Week 2 - Converging diverging nozzle

AIM: To stimulate the convergence_diverging nozzle by using ANSYS Fluent and plot the results.

Geometry:

Objectives:

• The pressure, velocity and temperature variations across the domain
• The variation of Mach number across the domain and at what distance from the inlet does the flow become supersonic.

Boundary Conditions:

• At Inlet, Pressure = 1atm and Temperature = 300K. The outlet pressure= 0.027 atm.

• In the operating conditions, consider the reference pressure to be zero.

Procedure:

GEOMETRY:

• Create the given geometry in the Ansys Fluent space claim with given dimensions by using line, arc tools.
  
• Then the created geometry is imported into the Mesh tool GUI, then meshed the model with an element length of 0.005mm and defined the element type as Quad.

Meshing:

• After meshing the number of elements generated are 6977, and the number of nodes are 7198, the final mesh is displayed as below.
  
• The mesh is fine, and the mesh metric element quality is resulted as follows
  
• And also, named the edges of the model as inlet, outlet, nozzle wall, asymmetric wall respectively.
  

Solution:

• The mesh is imported into the solution setup
  
• solver type = Density based solver
• And turned on the energy equation.
• Viscous model
  
• And selected the Fluid material as "air" and the properties of the fluid is taken as Ideal-Gas properties.

Boundary Conditions:

• inlet as pressure-inlet type
  
• outlet as pressure-outlet type
  
• Nozzle wall as wall type
• asymmetric wall as symmetry

And then initialized the solution by Hybrid method and calculated the solution with 500 iterations.

Contour and plots:

• And created contours of temperature, pressure, velocity along the nozzle surface.
• Also, plotted the total pressure, temperature, velocity and Mach number. In the x-axis the direction vector is plotted, and along the Y axis the parameters are plotted.

Results:

Residuals:

Pressure plot:

Temperature plot:


Velocity plot:

Temperature Contour:

Here, the temperature is high at the inlet and gradually

Pressure contour:

Here, the pressure is decreasing troughtout the nozzle.

Velocity contour:

Here, the velocity is increased throughout the nozzle and at the outlet the velocity is low at the top.

Mach Number plot:

Here, Mach number results less than 1, that means the flow is subsonic, and at length 0.5 the Mach Number is >1 that means the flow is changes from subsonic to supersonic.

Means at the converging nozzle side the Mach number is less than 1 and the flow is Subsonic, and then the flow is changing to supersonic by increasing the mach number greater than 1.

We know that for isentropic flow

`\frac{d A}{A}=(M^2-1) \frac{d V}{V}`

So, here at the converging nozzle side the Area and the volume is decreasing gradually along the length, so the ratio of (Area/Volume) results in a positive value. That means `1-M^2`is positive when M must be 0 are 1.

Similarly, at the diverging nozzle side the Area and the volume is increasing gradually along the length, so the ratio of (Area/Volume) results in a negative value. That means `1-M^2`is negative when M must be >1.