Chapter 3

57

Chapter 3

Steady and transient analyses at

Mach 0.76, buffet investigation

3.1 Results at Mach equal to 0.76

The series of conducted analyses are specified in Table 2.5. Figure 3.1 shows contour

of static pressure in each condition starting from right to left with increasing incidence

angle:

Figure3.1

Contours of static pressure at Mach = 0.76 (from left to right at 2.975, 3, 3.01, 3.025, 3.03, 3.05, 3.2 degrees).

58

Figure 3.2

Normalised residual in steady analysis at Mach = 0.76 and α = 2.975°.

59

Figure 3.4

Normalised residual in steady analysis at Mach = 0.76 and α = 3.0°.

60

Figure 3.6

Normalised residual in steady analysis at Mach = 0.76 and α = 3.01°.

61

Figure 3.8

Normalised residual in steady analysis at Mach = 0.76 and α = 3.025°.

62

Figure 3.10

Normalised residual in steady analysis at Mach = 0.76 and α = 3.03°.

63

Figure 3.12

Normalised residual in steady analysis at Mach = 0.76 and α = 3.05°.

64

Figure 3.14

Normalised residual in steady analysis at Mach = 0.76 and α = 3.2°.

65

As can be noted from previous figures normalized residual are consistently higher in

the neighbourhood of 𝛼 = 3.025° giving a first indication of buffet onset point.

In following figures are shown charts obtained from transient analyses; for each

incidence condition are shown lift coefficient, drag coefficient, moment coefficient versus

time and power spectral density charts of previous parameters.

3.1.1 Simulation at

𝛂 = 2.975°

First series of charts refers to an incidence angle of 2.975 degrees.

Figure 3.16

Lift, drag and moment coefficients charts at Mach = 0.76 and α = 2.975°.

0,513 0,51302 0,51304 0,51306 0,51308 0 0,25 0,5 0,75 1 1,25 1,5 1,75 2 2,25 2,5 cl , l ift co e ff ic ie n t time [s]

Cl time history

0,034615 0,03462 0,034625 0,03463 0 0,25 0,5 0,75 1 1,25 1,5 1,75 2 2,25 2,5 cd , d rag c o e ff ic ie n t time [s]

Cd time history

-0,00559000 -0,00558000 -0,00557000 0 0,25 0,5 0,75 1 1,25 1,5 1,75 2 2,25 2,5 cm , m o m e n t co e ff ic ie n t time [s]

Cm time history

66

Figure 3.17

Lift, drag and moment coefficients PSD charts at Mach = 0.76 and α = 2.975°.

1,00E-06 1,00E-05 1,00E-04 1,00E-03 1,00E-02 1,00E-01 1,00E+00 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000

P

SD o

f

cl

[

1/Hz]

frequency [Hz]

PSD of Cl

1,00E-19 1,00E-18 1,00E-17 1,00E-16 1,00E-15 1,00E-14 1,00E-13 1,00E-12 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000

P

SD o

f

cd

[

1/Hz]

frequency [Hz]

PSD of Cd

1,00E-20 1,00E-19 1,00E-18 1,00E-17 1,00E-16 1,00E-15 1,00E-14 1,00E-13 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000

P

SD o

f

cm

[

1/Hz]

frequency [Hz]

PSD of Cm

67

PSD of lift coefficient at Mach equal to 0.76 and incidence angle of 2.975 degrees is

zero for all frequencies because there are not oscillations in lift coefficient value while for

the other parameters although PSDs are different from zero, their values are so small that

can be neglected.

3.1.2 Simulation at

𝛂 = 3°

Next charts refer to an incidence angle of 3 degrees; furthermore, in this condition are

reported charts of upper and lower surfaces coefficients of the airfoil to separate

contributes to unsteadiness and identify frequencies introduced individually by that

surfaces.

Figure 3.18

Lift, drag and moment coefficients charts at Mach = 0.76 and α = 3.0°.

0,5154394 0,5154395 0,5154396 0,5154397 0,3 0,3025 0,305 0,3075 0,31 0,3125 0,315 0,3175 0,32 0,3225 0,325 0,3275 0,33 cl , l ift co e ff ic ie n t time [s]

Cl time history

0,03498794 0,03498795 0,03498796 0,03498797 0,3 0,3025 0,305 0,3075 0,31 0,3125 0,315 0,3175 0,32 0,3225 0,325 0,3275 0,33 cd , d rag c oe ff icient time [s]

Cd time history

-0,00560075 -0,00560065 -0,00560055 0,3 0,3025 0,305 0,3075 0,31 0,3125 0,315 0,3175 0,32 0,3225 0,325 0,3275 0,33 cm , m om en t co e ff ic ie n t time [s]

Cm time history

68

Figure 3.19

Lift and drag coefficients PSD charts at Mach = 0.76 and α = 3.0°.

1,00E-17 1,00E-16 1,00E-15 1,00E-14 1,00E-13 1,00E-12 1,00E-11 1,00E-10 1,00E-09 1,00E-08 1,00E-07 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 P SD of c l [1/H z] frequency [Hz]

PSD of cl

1,00E-18 1,00E-17 1,00E-16 1,00E-15 1,00E-14 1,00E-13 1,00E-12 1,00E-11 1,00E-10 1,00E-09 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 P SD of c d [1/H z] frequency [Hz]

PSD of cd

69

Figure 3.20

Moment coefficient PSD chart at Mach = 0.76 and α = 3.0°.

Figure 3.21

Lift coefficient of upper and lower airfoil surfaces charts at Mach = 0.76 and α = 3.0°.

1,00E-18 1,00E-17 1,00E-16 1,00E-15 1,00E-14 1,00E-13 1,00E-12 1,00E-11 1,00E-10 1,00E-09 1,00E-08 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 PS D o f c m [ 1/Hz] frequency [Hz]

PSD of cm

0,6244243 0,6244244 0,6244245 0,6244246 0,3 0,305 0,31 0,315 0,32 0,325 0,33 0,335 0,34 0,345 0,35 0,355 cl _u p ,u p p e r su rface li ft co e ff ic ie n t time [s]

Cl upper surface time history

-0,10898495 -0,10898494 -0,10898493 -0,10898492 0,3 0,305 0,31 0,315 0,32 0,325 0,33 0,335 0,34 0,345 0,35 0,355 cl_ low ,low er sur face lift co e ff ic ie n t time [s]

70

Figure 3.22

Lift upper and lower coefficient PSD charts at Mach = 0.76 and α = 3.0°.

1,00E-17 1,00E-16 1,00E-15 1,00E-14 1,00E-13 1,00E-12 1,00E-11 1,00E-10 1,00E-09 1,00E-08 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 P SD of c l_ u p [1/H z] frequency [Hz]

PSD of Cl upper surface

1,00E-18 1,00E-17 1,00E-16 1,00E-15 1,00E-14 1,00E-13 1,00E-12 1,00E-11 1,00E-10 1,00E-09 1,00E-08 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 P SD of c l_ low [1/H z] frequency [Hz]

PSD of Cl lower surface

71

As can be seen from previous charts an oscillation of the parameters starts although of

very little amplitude, moreover, velocities of amplitude oscillation of lift coefficient and

PSDs of upper and lower surfaces locate most of pressure disturbances on the upper one as

is shown in Figures 3.22 and 3.23.

Figure 3.23

Lift coefficient Limit Cycle Oscillation of upper and

lower surfaces at Mach = 0.76 and α = 3.0°.

3.1.3 Simulation at

𝛂 = 3.01°

Next figures show data obtained at incidence angle of 3.01 degrees. As can be noted

no important oscillations were found; PSDs charts confirm this behaviour.

0,624422 0,624423 0,624424 0,624425 0,624426 -0,0015 -0,0005 0,0005 0,0015 cl _u p Δcl_up/Δt

Δcl_up/Δt

-0,10898700 -0,10898600 -0,10898500 -0,10898400 -0,10898300 -0,0015 -0,0005 0,0005 0,0015 cl _l o w Δcl_low/Δt

Δcl_low/Δt

72

Figure 3.24

Lift, drag and moment coefficients charts at Mach = 0.76 and α = 3.01°.

0,51639 0,516395 0,5164 0,516405 0,51641 0,516415 0,51642 0,516425 0,51643 0 0,25 0,5 0,75 1 1,25 1,5 1,75

cl

, l

if

t

co

ef

fi

ci

e

n

t

time [s]

Cl time history

0,03513 0,035132 0,035134 0,035136 0,035138 0,03514 0,035142 0,035144 0 0,25 0,5 0,75 1 1,25 1,5 1,75

cd

, d

ra

g

co

ef

fi

ci

e

n

t

time [s]

Cd time history

-0,005624 -0,005622 -0,00562 -0,005618 -0,005616 -0,005614 -0,005612 -0,00561 -0,005608 0 0,25 0,5 0,75 1 1,25 1,5 1,75

cm,

m

ome

n

t

co

ef

fi

ci

e

n

t

time [s]

Cm time history

73

Figure 3.25

Lift, drag and moment coefficients PSD charts at Mach = 0.76 and α = 3.01°.

1,E-17 1,E-16 1,E-15 1,E-14 1,E-13 1,E-12 1,E-11 1,E-10 1,E-09 1,E-08 0 50 100 150 200 250 300 350 400 450 500

PS

D

of

cl

[

1/Hz

]

frequency [Hz]

PSD of Cl

1,E-16 1,E-15 1,E-14 1,E-13 1,E-12 1,E-11 1,E-10 0 50 100 150 200 250 300 350 400 450 500

PS

D

of

cd

[

1/Hz

]

frequency [Hz]

PSD of Cd

1,E-16 1,E-15 1,E-14 1,E-13 1,E-12 1,E-11 1,E-10 0 50 100 150 200 250 300 350 400 450 500

PS

D

of

cm

[1/Hz

]

frequency [Hz]

PSD of Cm

74

In next Figure 3.26 are shown lift, drag and moment coefficient, at incidence angle of

3.025 degrees, oscillating with a higher order of amplitude than other simulation analyses

at the same Mach number.

Figure 3.26

Lift, drag and moment coefficients charts at Mach = 0.76 and α = 3.025°.

0,518084 0,518085 0,518086 0,518087 0,518088 4,75 4,8 4,85 4,9 4,95 5

cl

, l

if

t

co

ef

fi

ci

e

n

t

time [s]

Cl time history

0,0353704 0,0353706 0,0353708 0,035371 0,0353712 4,75 4,8 4,85 4,9 4,95 5

cd

, d

ra

g

co

ef

fi

ci

e

n

t

time [s]

Cd time history

-0,005677 -0,005677 -0,005676 -0,005676 -0,005675 -0,005675 4,75 4,8 4,85 4,9 4,95 5

cm

, m

om

en

t

coe

ff

ici

en

t

time [s]

Cm time history

75

Figure 3.27

Lift and drag coefficients PSD charts at Mach = 0.76 and α = 3.025°.

181,73 363,46 545,19 727,89 909,62 1,E-13 1,E-12 1,E-11 1,E-10 1,E-09 1,E-08 1,E-07 1,E-06 1,E-05 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000

PS

D

of

cl

[

1/Hz

]

frequency [Hz]

PSD of Cl

1,E-14 1,E-13 1,E-12 1,E-11 1,E-10 1,E-09 1,E-08 1,E-07 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000

PS

D

of

cd

[

1/Hz

]

frequency [Hz]

PSD of Cd

76

Figure 3.28

Moment coefficient PSD charts at Mach = 0.76 and α = 3.025°.

As expected from inspection of Figure 3.26, from Figures 2.27 and 3.28 can be seen

well defined frequencies, moreover the oscillation rate chart of lift and moment coefficient

indicate a quasi-perfect repetition of the disturbance as shown in Figure 3.29.

Figure 3.29

Lift and moment coefficients Limit Cycle Oscillation at Mach = 0.76 and α = 3.025°.

1,E-14 1,E-13 1,E-12 1,E-11 1,E-10 1,E-09 1,E-08 1,E-07 1,E-06 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000

PS

D

of

cm

[1/Hz

]

frequency [Hz]

PSD of Cm

0,518084 0,5180845 0,518085 0,5180855 0,518086 0,5180865 0,518087 0,5180875 0,518088 -0,004 -0,002 0 0,002 0,004

cl

, l

if

t

coe

ff

ici

en

t

Δcl/Δt [1/s]

Δcl/Δt

-0,005677 -0,005677 -0,005676 -0,005676 -0,005675 -0,005675 -0,003 -0,002 -0,001 0 0,001 0,002 0,003

cm,

m

ome

n

t

co

ef

fi

ci

e

n

t

Δcm/Δt [1/s]

ΔCm/Δt

77

These considerations and the RMS chart led to take the critical incidence value for

buffet onset, at a Mach number of 0.76, equal to 3.025 degrees with a characteristic

frequency of 181.73 Hz accompanied by super harmonics. A further investigation on the

locus of origin of unsteadiness was conducted using the image of the RMSE (root mean

square error) of static pressure shown in Figure 3.30; this last in association with the

separated analysis of upper and lower surfaces lift coefficient of the airfoil demonstrate

that most of the phenomenon, in this condition, was concentrated on the upper surface.

Figure 3.31 indeed shows that lift coefficient oscillation amplitude on lower surface is one

order of magnitude lower than that on the upper one.

Figure 3.30

RMSE of static pressure at Mach = 0.76 and α = 3.025°.

Figure 3.31

Upper and lower surface lift coefficient at Mach = 0.76 and α = 3.025°.

0,626349 0,626351 0,626353 4,75 4,8 4,85 4,9 4,95 5 cl _u p , l ift co e ff ic ie n t u p p e r su rface

time [s]

Cl upper surface time history

-0,1082653 -0,1082651 4,75 4,8 4,85 4,9 4,95 5 cl _l o w, li ft co e ff ic ie n t lo we r su rface

time [s]

78

Figure 3.32

Lift coefficient of upper and lower surfaces PSD charts at Mach = 0.76 and α = 3.025°.

1,00E-14 1,00E-13 1,00E-12 1,00E-11 1,00E-10 1,00E-09 1,00E-08 1,00E-07 1,00E-06 1,00E-05 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000

P

SD o

f

cl

_up

[

1/Hz]

frequency [Hz]

PSD of Cl upper surface

1,00E-14 1,00E-13 1,00E-12 1,00E-11 1,00E-10 1,00E-09 1,00E-08 1,00E-07 1,00E-06 1,00E-05 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000

PS

D

of

cl

_l

ow

[

1/Hz

]

frequency [Hz]

PSD of Cl lower surface

79

Figure 3.33

Lift coefficient Limit Cycle Oscillation of upper and lower surfaces at Mach = 0.76 and α = 3.025°.

3.1.5 Simulation at

𝛂 = 3.03°

Next figures refer to analyses conducted for an incidence angle of 3.03 degrees.

Figure 3.34

Lift, drag and moment coefficients charts at Mach = 0.76 and α = 3.03°.

0,626349 0,6263495 0,62635 0,6263505 0,626351 0,6263515 0,626352 0,6263525 0,626353 -0,006 -0,004 -0,002 0 0,002 0,004

cl

_up

, l

if

t

coe

ff

ici

en

t

up

per

su

rf

ace

Δcl_up/Δt [1/s]

Δ(cl_up)/Δt

-0,108267 -0,108267 -0,108266 -0,108266 -0,108265 -0,108265 -0,108264 -0,108264 -0,108263 -0,004 0,001

cl

_l

ow

, l

if

t

co

ef

fi

ci

e

n

t

low

e

r

su

rf

ace

Δcl_low/Δt [1/s]

Δ(cl_low)/Δt

0,51853 0,51855 0,51857 0,51859 0 0,25 0,5 0,75 1 1,25 1,5 1,75 2 2,25 2,5 2,75 3

cl

, l

if

t

co

ef

fi

ci

e

n

t

time [s]

Cl time history

0,035441 0,035446 0,035451 0,035456 0 0,25 0,5 0,75 1 1,25 1,5 1,75 2 2,25 2,5 2,75 3

cd

, d

ra

g

co

ef

fi

ci

e

n

t

time [s]

Cd time history

-0,005700 -0,005690 -0,005680 -0,005670 0 0,25 0,5 0,75 1 1,25 1,5 1,75 2 2,25 2,5 2,75 3

cm,

m

ome

n

t

co

ef

fi

ci

e

n

t

time [s]

Cm time history

80

are null, confirming thus previous consideration.

3.1.6 Simulation at

𝛂 = 3.05° and 𝛂 = 3.2°

Last simulations of this series at Mach equal to 0.76, that having incidence angle of

3.05 and 3.2 degrees show a similar behaviour with respect to the previous one. They did

not show indeed unsteady solutions. For purpose of completeness, the following figures

show the time trend of lift, drag and moment coefficient without oscillations, PSDs were

not reported because were all null.

Figure 3.35

Lift, drag and moment coefficients charts at Mach = 0.76 and α = 3.05°.

0,52032 0,52033 0,52034 0,52035 0,52036 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2 cl , l ift co e ff ic ie n t time [s]

Cl time history

0,03573 0,035735 0,03574 0,035745 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2 cd , d rag c o e ff ic ie n t time [s]

Cd time history

-0,005690 -0,005685 -0,005680 -0,005675 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2 cm , m o m e n t co e ff ic ie n t time [s]

Cm time history

81

Figure 3.36

Lift, drag and moment coefficients charts at Mach = 0.76 and α = 3.2°.

3.2 Results of simulation series at Mach = 0.76

An overview of the overall results shows that, at Mach number equal to 0.76,

NACA0012 airfoil presents a quite sudden onset of buffet unsteadiness followed by a

steady zone. Root mean square of power spectral density of lift, drag and moment

coefficient, change in time rate of lift coefficient and maximum modulus of lift coefficient

variance indicate a critical incidence of 3.025 degrees in accordance with results given by

NASA in Ref. [5] and by Crouch, Garbaruk, Strelets in Ref. [7] and [8]. In Table 3.1 are

reported root mean square of power spectral density values and in Table 3.2 are shown

results of maximum oscillation and variance of time rate of lift coefficient found in each

simulation.

0,5327 0,53275 0,5328 0,53285 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2 2,1 cl , l ift co e ff ic ie n t time [s]

Cl time history

0,0379 0,03791 0,03792 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2 2,1 cd , d rag c o e ff ic ie n t time [s]

Cd time history

-0,005610 -0,005600 -0,005590 -0,005580 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2 2,1 cm , m o m e n t co e ff ic ie n t time [s]

Cm time history

82

RMS values of PSD of

α

Cl

Cd

Cm

2,975

0

1,784E-06 4,3805E-07

3

0,0001175 1,015E-05 7,1147E-05

3,01

0

0

8,7838E-07

3,025 0,0021668 0,0003774

0,001412

3,03

0

0

1,0539E-06

3,05

0

0

6,1071E-07

3,2

0

0

5,5161E-07

Table 3.1

Results of RMS of PSD values obtained in each simulation at Mach = 0.76.

α

Δ(Δcl/Δt) Δcl

2,975 0

0

3

0,0008345 5,96E-07

3,01

0

0

3,025 0,0066757 2,98E-06

3,03

0

0

3,05

0

0

3,2

0

0

Table 3.2

Results of LCO amplitude and maximum

modulus of oscillation of lift coefficient at Mach = 0.76.

83

Figure 3.37

LCO amplitudes and maximum oscillation of lift coefficient as a function of incidence at Mach = 0.76.

0 0,001 0,002 0,003 0,004 0,005 0,006 0,007 0,008 2,95 2,975 3 3,025 3,05 3,075 3,1 3,125 3,15 3,175 3,2 3,225

Δ

(Δ

cl

/Δ

t)

α, incidence [deg]

Δ(Δcl/Δt)

0 0,0000005 0,000001 0,0000015 0,000002 0,0000025 0,000003 0,0000035 2,95 2,975 3 3,025 3,05 3,075 3,1 3,125 3,15 3,175 3,2 3,225

Δ

cl

α, incidence [deg]

Δcl

84

Figure 3.38

Comparison between amplitudes of LCO of lift coefficient at Mach = 0.76.

0,510000 0,515000 0,520000 0,525000 0,530000 0,535000 -0,004 -0,003 -0,002 -0,001 0 0,001 0,002 0,003 0,004

cl

Δcl/Δt

Cl oscillation rate amplitude

2,975 deg

3 deg

3,01 deg

3,025 deg

3,03 deg

3,05 deg

3.2 deg

85

Figure 3.39

Comparison between amplitude and shape of Limit Cycle Oscillation of lift coefficient at Mach = 0.76.

0,513023 0,513025 0,513027 -0,004 0,001

cl

Δcl/Δt

Δcl/Δt at

α=2,975° [deg]

0,51543700 0,51543900 0,51544100 -0,004 0,001

cl

Δcl/Δt

Δcl/Δt at

α=3,000° [deg]

0,518556 0,518558 0,51856 -0,004 0,001

cl

Δcl/Δt

Δcl/Δt at

α=3,030° [deg]

0,518084 0,518086 0,518088 -0,004 0,001 0,006

cl

Δcl/Δt

Δcl/Δt at

α=3,025° [deg]

0,516393 0,516395 0,516397 -0,004 0,001

cl

Δcl/Δt

Δcl/Δt at

α=3,010° [deg]

0,520341 0,520343 0,520345 -0,004 0,001

cl

Δcl/Δt

Δcl/Δt at

α=3,050° [deg]

0,532787 0,532789 0,532791 -0,004 0,001

cl

Δcl/Δt

Δcl/Δt at

α=3,200° [deg]

86

Figure 3.40

Root Mean Squares of Power Spectral Density of lift, drag and moment coefficients at

Mach = 0.76 as a function of incidence.

-1,0E-05 2,4E-04 4,9E-04 7,4E-04 9,9E-04 1,2E-03 1,5E-03 1,7E-03 2,0E-03 2,2E-03 2,5E-03 2,95 2,975 3 3,025 3,05 3,075 3,1 3,125 3,15 3,175 3,2 3,225

R

M

S(

PS

D(cl

))

α, incidence [deg]

RMS of PSD of Cl at Mach=0.76

0,00E+00 5,00E-05 1,00E-04 1,50E-04 2,00E-04 2,50E-04 3,00E-04 3,50E-04 4,00E-04 2,95 2,975 3 3,025 3,05 3,075 3,1 3,125 3,15 3,175 3,2 3,225

R

M

S(

PS

D(cd

))

α, incidence [deg]

RMS of PSD of Cd at Mach=0.76

-1,00E-05 1,90E-04 3,90E-04 5,90E-04 7,90E-04 9,90E-04 1,19E-03 1,39E-03 1,59E-03 2,95 2,975 3 3,025 3,05 3,075 3,1 3,125 3,15 3,175 3,2 3,225

R

M

S(

PS

D(cm

))

α, incidence [deg]

RMS of PSD of Cm at Mach=0.76

87

As can be noted from previous figures there is a sudden increase of RMS values

followed by a drop and a next steep rise showing a clear peak that indicates buffet onset.

Last step was the study in MATLAB

®

_{of colours-map. Results of this last analysis,}

conducted in buffet onset condition, are reported in following figures.

Figure 3.41

Colours-map of upper (on top) and lower airfoil surfaces static pressure fluctuations at Mach = 0.76 and 𝛼 =

88