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
Reynolds stresses:
22
2
inertia press. visc. Reynolds stresses
mean values turb. fluctuations
uuu p u uuw
uw
txz xz xz
ρμρ
⎛⎞
′′′
⎛⎞
∂∂∂ ∂ ∂ ∂∂
++ =−+ − +
⎜⎟
⎜⎟
⎜⎟
∂∂ ∂ ∂ ∂ ∂∂
⎝⎠
⎝⎠

−−−−−−−−−−−−−−−−−−−−−− −−−−−−−−−
m * a = F
Exchange of momentum due to turbulence
Resistance in laminar and turbulent flow
2
f
cu
τ
ρ
=
Flow resistance:
In laminar flow the resistance, expressed as a
shear stress, is proportional with the flow velocity.
In turbulent flow, the quadratic terms in equation
become dominant and the relation between
τ
and u
becomes quadratic
2.3 Uniform wall flow
2.3 Uniform wall flow
Wall flow
Wall flow
2
2''
*
1
()
bf bb
f
ghI c u u u w u ghI

c
τρ ρ ρ ρ
== == ⇒=
2/3 1/6
Chezy: with:
1
Manning: with:
f
f
g
uCRI C
c
c
uRI nR
n
g
==
==
u
*
is the shear “velocity”
12 12
ln 18log ( is equivalent roughness)
r
rr
g
R R
C = k
kk
κ

≈
Nikuradse-Colebrook roughness:
*
/uu
g
C=
Example
Example
¾
¾
20 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 the
a bed slope of 1/1000 and a roughness of 0.2 m. What is the
depth, the velocity, the
depth, the velocity, the
Chezy
Chezy
-
-
value, the relative turbulence
value, the relative turbulence
intensity 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* = bhu
Q* = Q
Stop
non uniform flow
non uniform flow
The growth of a boundary layer when an
infinitely thin plate is placed in a flow with u = u
0
.
Influence of pressure gradient on velocity
Influence of pressure gradient on velocity
profile
profile
Uniform accelerated Decelerated
Turbulence in
Turbulence in
windtunnel
windtunnel
contraction
contraction
The total amount of turbulent kinetic energy, k, remains approximately
constant.
Due to the increased velocity in the contraction, the relative turbulence, r,
using the local mean velocity decreases.
2.4 Free flow
2.4 Free flow
Flow, velocities and turbulence in mixing layer
Z
5

0
10
0
Flow and velocities in jets
Flow and velocities in jets
2
2
0.693
0
0.693
0
3.5
0.1
6.3
0.1
z
b
mm
R
b
mm
u
Plane jets : u = b = x u = u e
xB
u
Circular jets : u = b = x u = u e
xD
⎛⎞
⎛⎞
⎜⎟

−
⎜⎟
⎜⎟
⎝⎠
⎝⎠
⎛⎞
⎛⎞
⎜⎟
−
⎜⎟
⎜⎟
⎝⎠
⎝⎠
Turbulent fluctuations in circular jet
Turbulent fluctuations in circular jet
instability of an
instability of an
axisymmetric
axisymmetric
jet
jet
effect of strong pressure gradients
effect of strong pressure gradients
2.5 Combination of wall flow and Free flow
2.5 Combination of wall flow and Free flow
Flow separation around blunt and round body