Introduction
In many countries, large flood, can inundate over thousands towns and a far greater number of rural communities. The devastating impact of a flood through these communities is large, and social effects last for many years. In addition, damages from one event typically may be achieved tens millions of dollars, in case of large cities, billions of dollars. Therefore, research that increases the understanding of water flow in floods has considerable social and economic value for the whole countries. Present study will improve our knowledge of the extent and depth of flooding that can occur on all the floodplains within the world, allowing communities to make more informed decisions and become more able to cope with and plan for future flood.
Open channel flow may be laminar or turbulent depending on the value of the Reynolds number. The nature of flow is depended on determines the value of Reynolds number. The most flow encountered in engineering practice is turbulent. Furthermore, open channel flow may be steady or unsteady. If the flow is a function of distance only (or constant) and unsteady if it is also a function of time. Additionally, steady flow may be uniform (with discharge and depth hence velocity constant), or non-uniform. Also non-uniform flow may be rapidly or gradually varying (discharge constant, velocity and depth varying with position). In general Q=f(x).
Computing the flow characteristics is more significant to the engineers during design an open channels or other hydraulic structures. The computational fluid dynamics rapidly developed thus because of computer invention. The experimental solution used in past to predict the flow characteristics. Now numerical solution available and we can simulate many practical cases in nature. This literature review discusses introduced a finite element method modelling for two-dimensional (2D) flow model for deference cross-section high velocity channel. Because there are just a fewer studies on trapezoidal cross-section channel with high velocity flow I'm choosing this type of cross-section channel in this study. The procedure is not easy and more complicated rather than we think. There are many scales may be broken the solution and we have to make calibration and verification for them.
High-velocity channels are exactly lined flood control channels designed to discharge supercritical flow through specific reaches. The designer of these channels is primarily concerned with the depth of flow for the design discharge. (Richard. L. S. 2000). Before hand minimum bridge soffit elevations and side wall heights are set the depth must be known. In case of trapezoidal cross-section channel the determination of the depth have been complicated by side slopes flow and boundary characteristics such as, contractions, expansions, bends, and obstructions to the flow. Such as bridge piers and truck access ramps. The local flow depth in a river increases as a result of these boundary features, while in other conveyance hydraulic structures the local depth increases as a result of slope varying from steep slope to the mild slope. The local depths are unknown quantities for solution of the two-dimensional (2D) open channels flow equations.
For the rectangular cross-section open channel flows (vertical side walls). The plan view domain is defined such that one easily been discretized the domain. In present study the channel has slopping side walls (trapezoidal-cross channel), so the plan view of the flow domain, as limited by the flow surface, bank interface (i.e. waterline) is not known a priori. The width of the flow unknown because it was depends on water surface elevation in channel. The steady state flow was demonstrates the adjustment of the side boundaries of the flow field as a result of the computed flow field development from the specific initial flow conditions and initial side wall boundary location to the steady state flow. This constitutes a movable boundary problem and thus is encouraging me to present this study.
Previous study
The prediction of velocity distribution field for an open channel flow has been investigated for many years. The problem is treated by solving the Navier-Stocks hydrodynamics equations combined with turbulent open channel model applying for solving this problem.
These models depend on the deterministic law of physics that treats fluid flow as a boundary-value problem and makes predictions with certainty. However to develop a velocity distribution model, Chiu, C. L. (1988) proposed a new approach to the problem based on a probability concept.
Three-dimensional flow mathematical models of open channel flow derived by many researchers and used to determine various hydraulic variables and process. Such as the distribution of primary flow velocity, secondary flow, shear stress distribution, normal stress, channel cross section, discharge rate, flow resistant, and sediment transport. These contributions made a better understanding of the three dimensional structure of open channel flow.
The type of mesh used in solving averaged depth is quite important to achieve solution or broken it. Mesh generation may be structured mesh, unstructured mesh, or unstructured hybrid meshes. Development of an unstructured hybrid mesh method has been used by (Lay, Y. G. 2009) to simulate open channel flow with a finite volume discretization to the two dimensional depth averaged equations such that mass conservation is satisfied both locally and globally. The method is applicable to both steady and unsteady flows and covers the entire's flow range subcritical, transcritical, and supercritical. One dimensional (1D) flow models usually used in practical. Example model include (HEC-RAS (Brunner, 2006), MIKE11 (DHI, 2002), CCHEID (WU and Vieria, 2002), and SRH-1D Huang, and Greimann, (2007) are these all in Lay, Y. G. (2009)).
Application of one-dimensional (1D) flow model remains, particularly for application with long reaches (more than 50 km) or over a long time period (over a year). Modelling with three-dimensional (3D)-Navier-Stocke,s equation is necessary if flow is the neighboured of hydraulic structures is of interest. In the other words means if the accuracy of more allergic for example the spillway's channel.
In the nature most open channel flows, however, water depth is shallow relative to width and vertical acceleration is negligible in comparison with gravitational acceleration. So three-dimensional (3D) flow can be exactly eliminate to two-dimensional flow. Chiu, C. L. (1988) Explained that the two-dimensional (2D) flow depth averaged model provides the next level of modelling accuracy for many practical open channel flows. Indeed with increasing computational resources two-dimensional (2D) flow model may soon be routinely used for river projects and man open channels with different cross-section.
Arrange of two-dimensional (2D) flow have been developed and applied to a wide range of problems since the work of Chaw and Ben-Zvi, (1973) in Lay, Y. G. (2009). Example include (Horrington et al. (1978), McGurrick and Rodi (1978), Vreugden Hil and wijbenga (1982), Jin and Steffler (1993), Ye and McCorquodale (1997), Gamry and Steffler (2005), Zarrati et al. (2005), Begnudelli and Sanders (2006) are these all in Lay, Y. G. (2009)). The ability of two-dimensional (2D) flow model to solve open channel flows with complex geometries has always been a thrust for improvement as it is relevant to practical applications. One of the recent advances is the use of hierarchical mesh approaches using the adapting meshing as reported by Kra,mar and Jo,sa (2007). An alternative approach is pursued by (Lay, Y. G. 2009) employing a hybrid mesh.
At present, non-orthogonal structured meshes with a curvilinear coordinates system have been widely used with the finite difference method and the finite method framework, while unstructured meshes with fixed cell shape quadrilaterals or triangles have been used with finite element method or finite volume method. Meshing method based on a fixed cell shape and be appropriate for one application but problematic for another?. (Lay, Y. G. 2009)
In general, near-orthogonal quadrilateral cells gives good solutions with added benefit of allowing mesh stretching along the river main channel. Such cells however are restrictive in representing a natural river which typically includes widely different geometric features such as main channels, side channels, and floodplains. Triangular cell are easy to generate and the method alleviates the rigidity of structured mesh in that it allows flexible mesh point clustering.
Unfortunately, stretched triangles are inefficient and less accurate (Baker, 1996, Lay, Y. G. etal. 2003), but mesh stretching is a desirable feature to represent slender characteristics such as channels and levees. For this reason in present study hybrid mesh which is a combination of quadrilaterals and triangles is used. Lay, Y. G. (2008) proved that a good meshing strategy, in terms of efficiency and accuracy, is to represent the main channel and important areas with quadrilaterals and the rest of areas with triangles. Specifically, quadrilateral cells may be used in the main channel and be stretched along the flow direction, while triangular cells may be used to fill the floodplains and bars with mesh density control. Also the advantage of hybrid mesh was recognized by Bernard, and Berger, (1999). They proposed the coupling of two codes: one with structured quadrilateral mesh and another with an unstructured triangular mesh. Lai, Y. G. etal. (2003) proposed methodology is applicable to arbitrary shaped mesh cells not limited to quadrilateral or triangles. The advantage of the arbitrarily shaped cell method is that the some numerical solver is used with most topologies in use, for example, the method may be appropriate with the orthogonal or non-orthogonal structured quadrilateral mesh, and the unstructured triangular mesh, while the hybrid meshes with mixed cell shapes, and the Cartesian mesh can be used with stair cases. Lay, Y. G. (2009) represented the numerical formulation applicable to arbitrary shaped cell for the two-dimensional (2D) depth averaged equations have been represented by . The method is implemented in to numerical model, SRH-2D, and it's applied to a numbers of open channels flow for the purpose of calibrations and verifications. Further validation and verification of the model are achieved by applying the model to a practical nature river flow. the depth averaged parabolic model and the two equation model. For the parabolic model have been developed by Rodi, (1993). The eddy viscosity is calculated as
Finally it has been said by many researchers that turbulent flow is probably the last unsolved problem in classical physics. Certainly it is one of the most important problems in physics and engineering nowadays, since it appears in almost all fluid flows. Many turbulence models have been developed and used in practical calculations. But we should not forget that they are still modes, and so, turbulent motions are not being resolved, but approximated by a model which was developed under some simplifying hypotheses. Nowadays, with the increase of computer power, turbulent flow is starting to be simulated rather than modelled. Which mean that the real equations which govern the fluid motion, including turbulent motion, are being solved? But it is still not possible to perform these kinds of calculations in practical engineering flows. Lay, (2009) argues the real direct equation it will not be possible for at least a hundred years. Thus, turbulence modelling is, and will be necessary for many years.
Conclusion
The main goal of this literature review is to gather more information around how researchers have been solved turbulent flow numerically. The two-dimensional flow modelling of open channel flow have been got accuracy results for classical flow characteristics. The Navier-Stocke,s equations was easy to simulate. The previous study remains unsolved turbulent flow with high value of Reynolds number. Effect of many kind of mesh on solution has been explained. The height of water depth is of most significant flow characteristics during abrupt flood, also for designer s for the purpose design open channels. The cross-section of the open channel especially trapezoidal cross-section has been made problematic during solution because of, unknown of water width. to solve the turbulent flow with long horizontal scale needs invention of computer with high velocity processors more than nowadays exist. amount of free time in the spring term.
