Experimental and numerical investigation on sound generation from airfoil-flow interaction

Appl. Math. Mech. -Engl. Ed., 32(6), 765–776 (2011)DOI 10.1007/s10483-011-1456-7c©Shanghai University and Springer-Verlag

Berlin Heidelberg 2011

Applied Mathematicsand Mechanics(English Edition)

Experimental and numerical investigation on sound generation fromairfoil-flow interaction∗

Min JIANG (� �), Xiao-dong LI (��), Jia-jian ZHOU (��)

(School of Jet Propulsion, Beihang University, Beijing 100191, P. R. China)

(Communicated by Wen-rui HU)

Abstract Aerodynamic noise due to interaction between incoming turbulence and

rotating blades is an important component in the wind turbine noise. The rod-airfoil

configuration is used to investigate the interactive phenomenon experimentally and nu-

merically. Distribution of unsteady pressure on the airfoil surface is measured for different

rod positions and airfoil attack angles. Two National Advisory Committee for Aeronat-

ics (NACA) airfoils, NACA0012 and NACA0018, and two wind turbine airfoils, S809

and S825 are investigated. In addition, for low angles of attack, the flow field around

the airfoil’s leading edge is investigated with the particle image velocimetry (PIV). The

experimental results indicate that unsteady pressure disturbances on the airfoil surface

are related to the rod vortex shedding. Meanwhile, the interaction flow field of the rod

and NACA0012 airfoil is simulated with the unsteady Reynolds averaged Navier-Stokes

method (URANS), and the obtained pressure spectra are compared with the experimen-

tal results.

Key words rod-airfoil interaction, unsteady Reynolds averaged Navier-Stokes method,

particle image velocimetry, unsteady pressure

Chinese Library Classification V211.7, V211.3

2010 Mathematics Subject Classification 76G25

1 Introduction

For wind turbines, the incoming turbulent flow interacts with the downstream blades andgenerates sound radiation to the far field which is one of the most important components ofwind turbine noise. This kind of interaction phenomena can also be found in aero-engines andhelicopters. Therefore, it has already been a very important topic to investigate this kind ofinteraction flow phenomena for the understanding of noise generation mechanism.

The rod-airfoil configuration is a basic model to study the effect of incoming turbulenceon the airfoil. A rod is embedded upstream of the airfoil, so the von Karman vortex street isformed and convects downstream, which is used to impinge on the leading edge of the airfoil.Subsequently, the vortex is extruded, stretched, and splited. This process affects the flow fieldaround the airfoil significantly. Recently, the rod-airfoil interaction model has been investigated

∗ Received Feb. 21, 2011 / Revised Apr. 20, 2011Project supported by the National Basic Research Program of China (973 Program) (No. 2007CB714604)Corresponding author Xiao-dong LI, Professor, E-mail: [email protected]

766 Min JIANG, Xiao-dong LI, and Jia-jian ZHOU

by many researchers due to the fact that on one hand this configuration is simple enough ingeometry, and on the other hand the rod wake combines the dominated periodic vortex sheddingwith random perturbations which could be observed in the incoming turbulence flow of windturbine applications. Jacob and Casalino[1] conducted a measurement of the rod/NACA0012interaction flow field via the particle image velocimetry (PIV) technique, and obtained the farfield noise spectra as well, which provided detailed database for the validation of numericalsimulation. Their numerical and experimental results show that the interaction of vortex withthe airfoil leading edge is the main characteristics of the rod-airfoil interaction flow and thedominant noise source. Meanwhile, the rod-airfoil case has also been investigated widely bynumerical approaches, such as Reynolds-averaged Navier-Stokes method (RANS)[1–2], largeeddy simulation method (LES)[1–3], and detached eddy simulation method (DES)[4–6]. However,those investigations are only concentrated on the case that the rod is fixed, which meansthere is no shift between the rod axis and the airfoil chord, and the angle of attack is zero.However, the incoming turbulence toward airfoil could be various in the practice. Therefore,the investigation of the rod-airfoil interaction process with different rod positions and angles ofattack has significant efects for the real application.

In the present work, the rod-airfoil interaction problem is investigated experimentally andnumerically. In the experiment, the unsteady pressure disturbances on the airfoil surface aremeasured by dynamic pressure transducers in consideration of different rod positions and anglesof attack of the airfoil. In addition, the flow field of 2D rod/NACA0012 airfoil interaction issimulated by URANS. For the cases of small angles of attack, the flow field around the airfoilleading edge is examined by the PIV technique.

2 Experimental set-up and measurement techniques

2.1 Flow configurationThe rod-airfoil experiment was carried out in the anechoic chamber of Fluid and Acoustic

Engineering Laboratory of Beihang University. A blow-down air supply system was used toprovide the airflow. The outlet section of the wind tunnel is 250 mm×150 mm. The windtunnel can supply air continuously for approximately two minutes at the Mach number of 0.1.The airfoil was fixed between two round plates (see Fig. 1), and the angle of attack θ couldbe changed in the range from –60◦ to 60◦ by rotating these two round plates. The rod wasinstalled on a slider and its transverse position (shift between the rod axis and the airfoil chord)could be varied in the range from –35 mm to 35 mm. The sketch of the rod and NACA0012airfoil interaction model is shown in Fig. 1, where D denotes the rod diameter. The chord c ofthe airfoil and the distance between the rod and the airfoil were both 10D. The rod diameterand the airfoil chord were 6 mm and 60 mm in the dynamic pressure measurements, while theywere 10 mm and 100 mm in the PIV experiment. The experimental model is geometricallysimilar to that of Jacob and Casalino[1].

Fig. 1 Sketch of experimental set-up

Experimental and numerical investigation on sound generation from airfoil-flow interaction 767

2.2 Dynamic pressure measurementsIn this paper, the unsteady pressure on the airfoil surface was measured by three Kulite

dynamic pressure transducers, of which the measurement range is from 89 kPa to 117 kPa andthe approximate sensitivity is 7 V/kPa. The installation positions of these dynamic pressuretransducers are shown in Fig. 2, where the signs of rod position and airfoil attack angle aredefined.

Fig. 2 Sketch of installation positions of transducers

2.3 Particle image velocityThe double pulsed laser light sheet that illuminates the flow field was created by two fre-

quency doubled Spectra-Physics Quanta-Ray Nd-YAG lasers. The charge coupled device (CCD)camera used to capture the images has a resolution of 640×480 pixels, and a maximum framerate of 30 Hz. The software for control and analysis is Microvec running with the operationsystem of Windows NT4.0. The tracer particles are smoke particles and the measuring planeis the vicinity of the airfoil leading edge, as shown in Fig. 3.

Fig. 3 Sketch of PIV measuring plane

3 Numerical approach

3.1 Governing equation and turbulence modelThe governing equation is compressible Reynolds averaged Navier-Stokes equation in the

form of finite volume,

∂(ρui)∂t

+ uj∂(ρui)∂xj

= − ∂p

∂xi+

∂

∂xj

(μ

∂ui

∂xj− ρu′

iu′j

). (1)


In order to solve closure problem, the Wilcox k-ω turbulence model[7] is introduced. Roescheme[8] is used for spatial discretization, and three-factor approximate factorization[9] com-bining with subiteration[10] is adopted for time marching.3.2 Computational domain and mesh

The computational domain is a quasi oval domain, whose center is at the airfoil leading edge,and its lengths in the flow direction and the longitudinal direction are 112D and 100D, respec-tively. The computational domain consists of multi-block grids. The O-grid systems are adoptedaround the rod and airfoil. These two O-grid systems are linked with an H-grid system and en-closed by another O-grid system. The total grid number is approximately 190 000 (see Fig. 4).The inflow and outflow boundary conditions are used at the inflow and outflow boundary re-gion, respectively. No slip wall boundary conditions are applied on the surfaces of the rod andairfoil.

Fig. 4 Computational mesh

4 Experimental results

4.1 Pressure spectraThe unsteady pressure disturbances on airfoil surface were measured, and the effects of

rod positions and angles of attack were investigated. Two NACA airfoils, NACA0012 andNACA0018, and two wind turbine airfoils, S809 and S825 are considered. The results ofNACA0012 airfoil are mainly discussed.

The comparison of the pressure spectra of airfoil leading edge between the case with andwithout rod is plotted in Fig. 5 , where the incoming Mach number is 0.1 and the airfoil angleof attack θ = 0◦, SPL represents sound pressure level. As shown in Fig. 5 , there is a pressurepeak around the Strouhal number (fD/U0) St = 0.183 in the case of rod-airfoil, correspondingto the value of St of the rod vortex shedding with Ma=0.1.

The pressure spectra at three different locations are shown in Fig. 6, where the incomingMach number is 0.1 and θ = 0◦. At St = 0.183 ±0.002 corresponding to the rod sheddingfrequency, the amplitude of main peak is largest at the leading edge of airfoil and decreasessignificantly along the chord direction, which indicates that airfoil leading edge is the main areafor the interaction of von Karman vortex street and airfoil. As a result, the following analysiswill mainly focus on the leading edge of airfoil.

In order to study the effect of the airfoil angle of attack on the rod-airfoil interaction flow,the pressure on airfoil surface is measured by changing the angle of attack. It is noted that there


is no shift between the rod axis and the airfoil chord in these cases. Sensor 1 is at the airfoilleading edge. The pressure spectra of Sensor 1 (on the suction surface) at angle of attack from0◦ to 60◦ are presented in Fig. 7. The pressure spectra of Sensor 1 (on the pressure surface) atangle of attack range from 0◦ to –60◦ are shown in Fig. 8. As shown in Fig. 7, at the leadingedge of the suction surface, the pressure amplitude of the peak at the rod vortex sheddingfrequency increases at first, and then decreases when the angle of attack varies from 0◦ to 60◦

degree. It reaches the maximum at θ = 15◦, while almost disappears at θ = 30◦. When θ =60◦, the low frequency part of the spectra decreases due to the flow separation on the suctionsurface. As shown in Fig. 9, at the leading edge of the pressure surface, the pressure level atStrouhal number corresponding to the vortex shedding frequency decreases with the increaseof the angle of attack. When θ = –30◦, due to the high pressure on the pressure surface, thestrength of the von Karman vortex street dissipates faster in the process of approaching theairfoil and thus has a less effect on the pressure surface, resulting in that the pressure level ofStrouhal number corresponding to vortex shedding frequency decreases dramatically. At theangle of attack of –60◦, the pressure spectrum is almost unchanged compared to that of theangle of attack of –30◦.

Fig. 5 Comparison of pressure spectra be-tween the case of airfoil and rod-airfoil (Ma�0.1, θ = 0◦)

Fig. 6 Pressure spectra at different loca-tions (Ma�0.1, θ = 0◦)

Fig. 7 Pressure spectra at airfoil leading edge with positive angles of attack

In order to study the effect of the variation of rod’s transverse position on the flow field,


the pressure spectra at several different transverse positions of the rod are measured, where theangle of attack remains unchanged. The pressure spectra of the airfoil leading edge at 0◦ and15◦ are shown in Fig. 9(a) and Fig. 9(b), respectively, where position 0D denotes that there isno shift between the rod axis and the airfoil chord, and position 1D denotes that the offset ofthe rod is D in the positive direction. According to Fig. 9, the pressure level of the Strouhalnumber corresponding to the vortex shedding frequency decreases when the offset of the rodincreases.

Fig. 8 Pressure spectra at the airfoil leading edge with negative angles of attack

Fig. 9 Pressure spectra at the airfoil leading edge with different transverse rod positions

The pressure spectra of different airfoils are collected in Fig. 10 to analyze the effect ofvariation of airfoil geometry on the flow field. Roughly speaking, for zero, small, medium andlarge angle of attack, the pressure spectra of two NACA airfoils are similar. The results of twowind turbine airfoils show small difference at θ = 0◦. When θ = 0◦, the amplitude of pressurepeak at the rod vortex shedding frequency of S825 is closer to that of NACA airfoil. For smalland medium angle of attack, the pressure load on the leading edge of NACA airfoil are largerthan that of wind turbine airfoil as wells as the amplitude of pressure peak at the rod vortexshedding frequency. Due to the flow separation on the suction surface at large angle of attack,the tendency of pressure spectra of different airfoils become identical.


Fig. 10 Pressure spectra of different airfoils

4.2 Instantaneous flow field obtained by PIVThe instantaneous velocity field and vorticity field around the airfoil leading edge obtained by

PIV are shown in Fig. 11, where θ = 6◦. The von Karman vortex street is clearly distinguishablein the plot of vorticity field.

A large set of instantaneous velocity fields obtained by PIV is averaged to attain the meanflow field shown in Fig. 12. The wake region of the rod varies with angle of attack. Comparedto the case of θ = 0◦, the wake region of the rod deflects slightly at θ = 6◦.

Fig. 11 PIV instantaneous field θ=6◦


Fig. 12 Mean velocity field around leading edge

5 Numerical simulation results

5.1 Validation exampleThe numerical simulation code is validated first using the experimental results of rod-airfoil

interaction by Jacob and Casalino[1]. The parameters of the incoming flow in this experimentare given in Table 1 and the Reynolds number is based on the rod diameter.

Table 1 Parameters of incoming flow θ = 0◦

Re Ma θ

4.417×104 0.205 0◦

The mean flow field is compared with the computational and experimental results by Ja-cob and Casalino[1]. The computational results of the x-direction velocity component (u-component) at the line of x/c=–0.255 and x/c=0.25 are compared with measurements in Fig. 13.As shown in Fig. 13, the computed profile of u-component at x/c=–0.255 line is steeper thanexperimental data, which is an indication of larger y-direction gradient of u-component, whereasthe result computed by Ecole Centrale de Lyon (ECL) indicates smaller y-direction gradient ofu-component compared to experiment. At the line of x/c=0.25, only the results in the range ofy �0 are plotted, due to that geometry configuration and mean flow are symmetry with respectto x-axis. The position of airfoil wall is y/c�0.064. In the vicinity of the airfoil wall, the com-puted results of this paper agree well with the experimental results, while there is a deviationbetween the results of ECL and measurements in the range of 0.077< y/c <0.29. Based on thecomparisons above, the computational results of this paper agree better with measurementsthan those of ECL using URANS.

Instantaneous vorticity contours at different time in one rod vortex shedding period aregiven in Fig. 14. The interaction process of von Karman vortex street with airfoil is shown:the vortices with positive vorticity and the vortices with negative vorticity interact with theairfoil leading edge alternatively, and then move downstream along with the airfoil surface. Inthis interaction process, the vortex is being weakened continually and almost disappears at themiddle of the airfoil. It is worthwhile to note that vortex with positive vorticity interacts withairfoil leading edge under the leading edge and move downstream along with the lower surfaceof the airfoil; while the vortex with negative vorticity interacts with the leading edge above theleading edge and moves downstream along with the upper surface of the airfoil.


Fig. 13 Profile of x-direction velocity component of mean flow

Fig. 14 Instantaneous vorticity field contours in one rod vortex shedding period (θ = 0◦)

Based on the comparison between the computation and experiment, the numerical results ofthis paper basically agree with the measurements, and the interaction process of von Karmanvortex street with airfoil is clearly shown, which demonstrates the feasibility of using the presentnumerical solver to compute the rod-airfoil interaction flow.5.2 Example of experimental condition

Rod-airfoil interaction flow is computed according to the incoming flow conditions inTable 2, and the Reynolds number is based on rod diameter.


Table 2 Parameters of incoming flow

Re Ma θ

1.4×104 0.2 6◦, 10◦, 15◦

Instantaneous vorticity contours at different time in a rod vortex shedding period at θ = 6◦

are plotted in Fig. 15. The effect of the angle of attack on von Karman vortex street is shown.Compared to the case of θ = 0◦, von Karman vortex street deflects, resulting from that the flowvelocity of suction surface is larger than that of pressure surface at non-zero angle of attack.The deflection of von Karman vortex street is enhanced by the increase of angle of attack. It isshown that the strength of the vortex near the pressure surface dissipates faster in the processof approaching the airfoil, which is different from that of the 0◦ case.

Based on the unsteady numerical results, the pressure spectra on the airfoil surface can beobtained by the fast Fourier transform (FFT). Three pressure spectra at different locationsare shown in Fig. 16, in which “Point 1”, ”Point 2”, and “Point 3” correspond to “Sensor1”,”Sensor 2”, and “Sensor 3” in Fig. 2. The level of the main peak is the largest at the leadingedge and decreases along with the chord direction, which agrees with that of the experimentalresults. However, the decreasing rate of the level of the main peak becomes less compared tothe experiment results.

Fig. 15 Instantaneous vorticity field contours in one rod vortex shedding period (θ = 6◦)


Fig. 16 Pressure spectra at different locations (θ=0◦)

The computed pressure spectra at the airfoil leading edge are compared with the experi-mental values in Fig. 17, corresponding to different angle of attack respectively. The numericalspectrum is that of a purely periodic signal, while the experimental spectrum is broadenedaround the shedding frequency. The shedding frequency is overpredicted by RANS, and thelevel of main peak is underpredicted except for the case of θ = 0◦.

Fig. 17 Pressure spectra of different θ

6 Conclusions

The unsteady pressure on the airfoil surface with different rod positions and angles of attackhas been measured by dynamic pressure transducers. Moreover, the flow field of 2D rod andNACA0012 airfoil interaction has been computed by URANS. In addition, the PIV techniquehas been implemented to present the flow around airfoil leading edge at small angles of attack.The airfoil leading edge is found to be the main area of the interaction between the von Karmanvortex street and the airfoil. The strength of the interaction reaches its maximum around 15◦

angle of attack and it also varies with the transverse position of the rod. To be specific, itdecreases with the increase of the offset of the rod. The obtained distribution of mean flowvelocity agrees well with the experimental measurements and the calculated frequency andamplitude of the pressure peak show slight difference with the experimental data. Besides,the interaction process of the vortex street with the airfoil is clearly displayed by the numericalsimulation. The results of PIV experiment also show that the angle of attack of airfoil has effecton the von Karman vortex street, which is similar to that obtained in the numerical simulation.


References

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[3] Boudet, J., Grosjean, N., and Jacob M. C. Wake-aifoil interaction as broadband noise source: alarge-edgy simulation study. International Journal of Aeroacoustics, 4(1), 93–115 (2005)

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[6] Carani, M., Dai, Y., and Carani, D. Acoustic investigation of rod airfoil configuration with DESand FWH. AIAA Paper, 2007-4016 (2007)

[7] Wilcox, D. C. Reassessment of the scale determining equation for advanced turbulence models.AIAA Journal, 26(11), 1299–1310 (1988)

[8] Roe, P. L. Approximate Riemann solvers, parameter vectors and difference schemes. Journal ofComputational Physics, 43(2), 357–372 (1981)

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Experimental and numerical investigation on sound generation from airfoil-flow interaction