AE 169

Professor Dr. Papadopoulos

Robin Dhillon

Duong Tang

1. NACA 0012 Airfoil

2. Analysis of De Laval Nozzle

● Using CFD to simulate the flow around a NACA 0012 airfoil

at Re=1,000,000

● Compare lift and drag coefficients from ESI/ACE+ with

published data

● Use CFD to simulate the flow around de laval nozzle

The NACA 0012 airfoil is a symmetrical airfoil that produces no

lift at zero angle of attack.

Specifications and parameters:

● Thickness: 12.0%

● Camber: 0.0%

● Trailing edge angle: 58.6o

● Leading edge radius: 1.7%

● Zero-lift angle: 0.0o

● Max CL: ~1.35

● Max CL angle:15.0o

● Max L/D:36.958

● Max L/D angle: 7.5o

● Max L/D CL:0.842

Grid independent study:

● Grid points: 100 for airfoil, 150 for nozzle

● Due to time constraints, 300 grid points was not used

Flow conditions to achieve Re=1,000,000:

● 𝑉 = 100𝑚/𝑠

● 𝐶 = 1𝑚

● 𝜌=1.164𝑘𝑔/𝑚3

● 𝜇 = 1.164 ∗ 10−4

● 𝑃 = 100,000𝑃𝑎

Simulation grid

● Divided into 4 sections

● Vertical divider connects

at trailing edge

Simulation geometry

Simulation geometry at an angle of attack (12AoA)

ACE simulation

NACA 0012:

•Lift and drag curve of airfoil

•Flow geometry

Velocity contours at 0 AoA

Pressure contours at 0 AoA

Pressure contours at 1 AoA

Pressure contours at 2 AoA

Pressure contours at 3 AoA

Pressure contours at 4 AoA

Pressure contours at 5 AoA

Pressure contours at 6 AoA

Pressure contours at 7 AoA

Pressure contours at 8 AoA

Pressure contours at 9 AoA

Pressure contours at 10 AoA

Pressure contours at 11 AoA

Pressure contours at 12 AoA

Pressure contours at 13 AoA

Pressure contours at 14 AoA

Pressure contours at 15 AoA

• Convergent-divergent Nozzle

• Nozzle was developed by Swedish

* inventor Gustaf De Laval in 1888

• This principle was first used in a rocket

* engine by Robert Goddard

http://www.academia.edu/7907376/cfd_analysis_of_rocket_nozzle

Parameter Dimension

Total Nozzle Length (mm) 484

Inlet Diameter(mm) 166.6

Throat Diameter(mm) 34.5

Outlet Diameter(mm) 183.0

Chamber Length(mm) 99.93

Convergent Angle (deg) 32

Divergent Angle(deg) 11.31

Static Inlet Pressure(N/m^2) 10000000

Static Outlet Pressure(N/m^2) 101325

Static Inlet Temperature (K) 3300

Grid independent study:

● 150 grid points were used (previously 100, but 150

gave more accurate results)

Simulation grid

● divided into different sections

● easier to achieve orthogonality

● Lift coefficient was more accurate than drag coefficient

● More grid points would have led to more accurate results

● Errors due to differences in Reynolds number and numbers of

iterations

● Adding Boundary Layer improves drag simulation accuracy