Week 2 - Converging diverging nozzle

Aim:

• To perform CFD analysis on Converging Diverging Nozzle.
• Plot variation of velocity, temperature and pressure along the length of the nozzle.
• Plot the variation of Mach Number along the length of the nozzle and identify at what distance from the inlet it becomes Supersonic.
• Understand the variation of change in area on the Mach Numeber.

Take away:

By the end of this article one will be able to,

• Simulate this particular case set up.
• Plot the graphs.

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Simulation Setup:

• Geometry:

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• Mesh:

Named Selection:

• Mesh element size is given as 4 mm.

• Mesh is shown below:

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Setting up the physics:

• Solver Type = Density Based solver. (Since Mach Number can exceed 0.3 and it is compressible flow)
• 2D space = Axisymmetric.
• Time = Steady State.

• Energy equation must be turned on.
• Viscous Model = K-Omega SST (default)

Boundary Condition:

• Inlet = Pressure inlet (101325 Pa); Temperature = 300 K

• Outlet = Pressure outlet (2735.775 Pa)

• Material Properties: Material = Air; Density = Ideal gas Law.

• Next step is to do a hybrid initialization.
• Make sure that Courant number is selected properly to avoid divergence.

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Results:

• Residual:

• Mach Number:

• Here the 0 point on the x axis is the throat section of the pipe.
• Since the area of the nozzle decreases the velocity increases to conserve the mass.
• Therefore, from the graph it is quite evident that the Mach number at the throat section exceeds 1 and the flow becomes supersonic.

• Pressure Contour:

• Temperature Contour:

• Velocity Contour:

• Pressure Graph:

• Temperature Graph:

• Velocity Graph:

• Comparing the above graphs with the below graph.

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Conclusion:

• As the crosectional area decreases, the velocity increases, hence, the Mach Number increases.