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THREE-DIMENSIONAL NUMERICAL MODELLING OF HYDRODYNAMICS AND MORPHODYNAMICS AROUND IN-STREAM STRUCTURES

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THREE-DIMENSIONAL NUMERICAL MODELLING OF HYDRODYNAMICS AND MORPHODYNAMICS AROUND IN-STREAM STRUCTURES

Abstract

In-stream structures include both engineered structures and naturally formed ones. Examples of engineered in-stream structures are bridge piers, abutments, dams, engineered log jams (ELJ), rock vanes, J-hook vanes, among many others. Naturally formed in-stream structures mainly refer to large woody debris (LWD), which consist of fallen trees, logs, stumps, root wads, and piles of branches along the river course. These in-stream structures play a very significant role in flow resistance, sediment transport, invertebrate habitats and other aspects of fluvial ecosystem. For example, LWDs can provide food sources for aquatic insects and create refuge and habitat for fishes. They also create hydraulic diversity and roughness along river banks. Due to the geometrical complexity of these in-stream structures, the surrounding stream flow is extremely complicated and turbulent. The flow around and through complex in-stream structures can also result in local scour, sedimentation, and other morphodynamic changes. Thus, the overarching goal of this thesis research is to model and understand the flow and sediment transport processes associated with in-stream structures.

This thesis is organized as three parts: (a) high resolution numerical investigations on the three-dimensional (3D) hydraulics of LWDs, with a focus on the importance of how to represent porosity in computational models, (b) a new immersed boundary (IB) method designed for the accurate prediction of local bed shear stress, which is the driver for sediment motion, and (c) development and application of a coupled hydro-morphodynamics model for complex in-stream structures.

The first part tackles the problem of how to represent the porosity of in-stream structures. In many existing literature, the geometry of LWDs are simplified as simple cylinders or solid blocks, which are far from the reality of their complex and irregular shapes. This research tries to understand how much geometric details are needed in the numerical studies of in-stream structures. Three different representations, fully resolved geometry, porosity approximation, and solid barrier

 

simplification, were tested and compared. It is found that the porous media model and the solid barrier model, which are computationally economic, can describe the flow dynamics only to some extent. From the calibration of drag force and wake length, it is found that the equivalent grain size d50 in the porosity model should scale as the key element diameter for the simulated ELJ. A wake length scale analysis was performed for the semi-bounded flow around this in-stream structure near the bank. The length estimator in the literature for unbounded vegetation patches can be used with modifications. The results also show that the flow passing through the porous in-stream structure has a significant impact on mean velocity, turbulence kinetic energy, sediment transport capacity and integral wake length. Since geometrically-fully-resolved simulations are not currently feasible for engineering practices, the following suggestions are made based on this study. If the near-field and wake are important for the purpose of the structure, the well-calibrated porosity model seems to perform better than the solid barrier model. However, care needs to be taken when interpreting the results because this work also identified substantial loss of physical information with the porosity model. When the emphasis is the far field away from the structure, both the porosity model and the solid barrier model give comparable results.

The second part focuses on the development of a versatile computational fluid dynamics (CFD) code which can be used to track and model the dynamic evolution of the sediment bed as the scour hole develops. The immersed boundary methodology was adopted because it can deal with large and arbitrary bed deformation. More importantly, IB method can easily deal with the interaction between evolving sediment bed and in-stream structures. One technical difficulty with IB method is that in the literature focus was not on the wall shear stress. The use of the IB methods in the literature gave very poor wall shear stress, which is important for sediment transport. The root of the problem is that the original wall functions for turbulent boundary layer flow lack smoothness due to the nonlinearity and discontinuity between the log-law layer and the laminar layer. In IB method, the wall function is enforced through IB cells. However, for complex and evolving surfaces, there is no control on where the IB cells will be located in the boundary layer. The IB cells located in the log-law layer and the laminar layer follow different functions and thus will give non-smooth wall shear distribution. To remedy this, this research introduces a new IB method with a y+-adaptation wall function. The basic idea is that when an IB cell is too close to the immersed boundary, it is automatically replaced by cells in the fluid region further away from the boundary. Thus, all IB cells are in the log-law layer and they use the same function to evaluate turbulent flow quantities. As a result, the wall shear stress is much smoother. In the new IB method, the enforcement of boundary conditions is through IB cells on which the variables are reconstructed (interpolated) from their neighbouring cells with an explicit, iterative scheme. Three interpolation schemes are provided, i.e., quadratic, linear and mixed. Example cases in 1D, 2D, and 3D show the new IB method together with the y+-adaptation wall function produces results compare well with theory and experiments.

The third part of the thesis is the utilization of the IB method developed above and the development of a three-dimensional local scour model. The bed is treated as immersed boundary. The major components of the 3D scour model are the CFD part for turbulent flow field and the sediment transport part for updating the bed location. During the simulation, a robust and parallel interpolation scheme between 3D background mesh and 2D immersed boundary mesh is implemented. An edge-center storage method is used to address the divergence calculation problem in the Exner equation. This problem is caused by mesh non-orthogonality. One unique feature of the model that that a diffusion-based sand-slide algorithm is adopted. The relationship between sand slide and the augmented angle of repose is analyzed inside the scour. The model is validated against experimental measurements and its capability is demonstrated with a case where local scour occurs around a bridge pier with complex geometry. The demonstration shows that the model has the capability of simulating the exposure of in-stream structure foundation, which is extremely difficult if other approaches, such as dynamic mesh, are adopted.

Table of Contents

List of Figures                                                                                                                   ix

List of Tables                                                                                                                  xiv

Acknowledgments                                                                                                          xv

Chapter 1

Introduction                                                                                                              1

1.1                  Motivations and methodology . . . . . . . . . . . . . . . . . . . . .                    1

1.2     Objective and research questions                . . . . . . . . . . . . . . . . . . .                 7

1.3                        Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                          8

Chapter 2

Hydrodynamics modeling of complex in-stream structures                         12

2.1                       Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                       12

2.2    Methodology                     . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                      17

2.2.1                  Governing Equations . . . . . . . . . . . . . . . . . . . . . .                   18

2.2.1.1      Hydrodynamic Model              . . . . . . . . . . . . . . . .              18

2.2.1.2                 Porosity Model . . . . . . . . . . . . . . . . . . . .                 20

2.2.1.3               Drag Force Calculation . . . . . . . . . . . . . . . .               21

2.2.2           Geometry Preparation and Mesh Generation . . . . . . . . .            22

2.2.3                  Boundary Conditions . . . . . . . . . . . . . . . . . . . . . .                   25

2.2.4      Configuration of the Porous Media Model           . . . . . . . . . .          27

2.2.5                  Computational Platform . . . . . . . . . . . . . . . . . . . .                  29

2.3     Results and Discussions                   . . . . . . . . . . . . . . . . . . . . . . . .                  30

2.3.1           Validation of the Fully-Resolved Configuration . . . . . . . .            30

2.3.2               Calibration of Porous Media Model . . . . . . . . . . . . . .               34

2.3.3         Evaluation of Different Representations in the CFD Model .         37

2.3.3.1                 Flow Adjustment . . . . . . . . . . . . . . . . . . .                 38

2.3.3.2      Near-Surface Velocity              . . . . . . . . . . . . . . . .             43

2.3.3.3               Near-Bed Turbulence . . . . . . . . . . . . . . . . .               44

2.3.3.4                  Flow Structure . . . . . . . . . . . . . . . . . . . .                  45

2.4                       Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                        49

Chapter 3

An immersed boundary method with smooth wall shear for

morphodynamics modeling                                                               55

3.1                       Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                       55

3.2              Governing equations and their discretization . . . . . . . . . . . . .              61

3.2.1         Governing equations for flow and turbulence model . . . . .          61

3.2.2     Discretization method                . . . . . . . . . . . . . . . . . . . . .                62

3.2.3        Iterative solution algorithm for pressure-velocity coupling . .        64

3.3     Treatment of immersed boundaries              . . . . . . . . . . . . . . . . . .               67

3.3.1            Representation of immersed boundaries . . . . . . . . . . . .            67

3.3.2                 Reconstruction algorithm . . . . . . . . . . . . . . . . . . . .                 69

3.3.2.1       Quadratic interpolation scheme for reconstruction .       70

3.3.2.2        Alternative linear interpolation scheme for recon-

struction                 . . . . . . . . . . . . . . . . . . . . . . .                  73

3.3.2.3      Interpolation scheme selection and iterative method      75

3.3.3               Coefficient matrix manipulation . . . . . . . . . . . . . . . .                76

3.4                y+-adaptation immersed wall model . . . . . . . . . . . . . . . . . .                 79

3.4.1          Basic wall function for immersed boundary method . . . . .          79

3.4.2       y+-adaptation wall model for immersed boundary method       .     81

3.4.3       Rough wall function for immersed boundary method        . . . .       85

3.5                        Test cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                        86

3.5.1      Pitz-Daily 2D case                  . . . . . . . . . . . . . . . . . . . . . . .                  86

3.5.2                   Flow over a 3D dune . . . . . . . . . . . . . . . . . . . . . .                   92

3.6     Summary and conclusions                                . . . . . . . . . . . . . . . . . . . . . . . 101

Chapter 4 Development and applications of a robust 3D local scour model

based on immersed boundary method                                         107

4.1                                           Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

4.2                                      Hydrodynamic model . . . . . . . . . . . . . . . . . . . . . . . . . . 112

4.2.1                    Governing equations and turbulence model . . . . . . . . . . 112

4.2.2                                   Rough wall models . . . . . . . . . . . . . . . . . . . . . . . 114

4.3                                  Bed morphodynamics model . . . . . . . . . . . . . . . . . . . . . . 120

4.3.1                        Exner equation and bed-load transport . . . . . . . . . . . . 120

4.3.2                                   Critical shear stress . . . . . . . . . . . . . . . . . . . . . . . 121

4.3.3                                   Sand-slide algorithm . . . . . . . . . . . . . . . . . . . . . . 125

4.4                            Immersed boundary implementation . . . . . . . . . . . . . . . . . . 128

4.4.1                               Sharp interface method . . . . . . . . . . . . . . . . . . . . . 128

4.4.2                          Immersed boundary wall function . . . . . . . . . . . . . . . 134

4.4.3                 Coupled hydrodynaic and morphodynamic models . . . . . . 136

4.4.4       Interpolation between 3D hydro mesh and 2D morpho mesh      138

4.4.5            Effect of mesh non-orthogonality on divergence calculation . 140

4.4.6                       Intersection between bed and object . . . . . . . . . . . . . . 144

4.4.7                                 Computational speed . . . . . . . . . . . . . . . . . . . . . . 151

4.4.7.1      Test cases description                        . . . . . . . . . . . . . . . . 151

4.4.7.2                         Effect of mesh resolution . . . . . . . . . . . . . . . 152

4.4.7.3       Effects of 3D-2D interpolation stencil size            . . . . . 157

4.5                                  Validations and disucssions . . . . . . . . . . . . . . . . . . . . . . . 158

4.5.1      Hydrodynamics modeling                            . . . . . . . . . . . . . . . . . . . 161

4.5.2                                     Scour modeling . . . . . . . . . . . . . . . . . . . . . . . . . 167

4.5.3                           A test case of complex bridge piers . . . . . . . . . . . . . . 173

4.6                                            Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

Chapter 5 Summary and future work          184

5.1     Summary                                          . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

5.2                                           Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

Appendix A FV discretization schemes         189

Appendix B Estimation of shear velocity in fully developed open channel flow191

Chapter 1 |

Introduction

1.1 Motivations and methodology

In the practice of stream restoration, the term “in-stream structure” usually refers to the engineered construction which are designed to change the physical characteristics of a channel. Furthermore, their existance will increase the stream habitat complexity. Natural in-stream structures are part of fluvial processes and they inspire the design and construciton of stream restoration measures. One example of engineered in-stream structure is the large woody debris (LWD). LWD usually refers to trees, stumps, root wads and logs that fall into and are stored along the streams. It often acts as an important eco-hydraulic element in natural streams. Its influence ranges from very locainpirelized effects, such as local scour, to watershed scale such as floodplain morphology (Abbe and Brooks, 2011). The ecological significance of LWD-like in-stream structures has been emphasized by many researchers since 1980s. One important effect is associated with the particulate organic matter (Bilby and Likens, 1980), providing food and habitats for invertebrates (Benke et al., 1985) and fishes (Shirvell, 1990; Dolloff and Warren, 2003). According to Tullos and Walter (2014), for the benefit of fish habitat, in-stream structures can provide shelters, abundant foraging, and macroinvertebrate biomass, among many others. In a much broader sense, in-stream structures also include anything that human placed in rivers for various purposes, e.g, bridge piers, abutments, dams, engineered log jams, rock vanes, and J-hook vanes. Their existence also alters the flow field, geomorphology, and ecology.

It is well accepted that local micro-scale and meso-scale flow structures induced by obstacles in streams have a significant impact on the physical habitat (Shen and Diplas, 2008). For example, through flume experiment, Cullen (1991) found the local vortex might promote the growth of fish population. The linkage between the flow and any ecological model is based on the premise that the detailed flow field can be either accurately measured or simulated. However, measurements around complex in-stream structure are difficult. In addition, due to the vast variations of natural in-stream structures, it is extremely difficult to make any generalization based on limited measurement data. Computational models are thus very attractive because they can potentially model any configuration.

Depending on the assumptions on the hydraulics around in-stream structures, computational models can be categorized into one-dimensional (1D), twodimensional (2D), and three-dimensional (3D) models. Currently, most habitat assessment models, such as the PHABSIM model (Waddle, 2001), simplify the hydraulics around in-stream structures as 1D, which is able to capture the bulk, global flow features but not detailed, local features. It is in fact those local flow features that have the most profound and direct impact to the environment. He et al. (2009) used a 2D depth-averaged model to analyze the effects of LWD on channel morphology. The LWDs in their model are simply represented as porous media and the flow experiences extra drag force in the LWD zone.

In comparsion with 1D and 2D models, 3D computational fluid dynmaics (CFD) technique might be the most suitable tool to obtain high-resolution, local flow features. Up until now, there are very limited studies using CFD for complex in-stream structures, such as LWDs. Smith et al. (2011) emphasized the difficulty of implementing the complex geometric roughness elements like LWD into CFD models. Another study is reported in Allen and Smith (2012) where a URANS turbulence model was used to evaluate the impact of the geometric simplification on LWDs. Neither of the above two researches considered morphological impact.

Besides LWDs, there are some computational simulation studies on other stream restoration structures in the literature. Kang et al. (2011), Kang and

Sotiropoulos (2012),Kang and Sotiropoulos (2015a), and Kang and Sotiropoulos

(2015b) developed a very high accuracy 3D computational model to simulate the turbulent free surface flow interacting with a cross vane. They used Curvilinear Immersed Boundary (CURVIB) method (Gilmanov and Sotiropoulos, 2005; Ge and Sotiropoulos, 2007; Borazjani et al., 2008) to treat the complex geometry and a level set method to capture the free surface. For morphodynamic modelling, Khosronejad et al. (2011) developed a CURVIB model coupled with sediment transport. With these computational modelling techniques, they investigated large dunes in meandering streams and the morphdynamic impact of J-hook vanes (Khosronejad et al., 2012, 2014, 2015b,a). Although limited, CFD studies of stream restoration projects have grown in recent years and computational models have been proven to be a very promising tool to investigate the local hydraulics and morphodynamic features around complex structures in streams.

On the other hand, in-stream structures also include man-made hydraulic infrastructures, such as bridges, gates, weirs, dams and so forth. Sometimes, their geometry can also be very complex. Like LWDs, these structures can also induce scour. Indeed, scour is one major cause for bridge failures and other structural damages. It was reported that 53% of all the bridge failures in United States were due to flood and scour (Wardhana and Hadipriono, 2003). The exact cause of scour and erosion may vary under different conditions (Richardson and Richardson, 2008). A recent review in Wang et al. (2017) classified scour events into three major forms,

i.e., contraction scour, general scour, and local scour. Among the three, contraction scour and local scour are directly linked the 3D turbulent flow around the structure, which highlights the need to consider the geometric details.

Regardless it is man-made hydraulic infrastructure, river restoration structure, or a natural woody debris, they share similar hydrodynamic and morphological characteristics to some extend. The overarching goal of this thesis work is to develop and utilize 3D computational models for the study and design of these in-stream structures. To be applicable for engineering practice, such models have to balance between accuracy and computational cost. In addition, in the course of this thesis research, some unexpected technical problems emerged during the development of the models. For example, the numerical method adopted in this work, the immersed boundary method, was invented in the field of biofluids and widely adopted in many other fields later on. Its use in the field of hydraulics and sediment transport is relatively limited. One major problem encountered is that the wall shear stress was not of as great interest in other fields as in hydraulics. The immersed boundary methods reported in the literature do not work well in terms producing smooth wall shear. Non-smooth and ill-behaving wall shear stress jeopardize the sediment transport calculation and consequently make the simulated scour result useless. To overcome this, a solution is proposed and tested in this work.

Another technical difficulty when simulating 3D scour process around a structure with complex geometry is how to deal with the dynamic interaction of the evolving bed and the structure. During the erosion process, a structure may be dynamic buried or exhumed depending on the flow and sediment transport condition. It is the result of the coupled process between flow and sediment. There are some existing 3D scour models reported in the literature for flow and sediment transport around simple vertical cylinders (Olsen and Kjellesvig, 1998; Roulund et al., 2005; Liu and García, 2008; Escauriaza and Sotiropoulos, 2011; Jacobsen and Fredsoe, 2014; Baykal et al., 2017). Most of the scour models use moving mesh technique to simulate the bed morphological changes. The mesh moves based on the deformation of the scoured bed. However, this moving mesh method is limited to simple geometries such as vertical cylinders. Even for the case of an inclined cylinder, it will be very difficult to simply moving grid points as the scour hole evolves. In recent years, a promising alternative is to use the immersed boundary method (Escauriaza and Sotiropoulos, 2011; Khosronejad et al., 2011, 2012). This method treats both the bed and the in-stream structure as immersed boundary. It has been applied in the morphodynamic modeling of stream restoration structures (Khosronejad et al., 2014, 2015b, 2018). Although their model can consider complex geometry such as rock vanes, which is a great improvement, their algorithm limits the bed motion only in the vertical direction. In other words, the bed surface in their model can not dynamically cut and slice through the structure, and thus can not simulate real burial or exhume. Such capability is important for the failure study of those complex hydraulic infrastructures. In addition, their immersed boundary method is limited by curvilinear mesh. In this work, a unstructured mesh is used and thus greatly improve the easiness of use for practice.

1.2 Objective and research questions

Based on the background and motivations described above, the objectives of this thesis research are (1) to better understand and quantify the hydrodynamics around and through in-stream structures with computational modeling, in particular the effects of how porosity is modeled, (2) to develop robust and computational affordable computational model for the simulation of scour process around in-stream structures. With these models, the specfic research questions to be addressed are as follows:

  • How necessary is it to fully resolve the geometric complexity of in-stream structures? What are the implications if the structures are modeled with porous media or solid?
  • How to improve the smoothness of the wall shear stress simulated with immersed boundary method? What is the cause of non-smooth wall shear and how to balance accuracy and smoothness?
  • How to incorporate the morphodynamics into immersed boundary method? And how to improve the efficiency of the scour modeling of complex in-stream structure such that it is affordable in practice?

1.3 Outline

This thesis is organized as follows:

Chapter 2 aims to study how much geometric details are needed in the numerical simulations of complex in-stream structures. Three different representations, i.e., fully resolved geometry, porosity approximation and solid barrier simplification, are tested and compared. The example of engineered log jam was used for the comparison, which focuses on the effect in the near- and far-fields.

Chapter 3 describes the development of a three-dimensional numerical model with immersed boundary method technique. This immersed boundary method is designed for high Reynolds number flows. A y+-adaptation wall function is proposed to improve the smoothness of the wall shear stress computed with IB method. Example cases in 1D, 2D, and 3D will be shown to demonstrate that the y+-adaptation wall function produces much improved wall shear results.

Chapter 4 introduces the develop and application of a three-dimensional local scour numerical model based on the immersed boundary method proposed in Chapter 3. This model is validated against experimental measurement and tested with a case of complex bridge pier. It has the capability of simulating the exposure of the bridge’s foundation which was initially buried. The main features of the 3D scour model to be introduced include:

  • a robust and parallel-able interpolation scheme between 3D background mesh and 2D surface mesh,
  • an edge-center storage method to address the bedload flux divergence calculation problem in the Exner equation, which is caused by mesh non-

orthogonality,

  • a numerical acceleration method related to morphological time step,
  • a physical acceleration method based on morphological scaling.

Chapter 5 summarizes the achievements and findings of this thesis research. It also discusses some future research needs and directions.

References

Abbe, T. and Brooks, A. (2011). Geomorphic, engineering, and ecological considerations when using wood in river restoration. Geophysical Monograph Series, 194:419–451.

Allen, J. B. and Smith, D. L. (2012). Characterizing the impact of geometric simplification on large woody debris using CFD. International Journal of Hydraulic Engineering, 1(2):1–14.

Baykal, C., Sumer, B. M., Fuhrman, D. R., Jacobsen, N. G., and Fredsøe, J. (2017). Numerical simulation of scour and backfilling processes around a circular pile in waves. Coastal Engineering, 122(May 2016):87–107.

Benke, A. C., Henry, R. L., Gillespie, D. M., and Hunter, R. J. (1985). Importance of snag habitat for animal production in southeastern streams. Fisheries, 10(5):8–13.

Bilby, R. E. and Likens, G. E. (1980). Importance of organic debris dams in the structure and function of stream ecosystems. Ecology, 61(5):1107–1113.

Borazjani, I., Ge, L., and Sotiropoulos, F. (2008). Curvilinear immersed boundary method for simulating fluid structure interaction with complex 3D rigid bodies. Journal of Computational Physics, 227(16):7587–7620.

Cullen, R. (1991). Vortex mechanisms of local scour at model fishrocks. In Fisheries Bioengineering Symposium: American Fisheries Society Symposium 10, pages 213–218.

Dolloff, C. A. and Warren, M. L. (2003). Fish relationships with large wood in small streams. American Fisheries Society Symposium, 37:179–193.

Escauriaza, C. and Sotiropoulos, F. (2011). Reynolds number effects on the coherent dynamics of the turbulent horseshoe vortex system, volume 86.

Ge, L. and Sotiropoulos, F. (2007). A numerical method for solving the 3D unsteady incompressible

Navier-Stokes equations in curvilinear domains with complex immersed boundaries. Journal of Computational Physics, 225(2):1782–1809.

Gilmanov, A. and Sotiropoulos, F. (2005). A hybrid Cartesian/immersed boundary method for simulating flows with 3D, geometrically complex, moving bodies. Journal of Computational Physics, 207(2):457–492.

He, Z., Wu, W., and Douglas Shields, F. (2009). Numerical analysis of effects of large wood structures on channel morphology and fish habitat suitability in a Southern US sandy creek. Ecohydrology, 2(3):370–380.

Jacobsen, N. G. and Fredsoe, J. (2014). Formation and development of a breaker bar under regular waves. Part 2: Sediment transport and morphology. Coastal Engineering, 88:55–68.

Kang, S., Lightbody, A., Hill, C., and Sotiropoulos, F. (2011). High-resolution numerical simulation of turbulence in natural waterways. Advances in Water Resources, 34(1):98–113.

Kang, S. and Sotiropoulos, F. (2012). Numerical modeling of 3D turbulent free surface flow in natural waterways. Advances in Water Resources, 40:23–36.

Kang, S. and Sotiropoulos, F. (2015a). Large-eddy simulation of three-dimensional turbulent free surface flow past a complex stream restoration structure. Journal of Hydraulic Engineering, 141(10):4015022.

Kang, S. and Sotiropoulos, F. (2015b). Numerical study of flow dynamics around a stream restoration structure in a meandering channel. Journal of Hydraulic Research, 53(2):178–185.

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THREE-DIMENSIONAL NUMERICAL MODELLING OF HYDRODYNAMICS AND MORPHODYNAMICS AROUND IN-STREAM STRUCTURES

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