Functional Beamforming for Aeroacoustic Source Distributions Robert P. Dougherty OptiNav, Inc.

Presentation for the 20th Legacy AIAA/CEAS Aeroacoustics Conference, June 2014. See the AIAA web site for the paper, AIAA-2014-3066.

Outline

•  Definition and Theory

•  Jet Example

•  Propeller Example

•  Edge Source Example

•  Wind Tunnel Speaker Example

•  Hot, high-speed jet

•  Model Rocket

•  Misc.

•  Recommendations

•  Conclusions and recommendations

2

Definition and Theory

3

CSM model

Remove the noise: adjust the diagonal elements to minimize trace while keeping CSM nonnegative definite. Different paper…

4

Beamforming 5

Functional Beamforming 6

Power Function of a Matrix 7

Sidelobe Performance

Source at k, steer to l

8

FDBF for multiple sources 9

The Löwner-Heinz inequality implies

This means

10

Functional Beamforming for multiple sources

On the other hand…

!! = !!!! !, ! = 1,… ,!!!!! !!!

!!!!!!= 1

!! Weighted power means inequality:

is a decreasing function of !

Eigenvalue form:

11

So…

!! ! is a decreasing function of ν  and

The exact answer is surrounded!

and

12

Effect of errors in the steering vectors

Consider an actual steering vector and a model steering vector

Errors in θ limit ν.

13

Jet Example

14

NASA Jet Noise Array/Shop Air 15

Jet Example: Simulated point source

16

NASA Jet Noise Array/Shop Air 17

!250%

!200%

!150%

!100%

!50%

0%

50%

!2.5% !2% !1.5% !1% !0.5% 0% 0.5% 1% 1.5% 2% 2.5%

Beam

form

ing+level,+dB

+

x+(transverse,+horizontal),+inches+

1%

2%

3%

4%

5%

6%

7%

8%

9%

10%

11%

12%

13%

14%

15%

18

Jet Example: Two simulated point sources 20 dB level difference

19

!250%

!200%

!150%

!100%

!50%

0%

50%

!2.5% !2% !1.5% !1% !0.5% 0% 0.5% 1% 1.5% 2% 2.5%

Beam

form

ing+level,+dB

+

x+(transverse,+horizontal),+inches+

1%

2%

3%

4%

5%

6%

7%

8%

9%

10%

11%

12%

13%

14%

15%

21

Jet Example: Simulated line source

22

50#

55#

60#

65#

70#

75#

80#

85#

90#

(2.5# (2# (1.5# (1# (0.5# 0# 0.5# 1# 1.5# 2# 2.5#

Beam

form

ing+level,+dB

+

x+(transverse,+horizontal),+inches+

1#

2#

3#

4#

5#

6#

7#

8#

9#

10#

11#

12#

13#

14#

15#

24

Jet Example: Shop air jet

25

ν = 1

ν = 4

ν = 16

ν = 2

ν = 8

ν = 32

16 kHz 15 dB scale

26

50#

55#

60#

65#

70#

75#

80#

85#

90#

(6# (4# (2# 0# 2# 4# 6#

Beam

form

ing+level,+dB

+

x+(transverse,+horizontal),+cm+

1#

2#

3#

4#

5#

6#

7#

8#

9#

10#

11#

12#

13#

14#

15#

ν 16 kHz, ν = 1-100

Propeller Example

28

29

FDBF 30

CLEAN-SC 31

Functional Beamforming 32

Robust Adaptive Beamforming 33

Source Integration

20#

25#

30#

35#

40#

45#

50#

55#

60#

6000# 8000# 10000# 12000# 14000#

Narrowvand

)array)average)SPL,)d

B)re)20)

micro)Pa,)47H

z)BW)

Frequency,)Hz)

Motor#Prop#

34

Edge Source Example

35

10 kHz 37

16 kHz 38

30 kHz 39

Wind Tunnel Speaker Example

40

Speaker enclosure fairing in center of wind tunnel test section

Level-sensing wall array: 24 microphones, 32 inch diameter, Kevlar cover

Speaker test in 40x80/NFAC

Data from Clifton Horne, Nathan Burnside, NASA Ames Experimental Aerophysics Branch

41

100 kt, Mach 0.15 32 W

Functional BF, ν = 32 FDBF

42

100 kt, Mach 0.15 3.6 W

Functional BF, ν = 32 FDBF

43

100 kt, Mach 0.15 3.6 W

Functional BF, ν = 64 CLEAN-SC

44

100 kt, Mach 0.15 0.32 W

Functional BF, ν = 32 FDBF

45

100 kt, Mach 0.15 0.32 W

Functional BF, ν = 64 CLEAN-SC

46

10#

20#

30#

40#

50#

60#

70#

1000# 10000#

SPL,%dB%Re

%20%micro%Pa%at%array,%1/12%OB%

Frequency%(Hz),%1/12%OB%

FDBF#32#W#

FDBF#3.6#W#

FDBF#0.32#W#

10#

20#

30#

40#

50#

60#

70#

1000# 10000#

SPL,%dB%Re

%20%micro%Pa%at%array,%1/12%OB%

Frequency%(Hz),%1/12%OB%

FBF#32#W#

FBF#3.6#W#

FBF#0.32#W#

FDBF Functional BF, ν = 32 Mic 1 in array Mic 1 in array

32 W 32 W 3.6 W 3.6 W

0.32 W

0.32 W

100 kt, Mach 0.15 47

Heated, supersonic jet at NASA-Glenn

48

49

50

FDBF Functional Beamforming

500 Hz

1 kHz

2 kHz

SP 44504 NPR = 3.5 NRT = 2.95

50

51

FDBF Functional Beamforming

5 kHz

8 kHz

10 kHz

SP 44504 NPR = 3.5 NRT = 2.95

51

Model Rocket Motor

52

53

Rocket Test

Remote control

Reflecting surface

53

FDBF 54

Functional Beamforming 55

56

Determine Surface Reflection Coefficient by Functional Beamforming Integration

Integral1 (f)

Integral2 (f)

56

Determine Surface Reflection Coefficient by Functional Beamforming Integration

50#

55#

60#

65#

70#

75#

80#

100# 1000# 10000# 100000#

Integrated

)source)strength,)d

B)

Frequency,)Hz)

Integral_1#

Integral_2#

57

Misc.

58

59

Mach 0.15 jet. 60 dB scale

FB

FDBF

60

Spatula at 0° AOA. 18.5 kHz, 20 dB range

FB

FDBF

61

747-8 model, 35.8 kHz, 50 dB range

Airbrush pump FDBF 10 dB

FDBF 60 dB

FB-40 60 dB

63

Airbrush pump/putty knife edge FDBF 10 dB

FDBF 40 dB

FB-40 40 dB

64

Recommendations

65

1-∞

Too small: still have sidelobes

Too large: some real sources go away if steering vectors not perfect

With a decent array and physical model there is lots of space

Suggest 32

What is ν ? 66

Integration probably works great for normal cases

Be sure to normalize to the trace

Research opportunity for mixed types of steering vectors

How about quantitative spectra? 67

Functional Beamforming changes everything

Best dynamic range

Same speed as FDBF

Better resolution than FDBR

CLEAN-SC competitive sometimes

Additional steps needed for best resolution and quantitative spectra

Ridge detection

Linear programming postprocessing (nonlinear issue)

Optimize steering vectors?

Applications should be amazing

Conclusions 68