flow induced vibration of trailing edges using air … · flow induced vibration of trailing edges...
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Flow Induced Vibration of Trailing Edges Using Air‐Analog Experiments
FLINOVIA Penn State University
28‐April, 2017
Scott C. MorrisProfessor
Department of Aerospace and Mechanical EngineeringUniversity of Notre Dame, Notre Dame, IN 46556
574‐631‐[email protected]
The importance of the trailing edge region in flow over a lifting surface
Approach flowTurbulent trailing edge flow
• Hydrodynamic issues: lift and drag are highly dependent on trailing edge shape.
• Acoustic issues unsteady surface pressure will radiate directly to the far field.
• Structural issues Unsteady surface pressure will result in structural forcing. High levels of forcing could lead to material failure
Flow visualization of two similar trailing edges
The flows are VERY different, although the geometry is nearly the same.
Questions In Flow‐Induced Vibrations1. How do we best characterize unsteady driving pressures in trailing
edge flows? What fidelity is required? 2. Can these representations be coupled with a structural model to
predict flow‐induced vibration? 3. Can this be generalized beyond a couple of simple test cases? 4. How does the turbulence field vary with different types of “blunt”
trailing edge flows5. How does the flow topology change the surface pressure
fluctuations and length scales? 6. How do we measure unsteady surface pressure with high
accuracy, resolution, and frequency range at low cost? 7. How do we measure the full auto‐spectral density of the
amplitude of each vibrational mode with random excitation?
Trailing Edge Geometry Definition
• All geometries have 25 degree trailing edge• The bottom, or “pressure side” is flat• The top, or “suction side” has a defined radius of curvature
Anechoic Wind Tunnel
Inlet
Acoustic baffle
Screen and honeycomb
End plate
Fan roomAcoustic wedgesReference LDV
Scanning LDV
Taxonomy of Pressure Scaling
Upstream attached flow
Fully separated flow
Separation point
Lower side attached flowCoherent structure in the
turbulent wake
Spanwise coherence exponential decay with spatial separation at various frequencies
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
z (m)
Magnitude‐Phase Identification (MPI)
• Determining frequency content of a mode requires the ability to decompose the vibration into its mode shapes.
• With LDV, only two points can be measured at a time.
Reference Laser
Scanning Laser
V1
V2
∅
Vibration velocity spectra under various tunnel speeds
200 400 600 800 1000 1200 140010-14
10-13
10-12
10-11
10-10
10-9
10-8
10-7
F (Hz)
vv
(m2 /s
2 /Hz)
Uo = 21.6 m/sUo = 26.8 m/sUo = 32.5 m/sUo = 35.9 m/s
• Assume all modes are orthogonal• Solving numerically for equally spaced points leads to
• Disadvantage: If modes are not perfectly orthogonal (such as due to experimental error), small portions of one mode will affect the decomposition of other modes.
Modal Projection
16
,1
Predicting the flow induced vibration
The governing equation for structural vibration is:
The vibration displacement patterns can be written as a general superposition of normal modes:
Mode shape functions
“Model pressure” forcing functionThe modal pressure is defined as:
The autospectral density of modal pressure is:
Cross‐spectral density of surface pressure, which can be estimated by an empirical model
Summary/Conclusions
• Flow field, unsteady pressure, radiated sounds, and vibration modes obtained for 7 trailing edge geometries.
• Four different types of spectra have been identified, each with their own unique scaling.
• Model spectral predictions show good agreement with lower order modes, and over predict for higher modes.
Two‐point correlation for separating flow (R4)
x/t
y/t
-3 -2 -1 0 1 2 3 4 5-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
-8
-6
-4
-2
0
2
4
6
8x 10
-3
y/t
-3 -2 -1 0 1 2 3 4 5-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
-8
-6
-4
-2
0
2
4
6
8x 10
-3
Streamwisevelocity correlation
Vertical velocity correlation
Two‐point Correlation for Attached Flow (R10)y/
t
-3 -2 -1 0 1 2 3 4 5 6-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2x 10
-3
x/t
y/t
-3 -2 -1 0 1 2 3 4 5 6-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
-1
-0.5
0
0.5
1x 10
-3
Vibration velocity spectra at various locations
200 400 600 800 1000 1200 140010-13
10-12
10-11
10-10
10-9
10-8
10-7
F (Hz)
vv
(m2 /s
2 /Hz)
point 1point 2point 3point 4point 5