Acoustic Resonance of Trapped Modes of Ducted Shallow Cavities

Transcription

1 Acoustic Resonance of Trapped Modes of Ducted Shallow Cavities K. Aly & S. Ziada McMaster University Hamilton, Canada 1

2 Contents Motivation: Industrial problems Investigation of excitation mechanism Trapped acoustic modes Nature of excited modes Effect of mean flow Counter-measures Summary 2

3 Motivation Acoustic Resonance of Isolation Valves in a BWR Power Station 3

4 Schematic of BWR Plant Source: US NRC 4

5 M S L s Main Steam Lines (MSLs) of a boiling water reactor Source: US NRC 5

6 Schematic of ESBWR Source: GE Hitachi 6

7 Typical isolation valve used in BWR plants 7

8 8

9 Acoustic FE model of isolation valve 9

10 Typical examples of trapped acoustic modes 10

11 Small Scale Model Tests 11

12 Typical PSD of pressure pulsation in the model valve 12

13 Other Industrial Applications of Axisymmetric Shallow Cavities Turbo-compressors Control Valves Jet Engines Rocket Engines 13

14 Investigation of Excitation Mechanism d L D 14

15 Steam Piping Systems in Power Plants Lafon et al. (JFS 2003) 15

16 Flow-Excited Acoustic Resonance Mechanism Interaction of Flow instability & Acoustic mode Unsteady vorticity field ( ) Acoustic particle velocity field ( u ) 16

17 Flow Instabilities Free shear layers Wakes Jets 17

18 Resonance mode of a closed side-branch 18

19 Mechanisms of Cavity Oscillations The Fluid-Resonant Mechanism Boundary layer Acoustic velocity, u u Standing acoustic wave P Howe s analogy of the aerodynamic sound ( t ) u ( v ) d 19

20 Shear Layer Instability Modes Resonant side-branch Two baffles in a pipeline m = 1 a1 b1 m = 2 a2 b2 m = 3 a3 b3 20

21 Diametral Modes of Axisymmetric Ducted Shallow Cavities (Trapped modes) d L D 21

22 Trapped diametral (or cross) modes First mode (m = 1) Second mode (m = 2) 22

23 Contour plots of the radial particle velocity (L/d = 1) Main pipe Cavity floor First diametral mode (n=1) Second diametral mode (n=2) Third diametral mode (n=3) 23

24 Axisymmetric Shallow Cavities Test Arrangement L A P res sure T rans ducers D=150mm d A A-A 24

25 General Acoustic Response Typical Pressure Spectrum Flow velocity = 70 m/s, L/d = 1 25

26 General acoustic Response for L/d = 1 26

27 SPL Contours 27

28 SPL Contours Acoustic modes (n)

29 SPL Contours Shear layer modes (m) 29

30 SPL Contours

31 n=4 m=3 m=2 Acoustic Response n=1 n=2 n=3 m=1 m = shear layer modes n = acoustic modes Strouhal number (slope) Strouhal number S S = f L / V 31

32 Normalized pressure (P/ ½ V 2 ) Acoustic resonances occur over well defined ranges of Strouhal number First shear layer mode Second shear layer mode Strouhal number (f n L / V) 32

33 Nature of the Excited Acoustic Modes Stationary mode Spinning mode 33

34 Amplitude and Phase Measurements Expectations verses Reality 34

35 Visual representation of measured sound Field in the cavity 35

36 Two Orthogonal Modes Model The velocity potential for the 2D-first mode case is: 2 c ~ A sin( t v1 1 ) 2 c ~ B sin( t v 2 2 ) ~ J r (1.841 ) sin( ) 1 R 36

37 Results of two orthogonal modes model Summary Stationary Spinning Partially spinning A/B = 0 D = 0 A/B = 1 D = 90 A/B = 0.5 D = 90 37

38 Validation of the Two Orthogonal Modes Model Tests with one splitter plate 38

39 Validation of the Two Orthogonal Modes Model Tests with one splitter plate 39

40 Validation of the two Orthogonal Modes Model Pressure spectra with a splitter plate 40

41 Effect of Mean Flow on Trapped Modes - Effect on frequency - Effect on mode shape Why? The excitation mechanism depends on the mode shape of the acoustic field. P ( t ) u ( v ) d 41

42 Simulation of the Acoustic Modes with Flow Two-step approach: First, mean flow from RANS equations Then, acoustic field from lineariezed Acoustic Perturbation Equations (APE) developed by Ewert & Schröder (2003) 42

43 Effect of Mean Flow on Acoustic Pressure of First Mode M =0 M =0.2 43

44 Effect of mean flow on radial component of acoustic particle velocity 44

45 Counter-Measures 45

46 Pulsation amplitude (Pa) Effect of rounded upstream edge Shap edges Sharp edge Round edge Round edges Flow velocity (m/s) 46

47 Pulsation amplitude (Pa) Effect of chamfer at upstream edge 8000 Sharp edges 6000 Chamfer Flow velocity (m/s) 47

48 Curved spoiler Delta spoiler 48

49 Pulsation amplitude (Pa) Effect of spoilers at upstream edge Sharp edges Delta Spoiler Curved Spoiler Flow velocity (m/s) 49

50 Effect of spoilers on pressure drop 50

51 Summary Ducted cavities introduce trapped x-modes Strong acoustic resonances observed in industry are caused by cavity trapped x-modes Resonances occur over well defined Strouhal number ranges (S=f L / V) Observed modes are neither stationary nor spinning Flow affects the resonance mode shapes 51

52 Summary Phenomenon is difficult to simulate because High Mach number High frequency (Short wavelength) Distributed aeroacoustic sources (i.e. not compact sources) Avoid resonance by selecting appropriate Strouhal number Effective spoiler size is proportional to cavity size 52

53 Thank you 53

54 54