Comparative Study of OpenFOAM Solvers on Separation Pattern and Separation Pattern Transition in Overexpanded Single Expansion Ramp Nozzle

Yu, T.; Yu, Y.; Mao, Y. P.; Yang, Y. L.; Xu, S. L.

doi:10.47176/jafm.16.11.1751

Comparative Study of OpenFOAM Solvers on Separation Pattern and Separation Pattern Transition in Overexpanded Single Expansion Ramp Nozzle

Document Type : Regular Article

Authors

¹ School of Aeronautics, Chongqing Jiaotong University, 400074, Chongqing, China

² The Green Aerotechnics Research Institute of Chongqing Jiaotong University, Chongqing Key Laboratory of Green Aviation energy and power, 401120, Chongqing, China

³ Nanjing University of Aeronautics and Astronautics, Jiangsu Province Key Laboratory of Aerospace Power System, 210016, Nanjing, China

10.47176/jafm.16.11.1751

Abstract

Flow separation in overexpanded single expansion ramp nozzles (SERN) involves complex phenomena, such as shock waves, expansion waves, turbulent boundary layers, and shear layers. Computational fluid dynamics plays a crucial role in studying unsteady flow behaviour in supersonic nozzles, allowing for an investigation into the dynamic flow field characteristics. However, the application of OpenFOAM as a numerical tool for studying SERN in the field of compressible flows, particularly in the overexpansion state where the flow field characteristics are more complex, has received relatively less attention. In this study, the flow field characteristics of an overexpanded SERN under different turbulence models are investigated through a combination of experiments and numerical calculations. The qualitative and quantitative predictive performance of two compressible flow solvers in OpenFOAM, namely, rhoCentralFOAM and sonicFOAM, are compared in terms of flow separation pattern and separation pattern transitions within the overexpanded SERN. The ability of rhoCentralFOAM and sonicFOAM to accurately predict complex flow states is evaluated. Results indicate that the numerical simulations conducted using rhoCentralFOAM and sonicFOAM successfully capture flow separation, separated shock waves, separated bubbles and shear layers for two types of restricted shock separation patterns at the same nozzle pressure ratio (NPR), demonstrating agreement with experimental results. However, sonicFOAM initiates the transition in the separation pattern 0.0773 NPR earlier than rhoCentralFOAM during the whole separation pattern transition process of the SERN. The transition process in sonicFOAM lasts longer and exhibits a greater variation in NPR. SonicFOAM fails to accurately predict certain aspects, such as the pressure rise after the separation bubble, the reattachment shock wave, and tends to overestimat the length of the separation shock length. Consequently, sonicFOAM cannot be recommended as a suitable solver for accurately capturing the separation pattern of an overexpanded nozzle.

Keywords

Main Subjects

Computational Fluid Dynamics

References

Bhattacharya, S., & Ahmed, A. (2010). Effect of sinusoidal forcing on the wake of a circular cylinder. 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2010-89##

Bhattacharya, S., & Ahmed, A. (2020). Effect of aspect ratio on the flow over a wall-mounted hemispherical turret. International Journal of Heat and Fluid Flow, 84, 108600. https://doi.org/10.1016/j.ijheatfluidflow.2020.108600##

Bhattacharya, S., & Gregory, J. W. (2020). The effect of spatially and temporally modulated plasma actuation on cylinder wake. AIAA Journal, 58(9), 3808–3818. https://doi.org/10.2514/1.J059269##

Edwards, C., Small, W., Weidner, J., & Johnston, P. (1975). Studies of scramjet/airframe integration techniques for hypersonic aircraft. 13th Aerospace Sciences Meeting (Vol. 1–0). American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.1975-58##

Gayathri, N., Senthilkumar, P., Dineshkumar, K., Purusothaman, M., & Sriharan, B. (2022). CFD analysis on flow through nozzle of conical type and truncated conical plug type. Materials Today: Proceedings. https://doi.org/10.1016/j.matpr.2022.09.407##

Hemmati, A., & Namazian, Z. (2021). Numerical analysis of shock wave train in single-expansion ramp nozzle under harmonic inlet and outlet conditions. Chemical Engineering Communications, 1–10. Https://Doi.Org/10.1080/00986445.2021.2007091##

Huang, S., Xu, J., Yu, K., Wang, Y., Pan, R., Chen, K., & Zhang, Y. (2022). Numerical study of a trapezoidal bypass dual throat nozzle. Chinese Journal of Aeronautics. https://doi.org/10.1016/j.cja.2022.11.015##

Huang, W., Wang, Z., Ingham, D. B., Ma, L., & Pourkashanian, M. (2013). Design exploration for a single expansion ramp nozzle (SERN) using data mining. Acta Astronautica, 83, 10–17. https://doi.org/10.1016/j.actaastro.2012.09.016##

Jia, K., Scofield, T., Wei, M., & Bhattacharya, S. (2021). Vorticity transfer in a leading-edge vortex due to controlled spanwise bending. Physical Review Fluids, 6(2), 024703. https://doi.org/10.1103/PhysRevFluids.6.024703##

John, B., & Vivekkumar, P. (2020). A Numerical investigation on the equivalence of shock−wave/ boundary-layer interactions using a two equations RANS model. Journal of Applied Fluid Mechanics, 14(3), 753–767. https://doi.org/10.47176/jafm.14.03.31722##

Joshi, K., & Bhattacharya, S. (2019). Large-eddy simulation of the effect of distributed plasma forcing on the wake of a circular cylinder. Computers & Fluids, 193, 104295. https://doi.org/10.1016/j.compfluid.2019.104295##

Kurganov, A., & Tadmor, E. (2000). New high-resolution central schemes for nonlinear conservation laws and convection–diffusion equations. Journal of Computational Physics, 160(1), 241–282. https://doi.org/10.1006/jcph.2000.6459##

Kurganov, A., Guergana, A., & Siam, P. (2000). Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton—Jacobi equations. SIAM Journal on Scientific Computing, 23, 707–740. https://doi.org/10.1137/S1064827500373413##

Lederer, R., & Krueger, W. (1993). Nozzle development as a key element for hypersonics. 5th International Aerospace Planes and Hypersonics Technologies Conference. American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.1993-5058##

Li, Z., Leng, J., Abu-Hamdeh, N. H., Abusorrah, A. M., & Musa, A. (2022). Effects of nozzle types on mass diffusion mechanism of hydrogen multi-jets at supersonic combustion chamber. International Communications in Heat and Mass Transfer, 139, 106509. https://doi.org/10.1016/j.icheatmasstransfer.2022.106509##

Liu, X. Y., Cheng, M., Zhang, Y. Z., & Wang, J. P. (2022). Design and optimization of aerospike nozzle for rotating detonation engine. Aerospace Science and Technology, 120, 107300. https://doi.org/10.1016/j.ast.2021.107300##

Mirjalily, S. A. A. (2023). Calibration of the k-ω shear stress transport turbulence model for shock wave boundary layer interaction in a SERN using machine learning. Engineering Analysis with Boundary Elements, 146, 96–104. https://doi.org/10.1016/j.enganabound.2022.10.009##

Mousavi, S. M., Pourabidi, R., & Goshtasbi-Rad, E. (2018). Numerical investigation of over expanded flow behavior in a single expansion ramp nozzle. Acta Astronautica, 146, 273–281. https://doi.org/10.1016/j.actaastro.2018.03.003##

Nair, P. P., Narayanan, V., Suryan, A., & Kim, H. D. (2022). Prediction and visualization of supersonic nozzle flows using OpenFOAM. Journal of Visualization, 25(6), 1227–1247. https://doi.org/10.1007/s12650-022-00856-5##

Nave, L., & Coffey, G. (1973). Sea level side loads in high-area-ratio rocket engines. 9th Propulsion Conference. American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.1973-1284##

Pathan, K. A., Dabeer, P. S., & Khan, S. A. (2019). Effect of nozzle pressure ratio and control jets location to control base pressure in suddenly expanded flows. Journal of Applied Fluid Mechanics, 12(4), 1127–1135. https://doi.org/10.29252/jafm.12.04.29495##

Rakhsha, S., Rajabi Zargarabadi, M., & Saedodin, S. (2023). The effect of nozzle geometry on the flow and heat transfer of pulsed impinging jet on the concave surface. International Journal of Thermal Sciences, 184, 107925. https://doi.org/10.1016/j.ijthermalsci.2022.107925##

Salimi, M. R., Askari, R., & Hasani, M. (2022). Computational investigation of effects of side-injection geometry on thrust-vectoring performance in a fuel-injected dual throat nozzle. Journal of Applied Fluid Mechanics, 15(4), 1137–1153. https://doi.org/10.47176/jafm.15.04.33354##

Shyji, S., Deepu, M., Kumar, N. A., & Jayachandran, T. (2017). Numerical studies on thrust augmentation in high area ratio rocket nozzles by secondary injection. Journal of Applied Fluid Mechanics, 10(6), 1605–1614. https://doi.org/10.29252/jafm.73.245.27309##

Yaravintelimath, A., B. N., R., & A. Moríñigo, J. (2016). Numerical prediction of nozzle flow separation: Issue of turbulence modeling. Aerospace Science and Technology, 50, 31–43. https://doi.org/10.1016/j.ast.2015.12.016##

Yu, K., Xu, J., Lv, Z., & Song, G. (2019). Inverse design methodology on a single expansion ramp nozzle for scramjets. Aerospace Science and Technology, 92, 9–19. https://doi.org/10.1016/j.ast.2019.05.054##

Yu, Y. (2020). Over-expanded separation transitions of single expansion ramp nozzle in the accelerating and decelerating processes. Aerospace Science and Technology, 98, 105674. https://doi.org/10.1016/j.ast.2019.105674##

Yu, Y., Xu, J., Mo, J., & Wang, M. (2014a). Numerical investigation of separation pattern and separation pattern transition in overexpanded single expansion ramp nozzle. The Aeronautical Journal, 118(1202), 399–424. Cambridge Core. https://doi.org/10.1017/S0001924000009192##

Yu, y., xu, j., mo, j., & wang, m. (2014b). Principal parameters in flow separation patterns of over-expanded single expansion RAMP nozzle. Engineering Applications of Computational Fluid Mechanics, 8(2), 274–288. https://doi.org/10.1080/19942060.2014.11015513##

Yu, Y., Xu, J., Yu, K., & Mo, J. (2015). Unsteady transitions of separation patterns in single expansion ramp nozzle. Shock Waves, 25(6), 623–633. https://doi.org/10.1007/s00193-015-0595-y##

Zang, B., U S, V., & New, T. H. D. (2017). OpenFOAM based numerical simulation study of an underexpanded supersonic jet. 55th AIAA Aerospace Sciences Meeting. American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2017-0747##

Zhou, L., & Wang, Z. (2019). Numerical investigation on the three-dimensional flowfield in the single expansion ramp nozzle with passive cavity flow control. Journal of Applied Fluid Mechanics, 12(4), 1115–1126. https://doi.org/10.29252/jafm.12.04.29320##