1. 2D Free Jet Simulations (FLUENT)
Oct
yan

2. Outline 2D Laminar Plane Jet 2D Laminar Round Jet
Theoretical Solutions
Numerical Calculations (FLUENT code)
Mean Stream Velocity
Jet Half Width
Momentum Thickness
2D Laminar Round Jet

3. 2D Laminar Plane Jet ― Theoretical Solutions
Air emerges into a still air from a 2D slot at x=0
Constant momentum flux (J) at any cross section
Spread at constant pressure (P = 1 bar)
Red = 400 ( ux = 0.64 m/s）
Temperature = 300 K
ρ = kg/m3；ν = ×10-5 m2/s；
Fig.1 Typical free 2D laminar plane jet streamline pattern
Laminar Plane Jet
(Schlichting 1933)

4. 2D Laminar Plane Jet ― Numerical Calculations
Inlet velocity
Wall
Pressure
outlet
Symmetrical axis
Interior
Halved geometry

5. 2D Laminar Plane Jet ― Numerical Calculations
Centerline Velocity( ) 𝒙
𝒖 𝒄
0.01
0.05
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
White’s book PDF page277 (J = )

6. 2D Laminar Plane Jet ― Numerical Calculations
Mean Stream Velocity ( )
x/d = 20
x/d = 10
The plot shows the flow profile along the radial direction of the flow.

7. 2D Laminar Plane Jet ― Numerical Calculations
Mean Stream Velocity ( )
x/d = 30
x/d = 40
The plot shows the flow profile along the radial direction of the flow.

8. 2D Laminar Plane Jet ― Numerical Calculations
Mean Stream Velocity ( )
x/d = 60
x/d = 50
The plot shows the flow profile along the radial direction of the flow.

9. 2D Laminar Plane Jet ― Numerical Calculations
Mean Stream Velocity ( )
x/d = 70
x/d = 80
The plot shows the flow profile along the radial direction of the flow.

10. 2D Laminar Plane Jet ― Numerical Calculations
Mean Stream Velocity ( )
x/d = 90
x/d = 100
The plot shows the flow profile along the radial direction of the flow.

11. 2D Laminar Plane Jet ― Numerical Calculations
Jet Half Width ( )
𝒙/d
𝒓 𝟏/𝟐 /d 1 5 10 20 30 40 50 60 70 80 90
100
Half Width: Radial distance from the axis to the position at the which the absolute value of the axial velocity drops to half its value on the axis. The plot shows the relationship between jet half width and distance from the jet nozzle.

12. 2D Laminar Plane Jet ― Numerical Calculations
Jet Self-similarity
The plot shows the flow profile along the radial direction of the flow.

13. 2D Laminar Plane Jet ― Numerical Calculations
Momentum Thickness ( ) 𝒙 𝜽
0.01
e-4
0.05
e-4
0.1
e-3
0.2
e-3
0.3
e-3
0.4
e-3
0.5
e-3
0.6
e-3
0.7
e-3
0.8
e-3
0.9
e-2
1.0
e-3
Plot shows the changes in momentum thickness at different locations downstream of the jet.

14. Outline 2D Laminar Plane Jet 2D Laminar Round Jet
Theoretical Solutions
Numerical Calculations (FLUENT code)
Mean Stream Velocity
Jet Half Width
Momentum Thickness
2D Laminar Round Jet

15. 2D Laminar Round Jet ― Theoretical Solutions
Air emerges into a still air from a circular orifice at x=0
Constant momentum flux (J) at any cross section
Spread at constant pressure (P = 1 bar)
Red = 400 ( u = 0.64 m/s）
Temperature = 300 K
ρ = 1.16 kg/m3；ν = 1.6×10-5 m2/s；
Narrow Axisymmetric Jet
(Schlichting 1933)

16. 2D Laminar Round Jet ― Numerical Calculations
Inlet velocity
Wall
Pressure
outlet
Axial symmetirc
Interior
Halved geometry

17. 2D Laminar Round Jet ― Numerical Calculations
Centerline Velocity( ) 𝒙
𝒖 𝒄
0.01
0.05
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9

18. 2D Laminar Round Jet ― Numerical Calculations
Mean Stream Velocity ( )
x/d = 20
x/d = 10
The plot shows the flow profile along the radial direction of the flow.

19. 2D Laminar Plane Jet ― Numerical Calculations
Mean Stream Velocity ( )
x/d = 30
x/d = 40
The plot shows the flow profile along the radial direction of the flow.

20. 2D Laminar Plane Jet ― Numerical Calculations
Mean Stream Velocity ( )
x/d = 60
x/d = 50
The plot shows the flow profile along the radial direction of the flow.

21. 2D Laminar Plane Jet ― Numerical Calculations
Mean Stream Velocity ( )
x/d = 70
x/d = 80
The plot shows the flow profile along the radial direction of the flow.

22. 2D Laminar Plane Jet ― Numerical Calculations
Mean Stream Velocity ( )
x/d = 90
x/d = 100
The plot shows the flow profile along the radial direction of the flow.

23. 2D Laminar Round Jet ― Numerical Calculations
Jet Half Width ( )
𝒙/d
𝒓 𝟏/𝟐 /d 1 5 10 20 30 40 50 60 70 80 90
100
Half Width: Radial distance from the axis to the position at the which the absolute value of the axial velocity drops to half its value on the axis. The plot shows the relationship between jet half width and distance from the jet nozzle.

24. 2D Laminar Round Jet ― Numerical Calculations
Jet Self-similarity
The plot shows the flow profile along the radial direction of the flow.

25. 2D Laminar Round Jet ― Numerical Calculations
Momentum Thickness ( ) 𝒙
𝜽/𝐝 1
e-2 5
e-1 10
e-1 20
e-1 30
e-1 40
e-1 50
e-1 60
e-1 70
e-1 80
e-1 90
e-1
100
e-1
Plot shows the changes in momentum thickness at different locations downstream of the jet.