AERO213 Aeroengines Assignment

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Reference no: EM133091025

AERO213 Aeroengines - University of Liverpool

CFD MODELING OF SUPERSONIC FLOW THROUGH A CONVERGENT-DIVERGENT NOZZLE AND COMPARISON WITH 1D THEORY

PROBLEM OUTLINE

We are interested in the supersonic flow of air through a convergent-divergent nozzle having a circular cross-sectional area, A, that varies with axial distance from the throat, x, according to the formula
A = C₁ + x²; -0.5 <x< 0.5
where A is in metres2 and x is in metres. C₁ is a constant which is different for each student. The stagnation temperature To at the inlet is 300 K. The stagnation pressure po at the inlet is given. The static pressure pe at the exit is also given. Your personal values are on VITAL.

We will calculate the Mach number, pressure and temperature distribution in the nozzle using FLUENT and compare the solution to quasi-1D nozzle flow results. Use an inviscid flow model for the CFD calculation.

EXPECTED SUBMISSION

1. A completed technical note for up to 85 marks.
2. FLUENT contour plot of static pressure for up to 5 marks.
3. FLUENT plot of velocity vectors coloured by static temperature for up to 5 marks.
4. FLUENT xy-plot of the y-coordinate of the wall for up to 5 marks.

SECTION 1: 1D THEORY

Q1. Assuming steady one-dimensional flow, calculate the Mach number at the exit of your nozzle. Show your working and briefly justify your choice of equation(s).

Q2. Determine the mass flow rate of air through your nozzle. Show your working.

Q3. Determine the Mach number variation through the nozzle at the following axial (x) locations.

x (m)	Mach number
-0.5 (inlet)
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5 (exit)

Section 2: CFD
Q4. Plot the variation of Mach number with axial location for the 1D theory (i.e. your results from Q3) together with the CFD results along the centerline and at the wall.

Q5a.Provide sufficient evidence (e.g. a plot with short comments) to justify the number of cells you used in your mesh.

Q5b.State and justify the discretisation scheme you used, e.g. first order upwind, and derive a simple discretised expression for d2u/dx2 that is second order accurate.

Q6a. You were instructed to use an inviscid flow model. Justify the use of that model for this calculation.

Q6b.Write down the simplifiedCartesianNavier-Stokes momentum equations that you think are the closest representation to the equations you actually solved in Fluent. State why these aren't actually the equations you solved.

Q6c.State whether you included the energy equation in your CFD calculation and the reason why you made that decision.

Q7.Briefly discuss, in less than 100 words, the main conclusions you draw from the plot in Q4. In particular explain the reason behind the differences between the CFD results and 1D theory. You should refer to your other FLUENT plots to explain your reasoning.

Q8.Explain, in less than 100 words, why the accuracy of CFD calculations increases as the mesh density increases.

Section 3: Physical understanding

Q9. Describe in detail one physical phenomenon your CFD analysis has neglected which may be important in the convergent-divergent nozzle problem.

Q10. State and explain the simple change you would have to make to your FLUENT setup to see a shock in the nozzle.

Attachment:- Aeroengines.rar

Reference no: EM133091025

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