chapter2 - flow_ loads

8/3/2019 Chapter2 - Flow_ Loads

http://slidepdf.com/reader/full/chapter2-flow-loads 1/32

BED, BANK & SHOREBED, BANK & SHORE

PROTECTIONPROTECTION

Lecturer:Lecturer: PhamThuPhamThu HuongHuong

Faculty of Coastal EngineeringFaculty of Coastal Engineering



Chapter 2Chapter 2

FlowFlow -- LoadsLoads(3 class hours)



ContentContent

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

Flowregular

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 experimentReynolds dye experiment



Reynolds numberReynolds number

• Laminar flow occurs at low Reynolds numbers (Re<1000)

• Turbulent flow occurs at high Reynolds numbers (Re>2000)

v s - mean fluid velocity,L - characteristic length (h: water depth)μ - (absolute) dynamic fluid viscosityν - 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:



( )2 2 2

2 2 21, , ,

2 u v w

u v wk u v w r r r

u u 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 aturbulent flow fluctuation intensities of

u, v and w, relatively



VelocityVelocity

2

2

inertia press. visc.

u u u p uu w

t x z x z

ρ μ ⎛ ⎞∂ ∂ ∂ ∂ ∂+ + =− +⎜ ⎟

∂ ∂ ∂ ∂ ∂⎝ ⎠

m * a = F



Reynolds stresses:

2 2

2

inertia press. visc. Reynolds stresses

mean values turb. fluctuations

u u u p u u u wu w

t x z x z x z ρ μ ρ

⎛ ⎞′ ′ ′⎛ ⎞∂ ∂ ∂ ∂ ∂ ∂ ∂+ + = − + − +⎜ ⎟⎜ ⎟ ⎜ ⎟∂ ∂ ∂ ∂ ∂ ∂ ∂⎝ ⎠ ⎝ ⎠

− − − − − − − − − − − − − − − − − − − − − − − − − − − − − − −

m * a = F



Exchange of momentum due to turbulence



Resistance in laminar and turbulent flow

2 f c uτ ρ =Flow resistance:

In laminar flow the resistance, expressed as ashear stress, is proportional with the flow velocity.

In turbulent flow, the quadratic terms in equationbecome dominant and the relation between τ and u becomes quadratic



2.3 Uniform wall flow2.3 Uniform wall flow



Wall flowWall flow

2

2 ' '* 1( )b f b b

f

g h I c u u u w u g h I cτ ρ ρ ρ ρ = = = = ⇒ =

2 / 3 1/ 6

Chezy: with:

1Manning: with:

f

f

gu C R I C

c

cu R I n R

n g

= =

= =

u* is the shear “velocity”

12 12ln 18 log ( is equivalent roughness )

r r r

g R RC = k

k k κ ≈

Nikuradse-Colebrook roughness:

* / u u g C =



ExampleExample20 m3/s of water flows in a 10 m wide channel with vertical bank 20 m3/s of water flows in a 10 m wide channel with vertical bank s,s,a bed slope of 1/1000 and a roughness of 0.2 m. What is thea bed slope of 1/1000 and a roughness of 0.2 m. What is thedepth, the velocity, thedepth, the velocity, the Chezy Chezy --value, the relative turbulencevalue, the relative turbulenceintensity and the relative turbulent shear stress? intensity and the relative turbulent shear stress?

Assume h R =bh/(b+2h) C=18log(12R/k r )

u= C √RI

Q* = bhuQ* = QStop



non uniform flownon uniform flow

The growth of a boundary layer when aninfinitely thin plate is placed in a flow with u = u 0 .



Influence of pressure gradient on velocityInfluence of pressure gradient on velocityprofileprofile

Uniform accelerated Decelerated



Turbulence inTurbulence in windtunnelwindtunnel contractioncontraction

The total amount of turbulent kinetic energy, k , remains approximatelyconstant.

Due to the increased velocity in the contraction, the relative turbulence, r ,using the local mean velocity decreases.



2.4 Free flow2.4 Free flow

Flow, velocities and turbulence in mixing layer

Z

50

10 0



Flow and velocities in jetsFlow and velocities in jets

2

2

0.6930

0.6930

3.50.1

6.30.1

zb

m m

Rb

m m

uPlane jets : u = b = x u = u e x B

uCircular jets : u = b = x u = u e

x D

⎛ ⎞⎛ ⎞⎜ ⎟− ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

⎛ ⎞⎛ ⎞⎜ ⎟− ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠



Turbulent fluctuations in circular jetTurbulent fluctuations in circular jet



instability of aninstability of an axisymmetricaxisymmetric jet jet



effect of strong pressure gradientseffect of strong pressure gradients



2.5 Combination of wall flow and Free flow2.5 Combination of wall flow and Free flow

Flow separation around blunt and round body



Vertical constriction and expansion (sill)Vertical constriction and expansion (sill)



Vertical expansionVertical expansion(backward(backward --facing step)facing step)



Horizontal constriction and expansionHorizontal constriction and expansion

(groyne(groyne ))



DetachedDetachedbodiesbodies



2.6 Load2.6 Load ReductionReduction



The end Chapter 2The end Chapter 2

chapter2 - flow_ loads

Documents