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**2D Free Jet Simulations (FLUENT)**

Oct yan

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**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

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**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)

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**2D Laminar Plane Jet ― Numerical Calculations**

Inlet velocity Wall Pressure outlet Symmetrical axis Interior Halved geometry

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**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 = )

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**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.

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**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.

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**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.

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**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.

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**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.

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**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.

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**2D Laminar Plane Jet ― Numerical Calculations**

Jet Self-similarity The plot shows the flow profile along the radial direction of the flow.

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**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.

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**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

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**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)

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**2D Laminar Round Jet ― Numerical Calculations**

Inlet velocity Wall Pressure outlet Axial symmetirc Interior Halved geometry

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**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

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**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.

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**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.

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**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.

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**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.

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**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.

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**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.

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**2D Laminar Round Jet ― Numerical Calculations**

Jet Self-similarity The plot shows the flow profile along the radial direction of the flow.

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**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.

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