Investigation of NACA 0012 Airfoil Periodic Flows in a Transonic Wind Tunnel

Transcription

1 5st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition 7 - January 23, Grapevine (Dallas/Ft. Worth Region), Texas AIAA Investigation of NACA 2 Airfoil Periodic Flows in a Transonic Wind Tunnel Downloaded by UNIVERSITY OF CALIFORNIA IRVINE on January 29, 25 DOI:.254/ Xudong Ren, Zijie Zhao, Chao Gao Northwestern Polytechnical University, Xi an 772, China Juntao Xiong, Feng Liu, and Shijun Luo University of California, Irvine, CA An experimental study of static and dynamic pressure distributions over a NACA 2 airfoil in the two-dimensional test section.8.4-meter of a transonic wind tunnel is presented. Tests are conducted at freestream Mach numbers from.35 to.89, and angle of attack between 2. and 5, and Reynolds number based on the airfoil chord length of 3. million. Tests are performed at boundary-layer transition free and transition fixed at 5% chord length conditions. Firstly, sublimating naphthalene visualization is performed to locate the transition position of the boundary layer over the airfoil at upper surface. Secondly, the chordwise static pressure distributions with transition fixed are validated by well-documented data in the literature. Thirdly, the dynamic pressure data at Mach numbers from.6 to.89 are analyzed. Finally, a numerical simulation at freestream Mach numbers from.82 to.89 are done. The unsteady computation results show a close trends as experimental measurements. Nomenclature b = airfoil span c = airfoil chord = pressure coefficient Ĉ p = Fourier transform of (t), C p (t)e i2πft dt f = frequency k = reduced frequency, 2πfc/U M exp = freestream Mach number M corr = corrected freestream Mach number Re = Reynolds number based on chord length t st = starting time of steady flow in sublimating visualization x = chordwise coordinate from airfoil leading edge towards downstream x sh = shock-wave position x tr = boundary-layer transition location y = upward coordinate perpendicular to airfoil plane α = angle of attack δ = boundary-layer displacement thickness on sidewall Graduate Student, Department of Fluid Mechanics Graduate Student, Department of Fluid Mechanics. Professor and Associate Director, National Key Laboratory of Science and Technology on Aerodynamic Design and Research. Postdoctoral Researcher, Department of Mechanical and Aerospace Engineering, Senior Member AIAA Professor, Department of Mechanical and Aerospace Engineering, Associate Fellow AIAA. Researcher, Department of Mechanical and Aerospace Engineering. of 22 Copyright 23 by The authors. Published by the, Inc., with permission.

2 I. Introduction Downloaded by UNIVERSITY OF CALIFORNIA IRVINE on January 29, 25 DOI:.254/ In transonic flow conditions, shock wave and turbulent boundary-layer interaction may induce flow separation and cause large scale instabilities on rigid airfoils which is known as transonic buffet. The problem has been studied for more than 5 years by a lot of different research groups. 8 Although a lot progresses have been achieved by using new experimental techniques, the mechanism of the unsteady shock wave oscillation phenomena has not been understood enough because of the nonlinearaity and complicate of flow structures. McDevitt and Okuno (985) 5 measured the onset of buffet over a NACA 2 airfoil with free boundarylayer transition at freestream Mach number of.7.82, at angles of of attack up to 6, and at Reynolds number from million to 4 million. They showed the buffet onset angle of attack is lower when the freesream Mach number is higher. However they did not test the buffet onsets above Mach number.82. While the multiple solutions have been found for the steady, inviscid flow at Mach numbers from and zero angle of attack. 9 Also the Navier-Stokes computational results reveal the transonic buffet occurs in a narrow range of freestream Mach numbers of at zero angle of attack and at Reynolds number million. In this paper in order to further study buffet onsets at high Mach numbers from.8.89 at zero angle of attack and low Mach number.6 at high angle of attacks to understand the shock wave unsteady motion mechanism, a experiment and computation combined approach is used. Firstly, sublimating naphthalene visualization is used to locate the transition position of the boundary layer over the airfoil at upper surface for fixed and free transition tests. Secondly, to evaluate wind-tunnel test techniques the comparison between data obtained in different wind tunnels,2 are performed. Thirdly, the dynamic pressure data are analyzed. In this paper a limit number of dynamic pressures were measured on the sidewalls at the locations near the upper surface of the airfoil to detect the buffet onset. Finally, a computation work is performed to offer more results to analyze the buffet phenomena. II.A. Wind Tunnel II. Experimental Setup The present study was carried out in the continuous closed-circuit transonic wind tunnel of the Northwestern Polytechnical University, Xi an, China. The two-dimensional test section size is of m. The stagnation pressure and the stagnation temperature of the tunnel air were controlled from.5 to 5.5 atmospheric pressure and between 283 K and 323 K, respectively, dependent on Reynolds number and Mach number. The air was dried until the dewpoint in the test section was reduced sufficiently to avoid condensation effects. The upper and lower walls are 6%-perforated. The holes are 6 inclined upstream. The ratio of sidewall-displacement-thickness to tunnel width is about 2δ /b.25. This facility is driven by a two-stage axial-flow compressor. Figure. Mach number distribution along the centerline of the empty test section of the wind tunnel. The flow uniformity in the test section was shown by measuring the centerline static pressure distribution from which the centerline Mach number distribution was calculated using an average total pressure measured in the stilling chamber. Figure gives the Mach number distribution along the centerline of the empty test section of the wind tunnel for a nominal Mach number from.2 to.5. The Reynolds number is about 2 of 22

3 5 6 m. The flow is uniform in the test section except within 2 mm from the entrance and the exit for Mach number between.2 and.. In the meantime, the static pressure on the sidewall center line at 2 mm from the entrance was measured. The correlation between the sidewall static pressure and the Mach number in the model region is used to determine the freestream Mach number in the airfoil model testing. II.B. Model Downloaded by UNIVERSITY OF CALIFORNIA IRVINE on January 29, 25 DOI:.254/ The model is an NACA 2 airfoil with a chord length c = 2 mm, a span of 4 mm (which gives an aspect ratio of 2.). The model blockage is 3.%. The central region of the model is equipped with 8 chordwise static pressure orifices among which 46 and 33 orifices are staggeredly located on the upper and lower surfaces of the airfoil, respectively, and a forward and a rearward facing orifices at the leading and trailing edges, respectively. Besides, there are spanwise static pressure orifices on the upper surface of the airfoil which are located at =.285 and.435 on the port and starboard side, respectively. The static pressure orifices were.3 mm in diameter. Figure 2 shows the location of the static pressure orifices on the upper and lower surfaces of the NACA 2 airfoil denoted by open and closed circles, respectively. The static pressure were measured with electronically actuated differential pressure-scanning-valve units with transducer ranges of ±3 kn/m 2, ±26 kn/m 2 and ±43 kn/m 2 (±5, ±3, ±6 lb/in 2 ). Accuracy of the transducers was within.5% of full scale. The sampling rate was 2 Hz. A limited number of kulites mounted on the sidewalls at the locations near the upper surface of the airfoil are used to measure dynamic pressure to detect the buffet onset. The dynamic Kulite pressure transducers are mounted close to the upper surface of the airfoil on the support on each sidewall at =.225,.5 and.775, and y/c =.7 as shown in Figure 3. The dynamic pressure orifice diameter was about 2.4 mm. Figure 2. Location of static pressure orifices on upper and lower surfaces of the model denoted by red and blue dots, respectively. Figure 3. Location of dynamic pressure orifices on the support sidewall The model was machined from stainless steel with embedded pressure tubes. The measured coordinates of the experimental model were deviated from the coordinates given in Ref. 3 nowhere greater than y/c =.2. Angle of attack was changed manually by rotating the model about pivots of the supports in the tunnel sidewalls. The model installed in the tunnel is shown in Figure 4. 3 of 22

4 Figure 4. Model in the wind tunnel. Downloaded by UNIVERSITY OF CALIFORNIA IRVINE on January 29, 25 DOI:.254/ II.C. Artificial Transition The artificial transition method is required to result in a negligible increase in drag other than that due to the change in the transition location. One satisfactory method is with the use of a strip of distributed particles of roughness designed according to the technique of Ref. 4. The roughness particle has a height of. mm and diameter of.2 mm. The roughness height is chosen less than the local laminar boundary-layer thickness which is estimated about.4 mm and larger than the minimum height to initiate turbulent spot, which is calculated 4 about.7 mm. The distance between the neighboring particles is.5 mm. The roughness particles are made of fiber poly putty mixed with a stiffener. The weight ratio of the putty and stiffer is about. The putty has good filling performance, wear-resisting, excellent adhesion and sandibility. The roughness strip is made using a narrow and long plastic strip of.3 mm thickness, upon which a series of holes are drilled for filling the putty when it is placed at the location of transition line on model surface. After the putty becomes stiff, the plastic strip is removed carefully and a distributed putty-particle strip is formed. Figure 5 shows NACA 2 airfoil model with transition strips. II.D. (a) Figure 5. Photos for making roughness strip: (a) holed plastic plate, and (b) airfoil model with strip. Sublimation Visualization The sublimating product flow visualization is used to determine the boundary-layer transition position on the model surfaces. 5 The chemical solid used for visual indication of boundary-layer transition in transonic flow is naphthalene (C H 8 ). A % solution of naphthalene is made in the solvent, acetone ((CH 3 ) 2 CO) and sprayed on the surfaces of the model by means of an ordinary paint spray-gun with a gun nozzle distance of 6 mm. Complete evaporation of the solvent occurs before the spray reaches the surface. By this procedure, uniformity of coating is attained with three or four passages of the gun and the coating is finely crystalline, uniformly greyish-white, and of aerodynamic smoothness. Immediately after application of the coating, the air blast is turned on rapidly until the required air speed is reached and then maintains the speed until the chemicals in the turbulent region have sublimated, showing the desired flow patterns. Photographs are taken in real time from a camera through an optical window mounted on the ceiling wall of the test section, (b) 4 of 22

5 Downloaded by UNIVERSITY OF CALIFORNIA IRVINE on January 29, 25 DOI:.254/ which clearly record the development of the boundary-layer transition over the starboard upper surface of the airfoil. Figure 6 shows the naphthalene-film sublimation over the upper surface of the NACA 2 airfoil model, (a) without naphthalene film, (b) with naphthalene film, (c) fixed transition at x tr /c = 5%, and (d) free transition, where (c) and (d) are taken at M exp =.8, α =, Re = In the still air, the model surface without and with the naphthalene film is dark and white, respectively, as shown in (a) and (b). As the air flows, the elevated shear and temperature associated with high turbulence of the boundary layer at the location of transition cause the naphthalene to increase its rate of sublimation in the turbulent region with respect to that of the laminar region. Consequently, the naphthalene is removed in the turbulent area before the naphthalene in the laminar area is appreciably affected. Under the fixed transition, the white coating immediately after the roughness strip disappears leaving a dark band which spreads downstream towards the airfoil trailing edge, while under the free transition, a dark area across the airfoil span appears near the airfoil trailing edge with acute-angled dark band diverging from micro surface-imperfection points at the airfoil leading edge. Under the fixed transition, the dark area on the model surface is two-dimensional. Under the free transition, the dark areas on the model surface is not two-dimensional. It is noted that there appears a narrow dark band over the airfoil surface immediately behind the leading edge for both the fixed and free transition as the air flows. (c) (a) Figure 6. Naphthalene-film sublimation: (a) without naphthalene film, (b) with naphthalene film, (c) fixed transition, x tr/c = 5%, and (d) free transition, NACA 2, M exp =.8, α =, Re = (b) (d) III. Computational Setup A computational fluid dynamics code is used to solves the unsteady three-dimensional compressible Navier-Stokes equations on structured multiblock grids using a cell-centered finite-volume method with artificial dissipation as proposed by Jameson et al. Information exchange for flow computation on multiblock grids using multiple CPUs is implemented through the MPI (Message Passing Interface) protocol. The Navier-Stokes equations are solved using the eddy viscosity type turbulence models. All computations presented in this work are performed using Menter SST k-ω model. 6 The flow and turbulence equations 5 of 22

6 are discretized in space by a structured hexahedral grid using a cell-centered finite-volume method. Since within the code each block is considered as a single entity, only flow and turbulence quantities at the block boundaries need to be exchanged. The governing equations are solved using dual-time stepping method for time accurate flow. At sub-iteration the five stage Runge-Kutta scheme is used with local-time stepping, residual smoothing, and multigrid for convergence acceleration. The turbulence model equations are solved using stagger-couple method. Further details of the numerical method can be found in Ref.. IV. Results and Discussion Downloaded by UNIVERSITY OF CALIFORNIA IRVINE on January 29, 25 DOI:.254/ IV.A. Experimental Results The static and dynamic pressures over the NACA 2 airfoil are measured for both the free and fixedtransition at x tr /c = 5% at M exp = and Re = IV.A.. Flow Angularity of the Wind Tunnel The flow angularity of the wind-tunnel test section was examined from comparison of the upper and lower surface pressure distributions over the symmetrical NACA 2 airfoil at specific angles of attack. Figure 7 presents the chordwise pressure distributions at M exp =.8, at α =., Re = 3. 6 and fixed transition at x tr /c = 5%. It is shown that the flow angularity of the wind tunnel is negligible fixed lower surface Figure 7. Chordwise pressure distributions at M exp =.8, α =, NACA 2, Re = 3. 6, x tr/c = 5%. IV.A.2. Two-dimensionality of the Flowfield The flow two-dimensionality was examined by measuring the spanwise pressure distributions at =.285 and.435 at the port and starboard sides of the airfoil upper surface. Figure 8 and 9 presents the spanwise pressure distributions for fixed x tr /c = 5% and free boundary-layer transition, at M exp =.35 and M exp =.8, α = 3 and α =, Re = 3. 6 over the NACA 2 airfoil upper surface. With boundary layer transition strips the two-dimensionality of the flowfield are improved because of the flow turns to turbulent at the same streamwise position along the spanwise direction of the airfoil which can be evidenced by Fig of 22

7 fixed_spanwise_cp fixed_spanwise_cp free_spanwise_cp free_spanwise_cp Downloaded by UNIVERSITY OF CALIFORNIA IRVINE on January 29, 25 DOI:.254/ z/c (a) Figure 8. Spanwise pressure distributions over the upper surface at M exp =.35, α = 3., (a)x tr/c = 5%, (b) free transition,, NACA 2, Re = fixed_spanwise_cp fixed_spanwise_cp z/c (b) free_spanwise_cp free_spanwise_cp z/c (a) z/c (b) Figure 9. Spanwise pressure distributions over the upper surface at M exp =.8, α =., (a)x tr/c = 5%, (b) free transition,, NACA 2, Re = of 22

8 IV.A.3. Chordwise Pressure Distribution, Transition Free, Compared with ONERA (979) Reference gave the ONERA S3MA wind-tunnel test results of a NACA 2 airfoil of height/chord ratio 3.7 and span/chord ratio The airfoil chord is 2 mm. Figure compares the chordwise pressure distributions with those obtained by ONERA tunnel (979) for the NACA 2 airfoil. It is free transition case. At subsonic conditions the comparisons are excellent. While at supercritical speed the shock positions are different although the pressures before and after the shock wave almost coincide. The present shock wave locates upstream to that of the ONERA tests. It may be caused by different endwall inferences and free transition positions Downloaded by UNIVERSITY OF CALIFORNIA IRVINE on January 29, 25 DOI:.254/ c p upper-re=239,onera lower-re=239,onera -.5 upper-re=2,nf lower-re=2,nf * c p (a) M exp =.5, α = (b) M exp =.6, α = 4 upper-re=465,onera lower-re=465,onera upper-re=482,nf-6 lower-re=482,nf upper-re=379,onera lower-re=379,onera upper-re=393,nf-6 lower-re=393,nf * (c) M exp =.7, α = (d) M exp =.8, α = Figure. Comparison of pressure distributions for free transition, NACA 2, M exp =.8, α =, Re = (2 5) 6. upper-re=49,onera lower-re=49,onera upper-re=43,nf lower-re=43,nf * * 8 of 22

9 IV.A.4. Chordwise Pressure Distribution, Transition Fixed and Free Effects of boundary-layer transition on the pressure distributions over the NACA 2 airfoil are investigated by comparing the experimental results of the transition fixed at x tr /c = 5% with those of free transition. Figures -3 compares the chordwise pressure distributions over the upper and lower surfaces of the NACA 2 airfoil at M exp =.35, M exp =.6, and M exp =.8, for free and fixed transition at x tr /c = 5% and Re = At subsonic conditions the pressure distribution differences are small. While at supercritical speed the shock wave is very sensitive to boundary layer condition which causes the large difference of pressure distribution between fixed and free transition cases Downloaded by UNIVERSITY OF CALIFORNIA IRVINE on January 29, 25 DOI:.254/ fixed lower surface (a) α = fixed lower surface (c) α = fixed lower surface (b) α = fixed lower surface (d) α = 3. Figure. Comparison of pressure distributions for free and fixed transition at x tr/c = 5%, NACA 2, M exp =.35, Re = of 22

10 Downloaded by UNIVERSITY OF CALIFORNIA IRVINE on January 29, 25 DOI:.254/ fixed lower surface (a) α = fixed lower surface (c) α = fixed lower surface (b) α = fixed lower surface (d) α =. Figure 2. Comparison of pressure distributions for free and fixed transition at x tr/c = 5%, NACA 2, M exp =.6, Re = of 22

11 fixed lower surface fixed lower surface Downloaded by UNIVERSITY OF CALIFORNIA IRVINE on January 29, 25 DOI:.254/ (a) α = fixed lower surface (c) α = (b) α = fixed lower surface (d) α = 4. Figure 3. Comparison of pressure distributions for free and fixed transition at x tr/c = 5%, NACA 2, M exp =.8, α =., Re = IV.A.5. Chordwise Pressure Distribution, Transition Fixed, Compared with NASA (98) 2 The NASA Langley 2.5-meter wind tunnel data 2 are chosen for validation of the present results. The test model of Ref. 2 has a large chord of 635 mm and a large span-chord ratio of 3.43, both of which are desirable for two-dimensional testing. The model blockage is 3.5%. The upper and lower test-section walls are axially slotted with an opening of 5%. The ratio of sidewall-displacement-thickness to tunnel width is small (2δ /b =.84), which tends to minimize sidewall-boundary-layer effects. The flow was shown to be two-dimensional even at maximum lift conditions, and the experimental data are not corrected for wall effects. In addition, data for boundary-layer transition fixed at 5% chord are provided in Ref. 2. For supercritical flow the transition position may significantly affect the shock wave and boundary layer interaction and thus the aerodynamic characteristics. Hence the data with known transition position are required for the correlation between experimental results of different wind tunnels. Figures 4-6 presents the chordwise pressure distribution over the upper and lower surfaces of the NACA 2 airfoil at M exp =.35, M exp =.6, and M exp =.8, Re = 3. 6, x tr /c = 5%, compared with the corresponding results of Ref. 2. Still the comparisons are good at subsonic conditions and the discrepancy are large at supercritical flow conditions. of 22

12 Downloaded by UNIVERSITY OF CALIFORNIA IRVINE on January 29, 25 DOI:.254/ (NF-6) -6 (Langley) -5 fixed lower surface (Langley) (a) (NF-6) -6 (Langley) -5 fixed lower surface (Langley) (c) (NF-6) -6 (Langley) -5 fixed lower surface (Langley) (b) (NF-6) -6 (Langley) -5 fixed lower surface (Langley) Figure 4. Pressure distributions at M exp =.35, (a) α = 4., (b) α = 8., (c) α =. and (d) α = 3., NACA 2, Re = 3. 6, x tr/c = 5%, compared with the data of Ref. 2. (d) 2 of 22

13 Downloaded by UNIVERSITY OF CALIFORNIA IRVINE on January 29, 25 DOI:.254/ (NF-6).4 (Langley) fixed lower surface (Langley) (a) (NF-6).4 (Langley) fixed lower surface (Langley) (c) (NF-6).4 (Langley) fixed lower surface (Langley) (b) (NF-6).4 (Langley) fixed lower surface (Langley) Figure 5. Pressure distributions at M exp =.6, (a) α = 4., (b) α = 6., (c) α = 8. and (d) α =., NACA 2, Re = 3. 6, x tr/c = 5%, compared with the data of Ref. 2. (d) 3 of 22

14 (NF-6).4 (Langley) fixed lower surface (Langley) (NF-6).4 (Langley) fixed lower surface (Langley) Downloaded by UNIVERSITY OF CALIFORNIA IRVINE on January 29, 25 DOI:.254/ (a) (NF-6).4 (Langley) fixed lower surface (Langley) (c).2.2 (b) (NF-6).4 (Langley) fixed lower surface (Langley) Figure 6. Pressure distributions at M exp =.8, (a) α =., (b) α = 2., (c) α = 3. and (d) α = 4., NACA 2, Re = 3. 6, x tr/c = 5%, compared with the data of Ref. 2. IV.A.6. Sidewall Interference Correction with Root Mean Square (RMS) Method At transonic speeds, the wall interference problem is complicated by the possible nonlinear interaction of the model flow field with the near-wall flow field. The interference may cause the discrepancy of shock wave positions. So it is necessary to investigate the effects of sidewall interferences. In this paper, a very simple method is used. Based on NASA Langley wind tunnel experimental data, a root mean square of the difference of pressure distribution is calculated for each case. The minimum RMS determines the amount of Mach number correction. Table presents correction results of different Mach number. Its shown that the corrections are small at subsonic conditions and the corrections increase as Mach number increasing. Figure 7 shows the comparison of pressure distribution on the NACA2 surface between NF-6 data with corrected Mach number and NASA Langley data. With Mach number corrections the discrepancy become much smaller. (d) 4 of 22

15 Downloaded by UNIVERSITY OF CALIFORNIA IRVINE on January 29, 25 DOI:.254/ Table. Correction results of some Mach number, NACA 2, Re = 3. 6, x tr/c = 5%. M exp M corr upper surface,m=.8 (Langley).5 lower surface,m=.8 (Langley) upper surface,m=.82 (NF-6) lower surface,m=.82 (NF-6) (a) M exp = upper surface,m=.84 (Langley).5 lower surface,m=.84 (Langley) upper surface,m=.86 (NF-6) lower surface,m=.86 (NF-6) upper surface,m=.82 (Langley).5 lower surface,m=.82 (Langley) upper surface,m=.84 (NF-6) lower surface,m=.84 (NF-6) (b) M exp = upper surface,m=.86 (Langley) lower surface,m=.86 (Langley) upper surface,m=.89 (NF-6) lower surface,m=.89 (NF-6) (c) M exp =.86 (d) M exp =.89 Figure 7. Pressure distribution at NACA 2, M exp =.86.89, α =., Re = 3. 6, x tr/c = 5%. 5 of 22

16 IV.A.7. NACA 2 Airfoil Dynamic Pressure Data Unsteady pressure data on the NACA 2 airfoil are obtained from 6 dynamic pressure Kulite transducers installed at =.25,.5 and.75 on the upper surface and on the two side walls. As the flow about the model is two-dimensional, the ensemble-averaged pressure coefficient obtained from the side wall Kulite measurement lies close to the steady pressure distribution measured along the central station of the airfoil. The two foremost transducers ( =.25) are found defective in the present tests. Spectral analysis of the individual unsteady pressures at various test cases is made. In this section, the experimental freestream Mach numbers are not corrected. Figure 8 gives the freestream Mach number and angle of attack of the test cases, where the open and solid symbols denote no buffet and buffet, respectively. Table 2 presents the buffet frequency f and reduced frequency k = 2πfc/U for the NACA 2 airfoil at Re = 3. 6 and x tr /c = 5%. Downloaded by UNIVERSITY OF CALIFORNIA IRVINE on January 29, 25 DOI:.254/ α ( ) without buffet with buffet M exp Figure 8. Freestream Mach number and angle of attack, where the open and solid symbols denote no buffet and buffet cases, respectively, NACA 2, Re = 3. 6, x tr/c = 5%. Table 2. Buffet reduced frequency k = 2πfc/U infty, NACA 2, Re = 3. 6, x tr/c = 5%. M exp α f(hz) k , The spectral analysis of the individual unsteady pressures is done with a discrete Fourier transform. The sampling rate is set to 2, Hz and low-pass filtered at 2, Hz. The sampling length is fixed to 2s. Fig. 9 presents the resulting modulus squared of the unsteady pressure coefficient Ĉp 2 versus frequency f for M exp =.8.89, α =, at Re = 3. 6, x tr /c = 5%. In the figure denotes the location of the Kulite transducer. In Fig. 9, at =.75 a prominent spectral peak with large amplitude near Hz is seen for M exp =.88 and.89 at α =, and no large amplitude spectral peak is found for M exp = The buffet frequencies are summarized in Table 2. The unsteady pressures at the location =.5 yield no prominent spectral peak. In Fig. 2 (a) and Fig. 2 (a), multiple large-amplitude spectral peaks appear for M exp =.6 and M exp =.8. The fundamental shock oscillation mode frequencies listed in Table 2. The RMS value of the pressure fluctuations could also characterize buffet onset. Figure 22 presents the RMS value of the pressure fluctuations measured by the Kulite transducer for M exp =.8, α = of 22

17 .. 8E-5 6E-5 cp 2 (Hz ) cp 2 (Hz ) 8E-5 6E-5 4E-5 4E-5 2E-5 2E f(h z) M exp f(h z) (a) = M exp (b) =.75 Figure 9. Unsteady pressure coefficient modulus squared Cˆp 2 vs. frequency f, NACA 2, Mexp =.8.89, α =, Re = 3. 6, xtr /c = 5%.. 8E-5 6E-5 cp (Hz ) 8E-5 2 4E-5 4E-5 2 cp (Hz ) 6E-5 2E-5 2 2E f(h z) f(h z) ) α ( ) α ( (a) =.5 (b) =.75 Figure 2. Unsteady pressure coefficient modulus squared Cˆp vs. frequency f, NACA 2, Mexp =.6, α = 9., Re = 3. 6, xtr /c = 5%.. 8E-5 8E-5 6E-5 6E E-5 4E-5 2E-5 2E f(h z) cp (Hz ) 2 cp (Hz ) Downloaded by UNIVERSITY OF CALIFORNIA IRVINE on January 29, 25 DOI:.254/ α 8 f(h z) 3 4 (a) = α 3 4 (b) =.75 Figure 2. Unsteady pressure coefficient modulus squared Cˆp 2 vs. frequency f, NACA 2, Mexp =.8, α =, Re = 3. 6, xtr /c = 5% 7 of 22

18 When the angle of attack changes, the rms value does not change at the location =.75. But, at =.5, when α = 2, the rms value increases with the angle of attack increasing. So the buffet onset occurs at α = 2 at M exp =.8. The RMS value of the pressure fluctuations at the location =.75 for M exp =.8.89, α = are shown in Figure =.5 =.75 Downloaded by UNIVERSITY OF CALIFORNIA IRVINE on January 29, 25 DOI:.254/ Prms/q α ( ) Figure 22. angle of attack distribution of rms value of the pressure fluctuation, M exp =.8, Re = 3. 6, x tr/c = 5%. Prms/q M exp Figure 23. rms value of the pressure fluctuation at the location =.75, M exp =.8.89, α =, Re = 3. 6, x tr/c = 5%. Buffet onset is also characterized by the chordwise distributions of the mean pressure coefficient. Figure 24 compares the static pressures measured on the central section of the NACA 2 airfoil for M exp =.86,.87,.88 and.89 at α =, Re = 3. 6 and x tr /c = 5%. The spreading of the recompression region for M exp =.88 and.89 is resulted from the temporal integration of the intermittence during shock oscillation, and indicates buffet occurrence. Note also that the thickening of the mean separated region during buffet leads to a pressure decrease at the trailing edge. The time-averaged results of the unsteady pressure measurements on the wind tunnel side walls are also shown in Fig. 24. They lie close to the static pressure curve of the model central section, which indicates that the flow is essentially two dimensional. 8 of 22

19 Downloaded by UNIVERSITY OF CALIFORNIA IRVINE on January 29, 25 DOI:.254/ upper_surface lower_surface North_wall South_wall (a) M exp = upper_surface lower_surface North_wall South_wall (c) M exp = upper_surface lower_surface North_wall South_wall (b) M exp = upper_surface lower_surface North_wall South_wall (d) M exp =.89 Figure 24. Mean surface pressure coefficient, NACA 2, M exp =.86.89, α =., Re = 3. 6, x tr/c = 5% of 22

20 Downloaded by UNIVERSITY OF CALIFORNIA IRVINE on January 29, 25 DOI:.254/ IV.B. Numerical Simulation Results In this section the unsteady flow field simulations for NACA2 airfoil at freestream Mach numbers from.82 to.89 at zero angle of attack for Reynolds numbers 3. 6 with transition fixed at 5% chord length are performed to study unsteady viscous flow behaviors. The computational results reveal that the flow is steady when the Mach number is between.82 and.84. When the Mach number gets to.85, the flow suddenly changes into an unsteady oscillatory mode. The shock waves on the upper and lower surfaces of the airfoil begin to move back and forth in a periodic motion. The unsteadiness is caused by the shock wave interaction with the boundary layer over the airfoil surface. It can be categorized to type A shock wave motion. The unsteady flow pattern persists as the Mach number is further increased until it gets to.88 where the flow becomes steady again. The buffet occurs in a narrow band of freestream Mach numbers of Figure 25 shows the lift coefficients evolution history for the three Mach numbers of.85,.86, and.87. Figure 26 shows FFT analysis of lift coefficients. The FFT amplitudes are normalized by largest peak between the three Mach numbers. Figure 27 shows the comparison of time-averaged pressure distribution on the NACA2 surface between computational and experimental data. The time-averaged shock wave positions are very close. In the figure the computational Mach number is.85 and the experimental Mach number is.88. The Mach number discrepancy is caused by the endwall interference of wind tunnel test. After Mach number correction, the experimental Mach number.88 is corrected to.85 which is the same as computational Mach number. c l t (s) Ma =.85 Ma =.86 Ma =.87 Figure 25. Evolution of lift coefficients for NACA2 airfoil, α =., Re = Normalized magnitude Ma =.85 Ma =.86 Ma = Reduced Frequency Figure 26. FFT analysis of lift coefficients for NACA2 airfoil, α =., Re = of 22

21 Experiment (lower_surface) Experiment (upper_surface) Computation - c p Downloaded by UNIVERSITY OF CALIFORNIA IRVINE on January 29, 25 DOI:.254/ Figure 27. Comparison of time-averaged pressure distribution around NACA2 airfoil, α =., Re = V. Conclusions A NACA 2 airfoil model is tested in a transonic wind tunnel with free and fixed boundary-layer transitions at freestream Mach number of.35 to.89, and Reynolds number about 3 6. The fixed transition is set at 5% chord on the airfoil. The static pressure are measured and verified using other wind tunnel test results. With transition fixed the two-dimensionality is improved especially at supercritical flow conditions. Dynamic pressure measurements show that the buffet starts at different angle of attack at different freestream Mach number. The buffet onset angle of attack is about α exp = 9. when the experimental freestream Mach number is M exp =.6. At this lower Mach number condition, at the higher angle of attack a sharp suction peak of pressure cause a supersonic pocket with a shock wave which interacts with boundary layer. Then the buffet happens. At supercritical condition such as freestream Mach number M exp =.8, the shock wave is stronger at small angle of attack. So the buffet onset angle of attack is about α exp = 2. at freestream Mach number M exp =.8. For this symmetric airfoil NACA 2 the buffet even occurs at zero angle of attack in a narrow band of freestream Mach numbers from.88 to.89. At these conditions the shock waves are strong enough to induce the flow separation at zero angle of attack. The numerical simulations also show the close trend as experiment results at higher freestream Mach number. It can be conjectured there may be a close relationship between inviscid multiple solutions and unsteady buffet of viscous flow. VI. Acknowledgment The present work is supported by the Foundation for Fundamental Research of the Northwestern Polytechnical University No. JC3 and Nation Key Laboratory Research Foundation of China No. 94C 423C42. References McDevitt, J. B., Supercitical Flow About a Thick Circular-Arc Airofil, NASA TM 78549, McDevitt, J. B., Levy, J. J., and Deiwert, G. S., Transonic flow about a thick circular-arc airfoil, AIAA Journal, Vol. 4, No. 5, 976, pp Levy, J. J., Experimental and computational steady and unsteady transonic flows about a thick airfoil, AIAA Journal, Vol. 6, No. 6, 978, pp Marvin, J. G. and Levy, J. J., Turbulence modelling for unsteady transonic flows, AIAA Journal, Vol. 8, No. 5, 98, pp McDevitt, J. B. and Okuno, A. F., Static and Dynamic Pressure Measurements on a NACA 2 Airfoil in the Ames High Reynolds Number Facility, NASA TP 2485, K. Yamamoto, Y. T., Self-excited Oscillation of Transonic Flow Around an Airfoil in Two-Dimensional Channels, 2 of 22

22 Downloaded by UNIVERSITY OF CALIFORNIA IRVINE on January 29, 25 DOI:.254/ Journal of Turbomachinery, Vol. 2, No., 99, pp Jacquin, L., Molton, P., Deck, S., Maury, B., and Soulevant, D., Experimental Study of Shock Oscillation over a Transonic Supercritical Profile, AIAA Journal, Vol. 47, No. 9, 29, pp Hartmann, A., Steimle, P. C., Klaas, M., and Schroder, W., Time-Resolved particle Image Velocimetry of Unsteady Shock Wave-Boundary Layer Interaction, AIAA Journal, Vol. 49, No., 2, pp Liu, Y., Liu, F., and Luo, S., Abstract: MX.4 : Linear Stability Analysis on Multiple Solutions of Steady Transonic Small Disturbance Equation, APS, Nov. 2. Xiong, J., Liu, F., and Luo, S., Computation of NACA2 Airfoil Transonic Buffet Phenomenon with Unsteady Navier-Stokes Equations, AIAA paper , January 22. Thibert, J., Grandjacques, M., and Ohman, L., NACA 2 Airfoil, Experiment Data Base for Computer Program Assassment, AGARD-AR-38 A- to A-9, Harris, C., Two-Dimensional Aerodynamics of the NACA 2 Airfoil in the Langley 8-Foot Transonic Pressure Tunnel, NACA TM 8927, Abbott, I. H. and Von Doenhoff, A. E., Theory of Wing Sections, Dover Publications, Inc., New York, Braslow, A. and Knox, E., Simplified Method for Determination of Critical Height of Distributed Roughness Particles for Boundary-Layer Transition at Mach Numbers from to 5, NACA TN 4363, Main-Smith, J., Chemival Solids as Diffusible Coating Films for Visual Indications of Boundary-Layer Transition in Air and Water, ARC Reports and Memoranda 2755, Menter, F., Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications, AIAA Journal, Vol. 32, No. 8, 994, pp of 22