DOI : 10.17577/IJERTCONV7IS11016
- Open Access
- Authors : K.M. Sridhar, P.Palanisamy, M.Prasanth, B.Sajahan
- Paper ID : IJERTCONV7IS11016
- Volume & Issue : CONFCALL – 2019 (Volume 7 – Issue 11)
- Published (First Online): 20-11-2019
- ISSN (Online) : 2278-0181
- Publisher Name : IJERT
- License:
This work is licensed under a Creative Commons Attribution 4.0 International License
Flutter Prediction Based on Fluid-Structural Interactions of Wing with Winglet
K. M. Sridhar
Assistant Professor of Aero Dept
M.A.M School of Engineering
P. Palanisamy
Dept. of Aero Eng
M.A.M School of Engineering
M. Prasanth
Dept .of Aero Eng
M.A.M School of Engineering
B. Sajahan
Dept. of Aero Eng
M.A.M School of Engineering
Abstract:- Aircraft components are naturally elastic which has its own natural frequency. When the source frequency is equal to objects natural frequency, the object may be tends to vibrate and deform. This may result in flutter. Flutter is an oscillatory instability occurs in airplane wing and control surfaces. The oscillatory motion of fluttering cantilever beam has both flexural and torsional component. The aircraft wing has infinitely many degrees of freedom due to cantilever beam structure. The main focus of this article is to predict the flutter of an aircraft wing with combination of winglet for different mach number and different altitude. Modelling of fluid and structural domain are required to solve FSI phenomena. The wing model has been analysed at certain constant altitude in subsonic range using optimization CFD and FEA tools. The deformation exist in a wing with winglet model caused by dynamic aeroelastic effects. The resulting structural deformation and stress variation corresponding to the flow are fully studied and validated with the help of numerical analysis.
Keywords: Aeroelasticity, deformation, flutter, FSI, stress variation
-
The aerodynamic forces are solved by using flow field governing equations. The structural displacement are solved by using structural governing equations.
Designed Initial Flow Field and Structural Models
Designed Initial Flow Field and Structural Models
Initial Flow Field model for CFD Residual
Initial Flow Field model for CFD Residual
Solving Flow Field Governing Equations for Aerodynamic Forces
Solving Flow Field Governing Equations for Aerodynamic Forces
CFD Residuals
CFD Residuals
-
INTRODUCTION
If Converged
If Converged
Wing are the sources for lift in an aircraft. Due to the aeroelastic characteristics and stress distribution of wing, it may deform. The aircraft performance may change or decrease due to this
Initial Structural Model for Structural Residual
Initial Structural Model for Structural Residual
deformation. In this article, the flutter predicted interms of deformation and stress distribution over a wing model. There are two ways to calculate fluid structural interaction i.e., strongly coupled fluid structural interaction and partly coupled fluid structural interaction [1].
1.1 PREDICTING THE EFFECTS OF AEROELASTICITY
The aeroelastic effect occurring on a wing with winglet model due to the flow separation is considered for present analysis. The aerodynamic force predictions and their influence is done using a three-dimensional Navier- Stroke model with fully coupled iterations to identify the physical phenomena. Once the flow field solutions are converged using CFD tool, then the flexural motion of the wing caused by the influence of aerodynamic forces will be computed using FEA tool. The algorithm for partly coupled fluid structural interaction analysis is presented in figure
Solving Structural Governing Equations for Structural Displacements
Solving Structural Governing Equations for Structural Displacements
Structural Residuals
Structural Residuals
If Converged
If Converged
Post processing Result
FIGURE 1: ALGORITHM FOR PARTLY COUPLED FOR FLUID STRUCTURAL INTERACTION ANALYSIS
-
PROBLEM DESCRIPTION
-
MODEL DESCRIPTION
Rectangular wing with 60º cant angle winglet is used for aeroelastic analysis. The airfoil used was a NACA 653218. The wing model were modelled using design software. NACA six series, NACA 653218 is used to model the rectangular wing with elliptical winglet. In NACA 653218 airfoil, the position of minimum pressure is 0.5, design lift coefficient is 0.2, range of lift coefficient is 0.3, maximum thickness is 18% at 39.9% chord and maximum camber is 1.1% at 50% chord. The specification of wing and winglet are shown in table 1 and 2.
TABLE 1: SPECIFICATION OF WING
SI.
NO.
PARAMETERS OF MODEL
TYPES AND DIMENSIONS
1.
Wing type
Rectangular wing model
2.
Airfoil type
NACA 653218 airfoil
3.
Chord length
121mm
4.
Wing span length
660mm
5.
Semi-span length
330mm
FIGURE 2: NACA 653218 AIRFOIL
TABLE 2: SPECIFICATION OF WINGLET
SI. NO
.
PARAMETERS OF MODEL
TYPES AND DIMENSIONS
1.
Winglet type
Elliptical winglet
2.
Airfoil type
NACA 653218 airfoil
3.
Winglet root chord
121mm
4.
Winglet tip chord
60.5mm
5.
Angled height
55.1mm
6.
Vertical height
47.7mm
7.
Horizontal height
27.6mm
8.
Cant angle
60
Using the specification which is tabulated in table I and II, the wing with winglet model is designed using modelling software. The designed wing model is shown in figure 3.
FIGURE 3: DESIGNED RECTANGULAR WING WITH ELLIPTICAL WINGLET MODEL IN 3D VIEW
A C-Domain control volume is used for flow field analysis. The wing with winglet model including the C-Domain Control Volume is depicted in figure 4. The control volume and the wing with winglet model are subtracted with each other. The total wing with winglet model area is immersed inside the control volume and one face of the wing model is attached with the side face of the control volume.
-
GRID GENERATION
A fine tetrahedron grid is generated for both the control volume and wing model as shown in figure 5. Tetrahedron grid is preferred for 3-D solid structures. Totally 178484 nodes and 703930 elements are generated for the control volume which is used for flow field analysis as shown in figure 4.
FIGURE 4: FINE GRID VIEW OF CONTROL VOLUME WITH THE WING STRUCTURE
Totally 199675 nodes and 126597 elements are generated for wing which is used for structural analysis as shown in figure 5.
FIGURE 5: FINE GRID VIEW OF WING STRUCTURE
-
BOUNDARY CONDITION
In the control volume the face upright to the leading edge is considered as velocity inlet, the face just opposite to the velocity inlet is taken as pressure outlet and the remaining four faces of the
control volume are considered as symmetry faces. The upper and lower faces of the wing model are taken as fluid solid interface faces. The numerical
values of the boundary conditions are given as the International Standard Atmospheric (ISA) properties at 0km to 11km altitude which values are taken from reference 4. The velocity range is considered from 0.05 Mach to 0.75 Mac.
One face of the wing model attached to one face of the control volume and the symmetry face is converted into a fixed support for the structural analysis. The imported pressure load from the fluid flow solver is applied on the fluid- solid interface faces. Aluminium alloy is the material used on wing model design and its properties are shown in table 3.
TABLE 3: PROPERTIES OF MATERIAL
N
o
Variables
Properties of material
1
Material
Aluminium alloy
2
Youngs Modulus
71GPa
3
Density
2770 kg/m3
4
Bulk Modulus
69.608GPa
5
Poissons Ratio
0.33
-
-
RESULTS AND DISCUSSIONS
-
FUNDAMENTAL VIBRATION ANALYSIS
The fundamental vibrational analysis of wing model carried out using modal analysis software package. The vector contour of Mode Shape 4 is shown in figure 6.
TABLE 4: FIRST TEN VIBRATIONAL ANALYSIS DATA
SI. NO.
MODE SHAPE
FREQUENCY (Hz)
1.
1
106.84
2.
2
513.6
3.
3
651.08
4.
4
807.35
5.
5
1752.8
6.
6
2385.2
7.
7
2700.7
8.
8
3063.00
9.
9
3455.6
10.
10
4066.9
FIGURE 6: VECTOR CONTOUR OF MODE SHAPE 4
The main objective of modal analysis is to determine the dynamic characteristics of aircraft wing such as natural frequency, deformation and mode shapes. First ten vibrational analysis data are shown in table 4.
-
FLOW FIELD ANALYSIS
The flow field analysis are carried out for wing with winglet model at various mach numbers from 0.05 to 0.75 and at different altitude from 0km to 11km using Computational fluid dynamics tool.
Mach Numbe r
Maximum Static Pressure (Pa)
Altitud e
h = 0km
Altitud e
h= 1km
Altitud e
h= 2km
Altitud e
h= 3km
Altitud e
h= 4km
Altitud e
h= 5km
0.05
1131.0
3
991.61
9
877.40
786.34
3
676.68
597.55
0.10
4580.0
9
4052.6
7
3584.2
3155.8
2859.2
2484.8
0.15
10352.
30
9170.0
4
8116.2
7158.8
6349.3
5611.4
0.20
18263.
50
16188.
00
14487
12643
11196
9775.5
0.25
28542.
70
25145.
60
22275
21226
17320
15133
0.30
40454.
20
35901.
10
32087
28096
24820
21883
0.35
54589.
90
48530.
60
42925
38245
33521
29294
0.40
71616.
20
62898.
00
55683
49153
43495
37979
0.45
90245.
10
79145.
30
70611
62252
54688
47717
0.50
111435
.0
97680.
00
86310
76143
67308
58993
0.55
134176
.0
118918
.00
104160
91713
81113
71197
0.60
158012
.0
139805
.00
123350
108730
96147
84253
0.65
184838
.0
163612
.00
144400
127130
112480
98507
0.70
213681
.0
189334
.00
167110
147150
130190
113120
0.75
244942
.0
218313
.00
191430
168480
148990
129460
TABLE 5: MAXIMUM STATIC PRESSURE VS MACH NUMBERS FOR 0KM TO 5KM ALTITUDE
The maximum static pressure variation
increases while mach number increases and decreases while altitude (h) increases as shown in figure 7. The minimum static pressure variation against mach number is shown in figure 9. The static pressure variation over the wing at 0.2 and 0.6 Mach number at 4km altitude is shown in figure 8 and 10 as a vector contour.
From this vector representation, it is evident that the maximum static pressure variation occurs at wing leading edge and minimum static pressure variation occurs at wing trailing edge. The pressure occurred at winglet region is less while compare with wing region as shown in figure 10 and 11. The computed maximum static pressure value against mach number is shown in table 5 and 6. The computed minimum static pressure value against mach number is shown in table 7 and 8.
Mach Numb er
Maximum Static Pressure (Pa)
Altitud e
h = 6km
Altitud e
h= 7km
Altitud e
h= 8km
Altitud e
h= 9km
Altitud e
h= 10km
Altitud e
h= 11km
0.05
517.94
450.05
388.53
336.45
288.36
246.66
0.10
2115.9
1886.3
1596.9
1377.9
1181.8
1010.4
0.15
4901.4
4184.2
3699.9
3132.0
2691.8
2304.2
0.20
8652.0
7478.2
6474.1
5591.6
4811.5
4119.6
0.25
13287
11586
10069
8707.5
7495.5
6446.0
0.30
19142
16536
14499
12439
10716
9201.8
0.35
25851
22528
19561
16773
14461
12415
0.40
33221
28962
25152
21932
18747
16086
0.45
42089
p>36382 31878
27349
23549
20210
0.50
51233
44634
39077
33534
28902
24780
0.55
62263
54274
47145
40489
34763
29835
0.60
73634
64187
55770
48243
41302
35430
0.65
85994
74917
65049
56270
48500
41354
0.70
98941
86484
75075
64951
55714
47769
0.75
11369
0
98684
85829
74046
63750
54629
TABLE 6: MAXIMUM STATIC PRESSURE VS MACH NUMBERS FOR 6KM TO 11KM ALTITUDE
FIGURE 7: MAXIMUM PRESSURE VARIATION ABOUT MACH NUMBER AT 0KM TO 11KM ALTITUDE
FIGURE 8: COMPUTED STATIC PRESSURE VARIATION AT 0.2 MACH NUMBER AT 4KM ALTITUDE
ach Numbe
r
Minimum Static Pressure (Pa)
h = 0km
h= 1km
h= 2km
h= 3km
h= 4km
h= 5km
0.05
2.6261
6
2.3985
5
2.1787
0
1.8895
1.7551
1.5694
0.10
10.692
0
9.6941
5
8.5818
6.6773
7.3119
5.8982
0.15
19.453
2
17.520
8
15.991
15.36
15.459
12.880
0.20
37.349
4
35.743
1
26.447
27.627
27.179
19.406
0.25
52.998
5
49.072
0
44.845
45.723
45.415
29.455
0.30
68.678
0
63.391
6
58.942
49.057
62.412
45.306
0.35
88.147
2
89.423
1
75.806
69.473
80.699
48.374
0.40
127.96
1
99.825
9
93.983
88.543
102.55
60.474
0.45
111.22
3
128.20
8
116.56
102.04
128.24
87.783
0.50
207.65
6
150.89
0
122.6
132.40
146.72
108.91
0.55
236.42
6
233.57
3
206.31
116.83
140.44
126.55
0.60
179.73
4
177.51
6
221.45
211.13
158.78
141.10
0.65
237.93
4
195.09
5
175.22
231.85
135.80
124.74
0.70
310.69
4
208.15
3
246.60
175.93
252.72
210.99
0.75
371.29
7
314.84
4
218.78
249.19
264.24
246.61
TABLE 7: MINIMUM STATIC PRESSURE VS MACH NUMBERS FOR 0KM TO 5KM ALTITUDE
Mach Numbe r
Minimum Static Pressure (Pa)
h = 6km
h= 7km
h= 8km
h= 9km
h= 10km
h= 11km
0.05
1.4678
1.2543
1.0382
0.9288
6
0.9004
6
0.83003
0.10
4.9476
4.7553
4.7218
4.0647
0
3.4839
0
2.97210
0.15
11.776
10.285
9.3470
8.1781
0
7.2082
0
6.24590
0.20
22.837
18.727
14.422
12.683
11.254
0
10.1430
0.25
25.80
4
26.00
2
22.55
3
20.06
1
18.89
40
14.68
60
0.30
35.75
8
31.88
7
36.30
2
31.57
6
28.48
60
22.53
00
0.35
48.12
4
40.80
9
36.35
5
38.44
4
37.64
80
32.41
90
0.40
53.41
0
53.97
2
55.57
6
40.63
1
43.09
80
40.65
20
0.45
80.55
6
58.98
2
53.64
6
65.95
5
58.31
70
47.35
40
0.50
78.18
6
69.41
9
64.57
9
77.36
5
68.73
40
60.39
10
0.55
117.8
6
100.3
0
79.36
5
74.84
4
81.76
50
70.63
00
0.60
129.6
6
115.0
8
96.85
3
78.61
6
86.48
70
82.95
10
0.65
145.6
5
129.8
1
108.8
6
88.21
3
79.80
70
98.30
50
0.70
123.2
6
135.8
3
117.3
2
96.14
8
126.6
7
110.4
3
0.75
184.6
3
126.0
6
127.7
8
123.2
5
143.6
9
122.2
3
Mach Numbe r
Minimum Static Pressure (Pa)
h = 6km
h= 7km
h= 8km
h= 9km
h= 10km
h= 11km
0.05
1.4678
1.2543
1.0382
0.9288
6
0.9004
6
0.83003
0.10
4.9476
4.7553
4.7218
4.0647
0
3.4839
0
2.97210
0.15
11.776
10.285
9.3470
8.1781
0
7.2082
0
6.24590
0.20
22.837
18.727
14.422
12.683
11.254
0
10.1430
0.25
25.80
4
26.00
2
22.55
3
20.06
1
18.89
40
14.68
60
0.30
35.75
8
31.88
7
36.30
2
31.57
6
28.48
60
22.53
00
0.35
48.12
4
40.80
9
36.35
5
38.44
4
37.64
80
32.41
90
0.40
53.41
0
53.97
2
55.57
6
40.63
1
43.09
80
40.65
20
0.45
80.55
6
58.98
2
53.64
6
65.95
5
58.31
70
47.35
40
0.50
78.18
6
69.41
9
64.57
9
77.36
5
68.73
40
60.39
10
0.55
117.8
6
100.3
0
79.36
5
74.84
4
81.76
50
70.63
00
0.60
129.6
6
115.0
8
96.85
3
78.61
6
86.48
70
82.95
10
0.65
145.6
5
129.8
1
108.8
6
88.21
3
79.80
70
98.30
50
0.70
123.2
6
135.8
3
117.3
2
96.14
8
126.6
7
110.4
3
0.75
184.6
3
126.0
6
127.7
8
123.2
5
143.6
9
122.2
3
TABLE 8: MINIMUM STATIC PRESSURE VS MACH NUMBERS FOR 6KM TO 11KM ALTITUDE
FIGURE 9: MINIMUM PRESSURE VARIATION ABOUT MACH NUMBER AT 0KM TO 11KM ALTITUDE
0.70
352100
00
314100
00
277720
00
245680
00
214900
00
1892000
0
0.75
404980
00
363700
00
319710
00
281900
00
248230
00
2182600
0
0.70
352100
00
314100
00
277720
00
245680
00
214900
00
1892000
0
0.75
404980
00
363700
00
319710
00
281900
00
248230
00
2182600
0
FIGURE 10: COMPUTED STATIC PRESSURE VARIATION AT 0.6 MACH NUMBER AT 4KM ALTITUDE
-
STRUCTURAL ANALYSIS
The total deformation and the equivalent Von- Mises stress distributions of the wing with winglet model are computed using Finite Element Analysis tool. The computed pressure load imported over wing with winglet model as shown in figure 8 and 10.
Mach Number
Equivalent Von – Mises Maximum Stress (Pa)
h = 0km
h= 1km
h= 2km
h= 3km
h= 4km
h= 5km
0.05
147600
122500
107150
98979
83749
72039
0.10
585780
515680
453330
394440
385790
328490
0.15
138360
0
120980
0
106170
0
931680
913050
769740
0.20
262910
0
229790
0
213500
0
178600
0
165540
0
1341000
0.25
435730
0
372340
0
323330
0
323290
0
263110
0
2184500
0.30
617220
0
543240
0
496680
0
418050
0
381220
0
3357300
0.35
849550
0
748730
0
661280
0
601110
0
524330
0
4432400
0.40
114590
00
994810
0
874980
0
767210
0
689370
0
5876500
0.45
145520
00
126300
00
114340
00
100790
00
876360
0
7529700
0.50
179900
00
156270
00
138230
00
121870
00
108560
00
9616700
0.55
218980
00
194540
00
168740
00
148320
00
131980
00
1171300
0
0.60
255810
00
227380
00
201340
00
178410
00
157450
00
1399800
0
0.65
302790
00
268710
00
237720
00
210000
00
186390
00
1649000
0
Mach Number
Equivalent Von – Mises Maximum Stress (Pa)
h = 0km
h= 1km
h= 2km
h= 3km
h= 4km
h= 5km
0.05
147600
122500
107150
98979
83749
72039
0.10
585780
515680
453330
394440
385790
328490
0.15
138360
0
120980
0
106170
0
931680
913050
769740
0.20
262910
0
229790
0
213500
0
178600
0
165540
0
1341000
0.25
435730
0
372340
0
323330
0
323290
0
263110
0
2184500
0.30
617220
0
543240
0
496680
0
418050
0
381220
0
3357300
0.35
849550
0
748730
0
661280
0
601110
0
524330
0
4432400
0.40
114590
00
994810
0
874980
0
767210
0
689370
0
5876500
0.45
145520
00
126300
00
114340
00
100790
00
876360
0
7529700
0.50
179900
00
156270
00
138230
00
121870
00
108560
00
9616700
0.55
218980
00
194540
00
168740
00
148320
00
131980
00
1171300
0
0.60
255810
00
227380
00
201340
00
178410
00
157450
00
1399800
0
0.65
302790
00
268710
00
237720
00
210000
00
186390
00
1649000
0
TABLE 9: EQUIVALENT VON MISES MAXIMUM STRESS VS MACH NUMBERS FOR 0KM TO 5KM ALTITUDE
The equivalent Von – Mises stress variation caused by the pressure load acting on the wing at the inlet velocity of
0.2 and 0.6 Mach at 4km altitude is illustrated in figure 12 and 114. The maximum stress variations are tabulated which is shown in table 9 and 10 and minimum stress variations are tabulated which is shown in table 11 and 12. The maximum and minimum equivalent Von Mises Stress variation increase while Mach number increases and also decreases while altitude increases as shown in figure 11 and 13.
Mach Numbe r
Equivalent Von – Mises Maximum Stress (Pa)
h = 6km
h= 7km
h= 8km
h= 9km
h= 10km
h= 11km
0.05
60944
52277
44329
37964
32008
26838
0.10
260750
248790
195270
167090
142910
121680
0.15
671150
535960
502440
395620
337310
288480
0.20
124420
0
994660
854680
733060
626300
533630
0.25
188260
0
163000
0
140310
0
120660
0
102900
0
864720
0.30
292410
0
241240
0
218550
0
178730
0
153080
0
129740
0
0.35
402570
0
349600
0
301870
0
248750
0
212990
0
181170
0
0.40
511280
0
443110
0
382500
0
343540
0
282100
0
240460
0
0.45
675280
0
567500
0
507890
0
421460
0
361940
0
308630
0
0.50
816150
0
708430
0
630260
0
526590
0
450610
0
385100
0
0.55
102060
00
885490
0
765760
0
641660
0
550290
0
468650
0
0.60
121960
00
105930
00
917540
0
791380
0
659100
0
561940
0
0.65
143920
00
125190
00
108530
00
928340
0
800230
0
665850
0
0.70
164350
00
145790
00
126380
00
108710
00
910380
0
776800
0
0.75
193410
00
164700
00
145470
00
122500
00
105260
00
896070
0
TABLE 10: EQUIVALENT VON – MISES MAXIMUM STRESS VS MACH NUMBERS FOR 6KM TO 11KM ALTITUDE
0.35
6574.6
5767.0
5093
4766.3
4014.8
3362.7
0.40
8877.8
7758.5
6824.4
5952.8
5170.9
4517.4
0.45
11186.
0
9864.1
8705.2
7655.7
6455.0
5850.8
0.50
13813.
0
12203
10831
9598.3
7911.1
7257.9
0.55
16657.
0
14692
13155
11635
9552.2
8679.2
0.60
19720.
0
17531
15576
13815
11375
10243
0.65
23185.
0
20585
18266
16157
13292
11976
0.70
26979.
0
23935
21195
18713
15368
14503
0.75
30940.
0
26964
24305
21456
17712
16607
0.35
6574.6
5767.0
5093
4766.3
4014.8
3362.7
0.40
8877.8
7758.5
6824.4
5952.8
5170.9
4517.4
0.45
11186.
0
9864.1
8705.2
7655.7
6455.0
5850.8
0.50
13813.
0
12203
10831
9598.3
7911.1
7257.9
0.55
16657.
0
14692
13155
11635
9552.2
0.60
19720.
0
17531
15576
13815
11375
10243
0.65
23185.
0
20585
18266
16157
13292
11976
0.70
26979.
0
23935
21195
18713
15368
14503
0.75
30940.
0
26964
24305
21456
17712
16607
FIGURE 11: MAXIMUM STRESS VARIATION ABOUT MACH NUMBER AT 0KM TO 11KM ALTITUDE
Mach Numbe r
Equivalent Von – Mises Minimum Stress (Pa)
h = 0km
h= 1km
h= 2km
h= 3km
h= 4km
h= 5km
0.05
90.017
69.613
58.953
61.813
44.476
34.107
0.10
372.77
326.01
283.57
243.30
262.79
212.76
0.15
939.64
805.10
699.28
606.32
677.10
522.19
0.20
1926.6
1659.4
1642.5
1248.2
1299.8
902.08
0.25
3465.1
2792.6
2393.8
2541.8
2115.0
1552.3
0.30
4743.6
4145.6
3974
3150.1
3007.6
2642.1
Mach Numbe r
Equivalent Von – Mises Minimum Stress (Pa)
h = 0km
h= 1km
h= 2km
h= 3km
h= 4km
h= 5km
0.05
90.017
69.613
58.953
61.813
44.476
34.107
0.10
372.77
326.01
283.57
243.30
262.79
212.76
0.15
939.64
805.10
699.28
606.32
677.10
522.19
0.20
1926.6
1659.4
1642.5
1248.2
1299.8
902.08
0.25
3465.1
2792.6
2393.8
2541.8
2115.0
1552.3
0.30
4743.6
4145.6
3974
3150.1
3007.6
2642.1
FIGURE 12: COMPUTED EQUIVALENT VON – MISES STRESS VARIATION AT 0.2 MACH NUMBER AT 4KM ALTITUDE
TABLE 11: EQUIVALENT VON MISES MINIMUM STRESS VS MACH NUMBERS FOR 0KM TO 5KM ALTITUDE
MAC H NUMB ER
EQUIVALENT VON – MISES MINIMUM STRESS (PA)
h = 6km
h= 7km
h= 8km
h= 9km
h= 10km
h= 11km
0.05
27.483
22.632
18.121
14.617
11.356
9.1446
0.10
163.91
162.27
128.53
109.14
87.708
70.593
0.15
449.57
339.42
333.94
251.65
216.07
188.50
0.20
892.36
634.10
552.60
471.25
400.90
341.09
0.25
1324.2
1124.6
949.73
803.48
677.60
562.41
0.30
2287.1
1745.1
1650.9
1244.9
1047.7
869.08
0.35
3183.7
2750.2
2335.0
1795.4
1509.3
1260.6
0.40
3910.1
3368.3
2887.9
2682.4
2061.8
1723.7
0.45
5247.4
4359.5
3999.8
3196.0
2693.8
2259.0
0.50
6355.7
5490.8
4878.5
4030.6
3428.2
2875.5
0.55
7614.3
6660.3
5814.3
4954.6
4218.3
3564.4
0.60
8966.0
7836.6
6837.9
5928.1
5098.5
4314.1
0.65
10434
9109.6
7932.3
6903.3
5981.9
5135.6
0.70
12699
10478
9123.0
7930.6
7081.4
6016.9
0.75
13797
12679
10392
9535.6
8207.3
6958.9
TABLE 12: EQUIVALENT VON MISES MINIMUM STRESS VS MACH NUMBERS FOR 6KM TO 11KM ALTITUDE
FIGURE 13: MINIMUM STRESS VARIATION ABOUT MACH NUMBER AT 0KM TO 11KM ALTITUDE
70
600
20
100
500
800
0.55
0.8762
60
0.7785
000
0.6734
10
0.5921
500
0.5305
500
0.4687
300
0.60
1.0190
00
0.9056
800
0.8024
30
0.7118
100
0.6327
900
0.5601
200
0.65
1.2065
00
1.0704
000
0.9474
60
0.8371
200
0.7485
000
0.6596
900
0.70
1.4042
00
1.2523
000
1.1071
00
0.9790
500
0.8641
300
0.7546
700
0.75
1.6157
00
1.4564
000
1.2744
00
1.1237
000
0.9972
000
0.8700
300
70
600
20
100
500
800
0.55
0.8762
60
0.7785
000
0.6734
10
0.5921
500
0.5305
500
0.4687
300
0.60
1.0190
00
0.9056
800
0.8024
30
0.7118
100
0.6327
900
0.5601
200
0.65
1.2065
00
1.0704
000
0.9474
60
0.8371
200
0.7485
000
0.6596
900
0.70
1.4042
00
1.2523
000
1.1071
00
0.9790
500
0.8641
300
0.7546
700
0.75
1.6157
00
1.4564
000
1.2744
00
1.1237
000
0.9972
000
0.8700
300
FIGURE 14: COMPUTED EQUIVALENT VON – MISES STRESS VARIATION AT 0.6 MACH NUMBER AT 4KM ALTITUDE
The total deformation distribution produced on the wing because of the pressure load acting on it (0.2 and 0.6 Mach number) is shown in figure 16 and 17. The total deformation value increases gradually from the wing root to winglet tip. The maximum deformation occurs at trailing edge wing tip to winglet tip. The wing for various velocity inlet conditions at different altitude, deformations values are computed as illustrated and tabulated in figure 15 and table 13 and 14.
TABLE 13: TOTAL DEFORMATION VS MACH NUMBERS FOR 0KM TO 5KM ALTITUDE
Mach Number
Total Deformation (mm)
h = 6km
h= 7km
h= 8km
h= 9km
h= 10km
h= 11km
0.05
0.00225
83
0.00192
87
0.00162
88
0.00139
51
0.00116
97
0.00097
594
0.10
0.00988
58
0.00959
86
0.00739
32
0.00631
34
0.00538
87
0.00458
060
0.15
0.02616
30
0.02059
00
0.01955
70
0.01514
90
0.01289
30
0.01102
000
0.20
0.04893
50
0.03856
70
0.03307
90
0.02833
70
0.02418
00
0.02057
100
0.25
0.07380
20
0.06383
50
0.05487
00
0.04713
40
0.04014
10
0.03360
700
0.30
0.11610
00
0.09496
10
0.08661
40
0.07020
40
0.06007
50
0.05081
300
0.35
0.16025
00
0.13909
00
0.12000
00
0.09811
80
0.08392
70
0.07130
400
0.40
0.20279
00
0.17559
00
0.15143
00
0.13681
00
0.11151
00
0.09495
000
0.45
0.26971
00
0.22551
00
0.20266
00
0.16716
00
0.14347
00
0.12222
000
0.50
0.32535
00
0.28223
00
0.25167
00
0.20941
00
0.17900
00
0.15289
000
0.55
0.40836
00
0.35428
00
0.30627
00
0.25576
00
0.21906
00
0.18633
000
0.60
0.48804
00
0.42383
00
0.36700
00
0.31645
00
0.26299
00
0.22396
000
0.65
0.57586
00
0.50080
00
0.43396
00
0.37146
00
0.31982
00
0.26562
000
0.70
0.65648
00
0.58326
00
0.50541
00
0.43469
00
0.36341
00
0.31002
000
0.75
0.77335
00
0.65810
00
0.58193
00
0.48940
00
0.42025
00
0.35764
000
TABLE 14: TOTAL DEFORMATION VS MACH NUMBERS FOR 6KM TO 11KM ALTITUDE
Mach Numbe r
Total Deformation (mm)
h = 0km
h= 1km
h= 2km
h= 3km
h= 4km
h= 5km
0.05
0.0056
263
0.0045
788
0.0039
96
0.0037
463
0.0031
535
0.0026
795
0.10
0.0224
03
0.0196
940
0.0172
87
0.0150
140
0.0150
930
0.0126
910
0.15
0.0535
40
0.0466
990
0.0409
48
0.0359
070
0.0360
840
0.0300
380
0.20
0.1031
50
0.0899
320
0.0843
01
0.0698
390
0.0657
160
0.0522
480
0.25
0.1730
50
0.1468
700
0.1271
60
0.1283
000
0.1048
500
0.0857
310
0.30
0.2446
10
0.2149
800
0.1977
00
0.1650
300
0.1522
700
0.1334
000
0.35
0.3374
80
0.2972
100
0.2623
70
0.2397
300
0.2098
600
0.1753
900
0.40
0.4581
90
0.3961
400
0.3482
20
0.3049
900
0.2763
500
0.2332
800
0.45
0.5820
10
0.5033
600
0.4572
00
0.4030
500
0.3530
000
0.2997
800
0.50
0.7202
0.6231
0.5516
0.4866
0.4362
0.3844
FIGURE 15: TOTAL DEFORMATION ABOUT MACH NUMBER AT 0KM TO 11KM ALTITUDE
FIGURE 16: TOTAL DEFORMATION CONTOUR AT
0.2 MACH NUMBER AT 4KM ALTITUDE
FIGURE 17: TOTAL DEFORMATION CONTOUR AT
0.6 MACH NUMBER AT 4KM ALTITUDE
-
-
CONCLUSION
-
The considered rectangular wing with winglet model is kept at 0º Angle of Attack throughout the analysis. Therefore, the pressure distributions obtained for the subsonic Mach numbers from 0.05 to 0.75 at different altitude are verified with the available historical data. The results are fully agreed with the data exist in the NACA report and verified with the fifteen inlet velocity conditions. From the results and contours, it is identified that the non-linear aeroelastic effects in the both incompressible and compressible subsonic velocities are negligible. The methodology used in this article can be implemented for Taper, Swept back and Delta wings with different wingtips with high subsonic Mach numbers to study the aeroelastic nature of such designs.
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