Abstract
At low altitudes during rocket flight, the atmospheric pressure is higher compared to the design pressure of the nozzle at the exit. This leads to the formation of overexpansion shock, and consequently, flow separation. When the separation is asymmetric, the lateral force acts on the nozzle wall, and the magnitude of the lateral force depends on the extent of asymmetry. Hence, accurate prediction of the flow separation is essential to estimate side loading. This study uses OpenFOAM and ANSYS to analyze flow separation. OpenFOAM offers the flexibility to modify the code as per the requirements of the problem, as the code is readily available. There is only a limited number of studies conducted on supersonic nozzles using OpenFOAM. This study addresses the choice of solver, discretization method, and boundary conditions to be implemented for accurately predicting supersonic flow through different nozzle geometries. The analysis is conducted on cold flow through planar convergent-divergent, planar expansion-deflection, and conical aerospike nozzle geometries. Reynolds-averaged Navier–Stokes equations are solved along with turbulence models. Compressible solvers sonicFOAM and rhoCentralFOAM are used for the simulations with OpenFOAM. Different turbulence models are tested and validated for the planar convergent-divergent nozzle and compared with the expansion-deflection nozzle and aerospike nozzle. The results are validated with available experimental data. While comparing the supersonic flow through the different nozzles, it is observed that rhoCentralFOAM captures flow separation, shocks, shear layer, and pressure profile better in comparison to sonicFOAM.
Graphical abstract
Similar content being viewed by others
Abbreviations
- A e :
-
Area at nozzle exit, mm2
- A t :
-
Area at nozzle throat, mm2
- c p :
-
Specific heat at constant pressure, J/kgK
- D :
-
Exit nozzle diameter, mm
- E :
-
Total energy, J
- FSS :
-
Free Shock Separation
- I :
-
Unit tensor
- k :
-
Turbulence kinetic energy, J/kg
- k T :
-
Thermal conductivity, W/(mK)
- L :
-
Axial length of divergent section of the nozzle, mm
- LW :
-
Lower Wall
- NPR :
-
Nozzle Pressure Ratio
- P a :
-
Atmospheric pressure, Pa
- P e :
-
Pressure at the exit of the nozzle, Pa
- P o :
-
Jet stagnation pressure, Pa
- P w :
-
Wall pressure on nozzle profile, Pa
- p :
-
Static pressure, Pa
- Pr t :
-
Turbulent Prandtl number
- RANS :
-
Reynolds-Averaged Navier–Stokes
- RSS :
-
Restricted Shock Separation
- R e :
-
Radius of the nozzle exit, mm
- SA :
-
Spalart–Allmaras
- SST :
-
Shear Stress Transport
- T h :
-
Height of the throat, mm
- UW :
-
Upper Wall
- ν :
-
Molecular kinematic viscosity
- v e :
-
Velocity at the exit, m/s
- X :
-
Coordinate along X-axis, mm
- Y :
-
Coordinate along Y-axis, mm
- γ:
-
Ratio of the specific heats
- ρ :
-
Density, kg/m3
- μ :
-
Dynamic viscosity, Pa.s
- μ t :
-
Turbulent viscosity, Pa.s
- μ eff :
-
Effective viscosity, Pa.s
References
Abed N, Afgan I, Cioncolini A, Iacovides H, Nasser A, Mekhail T (2020) Thermal performance evaluation of various nanofluids with non-uniform heating for parabolic trough collectors. Case Stud Therm Eng 22:100769. https://doi.org/10.1016/j.csite.2020.100769
Agarwal R (1999) Computational fluid dynamics of whole body aircraft. Annu Rev Fluid Mech 31:125–169. https://doi.org/10.1146/annurev.fluid.31.1.125
Ali AE, Afgan I, Laurence D, Revell A (2021) A dual-mesh hybrid RANS-LES simulation of the buoyant flow in a differentially heated square cavity with an improved resolution criterion. Comput Fluids 224:104949. https://doi.org/10.1016/j.compfluid.2021.104949
Ashton N, Skaperdas V (2019) Verification and validation of OpenFOAM for high-lift aircraft flows. J Aircr 56(4):1641–1657. https://doi.org/10.2514/1.C034918
Cao Y, Tamura T (2016) Large-eddy simulations of flow past a square cylinder using structured and unstructured grids. Comput Fluids 137:36–54. https://doi.org/10.1016/j.compfluid.2016.07.013
Cao Z, White C, Kontis K (2021) Numerical investigation of rarefied vortex loop formation due to shock wave diffraction with the use of rorticity. Phys Fluids 33(6):067112. https://doi.org/10.1063/5.0054289
Cao Z, Agir MB, White C, Kontis K (2022) An open source code for two-phase rarefied flows: rarefiedMultiphaseFoam. Comput Phys Commun 276:108339. https://doi.org/10.1016/j.cpc.2022.108339
Choudhury SP, Suryan A, Pisharady JC, Jayashree A, Rashid K (2018) Parametric study of supersonic film cooling in dual bell nozzle for an experimental air–kerosene engine. Aerosp Sci Technol 78:364–376. https://doi.org/10.1016/j.ast.2018.04.038
Chutkey K, Viji M, Verma SB (2018) Interaction of external flow with linear cluster plug nozzle jet. Shock Waves 28(6):1207–1221. https://doi.org/10.1007/s00193-018-0849-6
Constant E, Favier J, Meldi M, Meliga P, Serre E (2017) An immersed boundary method in OpenFOAM: verification and validation. Comput Fluids 157:55–72. https://doi.org/10.1016/j.compfluid.2017.08.001
D’Alessandro V, Montelpare S, Ricci R (2016) Detached–eddy simulations of the flow over a cylinder at Re= 3900 using OpenFOAM. Comput Fluids 136:152–169. https://doi.org/10.1016/j.compfluid.2016.05.031
Damgaard T, Östlund J, Frey M (2004) Side-Load phenomena in highly overexpanded rocket nozzles. J Propuls Power 20(4):695–704. https://doi.org/10.2514/1.3059
Doolan C (2009) Flow and noise simulation of the NASA tandem cylinder experiment using OpenFOAM, Proc. of 15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference), Miami, Florida, USA, AIAA Paper 2009–3157, 2009 https://doi.org/10.2514/6.2009-3157
Droeske N, Makowka K, Nizenkov P, Vellaramkalayil JJ, Sattelmayer T, von Wolfersdorf J (2014) Validation of a novel OpenFOAM solver using a supersonic, non-reacting channel flow, Proc. of 19th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, Atlanta, GA, USA, AIAA Paper 2014–3088 https://doi.org/10.2514/6.2014-3088
Flores F, Garreaud R, Muñoz RC (2014) OpenFOAM applied to the CFD simulation of turbulent buoyant atmospheric flows and pollutant dispersion inside large open pit mines under intense isolation. Comput Fluids 90:72–87. https://doi.org/10.1016/j.compfluid.2013.11.012
Fluent user’s guide, (2013) ANSYS, Inc., Canonsburg, PA:1–1146
Frey M, Hagemann G (1999) Flow separation and side-loads in rocket nozzles, Proc of 35th Joint Propulsion Conference and Exhibit, Los Angeles, CA, USA, AIAA Paper 1999–2815 https://doi.org/10.2514/6.1999-2815
Frey M, Hagemann G (2000) Restricted shock separation in rocket nozzles. J Propuls Power 16(3):478–484. https://doi.org/10.2514/2.5593
George J, Nair PP, Soman S, Suryan A, Kim HD (2021) Visualization of flow through planar double divergent nozzles by computational method. J vis 24(4):711–732. https://doi.org/10.1007/s12650-020-00729-9
Gramola M, Bruce PJK, Santer M (2020) Off-design performance of 2D adaptive shock control bumps. J Fluids Struct 93:102856. https://doi.org/10.1016/j.jfluidstructs.2019.102856
Greenshields CJ (2020) OpenFOAM User Guide v8.0. OpenFOAM Foundation Ltd. http://foam.sourceforge.net/docs/Guides-a4/OpenFOAMUserGuide-A4.pdf. Assessed on 1 August 2020
Hagemann G, Immich H, Nguyen TV, Dumnov GE (1998) Advanced rocket nozzles. J Propuls Power 14(5):620–634. https://doi.org/10.2514/2.5354
Han X, Li J, Morgans AS (2015) Prediction of combustion instability limit cycle oscillations by combining flame describing function simulations with a thermoacoustic network model. Combust Flame 162(10):3632–3647. https://doi.org/10.1016/j.combustflame.2015.06.020
Han X, Laera D, Yang D, Zhang C, Wang J, Hui X, Lin Y, Morgans AS, Sung CJ (2020) Flame interactions in a stratified swirl burner: flame stabilization, combustion instabilities and beating oscillations. Combust Flame 212:500–509. https://doi.org/10.1016/j.combustflame.2019.11.020
Hunter CA (2004) Experimental investigation of separated nozzle flows. J Propuls Power 20(3):527–532. https://doi.org/10.2514/1.4612
Hunter C (1998) Experimental, theoretical, and computational investigation of separated nozzle flows, Proc. of 34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Cleveland, OH, USA, AIAA Paper 98–3107 https://doi.org/10.2514/6.1998-3107
Jinks ER, Bruce PJK, Santer M (2018) Optimisation of adaptive shock control bumps with structural constraints. Aerosp Sci Technol 77:332–343. https://doi.org/10.1016/j.ast.2018.03.018
Jinks ER, Bruce PJK, Santer M, (2014) Adaptive shock control bumps, In: 52nd Aerospace Sciences Meeting, AIAA 2014–0945, (p 0945) https://doi.org/10.2514/6.2014-0945
Kadu PA, Sakai Y, Ito Y, Iwano K, Sugino M, Katagiri T, Nagata K (2019) Numerical investigation of passive scalar transport and mixing in a turbulent unconfined coaxial swirling jet. Int J Heat Mass Transf 142:118461. https://doi.org/10.1016/j.ijheatmasstransfer.2019.118461
Kadu PA, Sakai Y, Ito Y, Iwano K, Sugino M, Katagiri T, Hayase T, Nagata K (2020) Application of spectral proper orthogonal decomposition to velocity and passive scalar fields in a swirling coaxial jet. Phys Fluids 32(1):015106. https://doi.org/10.1063/1.5131627
Karthikeyan N, Kumar A, Verma SB, Venkatakrishnan L (2013) Effect of spike truncation on the acoustic behavior of annular aerospike nozzles. AIAA J 51(9):2168–2182. https://doi.org/10.2514/1.J052139
Kurganov A, Tadmor E (2000) New high-resolution central schemes for nonlinear conservation laws and convection–diffusion equations. J Comput Phys 160(1):241–282
Kurganov A, Noelle S, Petrova G (2001) Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations. SIAM J Sci Comput 23(3):707–740. https://doi.org/10.1137/S1064827500373413
Lysenko DA, Ertesvåg IS, Rian KE (2010) Modeling of turbulent separated flows using OpenFOAM. Comput Fluids 80:408–422. https://doi.org/10.1016/j.compfluid.2012.01.015
Mukundhan D, Kumar R, (2017) Preliminary design and optimization of 2D supersonic intake using OpenFOAM, Proc. of 30th International Symposium on Shock Waves 2, Springer, Cham: 1047–1051 https://doi.org/10.1007/978-3-319-44866-4_46
Muntean S, Nilsson H, Susan-Resiga R (2009) 3D numerical analysis of the unsteady turbulent swirling flow in a conical diffuser using Fluent and OpenFOAM, Proc. of 3rd IAHR International Meeting of the Workgroup on Cavitation and Dynamic Problem in Hydraulic Machinery and Systems, Brno, Czech Republic
Nair PP, Suryan A, Kim HD (2017) Computational study of performance characteristics for truncated conical aerospike nozzles. J Therm Sci 26(6):483–489. https://doi.org/10.1007/s11630-017-0965-0
Nair PP, Suryan A, Kim HD (2019a) Study of conical aerospike nozzles with base-bleed and freestream effects. J Spacecr Rockets 56(4):990–1005. https://doi.org/10.2514/1.A34256
Nair PP, Suryan A, Kim HD (2019b) Computational study on flow through truncated conical plug nozzle with base bleed. Propuls Power Res 8(2):108–120. https://doi.org/10.1016/j.jppr.2019.02.001
Nair PP, Suryan A, Kim HD (2020a) Computational study on reducing flow asymmetry in over-expanded planar nozzle by incorporating double divergence. Aerosp Sci Technol 100:105790. https://doi.org/10.1016/j.ast.2020.105790
Nair PP, Suryan A, Chandran R (2020b) A numerical study on planar nozzles with different divergence angles, Recent asian research on thermal and fluid sciences, Springer, Singapore, 133-146 https://doi.org/10.1007/978-981-15-1892-8_12
Nakao S, Kashitani M, Miyaguni T, Yamaguchi Y (2014) A study on high subsonic airfoil flows in relatively high reynolds number by using openfoam. J Therm Sci 23(2):133–137. https://doi.org/10.1007/s11630-014-0687-5
Nave LH, Coffey GA (1973) Sea level side loads in high-area-ratio rocket engines, Proc of 9th Propulsion Conference, Las Vegas, NV, USA, AIAA Paper 1973–1284. https://doi.org/10.2514/6.1973-1284
Palharini RC, White C, Scanlon TJ, Brown RE, Borg MK, Reese JM (2015) Benchmark numerical simulations of rarefied non-reacting gas flows using an open-source DSMC code. Comput Fluids 120:140–157. https://doi.org/10.1016/j.compfluid.2015.07.021
Papamoschou D, Zill A, Johnson A (2009) Supersonic flow separation in planar nozzles. Shock Waves 19(3):171–183. https://doi.org/10.1007/s00193-008-0160-z
Papamoschou D, Zill A (2004) Fundamental investigation of supersonic nozzle flow separation, Proc. of 42nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada , USA, AIAA Paper 2004–1111 https://doi.org/10.2514/6.2004-1111
Paul PJ, Nair PP, Suryan A, Martin MJP, Kim HD (2020) Numerical simulation on optimization of pintle base shape in planar expansion-deflection nozzles. J Spacecr Rockets 57(3):539–548. https://doi.org/10.2514/1.A34559
Putra YS, Beaudoin A, Rousseaux G, Thomas L, Huberson S (2019) 2D numerical contributions for the study of non-cohesive sediment transport beneath tidal bores. Comptes Rendus Mécanique 347(2):166–180. https://doi.org/10.1016/j.crme.2018.11.004
Rabbani HS, Joekar-Niasar V, Shokri N (2016) Effects of intermediate wettability on entry capillary pressure in angular pores. J Colloid Interface Sci 473:34–43. https://doi.org/10.1016/j.jcis.2016.03.053
Robertson E, Choudhury V, Bhushan S, Walters DK (2015) Validation of OpenFOAM numerical methods and turbulence models for incompressible bluff body flows. Comput Fluids 123:122–145. https://doi.org/10.1016/j.compfluid.2015.09.010
Ruf, J., McDaniels, D. & Brown A (2010) Details of side load test data and analysis for a truncated ideal contour nozzle and a parabolic contour nozzle, Proc of 46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Nashville, TN, USA, AIAA Paper 2010–6813 https://doi.org/10.2514/6.2010-6813
Soman S, Suryan A, Nair PP, Kim HD (2021) Numerical analysis of flowfield in linear plug nozzle with base bleed. J Spacecr Rockets 58(6):1786–1798. https://doi.org/10.2514/1.A34992
Stoldt H, Johansen, CT, Korobenko A, Ziade P (2020) Verification and validation of a high-fidelity open-source simulation tool for supersonic aircraft aerodynamic analysis, Proc. of 19th AIAA aviation 2020 forum, Virtual event, AIAA Paper 2020-2758. https://doi.org/10.2514/6.2020-2758
Sutherland W (1893) The viscosity of gases and molecular force, philosophical magazine series 5, 36 (223):507–531 https://doi.org/10.1080/14786449308620508
Suzuki YJ, Koyaguchi T (2013) 3D numerical simulation of volcanic eruption clouds using the 2011 Shinmoe-dake eruptions. Earth Planets Space 65(10):581–589. https://doi.org/10.5047/eps.2013.03.009
Taylor NV, Hempsell CM, Macfarlane J, Osborne R, Varvill R, Bond A, Feast S (2010) Experimental investigation of the evacuation effect in expansion deflection nozzles. Acta Astronaut 66(3–4):550–562. https://doi.org/10.1016/j.actaastro.2009.07.016
Taylor N, Steelant J, Bond R (2011) Experimental comparison of dual bell and expansion deflection nozzles, Proc. of 47th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, San Diego, California, USA, AIAA Paper 2011–5688 https://doi.org/10.2514/6.2011-5688
Tunstall R, Laurence D, Prosser R, Skillen A (2017) Towards a generalised dual-mesh hybrid LES/RANS framework with improved consistency. Comput Fluids 157:73–83. https://doi.org/10.1016/j.compfluid.2017.08.002
Verma SB (2009) Performance characteristics of an annular conical aerospike nozzle with freestream effect. J Propuls Power 25(3):783–791. https://doi.org/10.2514/1.40302
Verma SB, Manisankar C (2014) Origin of flow asymmetry in planar nozzles with separation. Shock Waves 24(2):191–209. https://doi.org/10.1007/s00193-013-0492-1
Verma SB, Viji M (2011) Freestream effects on base pressure development of an annular plug nozzle. Shock Waves 21(2):163–171. https://doi.org/10.1007/s00193-011-0305-3
Verma SB, Stark R, Haidn O (2006) Relation between shock unsteadiness and the origin of sideloads inside a thrust optimized parabolic rocket nozzle. Aerosp Sci Technol 10(6):474–483. https://doi.org/10.1016/j.ast.2006.06.004
Verma SB, Stark R, Haidn O (2017) Origin of side-loads in a subscale truncated ideal contour nozzle. Aerosp Sci Technol 71:725–732. https://doi.org/10.1016/j.ast.2017.10.014
Vuorinen V, Keskinen JP, Duwig C, Boersma BJ (2014) Boersma, On the implementation of low-dissipative Runge-Kutta projection methods for time dependent flows using OpenFOAM. Comput Fluids 93:153–163. https://doi.org/10.1016/j.compfluid.2014.01.026
Wagner B, Stark R, Schlechtriem S (2011) Experimental study of a planar expansion-deflection nozzle. Progress Propul Phys 2:641–654. https://doi.org/10.1051/eucass/201102641
Wagner B, Schlechtriem S (2011) Numerical and Experimental Study of the Flow in a Planar Expansion-Deflection Nozzle, Proc. of 47th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, San Diego, California, USA, AIAA Paper 2011–5942 https://doi.org/10.2514/6.2011-5942
Wang M, Freund B, Lele SK (2006) Computational prediction of flow-generated sound. Annu Rev Fluid Mech 38:483–512. https://doi.org/10.1146/annurev.fluid.38.050304.092036
Wang Y, Xu J, Huang S, Lin Y, Jiang J (2019) Computational study of axisymmetric divergent bypass dual throat nozzle. Aerosp Sci Technol 86:177–190. https://doi.org/10.1016/j.ast.2018.11.059
White C, Borg MK, Scanlon TJ, Longshaw SM, John B, Emerson DR, Reese JM (2018) dsmcFoam+: an OpenFOAM based direct simulation Monte Carlo solver. Comput Phys Commun 224:22–43. https://doi.org/10.1016/j.cpc.2017.09.030
Wojewodka MM, White C, Shahpar S, Kontis K (2022) Numerical study of complex flow physics and coherent structures of the flow through a convoluted duct. Aerosp Sci Technol 121:107191. https://doi.org/10.1016/j.ast.2021.107191
Xiao Q, Tsai HM, Papamoschou D (2007) Numerical investigation of supersonic nozzle flow separation. AIAA J 45(3):532–541. https://doi.org/10.2514/1.20073
Yang WJ, Yi W, Ren XG, Xu LY, Xu XH, Yuan XF (2015) Toward large scale parallel computer simulation of viscoelastic fluid flow: a study of benchmark flow problems. J Non-Newton Fluid Mech 222:82–95. https://doi.org/10.1016/j.jnnfm.2014.09.004
Zang B, Vevek US, Lim HD, Wei X, New TH (2018a) An assessment of OpenFOAM solver on RANS simulation of round supersonic free jet. J Comput Sci 28:18–31. https://doi.org/10.1016/j.jocs.2018.07.002
Zang B, Vevek US, Lim HD, Wei X, New TH (2018b) An assessment of OpenFOAM solver on RANS simulations of round supersonic free jets. J Comput Sci 28:18–31. https://doi.org/10.1016/j.jocs.2018.07.002
Zmijanovic V, Leger L, Sellam M, Chpoun A (2018) Assessment of transition regimes in a dual-bell nozzle and possibility of active fluidic control. Aerosp Sci Technol 82:1–8. https://doi.org/10.1016/j.ast.2018.02.003
Author information
Authors and Affiliations
Corresponding author
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
Nair, P.P., Narayanan, V., Suryan, A. et al. Prediction and visualization of supersonic nozzle flows using OpenFOAM. J Vis 25, 1227–1247 (2022). https://doi.org/10.1007/s12650-022-00856-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12650-022-00856-5