Download miễn phí Luận văn Stone Stability Under Non-Uniform Flow



Contents
Summary v
Samenvatting ix
Tom tat xiii
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Objectives of this study . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Research methodology . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Literature review 7
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Turbulence and flow properties . . . . . . . . . . . . . . . . . . . . . 7
2.2.1 Uniform open-channel flow over a rough bed . . . . . . . . 7
2.2.2 Non-uniform open-channel flow . . . . . . . . . . . . . . . . 11
2.3 Hydrodynamic forces on a single stone . . . . . . . . . . . . . . . . 13
2.4 Stability parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.1 Governing variables . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.2 The Shields stability parameter . . . . . . . . . . . . . . . . . 18
2.4.3 The Jongeling et al. stability parameter . . . . . . . . . . . . 18
2.4.4 The Hofland stability parameter . . . . . . . . . . . . . . . . 19
2.5 Mobility parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.6 Methods for stone stability assessment . . . . . . . . . . . . . . . . . 21
2.6.1 The stability threshold concept . . . . . . . . . . . . . . . . . 21
2.6.2 The stone transport concept . . . . . . . . . . . . . . . . . . . 26
2.6.3 Comparison and selection of methods . . . . . . . . . . . . . 29
2.7 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3 Experimental arrangement and data processing methods 33
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2 Experimental configuration . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.2 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3 Stones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.4 Test program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.4.1 Hydraulic conditions . . . . . . . . . . . . . . . . . . . . . . . 39
3.4.2 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.5 Selected time series . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.6 Data processing methods . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.6.1 Velocity and turbulence data . . . . . . . . . . . . . . . . . . 45
3.6.2 Stone entrainment rate data . . . . . . . . . . . . . . . . . . . 46
3.6.3 Correlation analysis . . . . . . . . . . . . . . . . . . . . . . . 47
4 Flow characteristics 49
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2 Flow quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.3 Shear velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.4 Mean flow velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.5 The eddy viscosity and mixing length . . . . . . . . . . . . . . . . . 55
4.6 Turbulence intensity data . . . . . . . . . . . . . . . . . . . . . . . . 59
4.7 Reynolds shear stress data . . . . . . . . . . . . . . . . . . . . . . . . 63
4.8 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5 Stone transport formulae 67
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.2 The proposed stability parameter . . . . . . . . . . . . . . . . . . . . 68
5.3 Final formulation of the proposed stability parameter . . . . . . . . 70
5.4 Evaluation of the available stability parameters . . . . . . . . . . . . 72
5.4.1 The Shields stability parameter . . . . . . . . . . . . . . . . . 72
5.4.2 The Jongeling et al. stability parameter . . . . . . . . . . . . 73
5.4.3 The Hofland stability parameter . . . . . . . . . . . . . . . . 75
5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.5.1 Comparison of the stability parameters . . . . . . . . . . . . 77
5.5.2 Sensitivity analysis of key parameters . . . . . . . . . . . . . 78
5.5.3 Entrainment correction . . . . . . . . . . . . . . . . . . . . . . 80
5.5.4 Data comparison . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6 Estimation of stone entrainment using numerical flow modeling 87
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.2 Flow conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6.3 Numerical model set-up . . . . . . . . . . . . . . . . . . . . . . . . . 88
6.3.1 Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.3.2 Boundary condition . . . . . . . . . . . . . . . . . . . . . . . 91
6.3.3 Model validation . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.3.4 Model calibration and verification . . . . . . . . . . . . . . . 94
6.4 Computation results . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.5 Estimation of bed damage . . . . . . . . . . . . . . . . . . . . . . . . 97
6.6 Conclusions and recommendations . . . . . . . . . . . . . . . . . . . 99
7 Conclusions and recommendations 101
7.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
7.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
7.3 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
References 106
A Stones 115
A.1 Artificial stones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
A.2 Stone gradation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
B Data 117
B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
B.2 Velocity and turbulence data . . . . . . . . . . . . . . . . . . . . . . . 117
B.3 Governing variables . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
C Numerical flow modeling 129
C.1 Turbulence modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
C.1.1 Mean-flow equations . . . . . . . . . . . . . . . . . . . . . . . 129
C.1.2 The two-equation k-ε model . . . . . . . . . . . . . . . . . . . 130
C.2 Deft input files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
C.2.1 Mesh description . . . . . . . . . . . . . . . . . . . . . . . . . 132
C.2.2 Problem description . . . . . . . . . . . . . . . . . . . . . . . 136
C.2.3 Typical sequence of an Deft session . . . . . . . . . . . . . . 139
List of symbols 141
List of figures 145
List of tables 148
Acknowledgements 151
Curriculum Vitae 153


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t the flow is in non-equilibrium (Clauser’s parameter β
in Eq. (4.1) varies along the flow direction), making it impossible to generalize
the results.
4.5 The eddy viscosity and mixing length
To assess the suitability of the Prandtl mixing length model to the present flow
conditions, the eddy viscosity νt and mixing length lm were determined from the
measured shear stress data and the mean velocity profile. The velocity gradient
du/dz used in the calculation can be obtained by applying a cubic spline data
interpolation technique to the measured velocity against ln z as described in Sec-
tion 4.3. Once the velocity gradient du/dz is available, the eddy viscosity νt and
the mixing length lm can be determined as follows. From Eqs. (2.6) and (2.7) one
has:
νt =
ν dudz − u′w′
du
dz
(4.6)
From Eqs. (2.6) and (2.9) one has:
lm =
√√√√ν dudz − u′w′∣∣∣ dudz
∣∣∣ dudz
(4.7)
where ν is the kinematic viscosity.
Figure 4.2 to 4.4 show the distributions of the eddy viscosity and the mix-
ing length at all measuring profiles together with theoretical curves according to
56 Chapter 4. Flow characteristics
0 0.05 0.1 0.15 0.2
0
0.5
1
lm/h
z
/
h
0 0.05 0.1 0.15
0
0.5
1
νt/hu∗
z
/
h
1AR1
1BR1
1CR1
1DR1
1ER1
1FR1
1GR1
1HR1
1IR1
1JR1
1KR1
1LR1
Π=0.0
Π=0.2
Π=0.5
l = κ z
Π=0.0
Π=0.2
Π=0.5
νt = κ u*z
0 0.05 0.1 0.15 0.2
0
0.5
1
lm/h
z
/
h
0 0.05 0.1 0.15
0
0.5
1
νt/hu∗
z
/
h
1AR2
1BR2
1CR2
1DR2
1ER2
1FR2
1GR2
1HR2
1IR2
1JR2
1KR2
1LR2
Π=0.0
Π=0.2
Π=0.5
l = κ z
Π=0.0
Π=0.2
Π=0.5
νt = κ u*z
0 0.05 0.1 0.15 0.2
0
0.5
1
lm/h
z
/
h
0 0.05 0.1 0.15
0
0.5
1
νt/hu∗
z
/
h
1AR3
1BR3
1CR3
1DR3
1ER3
1FR3
1GR3
1HR3
1IR3
1JR3
1KR3
1LR3
Π=0.0
Π=0.2
Π=0.5
l = κ z
Π=0.0
Π=0.2
Π=0.5
νt = κ u*z
0 0.05 0.1 0.15 0.2
0
0.5
1
lm/h
z
/
h
0 0.05 0.1 0.15
0
0.5
1
νt/hu∗
z
/
h
1AR4
1BR4
1CR4
1DR4
1ER4
1FR4
1GR4
1HR4
1IR4
1JR4
1KR4
1LR4
Π=0.0
Π=0.2
Π=0.5
l = κ z
Π=0.0
Π=0.2
Π=0.5
νt = κ u*z
Figure 4.2: Distributions of eddy viscosity and mixing length (set-up 1).
4.5. The eddy viscosity and mixing length 57
0 0.05 0.1 0.15 0.2
0
0.5
1
lm/h
z
/
h
0 0.05 0.1 0.15
0
0.5
1
νt/hu∗
z
/
h
2AR1
2BR1
2CR1
2DR1
2ER1
2FR1
2GR1
2HR1
2IR1
2JR1
2KR1
2LR1
Π=0.0
Π=0.2
Π=0.5
l = κ z
Π=0.0
Π=0.2
Π=0.5
νt = κ u*z
0 0.05 0.1 0.15 0.2
0
0.5
1
lm/h
z
/
h
0 0.05 0.1 0.15
0
0.5
1
νt/hu∗
z
/
h
2AR2
2BR2
2CR2
2DR2
2ER2
2FR2
2GR2
2HR2
2IR2
2JR2
2KR2
2LR2
Π=0.0
Π=0.2
Π=0.5
l = κ z
Π=0.0
Π=0.2
Π=0.5
νt = κ u*z
0 0.05 0.1 0.15 0.2
0
0.5
1
lm/h
z
/
h
0 0.05 0.1 0.15
0
0.5
1
νt/hu∗
z
/
h
2AR3
2BR3
2CR3
2DR3
2ER3
2FR3
2GR3
2HR3
2IR3
2JR3
2KR3
2LR3
Π=0.0
Π=0.2
Π=0.5
l = κ z
Π=0.0
Π=0.2
Π=0.5
νt = κ u*z
0 0.05 0.1 0.15 0.2
0
0.5
1
lm/h
z
/
h
0 0.05 0.1 0.15
0
0.5
1
νt/hu∗
z
/
h
2AR4
2BR4
2CR4
2DR4
2ER4
2FR4
2GR4
2HR4
2IR4
2JR4
2KR4
2LR4
Π=0.0
Π=0.2
Π=0.5
l = κ z
Π=0.0
Π=0.2
Π=0.5
νt = κ u*z
Figure 4.3: Distributions of eddy viscosity and mixing length (set-up 2).
58 Chapter 4. Flow characteristics
0 0.05 0.1 0.15 0.2
0
0.5
1
lm/h
z
/
h
0 0.05 0.1 0.15
0
0.5
1
νt/hu∗
z
/
h
3AR1
3BR1
3CR1
3DR1
3ER1
3FR1
3GR1
3HR1
3IR1
3JR1
3KR1
3LR1
Π=0.0
Π=0.2
Π=0.5
l = κ z
Π=0.0
Π=0.2
Π=0.5
νt = κ u*z
0 0.05 0.1 0.15 0.2
0
0.5
1
lm/h
z
/
h
0 0.05 0.1 0.15
0
0.5
1
νt/hu∗
z
/
h
3AR2
3BR2
3CR2
3DR2
3ER2
3FR2
3GR2
3HR2
3IR2
3JR2
3KR2
3LR2
Π=0.0
Π=0.2
Π=0.5
l = κ z
Π=0.0
Π=0.2
Π=0.5
νt = κ u*z
0 0.05 0.1 0.15 0.2
0
0.5
1
lm/h
z
/
h
0 0.05 0.1 0.15
0
0.5
1
νt/hu∗
z
/
h
3AR3
3BR3
3CR3
3DR3
3ER3
3FR3
3GR3
3HR3
3IR3
3JR3
3KR3
3LR3
Π=0.0
Π=0.2
Π=0.5
l = κ z
Π=0.0
Π=0.2
Π=0.5
νt = κ u*z
Figure 4.4: Distributions of eddy viscosity and mixing length (set-up 3).
4.6. Turbulence intensity data 59
Eqs. (2.13) and (2.14). These profiles show a high scatter level. This can be ex-
plained by the fact that small measurement errors occurring in velocity profiles
are enhanced in the calculation of du/dz. The scatter level is higher for the data at
profile 2 to 4 in set-up 2 and 3 compared to that of set-up 1. This agrees with the
higher non-uniformity of the flow in these two set-ups. However, a good agree-
ment between our data and literature can be seen for profile 1 at z/h < 0.2. This
explains the validity of the log law for our data in the inner region. The devia-
tions from the theoretical curves of the eddy viscosity and the mixing length in
the outer region show that the extension of the log law to the whole water depth
cannot be applied to the present flow conditions. The scatter in the outer region
reflects the fact that the Coles wake parameter Π varies considerably for all flow
conditions.
4.6 Turbulence intensity data
Figures 4.5, 4.6 and 4.7 show the turbulence intensities normalized by the shear
velocity (u∗1) for all flow conditions. From the measured turbulence intensity
distributions, the empirical constants α and β in Eq. (2.3) can be evaluated. This
equation is rewritten as
σ(ui)
u∗
= αie
−βi zh (4.8)
The empirical constants αi and βi were determined by least-square fitting to
the turbulence data in the range of 0.15 < z/h < 0.70. The fit analysis was
made as follows. By taking the logarithm of both sides of Eq. (4.8) and taking
Y = ln[σ(ui)/u∗ ], X = z/h, A = −βi, and B = ln(αi), we have
ln
[
σ(ui)
u∗
]
= ln(αi)− βi zh → Y = AX + B (4.9)
Table 4.4: The empirical constants α and β determined from the present data.
set-up 1 set-up 2 set-up 3 Nezu (1977)
profile 1 2 3 4 1 2 3 4 1 2 3 for uniform flow
αu 2.33 2.31 2.20 2.21 2.27 2.38 2.35 2.21 2.29 2.41 2.32 2.30
βu 1.61 1.48 1.35 1.23 1.50 1.49 1.32 1.05 1.41 1.45 1.30 1.00
R2u 0.92 0.95 0.93 0.92 0.90 0.95 0.88 0.85 0.89 0.96 0.89 -
αw 1.15 1.10 1.09 1.09 1.17 1.12 1.15 1.12 1.17 1.09 1.12 1.63
βw 1.06 0.83 0.77 0.65 1.03 0.90 0.83 0.61 0.95 0.80 0.78 1.00
R2w 0.92 0.91 0.93 0.84 0.91 0.94 0.88 0.81 0.89 0.94 0.90 -
From Eq. (4.9) a linear regression analysis was made for the present data. The
results are given in Table 4.4 and shown in Figure 4.5 to 4.7. For all profiles
60 Chapter 4. Flow characteristics
0.5 1 1.5 2 2.5
0
0.2
0.4
0.6
0.8
1
σ(u)/u∗
z
/
h
0 0.5 1 1.5 2
0
0.2
0.4
0.6
0.8
1
σ(w)/u∗
z
/
h
1AR1
1BR1
1CR1
1DR1
1ER1
1FR1
1GR1
1HR1
1IR1
1JR1
1KR1
1LR1
σ(u)/u
*
= 2.30 e−z/h
σ(u)/u
*
= 1.63 e−z/h
σ(u)/u
*
= 2.33e(−1.61z/h)
σ(u)/u
*
= 1.15e(−1.05z/h)
0.5 1 1.5 2 2.5
0
0.2
0.4
0.6
0.8
1
σ(u)/u∗
z
/
h
0 0.5 1 1.5 2
0
0.2
0.4
0.6
0.8
1
σ(w)/u∗
z
/
h
1AR2
1BR2
1CR2
1DR2
1ER2
1FR2
1GR2
1HR2
1IR2
1JR2
1KR2
1LR2
σ(u)/u
*
= 2.30 e−z/h
σ(u)/u
*
= 2.31e(−1.48z/h)
σ(u)/u
*
= 1.63 e−z/h
σ(u)/u
*
= 1.09e(−0.83z/h)
0.5 1 1.5 2 2.5
0
0.2
0.4
0.6
0.8
1
σ(u)/u∗
z
/
h
0 0.5 1 1.5 2
0
0.2
0.4
0.6
0.8
1
σ(w)/u∗
z
/
h
1AR3
1BR3
1CR3
1DR3
1ER3
1FR3
1GR3
1HR3
1IR3
1JR3
1KR3
1LR3
σ(u)/u
*
= 2.30 e−z/h
σ(u)/u
*
= 2.20e(−1.35z/h)
σ(u)/u
*
= 1.63 e−z/h
σ(u)/u
*
= 1.09e(−0.77z/h)
0.5 1 1.5 2 2.5
0
0.2
0.4
0.6
0.8
1
σ(u)/u∗
z
/
h
0 0.5 1 1.5 2
0
0.2
0.4
0.6
0.8
1
σ(w)/u∗
z
/
h
1AR4
1BR4
1CR4
1DR4
1ER4
1FR4
1GR4
1HR4
1IR4
1JR4
1KR4
1LR4
σ(u)/u
*
= 2.30 e−z/h
σ(u)/u
*
= 2.21e(−1.23z/h)
σ(u)/u
*
= 1.63 e−z/h
σ(u)/u
*
= 1.09e(−0.65z/h)
Figure 4.5: Turbulence intensity distributions (set-up 1).
4.6. Turbulence intensity data 61
0.5 1 1.5 2 2.5
0
0.2
0.4
0.6
0.8
1
σ(u)/u∗
z
/
h
0 0.5 1 1.5 2
0
0.2
0.4
0.6
0.8
1
σ(w)/u∗
z
/
h
2AR1
2BR1
2CR1
2DR1
2ER1
2FR1
2GR1
2HR1
2IR1
2JR1
2KR1
2LR1
σ(u)/u
*
= 2.30 e−z/h
σ(u)/u
*
= 2.27e(−1.50z/h)
σ(u)/u
*
= 1.63 e−z/h
σ(u)/u
*
= 1.17e(−1.03z/h)
0.5 1 1.5 2 2.5
0
0.2
0.4
0.6
0.8
1
σ(u)/u∗
z
/
h
0 0.5 1 1.5 2
0
0.2
0.4
0.6
0.8
1
σ(w)/u∗
z
/
h
2AR2
2BR2
2CR2
2DR2
2ER2
2FR2
2GR2
2HR2
2IR2
2JR2
2KR2
2LR2
σ(u)/u
*
= 2.30 e−z/h
σ(u)/u
*
= 2.38e(−1.49z/h)
σ(u)/u
*
= 1.63 e−z/h
σ(u)/u
*
= 1.12e(−0.90z/h)
0.5 1 1.5 2 2.5
0
0.2
0.4
0.6
0.8
1
σ(u)/u∗
z
/
h
0 0.5 1 1.5 2
0
0.2
0.4
0.6
0.8
1
σ(w)/u∗
z
/
h
2AR3
2BR3
2CR3
2DR3
2ER3
2FR3
2GR3
2HR3
2IR3
2JR3
2KR3
2LR3
σ(u)/u
*
= 2.30 e−z/h
σ(u)/u
*
= 1.63 e−z/h
σ(u)/u
*
= 1.15e(−0.83z/h)
σ(u)/u
*
= 2.35e(−...

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