ABSTRACT
The Hydraulics of flow in an open channel/waterway with flexible vegetation is studied. Vegetation along waterway has an ecological advantage; it enhances biodiversity, reduces erosion, and traps sediment. However, it has a hydraulic impact on flow. This study reviews hydrodynamics of vegetation along waterways (a concept to promote a sustainable green environment). It applies a modified one-dimensional (1-D) hydraulic model to replicate the vegetative velocity profile and Reynolds stresses using several laboratories experimental and field dataset found in the literature. Using this concept, a synthetic velocity profile is generated under varying hydraulic conditions. Using the concept of dimensional similarity, the vegetative parameters and flow resistance equation which relates these vegetation parameters, flow depth, and the zero- displacement parameter is proposed. The findings gave clear and comprehensive deduction, that mathematical model could to an extent replicate the rigorous experiments, as evaluations were parallel to the estimated laboratory values. It was concluded that at <10% slope, the flow channel can be construction without the use of concrete and other rigid materials.
CHAPTER ONE
1.0 INTRODUCTION
1.1 Background to the Study
Contrary to popular opinion, the vegetation in flow channels to a large extent does more good than harm to hydraulic systems. In the cause of achieving significant innovative solutions to the problems faced as a result of environmental conditions, the water infrastructures have become some of the key resources that require constant development and subsequent overhaul. The flow of fluid in systems is a phenomenon that is dependent on certain factors, some of which includes but not limited to, Velocity of flow, configuration of the system (that is size, shape and structure), geographical conditions, state of the fluid, and the likes. Out of the numerous benefits of Vegetation in flow Channels, the following are benefits derived by the aquatic habitats; to improve its ecosystem, to stabilize the bed slope and as a result curbs the likelihood of erosion, a reasonable amount of improved water quality, accumulation of sediment which may further enhance growth of vegetation. In any flow field, velocity is the most important characteristic to be identified, at any point (Featherstone & Nalluri, 1998). This has been the basis upon which all other flow conditions have been measured and studied. The effect of Velocity could affect a system in variety of ways (positively or negatively), when the flow is constant or gradually increases with pressure along the pathline, the next point of check is Erosion and Flood Control.
In a flood control system, for every (open) channel flow, the requirement for flood control is the fundamental necessity that governs its development. The design of flood- control systems will usually include a variety of conveyance channels that must behave in a stable and predictable way to ensure a known flow capacity will be available for an unplanned flood event. As soil erosion always occurs for a flood flow, channel linings are required either temporarily or permanently to attain channel stability. These linings may be classified as Rigid or Flexible. Rigid Linings such as, Channel Pavements of concrete or asphaltic concrete, a variety of precast interlocking blocks and articulated mats are encountered. Flexible Linings includes loose stones (ripraps) Vegetation, manufactured mats of lightweight materials, fabrics or a combination of these materials. The selection of a particular lining is a function of the design context, involving issues related to the consequences of flooding, the availability of land, and environmental needs.
A rigid lining can withstand high discharge and high velocity flow. Flood-control channels with rigid linings are often used to reduce the amount of land required for a surface drainage system. However, a flexible lining on the other hand can respond to a change in channel shape, and therefore, it is not so easy to subject it to local damage. It is used as temporary lining for control of erosion during construction or reclamation of disturbed areas. From environmental considerations, flexible linings are inexpensive, permit infiltration and exfiltration, and allow growth of vegetation. Flow conditions in the channel lined with flexible materials generally can be made to conform to conditions found in a natural channel, thus provide better habitat opportunities for local flora and fauna.
Rigid and flexible lining materials, Channel roughness is affected by the relative height of the roughness compared to the flow depth. Consequently channel roughness increases for shallow flow depths and decreases as flow depth increases.
Vegetative Lining; channel roughness varies significantly for vegetative linings, depending on the amount of submergence of the vegetation. As vegetation is flexible, the amount of submergence will increase as the drag force bends the plant stems toward the channel bed. The Manning’s coefficient can be determined practically by the Kouwen’s method (to be elaborated in Literature.
Vegetative canopy occurs in riverine environment such as in channels or on the flood plain, rivers and wetlands. It has a significant influence on the behaviour of the fluvial system. It increases the hydraulic resistance and reduces the inflow velocity, thereby causing problem on flood control. Meanwhile, it benefits as a storm surge protection, providing habitat for aquatic animals, reduce erosion (causing bank/channel stabilization) and water quality improvement motivate research of vegetated flows.
Several studies had been done on the resistance of vegetation to flow leading to established empirical relationships between vegetation parameters and the flow hydraulics (Cowna, 1956). Upon development of measuring devices, research interests have been extended to the study of velocity distributions and Reynolds stress. Based on this, theoretical analysis, Lopez and Garcia (2001) experimental study Stoesser et al. (2006) and mathematical model (Su Xiao-hui, 2003) have become the adopted study scheme. The classical issue of different vegetation type and hydraulic conditions of flows has restricted the generalization of experimental results. Hence, several mathematical models are been put forward based on the experimental results.
Many approaches have been proposed to develop the models. For example Naot, Huang (2002) used the continuity equation, energy equation and momentum equation in 3 dimensions to establish mathematical models. Among other 3-D models include two- equation � − 𝜔 turbulence model (Huai et al., 2009), large Eddy Simulation (LES) (Wang et al., 2009; Kubrak et al., 2008) etc. these models yielded results of high accuracy, but their limitation is based on complexity with large computation quantities and time.
Huai et al. (2009) developed a simpler mathematical model with restriction of rigid cylindrical stem of low vegetation density and not applicable to compound channel. Based on this, for sea grasses and other blade-type vegetation of high flexibility (that is, large deflection) and vegetation density, valid mathematical models are needed. Another approach regards vegetation layer and soil layer as homogenous and isotropic media, and applies the theory of turbulent flow and Biot’s poro-elastic theory to study the vegetated flow (Ghisalberti & Nepf, 2004). The method is, however, useful for soil of large porosity.
Recently, a one-dimensional numerical that combined the continuity equation and momentum equations with Spalart- Allmaras model with a modified length scale which is dependent on the vegetation density and vegetation height to water depth ratio as turbulence model (Busari & Li, 2015). The vegetation flexibility is accounted for using a large deflection analysis Based on the synthetic data an inducing equation is derived which relates the Manning roughness coefficient to the vegetation parameters, flow depth and a zero-plane displacement parameter. The predictions of the equation depend on the accuracy surrounding the estimation of plant’s drag coefficient.
In this study, the analysis of the turbulence structure in the vegetation region of the flow with submerged vegetation employs the mixing length approach and modifies its expression using Karman similarity theory base on the concept of zero-plane displacement to distinguish the regions in the vegetated area. The main force acting on a lining composed of large particles is the drag force. The effect is to increase the shear parameter and consequently Vegetation. Two major types of Vegetation are widely known Emergent Vegetation and Submerged Vegetation (Mazda et al., 1997).
The plant life, such as trees, grass, and bushes, always grows in the channels, rivers and wetlands. The vegetation can increase the resistance and reduce the velocity in flow, which has the negative influence on the flood control. However, the vegetation in flow can promote sediment deposition, reduces the river bed erosion, improves water environment and restores the river ecological systems. Therefore, it is important to study the influences of vegetation on the flow. At earlier time, researchers focused on the resistance of vegetation to flow and established some empirical relationships between the vegetation and the flow. With the development of measuring equipment, researchers became more interested in the distributions of the velocity and the Reynolds stress. They adopted three different study schemes, namely experimental study, theoretical analysis, and mathematical model. But the difference of vegetation types and experimental conditions restrict the generalization of the experimental results. So at present researchers put forward several mathematical models based on the experimental study. Many approaches have been proposed to construct the models. For example Naot et al. (2000) combined the continuity equation, energy equation, and momentum equations in three dimensions and established mathematical models, and other 3-D models include two-equation k – Z turbulence model and Large Eddy Stimulation (LES). The 3-D models can give relatively accurate results, but these models are complex with large computation quantities. So, simpler, valid mathematical models are needed. Another method is to derive the momentum equations regarding the flow with vegetation as a 1-D one. By adopting the mixing length expression, the model can give the vertical distributions of the stream-wise velocity and the Reynolds stress. To analyze the turbulence structure in the vegetated region of the flow with submerged vegetation, this work applies the mixing length approach and improves its expression according to the Karman similarity theory, and adopts the conception of penetrated distance to distinguish the regions in the vegetated area.
1.1.1 Mathematical modeling and simulation; numerical methods
In simple terms, a Mathematical Model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling.
Numerical Methods are techniques by which mathematical simulations/models are formulated so as to obtain their solutions using arithmetic operations. They usually comprise of large number of tedious calculations. Numerical solutions are often approximate values which may be the exact solutions, thus, are generally acceptable and valid. They can be determined either experimentally or analytically, the analytical method is applied in the case of this study as experimental methods have become more cumbersome and less economical, whose results are easily prone to error due to environmental conditions and human factors. A simple principle of numerical method is discretization, which is dependent on time and space of flow considered which gives an approximate result. It is also important to note, that the smaller the time interval, the more accurate the approximate result obtained.
In Hydraulics, Computational Fluid Dynamics is the use of computer aided design to determine, suggest and analyze fluid flow. It is the study of complex fluid flow, by solving the equations of flow velocity and motion, known as Navier-Stoke’s Equations (also referred to as Momentum equation, is used for the complete set of equations solved by numerical methods, which also includes the energy and continuity equations.), in a certain geometry and physical environment. Such flow environments could be considered waters channels with free surfaces, porous packed beds or porous concrete/metallic structures.
The presence of vegetation significantly have impact on flow conditions, while increasing flow resistance by (highly reducing erosion and stabilizing the earth through the plant root system), thereby improving the general purity of water.
Turbulent flows in such channels with submerged vegetation evidently have their structures depending on the nature of vegetation, its density and how it is arranged. Application of Computation Fluid Dynamics is of high significance as compared to physical experiment, due to its operation within the evolving Computer Aided Design/ Information Technology structure in conjunction with drawing and manufacturing tools, making it more accessible than experimental methods. The major issue in river modeling is the uncertainty in the predictions of resistance (Galema, 2009).
1.2 Aim and Objectives of the Study
1.2.1 Aim
The aim of this research is to obtain the Mathematical Model formulation for Submerged Aquatic Canopy (Flexible Vegetation).
1.2.2 Objectives of the study
This is guided by the following objectives;
1. To formulate the required theory of vegetated flow.
2. To evaluate significant hydraulic parameters using dimensional analysis.
3. To develop a Mathematical model for aquatic canopies.
4. To simulate mean velocity profile and Reynolds stress for different hydraulic conditions.
1.3 Statement of the Research Problem
In the cause of this study, it is likely to encounter some hindrances (not necessarily challenges) which may affect the expected outcomes of this research but not damaging to a viable result. The expected limitations may result from lack of access to accurate experimental findings, and hence the incorporation of Computational Fluid Dynamics to investigate the types of flow and further solve the flow equations. The Samples to be considered are restricted to blade-type flexible vegetation, whose model may have a certain level of variation with other types of vegetation (flexible or rigid). There is a likelihood of error due to experimental set-up, which may be experienced during physical sampling and hence may not be noticed immediately. Vegetation is observed to cause problem of flood control in a channel, which has further reinforced the lapses of vegetative cover in a flow channel.
1.4 Justification of the Study
With the recent intensity of discussions on flooding as a result Climate Change, the common acceptance that Vegetation is a cause of hindrance to flow or a cause of flow resistance is in high contrast to the findings by research and studies. This has further influenced the possibility that vegetation along a flow path or path line does not only have environmental benefits, but might also be a means of regulating excesses as a result of certain flow conditions.
The use of Mathematical Model shall further elaborate the significance of the need for more results and evidences to reinforce this theory.
The 3-D models can give relatively accurate results, but these models are complex with large computation quantities. So, simpler, valid mathematical models are needed. Another method is to derive the momentum equations regarding the flow with vegetation as a 1-Dimension. By adopting the mixing length expression, the model can give the vertical distributions of the stream-wise velocity and the Reynolds stress, though these models always involve some unknown parameters which are difficult to estimate.
1.5 Scope of the Study
With maximum accuracy, this Research is targeted at covering a wide range of situations and conditions; hence, it is not limited to a particular type or location of Vegetation. For the course of this research, we shall focus on the submerged aquatic canopy, study velocity, reconfiguration of flow channels to conserve aquatic life, alongside flood/erosion control by the application of Mathematical Model. This research shall be taken through the following stages
Stage one; The introduction and elaboration of aim and objectives
Stage Two; Detailed review of Literature available
Stage Three; Method of research process
Stage Four; Analysis and evaluation of results obtained
Stage Five; General observations and recommendations
This material content is developed to serve as a GUIDE for students to conduct academic research
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