Boundary layer Equations

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Boundary layer Equations. Contents : Boundary Layer Equations; Boundary Layer Separation; Effect of londitudinal pressure gradient on boundary layer evolution Blasius Solution Integral parameters: Displacement thickness and momentum thickness. - PowerPoint PPT Presentation

Text of Boundary layer Equations

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTBoundary layer EquationsContents:Boundary Layer Equations;Boundary Layer Separation;Effect of londitudinal pressure gradient on boundary layer evolutionBlasius SolutionIntegral parameters: Displacement thickness and momentum thickness

    Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/IST

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTLaminar Thin Boundary Layer Equations (d
  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTLaminar Thin Boundary Layer Equations (d
  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTTurbulent Thin Boundary Layer Equations (d
  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTBoundary Layer SeparationBoundary Layer Separation: reversal of the flow by the action of an adverse pressure gradient (pressure increases in flows direction) + viscous effects mfm: BL / Separation / Flow over edges and blunt bodies

    Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/IST

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTBoundary Layer SeparationBoundary layer separation: reversal of the flow by the action of an adverse pressure gradient (pressure increases in flows direction) + viscous effects

    Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/IST

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTBoundary Layer SeparationSimilar results to turbulent boundary layer - close to the wall there is laminar/linear sub-layer region.

    Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/IST

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTBoundary Layer SeparationThe external pressure gradient can be:dpe/dx=0 U0 constant (Paralell outer streamlines):dpe/dx>0 U0 decreases (Divergent outer streamlines):dpe/dx
  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTZero pressure gradient:dpe/dx=0 U0 constant (Paralell outer streamlines):Inflection point at the wallNo separation of boundary layerBoundary Layer SeparationCurvature of velocity profile is constant

    Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/IST

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTFavourable pressure gradient:dpe/dx
  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTAdverse pressure gradient:dpe/dx>0 U0 decreases (Divergent outer streamlines):Curvature of velocity profile can changeBoundary layer Separation can occurBoundary Layer Separation

    Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/IST

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTSum of viscous forces:Boundary Layer Separation

    Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/IST

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTEffect of longitudinal pressure gradient:Boundary Layer Separation

    Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/IST

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTEffect of longitudinal pressure gradient:Fuller velocity profilesLess full velocity profilesFuller velocity profiles more resistant to adverse pressure gradientsTurbulent flows (fuller profiles)- more resistant to adverse pressure gradientsBoundary Layer Separation

    Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/IST

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTBoundary Layer SepaationLongitudinal and intense adverse pressure gradient does not cause separation=> theres not viscous forces

    Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/IST

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTBlasius Solution to Laminar Boundary Layer Equation over a flat plate with dpe/dx=0 Bidimensional (2D) Thin Boundary Layer (d
  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTThe introdution of corresponds to recognize that the nondimension velocity profile is stabilized.A and n are unknownsBlasius Solution to Laminar Boundary Layer Equation over a flat plate with dpe/dx=0

    Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/IST

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTBlasius Solution to Laminar Boundary Layer Equation over a flat plate with dpe/dx=0 Procedure:

    Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/IST

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTBlasius Solution to Laminar Boundary Layer Equation over a flat plate with dpe/dx=0

    Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/IST

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTBlasius Solution to Laminar Boundary Layer Equation over a flat plate with dpe/dx=0 Boundary Conditions:

    Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/IST

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTGraphical Solution:Blasius Solution to Laminar Boundary Layer Equation over a flat plate with dpe/dx=0

    Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/IST

    Sheet1

    000.3321

    10.32980.323

    20.62980.2668

    30.84610.1614

    40.95550.0642

    50.99160.0059

    60.9990.0024

    70.9990.0002

    810.0001

    Sheet1

    F'

    F''

    Sheet2

    Sheet3

    MBD009F38F1.unknown

    MBD009F4981.unknown

    MBD009EC63A.unknown

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTSolution:Blasius Solution to Laminar Boundary Layer Equation over a flat plate with dpe/dx=0

    Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/IST

    Sheet1

    000.3321

    10.32980.323

    20.62980.2668

    30.84610.1614

    40.95550.0642

    50.99160.0059

    60.9990.0024

    70.9990.0002

    810.0001

    Sheet1

    F'

    F''

    Sheet2

    Sheet3

    MBD009F38F1.unknown

    MBD009F4981.unknown

    MBD009EC63A.unknown

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTSolution:Blasius Solution to Laminar Boundary Layer Equation over a flat plate with dpe/dx=0

    Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/IST

    Sheet1

    000.3321

    10.32980.323

    20.62980.2668

    30.84610.1614

    40.95550.0642

    50.99160.0059

    60.9990.0024

    70.9990.0002

    810.0001

    Sheet1

    F'

    F''

    Sheet2

    Sheet3

    MBD009F38F1.unknown

    MBD009F4981.unknown

    MBD009EC63A.unknown

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTSolution :Blasius Solution to Laminar Boundary Layer Equation over a flat plate with dpe/dx=0

    Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/IST

    Sheet1

    000.3321

    10.32980.323

    20.62980.2668

    30.84610.1614

    40.95550.0642

    50.99160.0059

    60.9990.0024

    70.9990.0002

    810.0001

    Sheet1

    F'

    F''

    Sheet2

    Sheet3

    MBD009F38F1.unknown

    MBD009F4981.unknown

    MBD009EC63A.unknown

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTDisplacement thickness:Blasius Solution to Laminar Boundary Layer Equation over a flat plate with dpe/dx=0

    Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/IST

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTDisplacement thickness :Blasius Solution to Laminar Boundary Layer Equation over a flat plate with dpe/dx=0

    Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/IST

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTBlasius Solution to Laminar Boundary Layer Equation over a flat plate with dpe/dx=0 Section where the streamline become part of boundary layer

    Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/IST

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTBlasius Solution to Laminar Boundary Layer Equation over a flat plate with dpe/dx=0 Blasius Solution for displacement thickness:com

    Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/IST

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTBlasius Solution to Laminar Boundary Layer Equation over a flat plate with dpe/dx=0 Momentum thickness:

    Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/IST

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTBlasius Solution to Laminar Boundary Layer Equation over a flat plate with dpe/dx=0 Momentum flow rate through a section of BD:

    Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/IST

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTBlasius Solution to Laminar Boundary Layer Equation over a flat plate with dpe/dx=0 Longitudinal momentum balance between the leading edge and a cross section at x:

    Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/IST

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTBlasius Solution to Laminar Boundary Layer Equation over a flat plate with dpe/dx=0 Blasius Solution to momentum thickness:with

    Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/IST

  • 2004Mecnica dos Fluidos II Prof. Antnio Sarmento - DEM/ISTLaminar Boundary Layer EquationsContents:Thin Boundary Layer Equations with Ze