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Compressible Flow in a Convergent-Divergent Nozzle

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In this project, the airflow will enter the convergent-divergent nozzle with a pressure of 70 bars and the Mach number of 0.2 with a temperature of 2735 K.

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

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Convergent-Divergent Nozzle Introduction

A de Laval nozzle (or convergent-divergent nozzle, CD nozzle, or con-di nozzle) is a tube that is pinched in the middle, making a carefully balanced, asymmetric hourglass shape. It is used to accelerate a hot, pressurized gas passing through it to a higher supersonic speed in the axial (thrust) direction, by converting the heat energy of the flow into kinetic energy. Because of this, the nozzle is widely used in some types of steam turbines and rocket engine nozzles.

Compressible Flow Project description

In this project, the airflow will enter the convergent-divergent nozzle with a pressure of 70 bars and the Mach number of 0.2 with a temperature of 2735 K. after passing the throat zone, the airflow will gain speed and lose its temperature as it passes through the diffuser.  The standard k-epsilon model with standard wall function is used to solve fluid flow equations. The energy model is activated and the ideal gas equation is exploited to calculate the density changes in the computational domain.

compressible flow

geometry and mesh

The geometry of this model is designed in ANSYS design modeler and meshed in ANSYS meshing®. The mesh type used for this geometry is unstructured and has great accuracy in sensitive sections. Also, the element number is 898906.

compressible flow

Compressible Flow CFD Simulation Settings

The key assumptions considered in this project are:

  • Simulation is done using Density-based solver.
  • The present simulation and its results are steady.
  • The effect of gravity is ignored.

The applied settings are summarized in the following table.

(Compressible Flow) Models
Viscous model k-epsilon
Model standard
Near wall treatment Standard wall function
Energy model On
(Compressible Flow) Boundary conditions
Inlet Pressure far-field
Gauge pressure 7000000 Pa
Mach number 0.21
temperature 2735 K
Outlet Pressure outlet
Gauge pressure 101325 Pa
Temperature 300 K
Walls wall motion stationary wall
New wall Heat flux 0 W/m2
(Compressible Flow) Solution Methods
Formulation Implicit
Flux type Roe-FDS
Spatial discretization Flow First order upwind
Turbulent kinetic energy First order upwind
Turbulent Dissipation rate First order upwind
(Compressible Flow) Initialization
Initialization method   standard
Gauge pressure 7000000 Pa
Y velocity 220.078
Turbulent kinetic energy 7.265146 m2/s2
Turbulent Dissipation rate 5107.493 m2/s3
Temperature 2735 K


The contours of, pressure, temperature, velocity, Mach number, etc. are presented.

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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