Hostname: page-component-77c89778f8-gq7q9 Total loading time: 0 Render date: 2024-07-20T06:27:29.002Z Has data issue: false hasContentIssue false
  • English
  • Français

Reacting flow analysis of a cavity-based scramjet combustor using a Jacobian-free Newton–Krylov method

Published online by Cambridge University Press:  27 December 2018

R. Rouzbar  and
S. Eyi
R. Rouzbar*
Affiliation:
Middle East Technical UniversityAnkaraTurkey
S. Eyi
Affiliation:
Middle East Technical UniversityAnkaraTurkey
*
ramin.rouzbar@metu.edu.tr
Get access Rights & Permissions [Opens in a new window]

Abstract

The scramjet is a rather a new technology and there are many issues related to their operation, especially when it comes to the combustion processes. Combustion in high-speed flows causes various problems such as flame instability and poor fuel–air mixing efficiency. One of the methods used to overcome these problems is to recess a cavity in the combustor wall where a secondary flow is generated. In this study, a computational fluid dynamics (CFD) code is developed to analyse the reacting flow passing through the cavity-based scramjet combustor. The developed code is based on three-dimensional coupled Navier–Stokes and finite rate chemistry equations. An ethylene-air reduced chemical reaction model is used as a fuel–air combination. The Spalart–Allmaras model is utilised for turbulence closure. The non-dimensional form of the flow and chemical reaction equations are discretised using a finite volume method. The Jacobian-Free Newton–Krylov (JFNK) method is used to solve the coupled system of non-linear equations. The JFNK is a matrix-free solution method which improves the computational cost of Newton’s method. The parameters that affect the performance of the JFNK method are studied in the analysis of a scramjet combustor. The influence of the forcing term on the convergence of the JFNK method is studied in the analysis of scramjet combustor. Different upwind flux vector splitting methods are utilised. Various flux limiter techniques are employed for the calculations of higher order flux vectors. The effects of flux vector splitting and flux limiter methods on the convergence and accuracy of the JFNK method are evaluated. Moreover, the variations of the mixing efficiency with fuel injection angles are studied.

Keywords

ScramjetJacobian-free Newton–KrylovJFNKComputational fluid dynamics
Type
Research Article
Information
The Aeronautical Journal , Volume 122 , Issue 1258 , December 2018 , pp. 1884 - 1915
Copyright
© Royal Aeronautical Society 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Heiser, W.H., Pratt, D.T., Daley, D.H. and Mehta, U.B. Hypersonic Airbreathing Propulsion, AIAA Education Series, 1994, AIAA, Washington, DC.Google Scholar
2. Segal, C. The Scramjet Engine: Processes and Characteristics, Cambridge Aerospace Series, Cambridge, UK, 2009, pp 1–253.Google Scholar
3. Smart, M. Scramjets. The Aeronautical J, 2007, 111, (1124), pp 605–619.Google Scholar
4. Baurle, R.A. and Eklund, D.R. Analysis of dual-mode hydrocarbon scramjet operation at Mach 4-6.5, J Propulsion and Power, 2002, 18, (5), pp 990–1002.Google Scholar
5. Dimotakis, P.E. Turbulent free shear layer mixing and combustion, High Speed Flight Propulsion Systems, Chapter 5 Pasadena, CA, 1991, pp. 265–340.Google Scholar
6. Bonanos, A.M. Scramjet Operability Range Studies of an Integrated Aerodynamic-Ramp-Injector/Plasma-Torch Igniter with Hydrogen and Hydrocarbon Fuels, PhD Dissertation, Aerospace Engineering Department, Virginia Polytechnic Institute and State University, Blacksburg, VI, 2005.Google Scholar
7. Pandey, K.M. and Sivasakthivel, T. Recent advances in scramjet fuel injection – a review, Int J Chemical Engineering and Applications, 2010, 1, (4), pp 294–301.Google Scholar
8. Dessornes, O. and Jourdren, C. Mixing Enhancement Techniques in a Scramjet, 1998, AIAA Paper 98-1517.Google Scholar
9. Tishkoff, J., Drummond, J., Edwards, T. and Nejad, A. Future Directions of Supersonic Combustion Research, 1997, AIAA Paper 97-1017.Google Scholar
10. Wang, Z., Wang, H. and Sun, M. Review of cavity-stabilized combustion for scramjet applications, Proceedings of the Institution of Mechanical Engineers, Part G: J Aerospace Engineering, 2014, 228, (14), pp 2718–2735.Google Scholar
11. Hsu, K.-Y., Goss, L.P. and Roquemore, W.M. Characteristics of a trapped-vortex combustor, J Propulsion and Power, 1998, 14, (1), pp 57–65.Google Scholar
12. Ben-Yakar, A. Experimental Investigation of Mixing and Ignition of Transverse Jets in Supersonic Crossflows, 2000, PhD Dissertation, Mechanical Engineering Department, Stanford University, Stanford, CA.Google Scholar
13. Baurle, R.A. Modeling of High Speed Reacting Flows: Established Practices and Future Challenges, 2004, AIAA Paper 2004-267.Google Scholar
14. Ladeinde, F. A Critical Review of Scramjet Combustion Simulation, 2009, AIAA Paper 2009-127.Google Scholar
15. Drummond, J.P. Methods for prediction of high-speed reacting flows in aerospace propulsion, AIAA J, 2014, 52, (3), pp 465–485.Google Scholar
16. Mura, A. and Izard, J.-F. Numerical simulation of supersonic nonpremixed turbulent combustion in a scramjet combustor model, J Propulsion and Power, 2010, 26, (4), pp 858–868.Google Scholar
17. Ghodke, C.D., Choi, J.J, Srinivasan, S. and Menon, S. Large Eddy Simulation of Supersonic Combustion in a Cavity-Strut Flameholder, 2011, AIAA Paper 2011-323.Google Scholar
18. Koo, H., Raman, V. and Varghese, P.L. Direct numerical simulation of supersonic combustion with thermal nonequilibrium, Proceedings of the Combustion Institute, 2015, 35, (2), pp 2145–2153.Google Scholar
19. Arnold-Medabalimi, N.A. and Duraisamy, K. Flamelet-Based RANS Computations of Supersonic Reacting Flows in a Model Scramjet Combustor, 2016, AIAA Paper 2016-3958.Google Scholar
20. Cheng, T.S., Wehrmeyer, J.A., Pitz, R.W., Jarrett, O.J.R. and Northam, G.B. Raman measurements of mixing and finite-rate chemistry in a supersonic hydrogen–air diffusion flame, Combustion and Flame, 1994, 99, (1), pp 157–173.Google Scholar
21. Berglund, M., Fedina, E., Fureby, C., Tegnér, J. and Sabel’nikov, V. Finite rate chemistry large-eddy simulation of self-ignition in supersonic combustion ramjet, AIAA J, 2010, 48, (3), pp 540–550.Google Scholar
22. Choi, J.-Y., Ma, F. and Yang, V. Combustion oscillations in a scramjet engine combustor with transverse fuel injection, Proceedings of the Combustion Institute, 2005, 30, (2), pp 2851–2858.Google Scholar
23. Potturi, A. and Edwards, J.R. Investigation of Subgrid Closure Models for Finite-Rate Scramjet Combustion, 2013, AIAA Paper 2013-2461.Google Scholar
24. Lin, K., Tam, C., Jackson, K., Kennedy, P., Williams, S., Olmstead, D. and Collatz, M. Fueling Study on Scramjet Operability Enhancement, 2009, AIAA Paper 2009-5116.Google Scholar
25. Mobus, H., Gerlinger, P. and Bruggemann, D. Scalar and joint scalar–velocity–frequency Monte Carlo PDF simulation of supersonic combustion, Combustion and Flame, 2003, 132, (1-2), pp 3–24.Google Scholar
26. Gerlinger, P. Investigation of an assumed PDF approach for finite-rate chemistry, Combustion Science and Technology, 2003, 175, (5), pp 841–872.Google Scholar
27. Baurle, R.A. and Girimajib, S.S. Assumed PDF turbulence–chemistry closure with temperature–composition correlations, Combustion and Flame, 2003, 134, (1-2), pp 131–148.Google Scholar
28. Gao, Z., Wang, J., Jiang, C. and Lee, C. Application and theoretical analysis of the flamelet model for supersonic turbulent combustion flows in the scramjet engine, Combustion Theory and Modelling, 2014, 18, (6), pp 652–691.Google Scholar
29. Li, W., Lou, Z. and Ladeinde, F. Comparison of Flamelet and Transported Species-Based Modeling of Scramjet Combustor, 2017, AIAA Paper 2017-4745.Google Scholar
30. Leveque, R.J. and Yee, H.C. Study of numerical methods for hyperbolic conservation laws with stiff source terms, J Computational Physics, 1990, 86, (1), pp 187–210.Google Scholar
31. Dembo, R.S., Eisenstat, S.C. and Steihaug, T. Inexact Newton methods, SIAM J Numerical Analysis, 1982, 19, (2), pp 400–408.Google Scholar
32. Chisholm, T.T. and Zingg, D.W. A Jacobian-free Newton–Krylov algorithm for compressible turbulent fluid flows, J Computational Physics, 2009, 228, (9), pp 3490–3507.Google Scholar
33. Eisenstat, S.C. and Walker, H.F. Choosing the forcing terms in an inexact Newton method, SIAM J Scientific Computing, 1996, 17, (1), pp 16–32.Google Scholar
34. Persson, P.O. and Peraire, J. Newton-GMRES preconditioning for discontinuous Galerkin discretizations of the Navier–Stokes equations, SIAM J Scientific Computing, 2008, 30, (6), pp 2709–2733.Google Scholar
35. Knoll, D.A., Mchugh, P.R. and Keyes, D.E. Newton–Krylov methods for low-Mach-number compressible combustion, AIAA J, 1996, 34, (5), pp 961–967.Google Scholar
36. Mchugh, P., Knoll, D. and Keyes, D. Application of Newton–Krylov–Schwarz algorithm to low-Mach-number compressible combustion, AIAA J, 1998, 36, (2), pp 290–292.Google Scholar
37. Yildizlar, B. and Eyi, S. Comparison of Newton and Newton-GMRES Methods for Three Dimensional Supersonic Nozzle Design, 2014, AIAA Paper 2014-3177.Google Scholar
38. Mcbride, B.J., Zehe, M.J. and Gordon, S. NASA Glenn Coefficients for Calculating Thermodynamic Properties of Individual Species, NASA/TP-2002-211556, Sept. 2002.Google Scholar
39. Yumuşak, M. and Eyi, S. Design optimization of rocket nozzles in chemically reacting flows, Computers & Fluids, 2012, 65, pp 25–34.Google Scholar
40. Zehe, M.J., Gordon, S. and Mcbride, B.J. CAP: A Computer Code for Generating Tabular Thermodynamic Functions from NASA Lewis Coefficients, NASA/TP-2001-210959/REV1, Feb. 2002.Google Scholar
41. Fry, R.S. A century of ramjet propulsion technology evolution, J Propulsion and Power, 2004, 20, (1), pp 27–58.Google Scholar
42. Lewis, M.J. Significance of fuel selection for hypersonic vehicle range, J Propulsion and Power, 2001, 17, (6), pp 1214–1221.Google Scholar
43. Powell, O.A., Edwards, J.T., Norris, R.B., Numbers, K.E. and Pearce, J.A. Development of hydrocarbon-fueled scramjet engines: the Hypersonic Technology (HyTech) Program, J Propulsion and Power, 2001, 17, (6), pp 1170–1176.Google Scholar
44. Eklund, D., Baurle, R. and Gruber, M. Numerical Study of a Scramjet Combustor Fueled by an Aerodynamic Ramp Injector in Dual-Mode Combustion, 2001, AIAA Paper 2001-379.Google Scholar
45. Spalart, P.R. and Allmaras, S.R. A One Equation Turbulence Model for Aerodynamic Flows, 1992,AIAA Paper 92-0439.Google Scholar
46. Steger, J.L. and Warming, R.F. Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods, J Computational Physics, 1981, 40, (2), pp 263–293.Google Scholar
47. Van Leer, B. Flux-vector splitting for the Euler equations, 8th International Conference on Numerical Methods in Fluid Dynamics, vol. 170, 1982, Springer, Berlin, pp 507–512.Google Scholar
48. Liou, M.-S. and Steffen, C.J. A new flux splitting scheme, J Computational Physics, 1993, 107, (1), pp 23–39.Google Scholar
49. Venkatakrishnan, V. Convergence to steady state solutions of the Euler equations on unstructured grids with limiters, J Computational Physics, 1995, 118, (1), pp 120–130.Google Scholar
50. Saad, Y. and Schultz, M.H. Gmres: a generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J Scientific and Statistical Computing, 1986, 7, (3), pp 856–869.Google Scholar
51. Knoll, D.A. and Keyes, D.E. Jacobian-free Newton–Krylov methods: a survey of approaches and applications, J Computational Physics, 2004, 193, (2), pp 357–397.Google Scholar