FLUID MECHANICS - KTH

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SG2214 Fluid MechanicsAnders DahlkildLuca BrandtTeachersFLUID MECHANICSAnders DahlkildLecturesLuca BrandtRecitationsIman LashgariRecitationsDepartment of MechanicsKTHwww.mech.kth.sePhoto: Rochester Institute of TechnologyFluid Mechanics, SG2214Fluid Mechanics: SG2214Fluid Mechanics: SG2214Course requirements (7.5 cr.) INL 1 (3 cr.)– 3 sets of home work problems (for 10 p. on written exam)– 1 laboration TEN1 (4.5 cr.)– 1 written exam (50 p.)The lab is scheduled ONCE a yearFluid Mechanics, SG2214(week 41)Book: Kundu & Cohen (5:th ed.)– E-book via KTH Social/Course home page– useful also in SG2218 Turbulence andSG2221 Wave motions and Hydrodynamic stabilityFluid Mechanics, SG2214“An in-depth introduction to fluid mechanics, with an emphasis of understandingfluid phenomena using the Navier-Stokes equations, the single set of partialdifferential equations governing all fluid flow”.1. Introduction, tensors,kinematics2. Conservation laws3. Laminar viscous flow4. Vorticity dynamics5. 2D irrotational flow6. Laminar boundary layers7. Introduction to turbulent flow- Fluid Mechanics, SG22141

Fluid MechanicsWhy Fluid Mechanics ?Fluid Engineers basic tools Atmosphere, OceanExperimental testing AerodynamicsComputational FluidDynamicsTheoretical estimates Energy conversion Transport of heat/other Numerous industrialprocessesFluid Mechanics, SG2214Fluid Mechanics, SG2214Fluid MechanicsFluid MechanicsDefinition of fluidNewton’s law of motion forsolid bodyFFsolid fluidG An elastic solid deforms afinite amount under theaction of a shear force, andreturns to its original shapeas F is withdrawn.A fluid deforms continuouslyunder the action of a shear force,however small.Fluid Mechanics, SG2214rGFluid Mechanics, SG22142

Fluid MechanicsFluid MechanicsContinuum hypothesis:Newton’s law of motion in fluid for:1. Open fix control volume(integral form) Momentum principleDiscrete molecular structure of matter is disregarded.Replaced by continuous distribution of matter.V2. Infinitesimal fluid element(differential form) Navier-Stokes equationsdVFluid Mechanics, SG2214Fluid Mechanics, SG2214Fluid MechanicsFluid MechanicsNewtons law of frictionyvvyuwuuw u(y)xxzFluid Mechanics, SG2214Fluid Mechanics, SG22143

Fluid MechanicsDifferent regimes of flow:Viscous flow: circular cylinderReynolds number p L2ma L2Stokes flow:Slow flow or large viscosity p L2ma L2From An Album of Fluid Motion Fluid Mechanics, SG2214Fluid Mechanics, SG2214Example: circular cylinderViscous flow: rotating tank Increasing viscosity Re Increasing Re From An Album of Fluid Motion Fluid Mechanics, SG2214Fluid Mechanics, SG22144

Thermal convectionHeated wallVorticies and vorticity: trailing-line vorticesCooled wallFrom www.efluids.comFrom www.efluids.comFluid Mechanics, SG2214Fluid Mechanics, SG2214Vorticies: wing tip vortexVorticies: hurricanes and tornadosFrom www.efluids.comFrom www.efluids.comFluid Mechanics, SG2214Fluid Mechanics, SG22145

Irrotational flow: 2D flow around airfoilBoundary layers LL From An Album of Fluid Motion From An Album of Fluid Motion Fluid Mechanics, SG2214Flow separationFluid Mechanics, SG2214Turbulent separationLaminar flow separatesfaster than turbulent flowAttached flowLaminar flowFrom An Album of Fluid Motion Turbulent flowSeparated flowFrom An Album of Fluid Motion From An Album of Fluid Motion Fluid Mechanics, SG2214Fluid Mechanics, SG22146

Surface waves: potential flow with free surfaceSG2221: Wave motions and hydrodynamic stability, 7.5 cr.Flow instability: von Karman vortex streetFrom www.eng.vt.edu/fluids/msc/galleryPerry, Chang & Lim, JFM 116From An Album of Fluid Motion From www.efluids.comFluid Mechanics, SG2214Fluid Mechanics, SG2214Flow instability: vortex breakdownTurbulence: jets and boundary layersFrom www.efluids.comFrom An Album of Fluid Motion From An Album of Fluid Motion Mount St Helen eruption, from www.efluids.comFrom www.efluids.comFrom www.efluids.comFluid Mechanics, SG2214Fluid Mechanics, SG22147

SG2218 Turbulence, 7.5 cr.Compressible flow: shock-wavesFrom www.efluids.comFrom www.efluids.comFluid Mechanics, SG2214Fluid Mechanics, SG2214Turbulent flow over high-lift profiles using RANSSG2215 Compressible Flow, 7.5 cr.Photo: NASA's Dryden Flight Research CenterTurbulent kinetic energy and streamlinesFluid Mechanics, SG2214Total pressure loss p-p0Fluid Mechanics, SG22148

SG2212 Computational Fluid dynamics, 7.5 cr.SG2224 Applied Computational Fluid Dynamics, 5 cr.Incompressible fluid elementFluid Mechanics, SG2214Fluid Mechanics, SG2214Navier-Stokes equationsVector formCartesian tensor formi 1,2,3VelocityDynamic viscosity μ GradientoperatorDensity PressurepLaplaceoperatorFluid Mechanics, SG22149

Fluid Mechanics Fluid Engineers basic tools Experimental testing Computational Fluid Theoretical estimates Dynamics Fluid Mechanics, SG2214 Fluid Mechanics Definition of fluid F solid F fluid A fluid deforms continuously under the action of a s

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