How Do You Analyze a 2-D Nozzle Operating at Critical Condition?

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SUMMARY

The discussion focuses on analyzing a 2-D convergent-divergent nozzle operating under critical conditions, specifically at the throat. Key parameters include a Reynolds number (ReD*) of 230,000, a throat diameter (D*) of 6 mm, and an initial temperature (T0) of 300 K. The analysis involves using equations for mass flow rate and Reynolds number, alongside computational simulations in StarCCM+ to validate analytical results. Participants are guided to solve for pressure and temperature at the exit, shock location, and pressure distributions.

PREREQUISITES
  • Understanding of gas dynamics, particularly convergent-divergent nozzles.
  • Familiarity with fluid mechanics equations, including mass flow and Reynolds number calculations.
  • Proficiency in using StarCCM+ for computational fluid dynamics simulations.
  • Knowledge of thermodynamic properties of air, including specific heat ratios and gas constants.
NEXT STEPS
  • Learn how to derive and apply the mass flow equation for compressible flow in nozzles.
  • Study shock wave theory and its implications in nozzle design and analysis.
  • Explore advanced features of StarCCM+ for simulating compressible flow scenarios.
  • Investigate methods for comparing analytical results with computational simulations effectively.
USEFUL FOR

Aerospace engineers, mechanical engineers, and students studying gas dynamics who are involved in nozzle design and performance analysis.

Maven.sharma
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Homework Statement


A 2-D nozzle shown in picture 1 is to be analyzed. The nozzle is working with critical condition at
the throat.
I haven attached a Pdf and .jpg file for the figure
ReD* :230000
D* :6mm
T0 :300 K
Diffusor half angle : 3°
Diffusor length :7D
Medium :Air
Κ :1,4
R :287 J/kgK
μ0 :18,6.10-6 Pas
ρ0 :1,2 kg/m³

Homework Equations


By using the following equations
m/A=P0√κ/√RT0(1+κ−1/2M2)κ+12(κ−1) (1)
ReDx= 4m/∏Dx ν (2)


The Attempt at a Solution


I have no idea how to solve analytically please guide me

1) Solve analyticaly the 1st, 2nd and 3rd critical poit. Choose a pressure ratio for a
shock in the diffusor part. Solve all the values (p, T) for the exit. Put the values in to
starCCM+ and compare your analytical results with the results from starCCM+.
2) Solve the location of the shock and compare the position from your result with
starCCM+.
3) Plot all the pressure distributions from starCCM+ along the axis in one graph. (p/p0
vs position).
4) Compare the time averaged massflowrate with the theoretical massflow. Do you
have some differences.
 

Attachments

  • gd_project1.pdf
    gd_project1.pdf
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  • j.jpg
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I'm sorry you are not finding help at the moment. Is there any additional information you can share with us?
 
Greg Bernhardt said:
I'm sorry you are not finding help at the moment. Is there any additional information you can share with us?

well i have uploaded the complete question detail more i could say is it is a convergent divergent nozzle this question is basically from gas dynamics convergent divergent nozzle topic