BED, BANK & SHORE BED, BANK & SHORE PROTECTION - CHAPTER 2 pps

BED, BANK & SHORE BED, BANK & SHORE PROTECTION PROTECTION Lecturer: Lecturer: PhamThu PhamThu Huong Huong Faculty of Coastal Engineering Faculty of Coastal Engineering Chapter 2 Chapter 2 Flow Flow - - Loads Loads (3 class hours) Content Content 2.1 Introduction 2.2 Turbulence 2.3 Wall flow 2.4 Free flow 2.5 Combination of wall flow and free flow 2.6 Load reduction 2.1 Introduction forces Structure Flow regular Fluctuation Hour tides Seconds short waves seconds turbulence Velocity field in various situations averaged velocity values (ū = Q/A) Chezy's law for uniform flow: ū = C √ (Ri) Reynolds dye experiment Reynolds dye experiment Reynolds number Reynolds number • Laminar flow occurs at low Reynolds numbers (Re<1000) • Turbulent flow occurs at high Reynolds numbers (Re>2000) vs - mean fluid velocity, L - characteristic length (h: water depth) μ - (absolute) dynamic fluid viscosity ν - kinematic fluid viscosity: ν = μ / ρ = 10 -6 m 2 /s (water) ρ - fluid density 2.2 Turbulence Turbulence motion: velocity and pressure show irregular fluctuations u = u + u v = v + v w = w + w p = p + p ′′ ′ ′ Turbulence variations: () 22 2 22 2 1 ,,, 2 uvw uvw kuvwr r r uu u ′ ′′ ′′ ′ =++ = = = Turbulence variations: u = u + u v = v + v w = w + w p = p + p ′′ ′ ′ Turbulence can then be expressed in various ways, such as: total kinetic energy in a turbulent flow fluctuation intensities of u, v and w, relatively Velocity Velocity 2 2 inertia press. visc. uuu p u uw txz xz ρμ ⎛⎞ ∂∂∂ ∂ ∂ ++ =−+ ⎜⎟ ∂∂ ∂ ∂ ∂ ⎝⎠ m * a = F [...]... turbulent flow 2. 3 Uniform wall flow Wall flow 2 τ b = ρ g h I = c f ρ u (= ρ u = ρ u w ) 2 * u* is the shear “velocity” Chezy: ' b u* = u u =C RI 1 2/ 3 Manning: u = R I n ' b 1 ⇒ u= cf g /C g cf with: C = with: n = R 1/ 6 cf g Nikuradse-Colebrook roughness: g 12 R 12 R ≈ 18 log C= ln kr kr κ ( kr is equivalent roughness ) ghI Example 20 m3/s of water flows in a 10 m wide channel with vertical banks, a bed...Reynolds stresses: m* a = F ⎛ ∂ u 2 ∂ u ′w′ ⎞ ⎛ ∂u ∂u ∂u ⎞ ∂p ∂ 2u ρ⎜ +u +w + μ 2 −ρ⎜ + ⎟ ⎟=− ⎜ ∂x ⎟ ∂x ∂z ⎠ ∂x ∂z ∂z ⎠ ⎝ ∂t ⎝ inertia press visc Reynolds stresses −−−−−−−−−−−−−−−−−−−−−− mean values −−−−−−−−− turb fluctuations Exchange of momentum due to turbulence Flow resistance: τ = cf ρ u 2 In laminar flow the resistance, expressed as a shear stress, is proportional... ghI Example 20 m3/s of water flows in a 10 m wide channel with vertical banks, a bed slope of 1/1000 and a roughness of 0 .2 m What is the depth, the velocity, the Chezy-value, the relative turbulence intensity and the relative turbulent shear stress? Assume h R =bh/(b+2h) C=18log(12R/kr) u= C√RI Stop Q* = Q Q* = bhu non uniform flow The growth of a boundary layer when an infinitely thin plate is placed... decreases 2. 4 Free flow 50 100 Z Flow, velocities and turbulence in mixing layer Flow and velocities in jets Plane jets : um = 3.5 u0 x B Circular jets : um = 6.3 u0 x D b = 0.1 x b = 0.1 x u = um e 2 ⎛ ⎛z⎞ ⎞ ⎜ − 0.693 ⎜ ⎟ ⎟ ⎜ ⎝b⎠ ⎟ ⎝ ⎠ u = um e 2 ⎛ ⎛R⎞ ⎞ ⎜ − 0.693 ⎜ ⎟ ⎟ ⎜ ⎝b⎠ ⎟ ⎝ ⎠ Turbulent fluctuations in circular jet instability of an axisymmetric jet effect of strong pressure gradients 2. 5 Combination... flow and Free flow Flow separation around blunt and round body Vertical constriction and expansion (sill) Vertical expansion (backward-facing step) Horizontal expansion Horizontal constriction and expansion (groyne) Detached bodies 2. 6 Load Reduction The end Chapter 2 . BED, BANK & SHORE BED, BANK & SHORE PROTECTION PROTECTION Lecturer: Lecturer: PhamThu PhamThu Huong Huong Faculty of Coastal Engineering Faculty of Coastal Engineering Chapter 2 Chapter. 2 Chapter 2 Flow Flow - - Loads Loads (3 class hours) Content Content 2. 1 Introduction 2. 2 Turbulence 2. 3 Wall flow 2. 4 Free flow 2. 5 Combination of wall flow and free flow 2. 6 Load reduction 2. 1. (Re> ;20 00) vs - mean fluid velocity, L - characteristic length (h: water depth) μ - (absolute) dynamic fluid viscosity ν - kinematic fluid viscosity: ν = μ / ρ = 10 -6 m 2 /s (water) ρ - fluid