Abstract
The turbulent wake of a planar generic space launcher equipped with a dual-bell nozzle is numerically investigated to examine the interaction of the dual-bell nozzle jet and the wake flow. The simulation is performed at transonic freestream condition, i.e., freestream Mach number \(Ma_{\infty }= 0.8\) and freestream Reynolds number based on the launcher thickness ReD = 4.3 ⋅ 105, with the dual-bell nozzle operating at sea-level mode. A zonal RANS/LES approach is used and the time-resolved flow field data is analyzed by classical spectral analysis and modal decomposition techniques, i.e., proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD). The overall flow topology of the recirculation region downstream of the base and the pressure loads on the outer nozzle fairing are only slightly affected by the modified nozzle shape. However, the changed nozzle flow topology characterized by the flow separation at the nozzle contour inflection leads to a backflow region and an entrainment of the outer flow into the nozzle extension which results in increased pressure loads on the inner nozzle wall. Using spectral, POD, and DMD analyses, the outer wake flow is investigated, revealing a growing and contracting of the separation bubble and an undulating motion of the shear layer similar to the “cross-pum**” and “cross-flap**” motion detected in previous investigations of a configuration with a classical nozzle and a jetless backward facing step setup. The spectral and modal analysis of the nozzle flow shows that the increased pressure loads detected at the inner wall of the nozzle extension are caused by an interaction of the separated shear layer inside the nozzle extension with the shock pattern that leads to a streamwise oscillation of the shock and a pum** or wave-like motion of the shear layer.
Similar content being viewed by others
References
Stark, R., Génin, C.: Sea-level transitioning dual bell nozzles. CEAS Space J. 9, 279–287 (2017)
Proshchanka, D., Koichi, Y., Tsukuda, H., Araki, K., Tsujimoto, Y., Kimura, T., Yokota, K.: Jet oscillation at low-altitude operation mode in dual-bell nozzle jet oscillation at low-altitude operation mode in dual-bell nozzle jet oscillation at low-altitude operation mode in dual-bell nozzle. J. Propuls. Power 28(5), 1071–1080 (2012)
Martelli, E., Nasuti, F., Onofri, M.: Numerical parametric analysis of dual-bell nozzle flows. AIAA J., 45(3) (2007)
Schneider, D., Génin, C.: Numerical investigation of flow transition behavior in cold flow dual-bell rocket nozzles. J. Propuls. Power 32(5), 1212–1219 (2016)
Bradshaw, P., Wong, F.: The reattachment and relaxation of a turbulent shear layer. J. Fluid Mech. 52(1), 113–135 (1972)
Eaton, J.K., Johnston, J.P.: A review of research on subsonic turbulent flow reattachment. AIAA J. 19(9), 1093–1100 (1981)
Driver, D.M., Seegmiller, H.L., Marvin, J.G.: Time-dependent behavior of a reattaching shear layer. AIAA J. 25(7), 914–919 (1987)
Friedrich, R., Arnal, M.: Analysing turbulent backward-facing step flow with the low-pass-filtered Navier-Stokes equations. J. Wind Eng. Ind. Aerodyn. 35, 101–128 (1990)
Silveria Neto, A., Grand, D., Metais, O., Lesieur, M.: A numerical investigation of the coherent vortices in turbulence behind a backward-facing step. J. Fluid Mech. 256, 1–25 (1993)
Le, H., Moin, P., Kim, J.: Direct numerical simulation of turbulent flow over a backward-facing step. J. Fluid Mech. 330, 349–374 (1997)
Lee, I., Sung, H.J.: Characteristics of wall pressure fluctuations in separated and reattaching flows over a backward-facing step: Part I. Time-mean statistics and cross-spectral analyses. Exp. Fluids 30, 262–272 (2001)
Statnikov, V., Bolgar, I., Scharnowski, S., Meinke, M., Kähler, C.J., Schröder, W.: Analysis of characteristic wake flow modes on a generic transonic backward-facing step configuration. Europ. J. Mech. B/Fluids 59, 124–134 (2016)
Scharnowski, S., Bolgar, I., Kähler, C.J.: Characterization of turbulent structures in a transonic backward-facing step flow. Flow, Turbul. Combust., 1–21 (2016)
Bolgar, I., Scharnowski, S., Kähler, C.J.: The effect of the mach number on a turbulent backward-facing step flow. Flow Turbul. Combust. 101(3), 653–680 (2018)
Deprés, D., Reijasse, P., Dussauge, J.P.: Analysis of unsteadiness in afterbody transonic flows. AIAA J. 42(12), 2541–2550 (2004)
Deck, S., Thorigny, P.: Unsteadiness of an axisymmetric separating-reattaching flow: Numerical investigation. Phys. Fluids, 19(065103) (2007)
Schrijer, F., Sciacchitano, A., Scarano, F.: Spatio-temporal and modal analysis of unsteady fluctuations in a high-subsonic base flow. Phys. Fluids, 26(086101) (2014)
Statnikov, V., Meinke, M., Schröder, W.: Analysis of spatio-temporal wake modes of space launchers at transonic flow. AIAA Paper, 2016–1116 (2016)
Statnikov, V., Meinke, M., Schröder, W.: Reduced-order analysis of buffet flow of space launchers. J. Fluid Mech. 815, 1–25 (2017)
Bolgar, I., Scharnowski, S., Kähler, C.J.: Experimental analysis of the interaction between a dual-bell nozzle with an external flow field aft of a backward-facing step. 21 DGLR-Fach-Symposium der STAB (2018)
Loosen, S., Statnikov, V., Meinke, M., Schröder, W.: Numerical investigation of the turbulent wake of a generic space launcher at transonic speed. In: 7th European Conference for Aeronautics and Aerospace Sciences, https://doi.org/10.13009/EUCASS2017-561 (2017)
David, S., Radulovic, S.: Prediction of buffet loads on the Ariane 5 afterbody. In: 6th International Symposium on Launcher Technologies. Munich, Germany 8-11 November (2005)
Fares, E., Schröder, W.: A general one-equation turbulence model for free shear and wall-bounded flows. Flow Turbul. Combust. 73, 187–215 (2004)
Statnikov, V., Sayadi, T., Meinke, M., Schmid, P., Schröder, W.: Analysis of pressure perturbation sources on a generic space launcher after-body in supersonic flow using zonal turbulence modeling and dynamic mode decomposition. Phys. Fluids, 27(016103) (2015)
Roidl, B., Meinke, M., Schröder, W.: A reformulated synthetic turbulence generation method for a zonal RANS-LES method and its application to zero-pressure gradient boundary layers. Int. J. Heat Fluid Flow 44, 28–40 (2013)
Roidl, B., Meinke, M., Schröder, W.: Boundary layers affected by different pressure gradients investigated computationally by a zonal RANS-LES method. Int. J. Heat Fluid Flow 45, 1–13 (2014)
Jarrin, N., Benhamadouche, S., Laurence, D., Prosser, R.: A synthetic-eddy-method for generating inflow conditions for large-eddy simulations. Int. J. Heat Fluid Flow 27, 585–593 (2006)
Choi, H., Moin, P.: Grid-point requirements for large eddy simulation: Champan’s estimates revisited. Phys. Fluids, 24(011702) (2012)
Berkooz, G., Holmes, P., Lumley, J.L.: The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25(1), 539–575 (1993)
Taira, K., Brunton, S.L., Dawson, S.T.M., Rowley, C.W., Colonius, T., McKeon, B.J., Schmidt, O.T., Gordeyev, S., Theofilis, V., Ukeiley, L.S.: Modal analysis of fluid flows: An overview. AIAA J (2017)
Schmid, P.J.: Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 5–28 (2010)
Jovanovic, M.R., Schmid, P.J., Nichols, J.W.: Sparsity-promoting dynamic mode decomposition. Phys. Fluids, 26(024103) (2014)
Winant, C.D., Browand, F.K.: Vortex pairing: The mechanism of turbulent mixing-layer growth at moderate Reynolds number. J. Fluid Mech. 63(2), 237–255 (1974)
Acknowledgements
Financial support has been provided by the German Research Foundation (Deutsche Forschungsgemeinschaft – DFG) in the framework of the Sonderforschungsbereich Transregio 40. The authors are grateful for the computing resources provided by the High Performance Computing Center Stuttgart (HLRS) and the Jülich Supercomputing Center (JSC) within a Large-Scale Project of the Gauss Center for Supercomputing (GCS)
Funding
This study was funded by the German Research Foundation (DFG).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interests
The authors declare that they have no conflict of interest.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Loosen, S., Meinke, M. & Schröder, W. Numerical Investigation of Jet-Wake Interaction for a Dual-Bell Nozzle. Flow Turbulence Combust 104, 553–578 (2020). https://doi.org/10.1007/s10494-019-00056-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10494-019-00056-6