuators via a control law so as to achieve a certain objective. For a convectively unstable flow, the crucial step in this approach is the correct estimation of the evolution of flow disturbances as they are convected downstream. Therefore, a model that provides an accurate

Domaines: Milieux fluides et réactifs

Igor Maia, Peter Jordan, Eduardo Martini, André Cavalieri, Aaron Towne, et al.. Real-Time Estimation in a Turbulent Jet Using Multiple-Input-Multiple-Output Transfer Functions. 25th AIAA/CEAS Aeroacoustics Conference, May 2019, Delft, Netherlands. ⟨10.2514/6.2019-2535⟩. ⟨hal-02378532⟩