Week 2 - Converging diverging nozzle

Objective:

1. To plot the pressure, velocity, and temperature variations across the domain
2. To plot the variation of Mach number across the domain and at what distance from the inlet does the flow become supersonic.

Geometry:

Mesh:

Geometry Setup:

• General Settings

• Since the flow is having a supersonic condition M>0.3 where the compressibility factor is taken into account thus using density-based formulation.

• Viscous Model

• Since this is a compressible flow viscosity has negligible effect thus using inviscid flow.

• Pressure Inlet

• Since at the inlet the stagnation pressure is atmospheric we use the value of the atmospheric condition.
• The Supersonic/Initial Gauge Pressure will be used in conjunction with the specified stagnation pressure to compute initial values according to the isentropic relations (for compressible flow) or Bernoulli's equation (for incompressible flow).

• Operating Condition:

• Any time an absolute pressure is needed, it is generated by adding the operating pressure to the relative pressure. Since here we are using absolute pressure and not atmospheric pressure.

• Pressure outlet

• Pressure outlet as specified in thequestion

Results:

Pressure Contour:

Pressure Graph:

Density Contour:

Density Graph:

Velocity Contour:

Velocity Graph:

Mach No. Contour:

Mach No. Graph:

Temperature Contour:

Temperature Graph:

Analytical graph:

`(1-M^2)(dv)/v = -(dA)/A`

When the flow in the throat is subsonic from the above relation as the area increases the dA>0 also M<1 also (1-M^2)>0 thus the velocity will tend to decrease. But when the flow is actually choked at the throat then a slight increase in the area causes the flow to go supersonic. For a supersonic flow (M > 1) the term multiplying velocity change is negative (1 - M^2 < 0). Then an increase in the area (dA > 0) produces an increase in the velocity (dV > 0).

In Supersonic flow to conserve mass, both the density and the velocity are changing as we change the area.

Inference:

From the results of the Mach number, it is clear that the Mach number becomes supersonic after the throat section.