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Characteristic timescales for detonation-based rocket propulsion systems

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Abstract

Characteristic timescales for rotating detonation rocket engines (RDREs) are described in this study. Traveling detonations within RDREs create a complex reacting flow field involving processes spanning a range of timescales. Specifically, characteristic times associated with combustion kinetics (detonation and deflagration), injection (e.g., flow recovery), flow (e.g., mixture residence time), and acoustic modes are quantified using first-principle analyses to characterize the RDRE-relevant physics. Three fuels are investigated including methane, hydrogen, and rocket-grade kerosene RP-2 for equivalence ratios from 0.25 to 3 and chamber pressures from 0.51 to 10.13 MPa, as well as for a case study with a standard RDRE geometry. Detonation chemical timescales range from 0.05 to 1000 ns for the induction and reaction times; detonation-based chemical equilibrium, however, spans a larger range from approximately 0.5 to \(200~\upmu \)s for the flow condition and fuel. This timescale sensitivity has implications regarding maximizing detonative heat release, especially with pre-detonation deflagration in real systems. Representative synthetic detonation wave profiles are input into a simplified injector model that describes the periodic choking/unchoking process and shows that injection timescales typically range from 5 to \(50~\upmu \)s depending on injector stiffness; for detonations and low-stiffness injectors, target reactant flow rates may not recover prior to the next wave arrival, preventing uniform mixing. This partially explains the detonation velocity deficit observed in RDREs, as with the standard RDRE analyzed in this study. Finally, timescales tied to chamber geometry including residence time are on the order of 100–10,000 \(\upmu \)s and acoustic resonance times are 10–\(1000~\upmu \)s. Overall, this work establishes characteristic time and length scales for the relevant physics, a valuable step in developing tools to optimize future RDRE designs.

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Data sets generated during the current study are available from the corresponding author on reasonable request.

References

  1. Stechmann, D.P., Heister, S.D., Harroun, A.J.: Rotating detonation engine performance model for rocket applications. J. Spacecr. Rocket. 56, 887–898 (2019). https://doi.org/10.2514/1.a34313

    Article  Google Scholar 

  2. Fievisohn, R.T., Hoke, J., Schumaker, S.A.: Product recirculation and incipient autoignition in a rotating detonation engine. AIAA Scitech 2020 Forum, AIAA Paper 2020-2286 (2020). https://doi.org/10.2514/6.2020-2286

  3. Wolański, P.: Research on Detonative Propulsion in Poland. Institute of Aviation, Warsaw (2021)

    Google Scholar 

  4. Bennewitz, J.W., Burr, J.R., Bigler, B.R., Burke, R.F., Lemcherfi, A., Mundt, T., Rezzag, T., Plaehn, E.W., Sosa, J., Walters, I.V., Schumaker, S.A., Ahmed, K.A., Slabaugh, C.D., Knowlen, C., Hargus, W.A.: Experimental validation of rotating detonation for rocket propulsion. Sci. Rep. 13, 14201 (2023). https://doi.org/10.1038/s41598-023-40156-y

    Article  Google Scholar 

  5. Hargus, W.A., Schumaker, S.A., Paulson, E.J.: Air force research laboratory rotating detonation rocket engine development. AIAA 2018 Joint Propulsion Conference, AIAA Paper 2018-4876 (2018). https://doi.org/10.2514/6.2018-4876

  6. Xu, R., Dammati, S.S., Shi, X., Genter, E.S., Jozefik, Z., Harvazinski, M.E., Lu, T., Poludnenko, A.Y., Sankaran, V., Kerstein, A.R., Wang, H.: Modeling of high-speed, methane-air, turbulent combustion, part II: reduced methane oxidation chemistry. Combust. Flame 263, 113380 (2024). https://doi.org/10.1016/j.combustflame.2024.113380

    Article  Google Scholar 

  7. Melguizo-Gavilanes, J., Boeck, L., Mével, R., Shepherd, J.: Hot surface ignition of stoichiometric hydrogen–air mixtures. Int. J. Hydrog. Energy 42, 7393–7403 (2017). https://doi.org/10.1016/j.ijhydene.2016.05.095

    Article  Google Scholar 

  8. Park, J.-W., Xu, R., Lu, T., Wang, H.: Skeletal and reduced model of NOx formation in RP-2 rocket fuel (2019). https://web.stanford.edu/group/haiwanglab/HyChem/pages/download.html

  9. Huber, M.L., Lemmon, E.W., Ott, L.S., Bruno, T.J.: Preliminary surrogate mixture models for the thermophysical properties of rocket propellants RP-1 and RP-2. Energy Fuels 23, 3083–3088 (2009). https://doi.org/10.1021/ef900216z

    Article  Google Scholar 

  10. Bigler, B.R., Burr, J.R., Bennewitz, J.W., Danczyk, S., Hargus, W.A.: Performance effects of mode transitions in a rotating detonation rocket engine. AIAA Propulsion and Energy 2020 Forum, AIAA Paper 2020-3852 (2020). https://doi.org/10.2514/6.2020-3852

  11. Burr, J.R., Paulson, E.: Thermodynamic performance results for rotating detonation rocket engine with distributed heat addition using cantera. AIAA Propulsion and Energy 2021 Forum, AIAA Paper 2021-3682 (2021). https://doi.org/10.2514/6.2021-3682

  12. Bigler, B.R., Bennewitz, J.W., Danczyk, S.A., Hargus, W.A.: Rotating detonation rocket engine operability under varied pressure drop injection. J. Spacecr. Rocket. 58, 316–325 (2021). https://doi.org/10.2514/1.a34763

    Article  Google Scholar 

  13. Bennewitz, J.W., Bigler, B.R., Ross, M.C., Danczyk, S.A., Hargus, W.A., Smith, R.D.: Performance of a rotating detonation rocket engine with various convergent nozzles and chamber lengths. Energies 14, 2037 (2021). https://doi.org/10.3390/en14082037

    Article  Google Scholar 

  14. Bennewitz, J.W., Bigler, B.R., Hargus, W.A., Danczyk, S.A., Smith, R.D.: Characterization of detonation wave propagation in a rotating detonation rocket engine using direct high-speed imaging. AIAA 2018 Joint Propulsion Conference, AIAA Paper 2018-4688 (2018). https://doi.org/10.2514/6.2018-4688

  15. Goodwin, D.G., Moffat, H.K., Schoegl, I., Speth, R.L., Weber, B.W.: Cantera: an object-oriented software toolkit for chemical kinetics, thermodynamics, and transport processes. Version 3.0.0 (2023). https://www.cantera.org

  16. Kao, S.: Detonation stability with reversible kinetics. Ph.D. Dissertation, California Institute of Technology (2008)

  17. Lietz, C., Ross, M., Desai, Y., Hargus, W.A.: Numerical investigation of operational performance in a methane-oxygen rotating detonation rocket engine. AIAA Scitech 2020 Forum, AIAA Paper 2020-0687 (2020). https://doi.org/10.2514/6.2020-0687

  18. Kaemming, T., Fotia, M.L., Hoke, J., Schauer, F.: Thermodynamic modeling of a rotating detonation engine through a reduced-order approach. AIAA J. Propul. Power 33, 1170–1178 (2017). https://doi.org/10.2514/1.b36237

    Article  Google Scholar 

  19. Kayser, J.C., Shambaugh, R.L.: Discharge coefficients for compressible flow through small-diameter orifices and convergent nozzles. Chem. Eng. Sci. 46, 1697–1711 (1991). https://doi.org/10.1016/0009-2509(91)87017-7

    Article  Google Scholar 

  20. E.P.A. Risk management program guidance for offsite consequence analysis. Tech. Rep. EPA 550-B-99-009, Chemical Emergency Preparedness and Prevention Office (1999)

  21. Zucrow, M.J., Hoffman, J.D.: Gas Dynamics, vol. 1. Wiley, Hoboken (1976)

    Google Scholar 

  22. Pal, P., Demir, S., Som, S.: Numerical analysis of combustion dynamics in a full-scale rotating detonation rocket engine using large eddy simulations. J. Energy Resour. Technol. 145(2), 021702 (2012). https://doi.org/10.1115/1.4055206

    Article  Google Scholar 

  23. Prakash, S., Raman, V.: The effects of mixture preburning on detonation wave propagation. Proc. Combust. Inst. 38, 3749–3758 (2021). https://doi.org/10.1016/j.proci.2020.06.005

    Article  Google Scholar 

  24. Ross, M., Karagozian, A., Burr, J.: Laser absorption characteristics of a simulated rotating detonation rocket engine. 29th ICDERS, SNU Siheung, Korea, ICDERS2023-072 (2023). http://www.icders.org/ICDERS2023/abstracts/ICDERS2023-072.pdf

  25. Bluemner, R., Gutmark, E.J., Paschereit, C.O., Bohon, M.D.: Stabilization mechanisms of longitudinal pulsations in rotating detonation combustors. Proc. Combust. Inst. 38, 3797–3806 (2021). https://doi.org/10.1016/j.proci.2020.07.063

    Article  Google Scholar 

  26. Ross, M., Burr, J., Desai, Y., Batista, A., Lietz, C.: Flow acceleration in an RDRE with gradual chamber constriction. Shock Waves 33, 253–265 (2023). https://doi.org/10.1007/s00193-022-01117-y

    Article  Google Scholar 

  27. Marble, F., Candel, S.: Acoustic disturbance from gas non-uniformities convected through a nozzle. J. Sound Vib. 55, 225–243 (1977). https://doi.org/10.1016/0022-460X(77)90596-X

  28. Dranovsky, M.L.: Combustion Instabilities in Liquid Rocket Engines. American Institute of Aeronautics and Astronautics, Reston (2007). https://doi.org/10.2514/4.866906

    Book  Google Scholar 

  29. Kim, J., Soedel, W.: General formulation of four pole parameters for three-dimensional cavities utilizing modal expansion, with special attention to the annular cylinder. J. Sound Vib. 129, 237–254 (1989). https://doi.org/10.1016/0022-460X(89)90580-4

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Acknowledgements

This work is sponsored by the Air Force Office of Scientific Research (AFOSR) under the AFOSR Energy, Combustion, Non-Equilibrium Thermodynamics portfolio with Chiping Li as program manager through the following Grants: (1) University of Alabama in Huntsville FA9550-23-1-0371 and (2) Air Force Research Laboratory (AFRL) Task 23RQCOR010.

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Author notes

  1. R. T. Dave, J. R. Burr, M. C. Ross, C. F. Lietz, and J. W. Bennewitz have contributed equally to this work.

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of Alabama in Huntsville, Huntsville, 35899, AL, USA

    R. T. Dave & J. W. Bennewitz

  2. Rocket Combustion Devices Branch, Air Force Research Laboratory, Edwards Air Force Base, 93524, CA, USA

    J. R. Burr, M. C. Ross & C. F. Lietz

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  1. R. T. Dave
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Correspondence to J. W. Bennewitz.

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Communicated by G. Ciccarelli.

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This paper is based on work that was presented at the 29th International Colloquium on the Dynamics of Explosions and Reactive Systems (ICDERS), Siheung, Korea, July 23–28, 2023.

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Dave, R.T., Burr, J.R., Ross, M.C. et al. Characteristic timescales for detonation-based rocket propulsion systems. Shock Waves (2024). https://doi.org/10.1007/s00193-024-01174-5

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