COMPRESSIBILITY EFFECTS ON TURBULENCE STRUCTURES OF AXISYMMETRIC MIXING LAYERS

1. COMPRESSIBILITY EFFECTS ON TURBULENCE STRUCTURES OF AXISYMMETRIC MIXING LAYERS PHYSICS OF FLUIDS (VOLUME 15) BRIAN THUROW, MO SAMIMY AND WALTER LEMPERT The Ohio State University, Columbus, Ohio 43210 (Received 17 September 2002; accepted 25 February 2003; published 6 May 2003) Presented by: ANIL THOMAS SU ID -790273351

2. OVERVIEW • GOAL • FACILITY AND DIAGNOSTICS • EXPERIMENTAL CONDITIONS • RESULTS a. Flow visualization b. Space-Time correlation results. • DISCUSSION • CONCLUSIONS

3. GOAL • To understand the dynamics of the turbulence structures in the regime of compressibility. • A real-time flow visualization system that produces 17 images over a time span of 150 microseconds is used to visualize the mixing layers. • Planer space-time correlations are used to track structures as the mixing layer convects downstream, determining their coherence and the changes in convective velocity with increasing compressibility.

4. Mixing layers of Mach 1.3(Mc=0.59) and Mach 2.0(Mc=0.87) ideally expanded high Reynolds number axisymmetric jets. Convective Mach number and Convective Velocity are given by: Mc= U1-U2 = U1-Uc,i = Uc,i-U2 -----(1) a1+a2 a1 a2 Uc,i= a1U2+a2U1 -----(2) a1+a2 U1&U2 – High and Low speed free stream velocities. a1&a2 - Speeds of sound Uc,i - Theoretical Isentropic convective velocity.

5. For Mc<0.5, turbulence structures are similar to the incompressible structures. They are two dimensional, coherent, and appear as large span wise rollers. The velocity of such large-scale structures is relatively accurately predicted by Eq.(2). For Mc>1.0, the flow is highly compressible and turbulence structures exhibit very little resemblance to their incompressible counterparts. Structures are smaller in scale, difficult to identify, more three-dimensional and lack coherence. Convective velocity measurements also deviate greatly from Eq. (2)

6. The compressibility range of 0.5<Mc<1.0, however, marks a transition between these two distinct regimes. The flow becomes more three-dimensional as Mc is increased from 0.5 toward 1.0, but elements of both incompressible and compressible flows are present, particularly at the lower end of the range. The convective velocity of structures also deviates from Eq. (2).

7. FACILITY AND DIAGNOSTICS • A jet stand and stagnation chamber to which a variety of nozzles may be attached. • Air is supplied from two four-stage compressors. • The stagnation chamber contains a perforated plate and two screens of varying porosity to condition the flow to be as uniform as possible prior to entering the nozzle. • A pulse burst laser and an ultra high-speed CCD camera were used to take sequences of 17 time-correlated flow visualization images.

8. For flow visualization, the laser beam was formed into a sheet and was directed through various slices in the flow field. Seeding was provided using product formation where water vapor contained in the warm moist ambient air condensed into nanometer-scale droplets upon entrainment into the jet and mixing with the cold and dry air of the jet core.

9. EXPERIMENTAL CONDITIONS The laser sheet was arranged to acquire images of both streamwise and cross-stream planes in the flow at a variety of downstream distances ranging from 3 to 12 jet diameters. Important parameters of two axisymmetric jets studied:

10. Convective velocities were calculated for downstream distances of 5.5 and 8 jet diameters for the Mach 1.3 and 2.0 jets, respectively. These locations are between 55% and 65% of the potential core length and allow structures to develop without interference from the other side of the mixing layer. A Non-dimensional time, t , is defined as - Jet exit velocity - Local mixing layer thickness - Time between two images obtained using the real-time visualization technique The value of t between each image is nearly same for both jets indicating that similar time span are being examined for both jets.

11. A. FLOW VISUALIZATION: A typical streamwise image sequence of Mach 1.3 (Mc=0.59) axisymmetric jet RESULTS

12. A typical cross-stream image sequence of Mach 1.3 (Mc=0.59) axisymmetric jet at x/D=6

13. A typical streamwise image sequence of Mach 2.0 (Mc=0.87) axisymmetric jet

14. A typical cross-stream image sequence of Mach 2.0 (Mc=0.87) axisymmetric jet at x/D=9

15. For a time separation of 10 microseconds, the maximum correlation level has dropped to about 0.83 and is located just under 3mm downstream. For increasing time separations, the correlation level continues to drop and the peak broadens. At Dt =140 microseconds, the maximum correlation is about 0.18 and the peak is quite broad. B. SPACE-TIME CORRELATION RESULT

16. The locations of these Peaks are plotted on an x-t diagram in Fig. 6. The slope of the linear fit through these points is the average convective velocity for the Mach 1.3 jet. The curve fit is very good and the average convective velocity is 266 m/s. This velocity is well above the theoretical prediction (Eq.2) of 206 m/s.

17. As the maximum correlation decreases and the peak becomes increasingly broad for increased time separations. Starting with a time separation of 80 microseconds, however, a very interesting event happens. This broad peak can now be clearly seen as consisting of two peaks. By individually charting the location of both peaks, two convective velocities can be calculated, a fast mode and a slow mode.

18. The points marking the fast mode do not appear until a time separation of 72 microsec. The linear fit to these points is quite good and the average convective velocity for the fast mode is 402 m/s while that of the slow mode is 190 m/s. The theoretical value for the convective velocity is calculated as 303 m/s, which is about halfway between the fast mode and the slow mode.

19. This is a plot of the maximum correlation levels Vs non-dimensional time for both jets. The non-dimensional time was defined in Eq.(2). The normalization collapses the results onto a single curve very well, except for the fast mode, which has a slightly lower correlation level.

20. This data include measurements from both the upper and lower halves of the mixing layer and consist of 354 cases. The peak of the histogram is centered at 250 m/s, which is close to the ensemble average convective velocity of 266 m/s, given earlier.

21. It consists of 151 individual measurements. The fast and slow modes observed in the ensemble-average data are manifested in the bimodal peaks. These peaks are centered at about 175 and 350 m/s and are close to the ensemble average values of 190 and 402 m/s, given earlier.

22. DISCUSSION • With increasing convective Mach number, structures become less organized and more three dimensional. • Double-pulsed flow visualizations indicate a suppression of interaction between turbulence structures. • There was a decrease in coherence of structures with changing compressibility. • The close match between the curves for Mc=0.59 and 0.87 seems to indicate that structures in either flow field evolve at approximately the same rate, when measured in units of non-dimensional time. • For the Mach 1.3 jet, we observe a fast mode in agreement with the stream selection rule. For the Mach2.0 jet, a fast mode is also observed. Contrary to the stream selection rule, however, a slow mode was also observed for the same flow field.

23. CONCLUSIONS • In the case of the Mach 1.3 jet, tearing and pairing occurred frequently. These types of events were also observed in the Mach 2.0 jet, but were less frequent and much more difficult to follow. • In both flow fields, the presence of streamwise vortices was observed in cross-stream images of the flow. These vortices seem to play a significant role in mixing layer dynamics, particularly in comparison with planar shear layers. • The lifetime of structures in both mixing layers was found to be about the same when using a non dimensional time scale based on the jet’s exit velocity and the local shear layer thickness.

24. Ensemble-average results show a single fast mode for the Mach 1.3 jet of 266 m/s, which is significantly higher than the theoretical velocity of 206 m/s. The same technique applied to the Mach 2.0 jet, however, revealed the presence of both a fast and a slow mode. These were measured to be 402and 190 m/s, respectively.

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