Transcription of BOUNDARY LAYER THEORY
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BOUNDARY LAYER THEORY
HIGH RENOLDS NUMBER FLOW BOUNDARY LAYERS(Re ) BOUNDARY LAYERThin region adjacent to surface of a body where viscous forces dominate over inertia forcesRe =Re>> 1 inertiaforcesviscousforces BoundarylayerseparationWake: viscouseffectsnot importantvorticitynot zeroFlowfieldaroundan arbitraryshapeInnerflowStrongviscouseffe ctsOuterflowViscouseffectsnegligibleVort icityzero(Inviscidpotentialflow) BOUNDARY LAYER THEORYS teady ,incompressible 2-D flow with no body forces. Valid for laminar flow for To solve eq. we first assume an approximate velocity profile inside the the wall shear stress to the velocity fieldTypically the velocity profile is taken to be a polynomial in y,and the degree of fluid this polynominaldetermines the number of BOUNDARY conditions which may be satisfied EXAMPLE:LAMINAR FLOW OVER A FLAT PLATE: *021(2)ddUdxdxU ++=0()nudy ()x 2()uabcfU =++=U U 0,99U ReUL =High Reynolds Number Flow Laminar BOUNDARY LAYER predictable Turbulent BOUNDARY layerpoor predictability Controlling parameter To get two BOUNDARY LAYER flows identical match Re(dynamic similarity) Although BOUNDARY LAYER s and prediction are complicated,simplifythe N-S equations to make job easier2-D , planar flow u* = , x*, y*= *,uvvU =,xyLDimensionless gov.
Boundary Layer Thickness : δ at 5 0.99 (Table) 5 5 Re Re x x U u yy xU UUx x x ηη δ ν δδ νν ∞ ∞∞ ==⇒=→= ≅≅= δ:defined as the distance from the wall for which u=0.99U∞ Boundary Layer Parameter (thicknesses) Most widely used is δ but is rather arbitrary y=δ when u=0.99 U∞
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