2D Free Jet Simulations (FLUENT) Oct. 31 2013 Yan Zhan Oct. 31, 2013
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
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 = 1.225 kg/m3;ν = 1.46073×10-5 m2/s; Fig.1 Typical free 2D laminar plane jet streamline pattern Laminar Plane Jet (Schlichting 1933)
2D Laminar Plane Jet ― Numerical Calculations Inlet velocity Wall Pressure outlet Symmetrical axis Interior Halved geometry
2D Laminar Plane Jet ― Numerical Calculations Centerline Velocity( ) 𝒙 𝒖 𝒄 0.01 0.6388123 0.05 0.63888186 0.1 0.63220511 0.2 0.6074034 0.3 0.5727235 0.4 0.537284 0.5 0.5115343 0.6 0.49355775 0.7 0.477681 0.8 0.4557375 0.9 0.44144434 White’s book PDF page277 (J = 0.0051)
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.
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.
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.
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.
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.
2D Laminar Plane Jet ― Numerical Calculations Jet Half Width ( ) 𝒙/d 𝒓 𝟏/𝟐 /d 1 0.539526 5 0.596278 10 0.65713 20 0.733453 30 0.836392 40 0.925598 50 1.00985 60 1.15413 70 1.21262 80 1.32187 90 1.74276 100 2.17414 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.
2D Laminar Plane Jet ― Numerical Calculations Jet Self-similarity The plot shows the flow profile along the radial direction of the flow.
2D Laminar Plane Jet ― Numerical Calculations Momentum Thickness ( ) 𝒙 𝜽 0.01 1.97590e-4 0.05 9.08948e-4 0.1 1.67433e-3 0.2 2.57365e-3 0.3 4.28040e-3 0.4 3.33453e-3 0.5 4.26769e-3 0.6 5.51115e-3 0.7 6.22347e-3 0.8 7.93727e-3 0.9 1.01272e-2 1.0 9.29760e-3 Plot shows the changes in momentum thickness at different locations downstream of the jet.
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
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)
2D Laminar Round Jet ― Numerical Calculations Inlet velocity Wall Pressure outlet Axial symmetirc Interior Halved geometry
2D Laminar Round Jet ― Numerical Calculations Centerline Velocity( ) 𝒙 𝒖 𝒄 0.01 0.63920647 0.05 0.63778848 0.1 0.610317 0.2 0.5230199 0.3 0.4403066 0.4 0.372688 0.5 0.32611621 0.6 0.2895635 0.7 0.260005 0.8 0.2357024 0.9 0.2153695
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.
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.
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.
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.
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.
2D Laminar Round Jet ― Numerical Calculations Jet Half Width ( ) 𝒙/d 𝒓 𝟏/𝟐 /d 1 0.462644 5 0.397387 10 0.603436 20 0.691654 30 0.822712 40 0.977359 50 1.07118 60 1.20262 70 1.33417 80 1.46478 90 1.59214 100 1.69765 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.
2D Laminar Round Jet ― Numerical Calculations Jet Self-similarity The plot shows the flow profile along the radial direction of the flow.
2D Laminar Round Jet ― Numerical Calculations Momentum Thickness ( ) 𝒙 𝜽/𝐝 1 4.879917e-2 5 1.429468e-1 10 2.109622e-1 20 2.877028e-1 30 3.523778e-1 40 4.257012e-1 50 4.583403e-1 60 5.047484e-1 70 5.455564e-1 80 5.808257e-1 90 6.108572e-1 100 6.309687e-1 Plot shows the changes in momentum thickness at different locations downstream of the jet.