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StanShock: a gas-dynamic model for shock tube simulations with non-ideal effects and chemical kinetics

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Abstract

A high-order, quasi-one-dimensional, reacting, compressible flow solver is developed to simulate non-ideal effects and chemical kinetics in shock tube systems. To this end, physical models for the thermoviscous boundary-layer development, area variation, gas interfaces, and reaction chemistry are considered. The model is first verified through simulations of steady isentropic nozzle flow, multi-species Sod’s problem, laminar premixed flame, and ZND detonation test cases. Comparisons with experiments are made by examining end-wall pressure traces that are gathered from shock tube experiments designed to test the code’s capabilities. Subsequently, the solver is utilized for uncertainty quantification and design optimization of a driver insert. Both applications prove to be highly efficient, indicating the utility of the solver for the design of experiments in consideration of non-ideal gas-dynamic effects.

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References

  1. Hanson, R.K., Davidson, D.F.: Recent advances in laser absorption and shock tube methods for studies of combustion chemistry. Prog. Energy Combust. Sci. 44, 103–114 (2014). https://doi.org/10.1016/j.pecs.2014.05.001

    Article  Google Scholar 

  2. Petersen, E.L., Hanson, R.K.: Nonideal effects behind reflected shock waves in a high-pressure shock tube. Shock Waves 10, 405–420 (2001). https://doi.org/10.1007/PL00004051

    Article  Google Scholar 

  3. Pang, G.A., Davidson, D.F., Hanson, R.K.: Experimental study and modeling of shock tube ignition delay times for hydrogen/oxygen/argon mixtures at low temperatures. Proc. Combust. Inst. 32, 181–188 (2009). https://doi.org/10.1016/j.proci.2008.06.014

    Article  Google Scholar 

  4. Davidson, D.F., Hanson, R.K.: Recent advances in shock tube/laser diagnostic methods for improved chemical kinetics measurements. Shock Waves 19, 271–283 (2009). https://doi.org/10.1007/s00193-009-0203-0

    Article  Google Scholar 

  5. Hong, Z., Pang, G., Vasu, S., Davidson, D., Hanson, R.: The use of driver inserts to reduce non-ideal pressure variations behind reflected shock waves. Shock Waves 19, 113–123 (2009). https://doi.org/10.1007/s00193-009-0205-y

    Article  Google Scholar 

  6. Li, H., Owens, Z.C., Davidson, D.F., Hanson, R.K.: A simple reactive gasdynamic model for the computation of gas temperature and species concentrations behind reflected shock waves. Int. J. Chem. Kinet. 40, 189–198 (2008). https://doi.org/10.1002/kin.20305

    Article  Google Scholar 

  7. Chaos, M., Dryer, F.L.: Chemical-kinetic modeling of ignition delay: considerations in interpreting shock tube data. Int. J. Chem. Kinet. 42(3), 143–150 (2010). https://doi.org/10.1002/kin.20471

    Article  Google Scholar 

  8. Weber, Y.S., Oran, E.S., Boris, J.P., Anderson, J.D.: The numerical simulation of shock bifurcation near the end wall of a shock tube. Phys. Fluids 7, 2475–2488 (1995). https://doi.org/10.1063/1.868691

    Article  MATH  Google Scholar 

  9. Yamashita, H., Kasahara, J., Sugiyama, Y., Matsuo, A.: Visualization study of ignition modes behind bifurcated-reflected shock waves. Combust. Flame 159, 2954–2966 (2012). https://doi.org/10.1016/j.combustflame.2012.05.009

    Article  Google Scholar 

  10. Grogan, K.P., Ihme, M.: Weak and strong ignition of hydrogen/oxygen mixtures in shock-tube systems. Proc. Combust. Inst. 35(2), 2181–2189 (2015). https://doi.org/10.1016/j.proci.2014.07.074

    Article  Google Scholar 

  11. Khokhlov, A., Austin, J., Knisely, A.: Development of hot spots and ignition behind reflected shocks in 2H\(_2\) + O\(_2\). 25th International Colloquium on the Dynamics of Explosions and Reactive Systems, Leeds, UK, Paper 20 (2015)

  12. Grogan, K.P., Ihme, M.: Regimes describing shock boundary layer interaction and ignition in shock tubes. Proc. Combust. Inst. 36(2), 2927–2935 (2017). https://doi.org/10.1016/j.proci.2016.06.078

    Article  Google Scholar 

  13. Lipkowicz, J.T., Wlokas, I., Kempf, A.M.: Analysis of mild ignition in a shock tube using a highly resolved 3D-LES and high-order shock-capturing schemes. Shock Waves 29, 511–521 (2019). https://doi.org/10.1007/s00193-018-0867-4

    Article  Google Scholar 

  14. Ben-Dor, G., Igra, O., Elpherin, T. (eds.): Handbook of Shock Waves. Elsevier, New York (2001). https://doi.org/10.1016/B978-0-12-086430-0.50045-2

    Book  Google Scholar 

  15. Alpher, R.A., White, D.R.: Flow in shock tubes with area change at the diaphragm section. J. Fluid Mech. 3(5), 457–470 (1958). https://doi.org/10.1017/S0022112058000124

    Article  Google Scholar 

  16. Saad, M.: Compressible Fluid Flow. Prentice-Hall, Englewood Cliffs (1985)

    Google Scholar 

  17. Kays, W., Crawford, M., Weigand, B.: Convective Heat and Mass Transfer. McGraw-Hill, New York (2005)

    Google Scholar 

  18. Mark, H.: The interaction of a reflected shock wave with the boundary layer in a shock tube. J. Aeronaut. Sci. 24, 304–306 (1957)

    Article  Google Scholar 

  19. Houim, R.W., Kuo, K.K.: A low-dissipation and time-accurate method for compressible multi-component flow with variable specific heat ratios. J. Comput. Phys. 230, 8527–8553 (2011). https://doi.org/10.1016/j.jcp.2011.07.031

    Article  MathSciNet  MATH  Google Scholar 

  20. Ziegler, J.: Simulations of compressible, diffusive, reactive flows with detailed chemistry using a high-order hybrid WENO-CD scheme. Ph.D. thesis, California Institute of Technology (2011)

  21. Lv, Y., Ihme, M.: Discontinuous Galerkin method for multicomponent chemically reacting flows and combustion. J. Comput. Phys. 270, 105–137 (2014). https://doi.org/10.1016/j.jcp.2014.03.029

    Article  MathSciNet  MATH  Google Scholar 

  22. Shu, C.W.: Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. Technical Report No. 97-65, Institute for Computer Applications in Science and Engineering NASA Langley Research Center (1997)

  23. Grogan, K.P.: Modeling and simulation of non-ideal combustion. Ph.D. thesis, Stanford University (2018)

  24. Glowinski, R., Osher, S.J., Yin, W. (eds.): Splitting Methods in Communication and Imaging, Science, and Engineering. Springer, New York (2016). https://doi.org/10.1007/978-3-319-41589-5

    Book  MATH  Google Scholar 

  25. Goodwin, D.G., Speth, R.L., Moffat, H.K., Weber, B.W.: Cantera: an object-oriented software toolkit for chemical kinetics, thermodynamics, and transport processes. https://www.cantera.org (2018). Version 2.4.0

  26. Abgrall, R.: How to prevent pressure oscillations in multicomponent flow calculations: a quasi conservative approach. J. Comput. Phys. 125, 150–160 (1996). https://doi.org/10.1006/jcph.1996.0085

    Article  MathSciNet  MATH  Google Scholar 

  27. Abgrall, R., Karni, S.: Computations of compressible multifluids. J. Comput. Phys. 169, 594–623 (2001). https://doi.org/10.1006/jcph.2000.6685

    Article  MathSciNet  MATH  Google Scholar 

  28. Billet, G., Abgrall, R.: An adaptive shock-capturing algorithm for solving unsteady reactive flows. Comput. Fluids 32, 1473–1495 (2003). https://doi.org/10.1016/S0045-7930(03)00004-5

    Article  MATH  Google Scholar 

  29. Toro, E.: Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction, 3rd edn. Springer, Berlin (2009). https://doi.org/10.1007/b79761

    Book  MATH  Google Scholar 

  30. Lam, S.K., Pitrou, A., Seibert, S.: Numba: a LLVM-based Python JIT compiler. LLVM@SC (2015)

  31. Hunter, J.D.: Matplotlib: A 2D graphics environment. Comput. Sci. Eng. 9(3), 90–95 (2007). https://doi.org/10.1109/MCSE.2007.55

    Article  Google Scholar 

  32. Sod, G.: A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws. J. Comput. Phys. 27, 1–31 (1978). https://doi.org/10.1016/0021-9991(78)90023-2

    Article  MathSciNet  MATH  Google Scholar 

  33. Laney, C.B.: Computational Gasdynamics. Cambridge University Press, Cambridge (1998). https://doi.org/10.1017/CBO9780511605604

    Book  MATH  Google Scholar 

  34. Hong, Z., Davidson, D., Hanson, R.: An improved \(\text{ H }_{2}/\text{ O }_{2}\) mechanism based on recent shock tube/laser absorption measurements. Combust. Flame 158, 633–644 (2011). https://doi.org/10.1016/j.combustflame.2010.10.002

    Article  Google Scholar 

  35. Lee, J.H.S.: The Detonation Phenomenon. Cambridge University Press, Cambridge (2008). https://doi.org/10.1017/CBO9780511754708

    Book  Google Scholar 

  36. Burke, M.P., Chaos, M., Ju, Y., Dryer, F.L., Klippenstein, S.J.: Comprehensive \(\text{ H }_{2}/\text{ O }_{2}\) kinetic model for high-pressure combustion. Int. J. Chem. Kinet. 44(7), 444–474 (2012). https://doi.org/10.1002/kin.20603

    Article  Google Scholar 

  37. Campbell, M.F.: Studies of biodiesel surrogates using novel shock tube techniques. Ph.D. thesis, Stanford University (2014)

  38. Tranter, R.S., Lynch, P.T.: A miniature high repetition rate shock tube. Rev. Sci. Instrum. 84, 094102 (2013). https://doi.org/10.1063/1.4820917

    Article  Google Scholar 

  39. Lee, D., Hochgreb, S.: Rapid compression machines: Heat transfer and suppression of corner vortex. Combust. Flame 114, 531–545 (1998). https://doi.org/10.1016/S0010-2180(97)00327-1

    Article  Google Scholar 

  40. Ihme, M.: On the role of turbulence and compositional fluctuations in rapid compression machines: Autoignition of syngas mixtures. Combust. Flame 159(4), 1592–1604 (2012). https://doi.org/10.1016/j.combustflame.2011.11.022

    Article  Google Scholar 

  41. Santer, T.J., Williams, B.J., Notz, W.I.: The Design and Analysis of Computer Experiments. Springer Series in Statistics. Springer, New York (2003). https://doi.org/10.1007/978-1-4757-3799-8

    Book  Google Scholar 

  42. Rasmussen, C.E., Williams, K.I.: Gaussian Processes for Machine Learning. MIT Press, Cambridge (2006)

    MATH  Google Scholar 

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Acknowledgements

The authors gratefully acknowledge financial support through the Air Force Office of Scientific Research under Award No. FA9550-14-1-0219. Additionally, we would like to thank Ronald K. Hanson, David F. Davidson, and Kenneth Brezinsky for invaluable discussions on shock tube experiments, which greatly informed this work.

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  1. Omniscience, Palo Alto, USA

    K. Grogan

  2. Stanford University, Stanford, USA

    M. Ihme

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Correspondence to K. Grogan.

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Communicated by H. Olivier.

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Grogan, K., Ihme, M. StanShock: a gas-dynamic model for shock tube simulations with non-ideal effects and chemical kinetics. Shock Waves 30, 425–438 (2020). https://doi.org/10.1007/s00193-019-00935-x

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