Akustische Rückkopplungen in laminar überströmten Spalten und Methoden zur Abschwächung von Tollmien-Schlichting Wellen

Transcription

1 Akustische Rückkopplungen in laminar überströmten Spalten und Methoden zur Abschwächung von Tollmien-Schlichting Wellen Acoustic Feedback in Gaps and Methods to Weaken Tollmien-Schlichting Waves J. Zahn, U. Rist, Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, D-70569, Germany Doktorandenseminar, , IAG Uni Stuttgart

2 Introduction 2/18 Motivation: Reduction of fuel consumption of aircrafts Reduction of friction drag Laminar flow instead of turbulent flow on the wing surface Challenge: Surface imperfections like steps and gaps lead to early laminar-turbulent transition Here: Gap between two wing elements Picture: Geza Schrauf, ECCOMAS 2012

3 Horizontal acoustic feedback 3/18 Two dimensional simulations of compressible laminar flow Increasing the gap width: Steady flow => unsteady flow

4 Horizontal acoustic feedback 4/18 Mechanism of horizontal acoustic feedback in a gap: Acoustic emission at the downstream edge Receptivity at the upstream edge Vortex amplification in the shear layer Same axis labeling as above

5 Horizontal acoustic feedback 5/18 Mechanism of horizontal acoustic feedback in a gap: Acoustic emission at the downstream edge Receptivity at the upstream edge Vortex amplification in the shear layer Same axis labeling as above

6 Horizontal acoustic feedback 6/18 Mechanism of horizontal acoustic feedback in a gap: Acoustic emission at the downstream edge Receptivity at the upstream edge Vortex amplification in the shear layer Same axis labeling as above

7 Horizontal acoustic feedback 7/18 Mechanism of horizontal acoustic feedback in a gap: Acoustic emission at the downstream edge Receptivity at the upstream edge Vortex amplification in the shear layer Same axis labeling as above

8 Horizontal acoustic feedback 8/18 Mechanism of horizontal acoustic feedback in a gap: Acoustic emission at the downstream edge Receptivity at the upstream edge Vortex amplification in the shear layer Same axis labeling as above

9 Horizontal acoustic feedback 9/18 Mechanism of horizontal acoustic feedback in a gap: Acoustic emission at the downstream edge Receptivity at the upstream edge Vortex amplification in the shear layer Same axis labeling as above

10 Horizontal acoustic feedback 10/18 Mechanism of horizontal acoustic feedback in a gap: Acoustic emission at the downstream edge Receptivity at the upstream edge Vortex amplification in the shear layer Same axis labeling as above

11 Horizontal acoustic feedback 11/18 Mechanism of horizontal acoustic feedback in a gap: Acoustic emission at the downstream edge Receptivity at the upstream edge Vortex amplification in the shear layer Same axis labeling as above

12 Horizontal acoustic feedback 12/18 Comparison with literature Equation for self-excited frequency f (J. E. Rossiter, 1966) Free-stream velocity U, gap width w, mode m, phase shift γ, normalized vortex velocity K, Mach number M Only 7% deviation between equation and simulation Minimum gap width wmin for self-excited acoustic feedback (V. Sarohia, 1977) Boundary-layer thickness δ, Reynolds number based on δ: Reδ Only 3% deviation between criterion and simulation U (m γ) f= w (1/ K + M ) w min =300 δ Reδ

13 Horizontal acoustic feedback 13/18 New finding: Influence of gap depth d at constant gap width w No feedback at middle deep gap even at increased width High amplitudes at shallowest gap

14 Vertical acoustic feedback 14/18 Disturbance amplitude downstream of gap varies with gap depth d periodically at constant w Minimum gap width wmin varies between approximately (d=24 000) and (d=48 000), prediction of Sarohia at wmin= Vertical resonance with respect to the gap depth d One side open tube: deff/λ=1/4, 3/4, Correction for the open end: deff=d+0,42w Wave length λ=a/f, with sonic speed a Resonant gap depth d = , Good agreement with high amplitudes!

15 Three dimensional acoustic feedback 15/18 Spanwise long gaps: Three dimensional mode as of w due to a centrifugal instability in the gap w<wmin: Only weak 3D flow (w/o acoustic feedback) w>wmin: Turbulent flow downstream of the gap in case of three-dimensional mode in combination with acoustic feedback

16 Ridge at downstream gap edge 16/18 Steady base flow (small gap width, w/o acoustic feedback and 3D mode) Ridge at the downstream gap edge causes additional separation Overall influence of ridge is only small due to its tiny dimension ridge

17 Ridge at downstream gap edge 17/18 Disturbance values of Tollmien-Schlichting (TS) wave with constant frequency Amplification without ridge (d/λ 1/4), however, elimination with ridge Explanation: New TS wave from the gap with same magnitude but 180 phase shift due to additional separation in the base flow ridge

18 Ridge at downstream gap edge 18/18 Measure for amplification of TS waves: 1. n-factor, valid for one frequency, 2. Nfactor valid for all relevant frequencies of TS waves Due to changing wave length λ=a/f, elimination not possible for other frequencies at constant gap depth d= Dependency on frequency reduced with short gap (d=10 000) that is open on both sides as d/λ is near to zero

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