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2D Free Jet Simulations (FLUENT) Oct. 31 2013 yan

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

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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) – Re d = 400 ( u x = 0.64 m/s ） – Temperature = 300 K – ρ = 1.225 kg/m 3 ； ν = 1.46073×10 -5 m 2 /s ； Laminar Plane Jet (Schlichting 1933) Fig.1 Typical free 2D laminar plane jet streamline pattern

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

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Centerline Velocity( ) 2D Laminar Plane Jet ― Numerical Calculations 0.010.6388123 0.050.63888186 0.10.63220511 0.20.6074034 0.30.5727235 0.40.537284 0.50.5115343 0.60.49355775 0.70.477681 0.80.4557375 0.90.44144434

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Mean Stream Velocity ( ) 2D Laminar Plane Jet ― Numerical Calculations x/d = 10 x/d = 20

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Mean Stream Velocity ( ) 2D Laminar Plane Jet ― Numerical Calculations x/d = 30 x/d = 40

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Mean Stream Velocity ( ) 2D Laminar Plane Jet ― Numerical Calculations x/d = 50 x/d = 60

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Mean Stream Velocity ( ) 2D Laminar Plane Jet ― Numerical Calculations x/d = 70 x/d = 80

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Mean Stream Velocity ( ) 2D Laminar Plane Jet ― Numerical Calculations x/d = 90 x/d = 100

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Jet Half Width ( ) 2D Laminar Plane Jet ― Numerical Calculations 10.539526 50.596278 100.65713 200.733453 300.836392 400.925598 501.00985 601.15413 701.21262 801.32187 901.74276 1002.17414

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Jet Self-similarity 2D Laminar Plane Jet ― Numerical Calculations

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Momentum Thickness ( ) 2D Laminar Plane Jet ― Numerical Calculations 0.011.97590e-4 0.059.08948e-4 0.11.67433e-3 0.22.57365e-3 0.34.28040e-3 0.43.33453e-3 0.54.26769e-3 0.65.51115e-3 0.76.22347e-3 0.87.93727e-3 0.91.01272e-2 1.09.29760e-3

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

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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) – Re d = 400 ( u = 0.64 m/s ） – Temperature = 300 K – ρ = 1.16 kg/m 3 ； ν = 1.6×10 -5 m 2 /s ； Narrow Axisymmetric Jet (Schlichting 1933) r

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

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Centerline Velocity( ) 2D Laminar Round Jet ― Numerical Calculations 0.010.63920647 0.050.63778848 0.10.610317 0.20.5230199 0.30.4403066 0.40.372688 0.50.32611621 0.60.2895635 0.70.260005 0.80.2357024 0.90.2153695

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Mean Stream Velocity ( ) 2D Laminar Round Jet ― Numerical Calculations x/d = 10 x/d = 20

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Mean Stream Velocity ( ) 2D Laminar Plane Jet ― Numerical Calculations x/d = 30 x/d = 40

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Mean Stream Velocity ( ) 2D Laminar Plane Jet ― Numerical Calculations x/d = 50 x/d = 60

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Mean Stream Velocity ( ) 2D Laminar Plane Jet ― Numerical Calculations x/d = 70 x/d = 80

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Mean Stream Velocity ( ) 2D Laminar Plane Jet ― Numerical Calculations x/d = 90 x/d = 100

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Jet Half Width ( ) 2D Laminar Round Jet ― Numerical Calculations 10.462644 50.397387 100.603436 200.691654 300.822712 400.977359 501.07118 601.20262 701.33417 801.46478 901.59214 1001.69765

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Jet Self-similarity 2D Laminar Round Jet ― Numerical Calculations

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Momentum Thickness ( ) 2D Laminar Round Jet ― Numerical Calculations 14.879917e-2 51.429468e-1 102.109622e-1 202.877028e-1 303.523778e-1 404.257012e-1 504.583403e-1 605.047484e-1 705.455564e-1 805.808257e-1 906.108572e-1 1006.309687e-1

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