Experimental Aerodynamics. Experimental Aerodynamics

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1 Lecture 3: Vortex shedding and buffeting G. Dimitriadis

2 Buffeting! All structures exposed to a wind have the tendency to vibrate.! These vibrations are normally of small amplitude and have stochastic character! They are by unsteadiness in the flow around the structure! There are two types of unsteadiness:! Unsteadiness in the oncoming free stream! Unsteadiness due to flow separation around the structure

3 Buffeting examples Buffeting of a rigid rectangular wing with 2 degrees of freedom Buffeting of a flexible Delta wing

4 Turbulence in the free stream! Unsteadiness in the free stream is generally caused by natural turbulence! In the atmosphere this turbulence is known as atmospheric turbulence and is related to the earth s boundary layer.! Wind tunnels always have a small amount of natural turbulence; in the ULg tunnel, the natural turbulence is of the order of 0.2% of the free stream airspeed.! Flow unsteadiness causes unsteady aerodynamic forces which excite the structure.

5 Von Karman Spectrum! The frequency content of atmospheric turbulence is usually modelled using the Von Karman spectrum! Where! is the angular frequency, L is the length scale of atmospheric turbulence, V is the aircraft s airspeed, " g is the turbulence intensity 2 L! 11 (" ) = # g $ 2 L! 22 (" ) = # g $ 1 % % ) " L & & V ' ( % " L & V % % ) " L & & V ' ( 2 5 / 6 Longitudinal turbulence ' * ( 2 2 ' ( 11/ 6 Lateral turbulence ' * (

6 Von Karman example Von Karman spectrum at an airspeed of 200m/s and " g =2.1. It can be seen that most of the power is concentrated at very low frequencies, less than 1Hz. The power at frequencies of 10Hz or more is very low

7 Separation-induced turbulence! Non-streamlined bodies and streamlined bodies at high angles of attack are characterized by flow separation! Flow separation generally causes the flow to become turbulent and, therefore, unsteady.! Again, separation-induced flow unsteadiness causes unsteady aerodynamic forces.! These forces in turn excite the structure.

8 Flow separation Separated flow behind truncated pyramid Separated flow behind circular cylinder

9 Structural response! Both free stream turbulence and separated flow have characteristic frequency spectra.! The structure itself has eigenmodes with characteristic eigenfrequencies (or natural frequencies).! It follows that the structure s response amplitude depends on the frequency content of the separated flow.! If the latter coincides with one of the natural frequencies of the structure, resonance can occur, leading to large amplitude oscillations.

10 The frequency content of the separated flow depends on the Reynolds Number.

11 Reynolds number dependence videos Re=272 Re=271, 594, 2902

12 Strouhal number! The Strouhal number is a measure of the unsteadiness of the flow.! It is defined as Str = f s D U! Where Str is the Strouhal number, f s is the fundamental frequency of the flow, D is a characteristic cross-flow dimension and U is the free stream airspeed

13 Str and Re! The Strouhal number also depends on the Reynolds number but less strongly than the frequency Strouhal number for circular cylinders

14 Str for circular cylinder! For low Re values (under Re=500) the Str dependence on Re can be approximated by: " Str = ! 19.7 % # $ Re & '! For Re between 500 and 10 5, Str can be taken as a constant equal to 0.2.! This means that, as the airspeed increases, so does the frequency of the unsteady flow

15 2D cylinder with 1-DOF Assume that L>>D so that the flow is nearly 2D One degree of freedom in y

16 Equation of motion! The structural equation of motion is of the form! Where! n is the wind-off natural frequency and " is the wind-off damping ratio.! When the wind is turned on the equation of motion becomes! Where l(t) is the lift force acting on the cylinder!!y +! n "!y +! n 2 y = 0!!y +! n!y +! 2 n y = l( t)

17 Lift force! The unsteady lift force can be written as l( t) = 1 2!U 2 Dc l cos" s t! Where c l is the sectional lift coefficient and! s is the separated flow fundamental frequency, given by the Strouhal number,! s = 2"Str U D

18 Response amplitude! The steady state response will be of the form y(t) = Y 1 sin! s t +Y 2 cos! s t! Where Y 1,2 are constants. The response amplitude is simply Y=(Y 1 +Y 2 ) 1/2. The equation of motion becomes!! s 2 Y 1 sin! s t!! s 2 Y 2 cos! s t +! n "! s Y 1 cos! s t!! n "! s Y 2 sin! s t +! n 2 Y 1 sin! s t +! n 2 Y 2 cos! s t = 1 2 #U 2 Dc l cos! s t

19 Amplitude values! After harmonic balancing:!! s 2 Y 1!! n "! s Y 2 +! n 2 Y 1 = 0! or " $ $ #! n 2!! s 2!! s 2 Y 2 +! n "! s Y 1 +! n 2 Y 2 = 1 2 #U 2 Dc l!! n!" s! n!" s! n 2!! s 2 %" ' $ ' &# $ Y 1 Y 2 % " ' &' = $ $ # $ 0 1 2!U 2 Dc l % ' ' &'

20 Solution! # "# Y 1 Y 2! # # # # = # # # # "# $ & %& = 1! 2 2 n '! s (( ) 2 + (! n "! s ) 2 ) 1 2 #U 2 Dc l! n "! s (! 2 2 n '! ) 2 s +! n "! s ( ( ) 2 ) 1 2 #U 2 Dc l! n (! 2 2 n '! ) 2 s +! n "! s ( 2 2 '! ) s ( ( ) 2 ) $ & & & & & & & & %&! # # "! n 2 '! s 2! n "! s '! n "! s! n 2 '! s 2 $! &# &# %"# #U 2 Dc l So that the maximum amplitude is obtained when dy d! s = 0 $ & & %&

21 Maximum amplitude! Working out the algebra gives the condition for maximum amplitude:! Or 2 (! 2 2 s!! ) n +! n2! 2 = 0! s =! n 1! " 2! Which occurs when 2 U res = D 2!Str " n 1! # 2 2

22 Lock-in! The result shown above assumes that the structure s response frequency is equal to the Strouhal frequency.! This is not always the case. Consider that the airspeed increases continuously from 0.! When it reaches U res, the cylinder will resonate. Any further small increases in airspeed will not affect the response frequency.! This phenomenon is called lock-in: the cylinder s response frequency locks in to the system s resonant frequency for a certain range of airspeeds higher than the resonance airspeed.

23 Lock-in diagram! s! n 1!" 2 / 2 1 Lock-in D Str 2!U " n 1!# 2 / 2

24 Practical Session! The ULg wind tunnel contains a circular cylinder. The cylinder is mounted on a support structure that can measure the aerodynamic loads.! The cylinder is also instrumented with accelerometers and a hot wire sensor in the wake.! Carry out a wind-off modal test to determine the wind-off natural frequency and damping ratio! Predict the resonance airspeed! Carry out wind-on tests:! What are the actual resonance frequency and airspeed values?! How do they compare with the predictions?! Does lock-in occur?

25 Estimating modal parameters! The free response of a dynamic system is an oscillation at the damped natural frequency and damping ratio of the system.! We can identify the natural frequency and damping ratio from this response.! One way of doing it is by taking the Fourier Transform of the response! The Fourier Transform is the Frequency Response Function (FRF) in this case.! The peaks of the FRF can be used to estimate the modal parameters.

26 Free response Recorded free response FFT of free response

27 The Half Power Point method is a graphical approach and, therefore, not very accurate. Nevertheless, it is always used, even when more sophisticated parameter estimation techniques are applied. The best algorithms and computers are no replacement for an engineer with a ruler and plotting paper, apparently. Half Power Point

28 Number of peaks! Note that most real structures will have more than one mode, therefore more than one peak.! Each peak will yield a natural frequency and a damping ratio.! We must choose which peak is relevant to our problem or treat all of them.! NB: When the wind is turned on the response is forced, not free!

Aeroelasticity. Lecture 4: Flight Flutter Testing. G. Dimitriadis. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 4

Aeroelasticity. Lecture 4: Flight Flutter Testing. G. Dimitriadis. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 4 Aeroelasticity Lecture 4: Flight Flutter Testing G. Dimitriadis AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 4 1 Main reference A Historical Overview of Flight Flutter Testing, Michael