1th AIAA/CEAS Aeroacoustics Conference, May 006 interactions Coupling of a Jet-Slot Oscillator With the Flow-Supply Duct: Interaction M. Glesser 1, A. Billon 1, V. Valeau, and A. Sakout 1 mglesser@univ-lr.fr 1 LEPTAB La Rochelle University, France LEA Poitiers University, France
Outline interactions 1 interactions 3
Basic principle interactions Scheme of the feedback loop [Powell, 1990] PSfrag replacements Flow perturbation Amplification Interaction frag replacements Indirect Feedback Oscillatory energy sourcce Highltly energetic whistling is produced Geometrical configuration producing flow-induced
Coupling of a Jet-Slot Oscillator With the Flow-Supply Duct interactions Flow PSfrag replacements y z x Billon et al. Two Feedback Paths for a Jet-Slot Oscillator Journal of Fluids and Structures, 1:11 13, 005.
An expression for the flow-acoustic interactions modeling interactions = acoustic resonance + flow-acoustic interactions Acoustic power generated or absorbed by flow-acoustic interactions: P = ρ 0 (ω v).u a dv V T 0 ω: vorticity field v: vortices convection speed u a : acoustic velocity field Emitted frequency => maximization of P
Vorticity Field replacements Vortex-point model [Nelson, 1983 & Bruggeman, 1987] interactions U c Γ Shedding Impact U t UU ct t + T 0 t Vortices convected in a straigth path Vorticity only concentrated on vortex cores Linear growth of the vortex circulation Saturation of the vortex circulation
Acoustic Field.5 interactions Vertical axis x, cm 1.5 1 0.5 0-0.5-1 -1.5-5 0 5 1 1.5.5 3 Horizontal axis x 1, cm 3.5 4 u a = ϕ (x, t) = cos(πf 0 t + θ) ( ϕ pot(x) )
Missing Parameters interactions Vertical axis x, cm?.5 1.5 1 0.5 0-0.5-1 -1.5? -5 0 5 1 1.5.5 3 3.5 4 Horizontal axis x 1, cm Shape of the potential flow? Acoustic field / vortex shedding synchronization? Jet mode & Vortices convection speed
Experimental Set-up interactions 90 Mobile hot-wire probe position (3 < x 1 < L, 80, 8) 150 100100 190 Static hot-wire probe position (3, 90, 8) x x 3 190 50 10 50 x 1 Mobile hot-wire probe x L % & % & % & % & %%%%% &&&&& H ((((( ''''' ((((( ' ( ' ( ' ( ' ( Static hot-wire probe Laser plane Laser source x 1 Camera
interactions Jet Oscillation Mode Symmetric jet mode Rather constant vortices convection speed
Vortices Convection Speed interactions Phase θ of cross-spectrum at f0 7π 6π 5π 4π 3π π π θ x 0 0 0, 0,4 0,6 0,8 1 Mobile probe position, x/l Convection speed: Uc = πf 0 ( θ x ) 1 Uc = 0.6U
Fields 1 Vorticity Field replacements interactions UU ct 777 U c = 0.6U 9 Γ Shedding Impact U c U 0.6U t t t + T 0 t
Fields I Acoustic J Field K interactions x 1 L x B L H B ξ η D D H Physical plane (z = x 1 + ix ) ϕ 0 (ζ) = M π log(ζ ξ b) D :;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;: D :;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;: <;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;< :;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;: <;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;< :;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;:;: <;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;< <;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;<;< H L B Canonical plane (ζ = ξ + iη) (1 α)m log(ζ ξ h ) π (α/)m log(ζ ξ l ) π
0 < θ < π Acoustic/Vorticity Fields Synchronisation 1 Principle replacements interactions 0 < θ < π Measured data U = 18. m/s L/H = 1.5 f 0 = 167 Hz Model Acoustic power P -1.5-1 -0.5 0 0.5 1 θ max P(θ) 1.5 π 0 π Phase shift θ 3π π
interactions f 0 = 1174 Hz Acoustic/Vorticity Fields Synchronisation.5 Result 3 3.5 4 0 π π 3π π L/H =.5 U = 18. m/s 0 < θ < π Measured data π U = 18. m/s 1 < L/H < 4 π 950 < f 0 < 1400 Hz Phase maximizing P, θmax L/H =.5 Model f 0 = 1174 Hz U = 18. m/s v05 3π π 1 < L/H < 4 P(θ) 950 < f 0 < 1400 Hz 0 θu max = 18. m/s 1 1.5.5 3 3.5 4 Normalized jet exit / obstacle distance L/H
Validation interactions replacements 0.1 1500 1 0. Input data 1400 1 < L/H < 5, U = 18. m/s 0.3 1300 500 Hz < f 0 < 1500 Hz 0.4 100 0.5 1100 1000 0.6 900 Model 0.7 800 0.8 700 600 0 0.9 500 11.5.5 3 3.5 4 4.5 5 P(L/H, f 0 ) Normalized jet exit / obstacle distance L/H Frequency, Hz
Summary interactions Development of a model for the flow-acoustic interactions involved in the coupling of a self-sustained oscillator with the flow-supply duct s resonance Frequency predictions Outlook Better understanding of the optimal lock-in conditions Emitted level prediction