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Large eddy simulation of acoustic waves generated from a hot supersonic jet

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Abstract

The effects of jet temperature on acoustic waves generated by a supersonic jet are investigated using large eddy simulation (LES) based on a high-fidelity computational code. The sixth-order compact scheme and the fourth-order Runge–Kutta scheme are employed for spatial derivatives and time integration, respectively. First, a verification and validation study is conducted using simulations of a cold supersonic jet with a jet Mach number of 2.0 and Reynolds number of \(9.0 \times 10^5\), and the effects of grid resolution and disturbance strength are evaluated. The verification and validation study shows that \(6.5 \times 10^8\) grid points are sufficient for qualitative discussion of acoustic wave generation phenomena and that the addition of disturbances is important for suppressing the acoustic waves caused by the turbulent transition at the nozzle exit, as seen in previous studies for a subsonic jet. Then, LESs of supersonic jets with a jet Mach number of 2.0 and Reynolds number of \(9.0 \times 10^5\) are performed for three temperature cases where the ratios of chamber to atmospheric temperature are 1.0, 2.7, and 4.0. The present results illustrate that different jet temperatures do not change the shear layer thickness, but the shear layer develops more inside the jet as the jet temperature increases, resulting in a shorter potential core for the hot jet. With regard to the acoustic fields, as the jet temperature increases, stronger Mach waves are emitted from a wider source region at wider radiation angles. We observe multiple Mach waves with different angles in the hot jet cases.

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Acknowledgements

This study was supported by Kakenhi Grants (17H03473 and 25709009). This study used computational resources of the “K” supercomputer provided by the Advanced Institute of Computational Science, RIKEN, through the High Performance Computing Initiative System Research Project (Project IDs: hp150125, hp160158, and hp170156). The authors are grateful for helpful comments from Mamori and Fukushima of the Tokyo University of Science (currently, the University of Electro-Communications and Tokai University, respectively) and preliminary computations conducted by P. Gabriel and K. Morihira, former graduate students at the University of Tokyo.

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Authors and Affiliations

  1. Department of Aerospace Engineering, Graduate School of Engineering, Tohoku University, 6-6-01 Aoba, Aramaki, Aoba, Sendai, 980-8579, Japan

    T. Nonomura & Y. Ozawa

  2. Tokyo University of Science, 3-1-1 Yoshinodai, Chuo, Sagamihara, Kanagawa, 229-8510, Japan

    H. Nakano

  3. Department of Aeronautics and Astronautics, Graduate School of Engineering, The University of Tokyo, 3-1-1 Yoshinodai, Chuo, Sagamihara, Kanagawa, 229-8510, Japan

    D. Terakado

  4. Department of Mechanical Engineering, Graduate School of Engineering, Tokyo University of Science, 6-3-1, Nijuku, Katsushika, Tokyo, 125-8585, Japan

    M. Yamamoto

  5. Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo, Sagamihara, Kanagawa, 229-8510, Japan

    K. Fujii & A. Oyama

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  1. T. Nonomura
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Appendix: Details of experiments conducted for validation study

Appendix: Details of experiments conducted for validation study

The computational results obtained in this study are compared with the results of experiments performed by the authors for the verification of the computation. A cold supersonic jet was reproduced with high-pressure air by a supersonic-jet-generating system in an anechoic room. We adjusted the pressure of the plenum chamber to realize an ideally expanded condition (\(M_{\mathrm{J}} = 2.0\), \(\hbox {Re} = 9.8 \times 10^5\)). To obtain the velocity field, particle image velocimetry (PIV) was performed at the supersonic-jet-generating system with a particle generator at Tohoku University. See reference [32] for more details. The diameter at the nozzle exit was 10 mm, and the Reynolds number of the supersonic jet was \(9.8 \times 10^5\). The design Mach number of all nozzles was 2.0. These nozzles are made with stereolithography. We employed a double-pulse laser system (LDY-300PIV, Litron Lasers) and a high-speed camera (V611, Phantom) to obtain particle images from the supersonic flow. The supersonic jet flow was very fast, which may have interfered with tracer particle mixing. Therefore, a premixing chamber was installed between the plenum chamber and tracer particle generator. Glycerin 50% aqueous solution was used for tracer particles. Particle size was approximately several micrometers. A Nikon lens and extension tube (Nikkor 300 mm f/4) were used. The resolution of all images was 1280 \(\times \) 800 pixels (120 \(\times \) 80 mm). The time \(\delta t\) between pulses of the lasers was set to be \(2\,\upmu \hbox {s}\), and the sampling frequency for each image was set to be 1000 Hz. In this study, a single-pixel ensemble correlation method [35] was adopted instead of a conventional spatial correlation method. The advantage of this correlation method is that it can image the velocity fields with fine spatial resolution corresponding to single pixels. However, only average velocity fields were obtained because temporal evolution information is used in the correlation calculation. This correlation method enabled us to obtain a detailed shear layer profile of a supersonic jet that has a large velocity gradient in the thin layer. In this study, we calculated cross-correlation from 2000 image pairs.

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Nonomura, T., Nakano, H., Ozawa, Y. et al. Large eddy simulation of acoustic waves generated from a hot supersonic jet. Shock Waves 29, 1133–1154 (2019). https://doi.org/10.1007/s00193-019-00895-2

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