# Supersonic Nozzle Flow Separation (Shock Wave) Simulation

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The present study simulates airflow within a supersonic convergent-divergent nozzle and examines the behavior of airflow separated from the nozzle in the surrounding environment (shock wave).

This ANSYS Fluent project includes CFD simulation files and a training movie.

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## Description

## Supersonic Nozzle Project Description

The present study simulates airflow within a supersonic convergent-divergent nozzle and examines the behavior of airflow separated from the nozzle in the surrounding environment. In order to simulate the present model, the pressure condition in the nozzle input section (pressure-inlet condition) and the ambient output sections (pressure-outlet condition) have been used. The nozzle pressure ratio (NPR) is equivalent to the ratio of the inlet air pressure of the nozzle, to the ambient pressure. Thus, the value of the nozzle pressure ratio in the current system is 1.5 and the amount of inlet air pressure is 153580.65 Pascals (NPR = P / Pambient = 1.5 and therefore P = 1.5 * 102387.146), as well as the pressure at the output, is equal to the ambient pressure, that is 102387.146 Pascal.

In addition, the inlet airflow has a temperature of 290 Kelvin. The functional structure of the nozzle is such that as the fluid enters it and passes through the convergent part of the nozzle, according to the continuity equation, it causes the velocity of the passing fluid to increase by decreasing the cross-sectional area of the flow; and therefore, due to the Bernoulli’s law, the fluid pressure decreases with increasing velocity, consequently. To analyze this model, parameters such as Mach number, velocity, and pressure based on the motion of the fluid flow in the longitudinal direction of the nozzle have been investigated. The following figure shows a schematic of the internal structure of a convergent-divergent nozzle and its components.

## Nozzle Geometry & Mesh

The present 2-D model is drawn using Design Modeler software. The geometric structure of the model consists of a convergent-divergent nozzle and the throat area, as well as a rectangular space containing the nozzle output. It should be noted that in the present model, the ratio of the cross-sectional area of the nozzle to the cross-sectional area of the throat area is assumed to be 1.5. The figure below shows a view of the geometry.

The meshing of the present model has been done using ANSYS Meshing software. The mesh type is structured and the element number is 9000. The size of the grids in the area adjacent to the nozzle output is smaller. The following figure shows the mesh. (Supersonic Nozzle)

## Shock Wave in a Supersonic Nozzle CFD Simulation

To simulate the present model, several assumptions are considered, which are:

- A density-based solver is performed because in models such as convergent-divergent nozzles, the airflow is considered to be quite compressible and the Mach number is significant.
- The present model is steady in terms of time and the time term is not considered in solving the problem.
- The effect of gravity on the fluid is not considered.

The following is a summary of the steps for defining a problem and its solution:

Models (Supersonic Nozzle) |
||

k-omega | Viscous model | |

standard | k-omega model | |

shear flow corrections | k-omega options | |

on | Energy | |

Boundary conditions (Supersonic Nozzle) |
||

pressure inlet | Inlet | |

153580.65 Pa | gauge total pressure | |

102387.146 Pa | supersonic/initial gauge pressure | |

290 K | Total temperature | |

pressure outlet | Surrounding | |

102387.146 Pa | gauge total pressure | |

wall | nozzle’s wall | |

0 W.m^{-2} (isolated) |
heat flux | |

Solution Methods (Supersonic Nozzle) |
||

Implicit | |
Solution methods |

first order upwind | flow | Spatial discretization |

first order upwind | turbulent kinetic energy | |

first order upwind | specific dissipation rate | |

Initialization (Supersonic Nozzle) |
||

Hybrid | Initialization method |

### Density-Based Solver

Due to the fact that in the present model, we use a convergent-divergent nozzle to enter the airflow, the fluid velocity increases significantly, so that the velocity of the fluid exceeds the speed of sound within the fluid. In such cases, where the Mach number is large, we apply the density-based solution solver.

### K-Omega Turbulence Model

In the present model, due to the presence of compressible flow and creating pressure gradient, we use the standard k-omega turbulent model with shear flow correction capability.

## Results

At the end of the solution process, we obtain two-dimensional contours of pressure, temperature, velocity, density, and Mach number, as well as two-dimensional path lines.

The following figure shows the contour of the Mach number in the specified state (NPR=1.5) in the specified area of the nozzle.

The following figure is the result of a reference article. (Supersonic Nozzle)

All files, including Geometry, Mesh, Case & Data, are available in Simulation File. By the way, Training File presents how to solve the problem and extract all desired results.

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