REACTOR
7.4. FLOW STRUCTURE ANALYSIS BY CROSS-CORRELATION IMAGE PROCESSING
S.B. Leonov, A.A. Firsov, M.A. Shurupov
alexander.a.firsov@gmail.com
The paper describes method of velocity profile measurements by processing of images obtained by schlieren optical system with using of line-scan camera. Image obtained by line-scan camera presents set of instantaneous states of flow disturbances: exposure time of one line is 6 μs at the f = 100 kHz scan rate. The velocity of each small disturbance in the flow is equal to velocity of flow. The method is based on determination of the shift of disturbance dx for two nearest lines of line- scan camera image. Typical line-scan camera image is presented in Fig. 1. Knowing the shift dx, we can find the velocity as V=f×dx. The image is divided to several parts by time and length to find out the local velocity for each part at fixed time. Utilizing the cross-correlation image processing of line-scan camera image, the time-depended lengthwise flow velocity profile averaged by flow width can be calculated. This approach is similar to the particle image velocimetry [1], but instead of introduced particles the natural disturbances are used as markers for velocimetry. In comparison with
correlation method, described in paper [2], presented method allows us to obtain the velocity profile instead of velocity in one point.
Figure 1. Typical image obtained by line-scan camera for subsonic flow.
Two-dimensional cross-correlation function (2D CCF) was used at image parts processing for determine dx:
Figure 2. Typical two-dimensional cross-correlation function.
Each 2D CCF calculation executed for two small parts of full image. These parts are equal by dimensions, but shifted by one line relative to each other in time (Fig. 1).
Typical 2D CCF is presented in Fig. 1.
Coordinate of each maximum at fixed time shift is multiple to dx, so that make possible find the dx by using 2D CCF.
Figure 3. Photo of down wall the channel.
Described method was applied for two experimental configurations. First experiment was provided with airfoil in the subsonic flow. Airfoil was installed into the subsonic flow with velocity V=100 m/s. Injection of weak CO2 jet was used for creation of flow disturbances above the airfoil plane. Field of view of line-scan camera was located in 5 mm above and parallel of the airfoil.
Velocity obtained by described method near the leading edge is in a good agreement with initial flow velocity, and along the chord of the wing profile the measured velocity decrease from 100m/s to 60 m/s and this fact corresponds to the used experimental configuration.
Second velocity measurement with using of cross-correlation image processing was provided in experiment on the plasma associated hydrogen burning in supersonic flow. Flow parameters were following: Mach number M ~ 2, velocity V ~ 490 m/s, To = 300 K. Plasma was produced by direct current electric discharge between 7 cooper electrodes located on the down wall of supersonic channel. Photo of discharge without hydrogen is presented in Fig. 4. Downstream of the electrodes 5 tubes for hydrogen injection was located as it shown in Fig. 3. Field of view of line scan camera was located in a plan parallel and 2 mm over down wall. Because the discharge produce a lot of density disturbances there is not necessary to introduce some foreign elements like a particles in PIV or CO2 jet like in previous experiment.
Figure 4. Photo of discharge without H2.
Measurements in the discharge and combustion area are accompanied by difficulties such as high temperature and voltage. Because of these problems utilization of other methods is difficult or impossible so the numerical simulation was used to obtain velocity field in reaction area.
Calculation of three-dimensional undisturbed flow in configuration close to experimental was performed by using FlowVision™ software. Numerical modeling of flow was based on solution of 3D time-dependent Navier-Stocks equations with the utilization of the wide used two-equation SST-model of turbulence.
Model of perfect gas was used at modeling of supersonic flow. No-slip and adiabatic conditions were specified on upper, lower, and on lateral walls of the duct. Direct current electric discharge was simulated by introducing volumetric heat source whose dimensions were 21 mm length × ∅ 3,4 mm and power was about 1 kW. This approach was tested previously in paper [3]. Combustion was simulated by one gross reaction in the combined Arrhenius-Magnussen model. Symmetry conditions were used on both side walls of the channel to decrease the calculation domain which contained about 9×106 mesh points, i.e. calculation was produced for thin 11 mm layer which contained only one discharge filament and one tube for hydrogen injection.
The results, obtained by cross-correlation image processing and by CFD simulation are presented in Fig. 5. Zero point on X axis corresponds to center of hydrogen injection tube.
Results obtained corresponds to each other, but numerical values have some variance because of some difference in experimental configurations, very simple model of combustion and absence of additional disturbances in numerical simulation introduced by electrical discharge. Main result of provided investigation is velocity values in two areas: 1) velocity in discharge area is 200-250 m/s;
2) velocity in combustion area is significantly lower than initial flow velocity (490 m/s) and it is in the range from 100 to 150 m/s, i.e. flow in combustion area is subsonic.
References
1. М. Raffel, C. Willert, S. Wereley, J. Kompenhans -Particle image velocimetry.
A practical guide. Berlin : Springer. 2007. P. 448 2. S.B. Leonov, A.A. Firsov, D.A. Yarantsev - Determining the Supersonic Flow Velocity Using the Correlation Function of Signals from Refraction
Sensors // Tech. Phys. Lett., 2009, Vol. 35, No. 6, PP. 548–551.
S.B. Leonov, A.A. Firsov, D.A. Yarantsev, F Falempin, M.A. Goldfeld - Plasma Effect on Shocks Configuration in Compression Ramp // 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, 11 - 14 April 2011, San Francisco, California, AIAA 2011- 2362.
Figure 5. Velocity profile for plasma assisted combustion zone in supersonic flo