CFDa.4.viscous

# CFDa.4.viscous - Fluids Review TRN-1998-004 Boundary-Layer...

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© Fluent Inc. 12/05/10 D1 Fluids Review TRN-1998-004 Boundary-Layer and Viscous Flows

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© Fluent Inc. 12/05/10 D2 Fluids Review TRN-1998-004 Overvie w Introduce the concept of the Boundary-Layer Introduce the Boundary-Layer Equations Laminar to Turbulence Transition Turbulent Boundary Layer Flow Separation
© Fluent Inc. 12/05/10 D3 Fluids Review TRN-1998-004 The Boundary-Layer Concepts (1) Prandtl (1904) introduced the concept of the boundary layer. The boundary layer is defined as the thin region on the surface of a body in which viscous effects are important. The fluid in the region outside the BL behaves as if inviscid (inertial dominated). The viscous effects, fluid friction, typically occur in flows at high Reynolds numbers. Using the above hypothesis, it is possible to simplify the analysis of high Reynolds number flow allowing for the analytical solution of external flow problems.

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© Fluent Inc. 12/05/10 D4 Fluids Review TRN-1998-004 Boundary-Layer Concepts (2) The BL increases in thickness from the leading edge. Near the leading edge the flow is laminar At a certain distance x from the leading edge the flow becomes turbulent A laminar sublayer exists in the turbulent BL where the flow is laminar
© Fluent Inc. 12/05/10 D5 Fluids Review TRN-1998-004 The Boundary-Layer Concepts (3) The BL allows the fluid to transition from the free stream velocity U to a velocity of zero at the wall The BL thickness δ is defined as the distance away from the surface where the velocity reaches 99% of the free-stream velocity, 99 . 0 , = = δ U u where y

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© Fluent Inc. 12/05/10 D6 Fluids Review TRN-1998-004 The Boundary-Layer Concepts (4) The BL displacement thickness δ is defined as the thickness of a zero- velocity layer which has the same mass flow defect as the BL - = δ 0 * 1 dy U u Equal Areas u = U μ = 0 u = u ( y ) μ = 0 δ u/U = 0.99
© Fluent Inc. 12/05/10 D7 Fluids Review TRN-1998-004 The Boundary-Layer Equations (1) The following analysis is for laminar flow

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