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Extended Abstract
This work was performed to have a more clear insight on transonic buffet phenomena using a numerical simulation approach. This method of analysis ensures a direct
observation of instabilities of the flow field and at the same time provides numerical data linked to those phenomena, making possible a comparison between tests (data and images) and CFD analyses (data, images and films).
Was selected the NACA0012 airfoil primarily cause of its high number of tests data available in the literature by virtue of the use of this airfoil to calibrate wind tunnels, secondly cause it is not a supercritical airfoil; this last ensured a not high resistance to flow unsteadiness. Furthermore, this body is quite “squat” compared to supercritical airfoils thus introducing a bigger disturbance in the flow field resulting in facilitating formation of unsteady flow.
The rigid model was validated using different Mach and Reynolds numbers, then was refined until it obtained a capability convergence to sixteenth decimal place in the pressure field, making possible to capture minimal perturbations triggering the onset of buffet phenomena.
It was maintained a symmetric mesh shape and a fine grid at a quite long distance from the solid body to capture the shock waves and little vibrational phenomena even far from the airfoil.
Were conducted a series of analyses based on the NACA technical paper 2485 (Ref. [5]) and results of Crouch, Garbaruk and other works (contained in two papers: ‘Predicting the onset of flow unsteadiness based on global instability’ and ‘Origin of transonic buffet on airfoils’, Ref. [7]-[8]); were analyzed conditions at high Mach numbers and relatively high Reynolds numbers finding a buffet boundary onset shown in the next figure. Were used the k-e model of turbulence (with URANS approach); was also conducted a study with the k-ω SST method showing no noteworthy differences between results of the two.
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As can be seen, CFD analyses demonstrate a very good accordance with experimental data; furthermore was captured the buffet onset at Mach = 0.80 for an incidence slightly below one degree. It was not found another work with this last onset point, the reason was found to be probably the origin of that unsteadiness. Upper and lower surfaces of the airfoil were divided to analyze individually the two contributions.
Buffet phenomenon was studied till today on the upper wall of the airfoils following the idea of a shift of the shock wave that would have to produce vortex shedding in accordance with a pulsing separation bubble growing and shrinking; these analyses demonstrate that at least at Mach = 0.80 there are multiple solutions for activation of buffet phenomenon as predicted by theory as can be seen in next figure (from Ref. [8]):
0 0,25 0,5 0,75 1 1,25 1,5 1,75 2 2,25 2,5 2,75 3 3,25 3,5 3,75 4 4,25 4,5 4,75 5 5,25 5,5 0,7 0,71 0,72 0,73 0,74 0,75 0,76 0,77 0,78 0,79 0,8 0,81 0,82 0,83 0,84 0,85 0,86 0,87 0,88 0,89 0,9 α , i n ci d e n ce [d e g] Mach number
Buffet boundary
Ref. [5] NASA experimental interpolated curve
Ref. [8] ROM
Ref. [5] NASA (PROBE 0,5*c) Ref. [5] NASA (PROBE 0,8*c) CFD
Ref. [8] CFD (steady) Ref. [8] CFD (unsteady) Ref. [12] CFD
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Furthermore, it was found that at least at Mach = 0.80 the phenomenon onset was triggered by the lower surface of the airfoil ( for a positive incidence ), so probably the buffet onset at this Mach number was not captured by other works because was hunted in a wrong part of the fluid flow.
For the other Mach numbers was found a “canonical behavior” with the major part of the instability concentrated on the upper side of the airfoil. Next figures show an example of repetitive signals of lift coefficients for two of the onset solutions at Mach = 0.80.
Were made fast Fourier transforms of the signals to recognize the frequencies involved and were calculated the power spectral density, to have an idea of how much energy each characteristic frequency was bringing, and the root mean square of that power spectral density to have an estimate of the energy contained in the whole signal. Were calculated also other parameters shown in detail in the thesis report. Some graph examples:
0,216536 0,216537 0,216538 0,216539 9,1 9,2 9,3 9,4 9,5 9,6 9,7 9,8 9,9 cl , l ift co e ff ic ie n t time [s]
Cl history at Mach=0.80, α=0.975º
0,305955 0,305956 0,305957 0,305958 9,5 9,55 9,6 9,65 9,7 9,75 9,8 9,85 9,9 9,95 10 cl , l ift co e ff ic ie n t time [s]Cl history at Mach=0.80, α=1.5º
1,00E-15 1,00E-13 1,00E-11 1,00E-09 1,00E-07 1,00E-05 0 50 100 150 200 250 300 350 400 450 500 PS D [1/ H z] frequency [Hz]PSD of Cl at Mach=0.80 and α=0.975º
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Other analyses of pressure and velocity fields indicate the loci of major disturbances and maps of dimensionless chord-time-pressure indicate repetitiveness of signals and the direction of propagation, as next figures that show a propagation inside the shear layer from the shock wave location upstream and downstream.
0,216536 0,2165365 0,216537 0,2165375 0,216538 0,2165385 0,216539 -0,0015 -0,001 -0,0005 0 0,0005 0,001 0,0015 cl Δcl/Δt
LCO at Mach=0.80 and
α=0.975º
-1,0E-05 9,0E-05 1,9E-04 2,9E-04 3,9E-04 4,9E-04 5,9E-04 6,9E-04 7,9E-04 8,9E-04 9,9E-04 1,1E-03 1,2E-03 1,3E-03 1,4E-03 1,5E-03 1,6E-03 1,7E-03 1,8E-03 1,9E-03 2,0E-03 2,1E-03 2,2E-03 2,3E-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 o f PS D o f c l incidence [deg]RMS of PSD of Cl at Mach=0.76
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Conducted analyses lead to think that buffet phenomenon doesn’t have its origin with the shock wave motion at least at onset, thus providing an idea that pressure disturbances trigger the buffet onset and wave motion, that was observed at higher incidence angles than that of buffet onset, could be only a consequence of the amplification of that disturbances involving, at sufficient incidence angles, the whole flow field.
