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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 = 1.225 kg/m 3 = 1.4607310 -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 = 1.16 kg/m 3 = 1.610 -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