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.
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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
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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
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DOI: https://doi.org/10.1007/s12650-022-00856-5