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Shock Wave CFD Simulation in Supersonic Airflow

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The problem is to simulate the supersonic airflow encountered by a two-way oblique airfoil barrier passing through a channel, thus investigating fluid behavior and creating a shock wave phenomenon.

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Shock Wave Project Description

The problem is to simulate the supersonic airflow encountered by a two-way oblique airfoil barrier passing through a channel, thus investigating fluid behavior and creating a shock wave phenomenon. The airflow in the simulation environment around the obstacles and canals has a temperature of 129.46 Kelvin and a Mach number of 2.49, and the direction of the airflow is generally assumed to be in the same direction. Mach number is a non-dimensional number that indicates the ratio of fluid velocity to sound velocity in the same fluid. This number is usually used when the velocity of the fluid flow is close to the sound velocity or more, and one of the major uses is aerospace applications.

Since the airflow in this model is supersonic, it has a larger Mach number than one; that is, the airflow speed is higher than the speed of sound in the air. Therefore, the pressure far-field boundary condition is used to define the mentioned boundary conditions and to consider the Mach number in the simulation. Ultrasonic airflow hits a diagonal barrier in its path, and then passes through the inner space of the square channel, and the collision with the sharp barrier creates a shock wave. The aim of the present study is to investigate the air pressure and velocity distribution around the barriers and inside the canal and also to study the shock wave phenomenon.

Shock Wave

Shock waves, like other flows, can carry the energy and propagate in an environment. Features of this type of wave include sudden and discrete changes in pressure, temperature, and density. In general, at supersonic velocities. There are two different types of designs for airfoils, including biconvex and double wedge airfoils. The biconvex type has convex flat surfaces and is curved, while the double wedge type, which is also used in the current model, has two sharp angles in the middle up and down. It can cause a triangular or rhombic shape in the airfoil.

It should be noted that since the present problem is done in the unsteady state, its time step is considered to be 0.025 seconds and the total time of the simulation process is 0.75 seconds.

Geometry & Mesh

The present 3-D model is drawn using the Design Modeler software. The geometric structure of the model includes a rectangular space for airflow and a double wedge airfoil barrier and a square channel with a wedge inside. The figure below shows a view of drawing geometry.

shock wave

The meshing of the present model has been done using ANSYS Meshing software. The mesh type is unstructured and the element number is 4466857. The size of the grids in the area adjacent to the barriers and channels is smaller. The following figure shows the mesh.


Shock Wave CFD Simulation

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

  • The Density-Based solver is performed because, in shock phenomenon, the airflow is considered to be quite compressible and the Mach number is significantly high.
  • Simulation has been performed in both fluid and thermal states (heat transfer).
  • The present model is unsteady in terms of time because the purpose of the problem is to study the behavior of shock over time.
  • 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 (Shock Wave)
k-omega Viscous model
SST k-omega model
compressiblity effects, production limiter k-omega options
on Energy
Boundary conditions (Shock Wave)
pressure far-field Inlet, Outlet, Side walls and top wall
26750 Pascal gauge pressure
2.49 makh number
129.46 K temperature
wall Ground
300 K temperature
wall Obstacle’s wall
0 W.m-2.K-1 heat flux
Solution Methods (Shock Wave)
Implicit   Solution methods
first order upwind flow Spatial discretization
first order upwind turbulent kinetic energy
first order upwind specific dissipation rate
Initialization (Shock Wave)
Standard Initialization method
26750.32 pascal gauge pressure
567.7385 m.s-1 x-velocity
0 m.s-1 y-velocity, z-velocity
129.4616 K temperature

Density-Based Solver

Due to the fact that in the present model, we use supersonic airflow to check the shock wave, so the Mach number of the airflow is significant. Therefore, to simulate the present model, we use a density-based solver.

K-Omega Turbulence Model

In the present model, since the flow has a significant Mach velocity and a transient shock wave is created, the k-omega SST type turbulent model is used.

Shock Wave Results

After the solution process is complete, we obtain two-dimensional and three-dimensional contours of pressure, temperature, velocity, density, and Mach number, as well as two-dimensional and three-dimensional pathlines. We obtain the resulting contours and pathlines in the final second of the unsteady simulation process. In addition, we present the two-dimensional contours and pathlines in the two sections of XY and XZ in the position of the surface passing through the middle of the obstacles and the canal.

There is a mesh file in this product. By the way, the Training File presents how to solve the problem and extract all desired results.


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