Skip to main content

Prediction and visualization of supersonic nozzle flows using OpenFOAM

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

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

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

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Abhilash Suryan.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Nair, P.P., Narayanan, V., Suryan, A. et al. Prediction and visualization of supersonic nozzle flows using OpenFOAM. J Vis (2022). https://doi.org/10.1007/s12650-022-00856-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

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

Keywords

  • Planar nozzle
  • Separated flow
  • OpenFOAM
  • Supersonic flow
  • Asymmetry
  • Advanced rocket nozzle