Week 2 - Converging diverging nozzle

Convergent Divergent Nozzle:

Consider the converging-diverging nozzle below with the dimensions. The throat radius of the nozzle is 0.1mm.

For the following 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.

We have to Plot:

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

From the above-derived variation, explain the variation of change in the area on mach number on the given geometry in a few words.

SOLUTION 1: Simulation

Step1: (creating and importing geometry)

• Create the geometry using design software for the above-mentioned dimensions.
• And import the geometry to Ansys-Spaceclaim as shown below,

Step2: (Meshing)

• Open meshing in the Ansys workbench and apply the suitable element size to deploy the mesh.
• The mesh we created is shown below,

Step3: (Setting up the simulations)

• Start the fluent simulation setup using 2D.
• Apply the boundary conditions for To the suitable boundaries as shown below.
• And run the calculation, for this case we get a converged solution at 73rd iterations.

Initial Setup

Boundary Conditions

Residuals plot after running the simulation

Step4: Post Processing the Results

• Here comes the main process of the entire project.
• We are going to analyze the results obtained from the simulations such as pressure, temperature, and mach number.
• Create a chart in the CFD-post processor as shown below, and various factors for the y-axis can be changed according to requirement.

1. Variation of pressure across the Nozzle Domain:

pressure contour

pressure plot

ii. Variation of temperature across the nozzle domain:

Temperature Contour

temperature plot

iii. Variation of velocity across the nozzle domain:

Velocity Contour

Velocity Plot

iv. Variation of mach number across the nozzle domain:

Mach number contour

Mach number Chart

SOLUTION 2: EXPERIMENTAL

• In this section we can able to find the experimental values of pressure, temperature and mach number variations for the C-D nozzle, which is available in the open sources.

• As we can see from the above graph the various factors like temperature, pressure, and velocity variations through the nozzle domain, will be taken as a reference for the comparison of simulation and analytical data which we are going to see in the next part.

SOLUTION 3: ANALYTICAL

• Variation of fluid velocity with the flow area of the nozzle is given below,
• `(dA)/A=-(Dv)/V(1-M^2)`

CONDITION 1

• Consider the first half of the nozzle (converging zone), the flow is isentropic
• `(dA)/(dV)=(A_2-A_1)/(V_2-V_1)`
• `(dA)/(dV)=(-_(ve))/(+_(ve))`
• So, `(dA)/(dV)=-_(ve)`

Since the `A_2 < A_1 and V_2>V_1`

• So if the above conditions are applied in the nozzle equation we will get dA/dV<0 and Mach number M<1.
• Hence it comes under subsonic flow.

CONDITION 2

• Consider the second half of the nozzle (diverging zone), the flow is isentropic
• `(dA)/(dV)=(A_2-A_1)/(V_2-V_1)`
• `(dA)/(dV)=(-_(ve))/(+_(ve))`
• So` `(dA)/(dV)=+_(ve)`

Since the `A_2 < A_1 and V_2>V_1`

• So if the above conditions are applied in the nozzle equation we will get dA/dV>0 and Mach number M>1.
• Hence it comes under supersonic flow.

CONDITION 3

• Consider the middel part of the nozzle (Throat zone), the flow is isentropic
• `(dA)/(dV)=(A_2-A_1)/(V_2-V_1)`
• `(dA)/(dV)=(0)/(0)`
• So,` `(dA)/(dV)=0`

Since the `A_2 = A_1 and V_2 = V_1`

• So if the above conditions are applied in the nozzle equation we will get dA/dV=0 and Mach number M=1.
• Hence it comes under sonic flow.

CONCLUSION:

• Hence, we plotted the various factors for the nozzle domain.
• And, also we have seen the effects on mach number on changing the area of the nozzles.
• Also we got the same solutions from the three different methods.