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High-Pressure Real-Gas Jet and Throttle Flow as a Simplified Gas Injector Model Using a Discontinuous Galerkin Method

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High Performance Computing in Science and Engineering ´16

Abstract

Industrial devices such as gas injectors for automotive combustion engines operate at ever-increasing pressures and already today reach regimes beyond the ideal-gas approximation. Numerical simulations are an important part of the design process for such components. In this paper, we present a case study with a computational fluid dynamics code based on the discontinuous Galerkin spectral element method with a real-gas equation of state. We assess a high-pressure throttle and jet flow as a basic model of a gas injector. We apply a shock-capturing method to achieve a robust simulation, and a newly developed method to maintain high efficiency despite load imbalances introduced by the shock capturing. The results indicate a dynamic mass flow rate at different pressure ratios between the inlet and outlet.

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  1. Adolf, M., Bargende, M., Becker, M., Bender, T.B., Budde, M., Ebner, A., Feix, F., Figer, G., Heine, P., Jauss, A., Kehler, T., Keskin, M.T., Köhler, E., Kufferath, A., Langer, W., Lejsek, D., Petersen, C., Philipp, U., Sarikaya, A., Sauerstein, R., Schaarschmidt, M., Schenk, A., Volz, P., Weiske, S., Winke, F., Winkelmann, H., Wollenhaupt, H., Wunderlich, K.: Natural gas and renewable methane for powertrains: future strategies for a climate-neutral mobility. In: Vehicle Development for Natural Gas and Renewable Methane, pp. 229–458. Springer, Cham (2016)

    Google Scholar 

  2. Allgeier, T., Haug, M., Frehoff, R., Weikert, M., Kröger, K., Langer, W., Förster, J., Thurso, J., Wörsinger, J.: Gasoline engine management: systems and components. In: Operation of Gasoline Engines on Natural Gas, pp. 122–135. Springer, Wiesbaden (2015)

    Google Scholar 

  3. Altmann, C., Beck, A.D., Hindenlang, F., Staudenmaier, M., Gassner, G.J., Munz, C.-D.: An efficient high performance parallelization of a discontinuous galerkin spectral element method. Lect. Notes Comput. Sci. 7686, 37–47 (2013)

    Article  Google Scholar 

  4. Beater, P.: Pneumatic Drives System Design, Modeling and Control. Springer, Berlin/London (2007)

    Book  Google Scholar 

  5. Bell, I.H., Wronski, J., Quoilin, S., Lemort, V.: Pure and pseudo-pure fluid thermophysical property evaluation and the open-source thermophysical property library coolprop. Ind. Eng. Chem. Res. 53 (6), 2498–2508 (2014)

    Article  Google Scholar 

  6. Boblest, S., Hempert, F., Hoffmann, M., Offenhäuser, P., Sonntag, M., Sadlo, F., Glass, C.W., Munz, C.-D., Ertl, T., Iben, U.: Toward a discontinuous galerkin fluid dynamics framework for industrial applications. In: High Performance Computing in Science and Engineering’15, pp. 531–545. Springer, Berlin/New York (2016)

    Google Scholar 

  7. Bolemann, T., Üffinger, M., Sadlo, F., Ertl, T., Munz, C.-D.: Direct visualization of piecewise polynomial data. In: IDIHOM: Industrialization of High-Order Methods – A Top-Down Approach, pp. 535–550. Springer, Cham (2015)

    Google Scholar 

  8. de Wiart, C., Hillewaert, K.: Development and validation of a massively parallel high-order solver for DNS and LES of industrial flows. In: Kroll, N., Hirsch, C., Bassi, F., Johnston, C., Hillewaert, K. (eds.) IDIHOM: Industrialization of High-Order Methods – A Top-Down Approach. Volume 128 of Notes on Numerical Fluid Mechanics and Multidisciplinary Design, pp. 251–292. Springer, Cham (2015)

    Google Scholar 

  9. Dumbser, M., Iben, U., Munz, C.-D.: Efficient implementation of high order unstructured {WENO} schemes for cavitating flows. Comput. Fluids 86, 141–168 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  10. Hempert, F., Hoffmann, M., Iben, U., Munz, C.-D.: On the simulation of industrial gas dynamic applications with the discontinuous Galerkin spectral element method. J. Therm. Sci. 25 (3), 1–8 (2016)

    Article  Google Scholar 

  11. Hindenlang, F., Gassner, G., Altmann, C., Beck, A., Staudenmaier, M., Munz, C.-D.: Explicit discontinuous Galerkin methods for unsteady problems. Comput. Fluids 61, 86–93 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  12. Huang, J., Crookes, R.: Assessment of simulated biogas as a fuel for the spark ignition engine. Fuel 77 (15), 1793–1801 (1998)

    Article  Google Scholar 

  13. Martin, T., Cohen, E., Kirby, R.M.: Direct isosurface visualization of hex-based high-order geometry and attribute representations. IEEE Trans. Vis. Comput. Graph. 18 (5), 753–766 (2012)

    Article  Google Scholar 

  14. McTaggart-Cowan, G., Mann, K., Huang, J., Singh, A., Patychuk, B., Zheng, Z.X., Munshi, S.: Direct injection of natural gas at up to 600 bar in a pilot-ignited heavy-duty engine. SAE Int. J. Engines 8 (3), 981–996 (2015)

    Article  Google Scholar 

  15. Nelson, B., Kirby, R.M., Haimes, R.: Gpu-based interactive cut-surface extraction from high-order finite element fields. IEEE Trans. Vis. Comput. Graph. 17 (12), 1803–1811 (2011)

    Article  Google Scholar 

  16. Nelson, B., Liu, E., Kirby, R.M., Haimes, R.: Elvis: a system for the accurate and interactive visualization of high-order finite element solutions. IEEE Trans. Vis. Comput. Graph. 18 (12), 2325–2334 (2012)

    Article  Google Scholar 

  17. Pagot, C., Osmari, D., Sadlo, F., Weiskopf, D., Ertl, T., Comba, J.: Efficient parallel vectors feature extraction from higher-order data. Comput. Graph. Forum 30 (3), 751–760 (2011)

    Article  Google Scholar 

  18. Persson, P.-O., Peraire, J.: Sub-cell shock capturing for discontinuous Galerkin methods. In: Proceedings of the American Institute of Aeronautics and Astronautics, Keystone, vol. 112 (2006)

    Google Scholar 

  19. Sonntag, M., Munz, C.-D.: Shock capturing for discontinuous Galerkin methods using finite volume subcells. In: Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems. Volume 78 of Springer Proceedings in Mathematics & Statistics, pp. 945–953. Springer, Cham (2014)

    Google Scholar 

  20. M. Sonntag and C.-D. Munz. Efficient parallelization of a shock capturing for discontinuous galerkin methods using finite volume sub-cells. J. Sci. Comput. 1–28 (2016)

    Google Scholar 

  21. Vuorinen, V., Yu, J., Tirunagari, S., Kaario, O., Larmi, M., Duwig, C., Boersma, B.: Large-eddy simulation of highly underexpanded transient gas jets. Phys. Fluids (1994-present) 25 (1), 016101 (2013)

    Google Scholar 

  22. Westerhoff, M., Holtmeier, G.: Erdgas Die greifbare Chance. MTZ – Motortechnische Zeitschrift 77 (2), 8–13 (2016)

    Article  Google Scholar 

  23. Yu, J., Vuorinen, V., Kaario, O., Sarjovaara, T., Larmi, M.: Visualization and analysis of the characteristics of transitional underexpanded jets. Int. J. Heat Fluid Flow 44, 140–154 (2013)

    Article  Google Scholar 

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Acknowledgements

This work is supported by the Federal Ministry of Education and Research (BMBF) within the HPC III project HONK “Industrialization of high-resolution numerical analysis of complex flow phenomena in hydraulic systems”. We also thank the Gauss Centre for Supercomputing (GCS) which provided us with the necessary computing resources on the Hazel Hen.

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Correspondence to Malte Hoffmann .

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Hempert, F. et al. (2016). High-Pressure Real-Gas Jet and Throttle Flow as a Simplified Gas Injector Model Using a Discontinuous Galerkin Method. In: Nagel, W.E., Kröner, D.H., Resch, M.M. (eds) High Performance Computing in Science and Engineering ´16. Springer, Cham. https://doi.org/10.1007/978-3-319-47066-5_20

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