Pressure Modulation of Weak Shock Waves through. Turbulent Flows

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1 4th Fluid Dynamics Conference and Exhibit 28 June - July 2, Chicago, Illinois AIAA Pressure Modulation of Weak Shock Waves through Turbulent Flows Daisuke Takagi, Atsushi Matsuda 2, Akihiro Sasoh 3, Shigeyoshi Ito 4, Kouji Nagata 5, Yasuhiko Sakai 6 Nagoya University, Furo-cho, Chikusa-ku, Nagoya, , Japan We performed experimental study about the interaction between a shock wave and atmospheric turbulence. A low speed wind tunnel with square grids (separation distance of mm) was used to generate turbulent flows. We generated a shock wave using an openend shock generator. We varied a flow velocity, shock Mach number and the size of square grids as control parameters, and measured an overpressure history on a flat plate located at 2 mm from the exit of the shock wave generator. After the shock wave passed through the grid turbulence, the standard deviation of the post-shock overpressure is increased to 7.3 % from.7% obtained without flow. A I. Introduction project of supersonic transport (SST) is currently run by Japan Aerospace Exploration Agency (JAXA). It is reported that large pressure modulation can occur when a shock wave interacts with atmospheric turbulence. In order to evaluate the effect of turbulence on sonic boom, experimental dataset about the interaction between a shock wave and turbulence warrants further investigations. The experimental result of interactions between shock wave and slit jet is reported by Lipkens et al. 2 According to this report, both the peak value and the rise time of a shock-induced overpressure exhibit large scatters, while the average value of the peak overpressure decreases and that of the rise time increases. Experimental study of interactions between slit jet and shock wave was conducted by Kim et al. 3 They succeeded to visualize the shock Graduate Student, Department of Aerospace Engineering, Nagoya University, AIAA Student Member. 2 Assistant Professor, Department of Aerospace Engineering, Nagoya University, AIAA Member. Currently, Assistant Professor, Department of Mechanical Engineering, Meijo University, AIAA Member. 3 Professor, Department of Aerospace Engineering, Nagoya University, Associate Fellow. 4 Graduate Student, Department of Mechanical Science and Engineering, Nagoya University. 5 Professor, Department of Mechanical Science and Engineering, ditto. 6 Professor, Department of Mechanical Science and Engineering, ditto. Copyright 2 by the, Inc. All rights reserved.

2 wave which is deformed by the interaction with slit jet. In their results, the average value and standard deviation of peak overpressure and its rise time agreed with Lipkens results. In order to obtain quantitative relationship between the overpressure and the turbulence in more general form, it is necessary to examine turbulent flows with better characterization. The purpose of this study is to obtain experimental relationships about the effect of the grid turbulence on the post-shock overpressure. PT- (PCB:3A2) 77 PT-2 (3A2) (a) Wind tunnel with square grids PT-3 (3A2) 32 Unit : mm 6 In wind tunnel SUS tube inner diameter: 5.35mm 46 y y Driver gas reservior x = 5 PT-4 (PCB:M2B8) (b) Test section (x=5mm) Figure. Schematics of experimental setup. z 2

3 II. Experimental Apparatus A. Wind Tunnel The wind tunnel used in this study is shown in Fig.(a). Its test length equals 4. m, and cross-section of 994mm 46mm. At the entrance of the wind tunnel, there are square grids made of aluminum. Here x-axis is along the test flow, y- and z-axes in the vertical and horizontal directions, respectively. Their origin is in the center of the tunnel width at the grid surface on the bottom wall. The square grids are placed with a separation distance of mm. Each of the grids has a 2mm 2mm square cross-section. Post-shock overpressure was measured at x =.5 m. The mean flow speed is denoted by U, its root mean square (r.m.s.) in the x and y directions U r.m.s. and V r.m.s., respectively. U was set to m/s or 7m/s. The turbulent flow characteristics were measured using an I-type and X-type hot wire anemometers. 4 In the range of 7mm y 3mm and -5mm z 5mm at x=.5 m, U r.m.s. /U which was measured using the I-type equaled 5.8.4[%]. Using the X-type in the range of 6 mm y 32mm at x=5mm and z=mm, U r.m.s. /U =5.9.2[%] and V r.m.s. /V =5.2.8[%]. Driver gas Atmosphere Piston (made of PC) Driven section (SUS tube) PI Atmosphere Driver section PI Figure 2. Driver gas reservoir with quick piston valve. B. Test Section In the wind tunnel, the test section (Fig.. (b)) is set to x=.5m. A shock wave generated in the shock wave generator exits at y=3 mm, and propagates a distance of 2 mm, impinging on a flat place at y= mm. The flat plate is made of aluminum, has dimensions of 2mm 2mm 8.8mm.(thickness). 3

4 In the shock wave generator, the driver gas reservoir is connected to a stainless-steel tube (inner diameter; 5.35mm). Dry air was used as the driver gas. A shock wave is generated by opening a quick-piston valve, see Fig. 2. Three pressure transducers (PT-, PT-2, and PT-3, PCB, H3A2, 3.6 mv/kpa, 5kHz) are set up in the tube to measure the velocity of the shock wave by the method of time of flight. A shock Mach number measured between PT- and PT-2 is denoted by M -2, that between PT-2 and PT-3 by M 2-3. The pressure transducer, PT-4 (PCB, M2B8, 4.9 mv/kpa, 5kHz), flush mounted on the plate at y= mm, measured the overpressure induced by the normal reflection of the shock wave, which was the primary interest in this study p p 2 p 3 p [kpa] Time ms Figure 3. Pressure traces measured with PT-,2,3 (without flow). III. Results A. Shock Wave Generator Performance Thirty experiments were under condition of U = m/s and p s =5kPa (initial pressure in the driver gas reservoir, absolute value,). Figure 3 shows overpressure histories measured in the shock wave generator, p, p 2 and p 3, respectively. Four waveforms are plotted in the figure. The reproducibility is sufficient. Due to pressure loss in the tube, the shock Mach number is decreased; M -2 =.86. (.%) and M 2-3 =.49.(.%), respectively. B. Post-Shock Overpressure Characteristics Figure 4 shows overpressure history measured with PT-4 ( p 4 ) without flow. In this case, p 4,peak =.39.8kPa(.7%). Four waveforms are plotted. Their reproducibility is also sufficient. With turbulent flow of U =.m/s, one hundred measurements were done. The initial pressure of the driver gas was set to p s =5kPa. The pressure histories at the PT-4 measured in four experiments are shown in Fig. 5. p 4,peak =.5.77 kpa(7.3%). The standard deviation in p 4,peak with the turbulent flow became larger by 4.3 times than that without flow. This result agrees with Lipken et al. and Kim et al. 4

5 .2.8 p4[kpa] main Time 5μs Figure 4. Pressure traces measured with PT-4 (without flow)..2.8 p 4 [kpa] Time 5μs Figure 5. Pressure traces measured with PT-4 (turbulent flow). IV. Conclusion The experiments about interactions between the grid turbulence and the shock wave were conducted. A large scatter in overpressure with the turbulent flow was 4.3 times larger than that without flow. Acknowledgments The authors would like to express our gratitude to Messrs. Akira Saito, Katsuyoshi Kumazawa, Takao Sumi, Technical Division, Graduate School of Engineering, Nagoya University for their valuable technical assistances. This research was supported by Japan Society for Promotion of Science, 92689, and Japan Aerospace Exploration Agency, project No. 27-J-J67. References Tatarski, V.I., Wave Propagation in a Turbulent Medium, McGraw-Hill Book Co. Inc., Lipkens, B., and Blackstock, D. T., Model Experiments to Study Sonic Boom Propagation through Turbulence, Part : General Results, J. Acoust. Soc. Am.Vol. 3, No., pp , J.H. Kim, et al., Shock Waves, submitted. 5