Newsletter 2014.11 Index
Theme : "Mechanical Engineering Congress, 2014 Japan (MECJ-14) Part 1"
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Particle Image Velocimetry for High Speed Air Flow and Uncertainty
Shunsuke Koike
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Abstract
Particle Image Velocimetry (PIV) is a powerful tool in wind tunnel experiments for aerospace engineering. In this paper, the PIV system in the JAXA 2m x 2m transonic wind tunnel is briefly described to show the important points of PIV for high-speed air flows. The traceability of the particles is essentially important in PIV for supersonic flows. The influence of the response delay of the particles on the velocity measurement and its uncertainty are described with a comparison between PIV and Molecular Tagging Velocimetry (MTV) data. A simple correction method for the response delay of the tracer particles is introduced. The corrected velocity calculated from PIV data is compared with the velocity using MTV.
The simplest equation for the PIV analysis is expressed by the next Eq. (1).
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(1) |
Here, u [m/s], α [m/pixel]，ΔX[pixel]，andΔt [s] are velocity, scaling factor, displacement of particles, and interval of the successive laser pulse, respectively. The uncertainty related to the measurement principle (e.g., traceability of particles), δu is also important. Uncertainty of those values should be reduced in order to reduce the total uncertainty of the velocity measurement.
Figure 1 shows the PIV system in the JAXA 2m x 2m transonic wind tunnel. As shown in Fig. 1, the PIV system is compose of seeding, laser sheet, and camera systems. In order to reduce the uncertainty of the values in Eq. (1) and δu, the following points are important. The major uncertainty was caused by the sub-pixel analysis in the vector calculation process when we implemented the following points.
First, the diameter of the tracer particle should be small to increase the traceability of the particles. In our case, oil particle (Dioctyl sebacate, DOS) which had a diameter of about 1 µm was used to reduce the uncertainty of δu. Although there are much smaller particles (e.g., TiO2 and Al2O3), these solid particles have risk to make some damage on the wind tunnel facility. Hence, we adopted the DOS.
Second, all components in Fig. 1 and vector processing method are important to reduce the uncertainty of the ΔX. We used our original focus control equipment for the camera system to obtain appropriate particle scattering light images. The several types of seeding rake were also used in order to make uniform seeding and to attain the appropriate number density of particles in a measurement area.
Third, we measured the interval of the successive laser pulse Δt at 2GHz sampling. The interval of the successive laser pulse for transonic flows is typically about several hundred nanoseconds. Hence, the error of several ten nanoseconds which is not a big problem for low speed flow measurement makes large uncertainty in the transonic flow measurement.
Fourth, the calibration of the camera system is also important to reduce the uncertainty related to the scaling factor α. Generally, it is difficult to set up the calibration board precisely in the large wind tunnel. We used the laser marking devices to set up the calibration board and the camera system precisely. The laser marking devices were also used for the positioning of the laser light sheet.
Major uncertainty in the PIV measurement for supersonic flows is caused by the response delay of the tracer particles. In supersonic flows, there are expansion fans and shock waves. These strong waves produce high acceleration and deceleration regions. The particles cannot follow the gas in those regions. Figure 2 directly represents this problem. So, in Fig 2, the PIV data is compared with the MTV data and the theoretical and empirical velocity curves for the underexpanded jet. Oil particles (DOS, of about 1µm) are used as tracers in the PIV measurements, and acetone is used as a molecular tracer in the MTV measurements. Hence, the velocity measured using MTV shows the actual velocity of the gas. As shown in Fig. 2(c), the velocity data measured using MTV agree with the theoretical and empirical velocity curves for the underexpanded jet. However, the data measured using PIV differ from the MTV data and the curves. The PIV data are lower than those in the acceleration region and higher in the deceleration region. Although the PIV data seem appropriate as shown in Fig. 2(b), it should be known that the PIV data have large uncertainties in the high acceleration and deceleration regions produced by the strong waves.
Generally, it is difficult to introduce the measurement system using molecular tracer into the large wind tunnels because of the molecular tracer harmfulness. Hence, the author considers that PIV is one of the most important tools to clarify the complex supersonic flow fields even if there is a problem in the particle traceability. Therefore, we are developing the simple correction methods using the theoretical and empirical drag laws of a sphere. In Fig. 2(c), the velocity corrected by the Stokes drag law is shown as red plots. Although several corrected data do not agree with the MTV data, it is clear from Fig. 2(c) that the PIV data are improved through the correction. The corrected data are useful to evaluate the uncertainty caused by the response delay of the particles. The author considers that the correction methods are useful in order to expand the measurement domain of PIV.
Reference
| (1) | Koike, S., Takahashi, H., Tanaka, K., Hirota, M., Takita, K., and Masuya, G., “Correction method for particle velocimetry data based on the Stokes drag law”, AIAA Journal, Vol. 45, No. 11, pp. 2770-2777, 2007. |
| (2) | Katsuhito Mii, Aoi Nakano, Shunsuke Koike, and Taro Handa, “Study on the correction method of PIV data measured in a supersonic region –comparison with MTV data–”, 45th Fluid Dynamics Conference/Aerospace Numerical Simulation Symposium 2013, 2B02, 2013. |
Key words
Particle Image Velocimetry, Transonic, Supersonic, Wind Tunnel
Figures
Fig. 1 JAXA 2m x 2m transonic wind tunnel and the PIV systems.
Fig. 2 Comparison between PIV and MTV data (2).
(a) Schematic of underexpanded jet,
(b) Velocity distribution measured using PIV,
(c) Velocity profile and their correction data on the center line
(broken line in Fig. 2(b)).