characteristics in channels with gradual width expansion and contraction are ...
The main difficulties in modeling complex open channel flows are dealing with.
CITY UNIVERSITY OF HONG KONG 香港城市大學
Experimental and Numerical Studies of Complex Open Channel Flows 複雜明渠水流的實驗與數值模擬研究
Submitted to Department of Civil and Architectural Engineering 土木及建築工程系 in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy 哲學博士學位
by
Yang Qingyuan 楊青遠
August 2012 二零一二年八月
Abstract The flow phenomena in three channel types, i.e., open channel, confluence channel, and bend channel are investigated in this project. Furthermore, flow characteristics in channels with gradual width expansion and contraction are also studied in both experimental and numerical ways. The flows, that rapidly change either directions or widths, induce strong secondary circulation, surface slope variation, and boundary separation. The flow structures in these channels are rather different from those in straight channels. In experimental study, a three dimensional, supersonic velocity detector (Acoustic Doppler Velocimeter, ADV) is used to obtain components of instantaneous velocity. A series of flume tests have been carried out to study turbulence, velocity distribution and energy dissipation of flows in the selected channels. The results not only provide detailed flow properties but sound base for verification and validation of numerical models. The main difficulties in modeling complex open channel flows are dealing with the free surface and eddy viscosity. In this study, both two-dimensional, depthaveraged models and three-dimensional models are adopted to simulate the flows in the three typical channels. For two dimensional simulations, a self-written program coupled with Large Eddy Simulation (LES) and implemented by several turbulence models is developed to investigate different scales of flow properties. For three dimensional simulations, commercial software Fluent coupled with selfprogrammed, free surface tracking is used. During the simulation, several turbulence models are adopted to estimate their impact on the simulation accuracy.
II Investigations of flow in confluence channels show that the strength of secondary circulation is flow-condition-dependent and is affected by the ratio flow rate of the branch channel to the main channel. The circulation is weak when the low flow rate ratio is low, confluence flow exhibits two-dimensional characteristics and can be approximately simulated by two-dimensional models. Under the case of high flow rate ratio, the circulation becomes strong, where the effects of secondary circulation cannot be neglected in the simulation. Reasonable results can be obtained only by using three-dimensional models together with proper free surface tracking. The key elements for simulation of confluence flow are also presented. The exploration of flow in bend channel demonstrates that the strength of secondary circulation and the transverse surface slope largely depend on the water level near the tail gate under the same flow rate. When the level is high, flow in bend channel moves slowly, circulation is weak, and the transverse surface is nearly flat. This situation can be modeled by the two-dimensional model without correction of secondary circulation; good agreement is found with the measurement. On the contrary, when the water level is low, flow in bend channel is faster, with strong secondary circulation and steep transverse surface slope. Hence, in numerical simulations, high accuracy can only be achieved by using three-dimensional or two-dimensional models with proper correction of the secondary circulation. Studies on flows in channels with changing widths indicate that the flow performs like hydraulic jump near the expansion and hydraulic fall in the vicinity of contraction. The transition from hydraulic fall to hydraulic jump generates rapid changes in water surface and velocity and induces strong secondary circulation.
III The two-dimensional simulations of water level present good agreement with the experimental data, but the simulated velocity profiles at expansion parts agree poorly with the experimental data. The accuracy of two-dimensional simulation is also flow-condition-dependent. The flow is also studied by three-dimensional simulations and the self-programmed codes perform well in tracking the water surface. The first major contribution of this study is that the characteristics of flows in three typical open channels are investigated, which provide references for further studies and solving similar problems in engineering applications. The second contribution is to develop and verify the self-written codes to tackle the depthaveraged shallow water equations and the complex open channel flows. Furthermore, codes for free surface tracking in three-dimensional simulations are also developed, which enhance accuracy and save computational time and resources in simulations compared to those utilizing the surface capturing methods.
IV
List of keywords Confluence river Open channel junction Surface tracking Pressure based surface tracking Bend flow Expansion Contraction LBM LES Depth-averaged models
VI
Contents
Abstract................................................................................................................ I List of keywords................................................................................................ IV Acknowledgments ............................................................................................... V Contents ............................................................................................................ VI List of figures .................................................................................................... IX List of tables.................................................................................................... XIII Nomenclature ..................................................................................................XIV Chapter 1
Introduction ....................................................................................1
1.1
Research motivation ...........................................................................1
1.2
Research objectives ............................................................................7
1.3
Outline of thesis ..................................................................................8
Chapter 2 2.1
2.2
Theoretical background .................................................................10 Governing equations .........................................................................10 2.1.1
Time-averaged equations .......................................................10
2.1.2
Space-averaged equation ........................................................12
2.1.3
Numerical solving of governing equations .............................14
2.1.4
Free surface tackling ..............................................................16
2.1.5
Depth-averaged equations ......................................................19
2.1.6
Lattice Boltzmann method .....................................................21
Flows in open channel ......................................................................27 2.2.1
Uniform open channel flow ....................................................27
2.2.2
Hydraulic jump ......................................................................31
2.2.3
Hydraulic fall .........................................................................31
2.2.4
Separation flow ......................................................................32
VII
Chapter 3 3.1
2.2.5
Free shear flow ......................................................................32
2.2.6
Equipment for velocity measurement .....................................33
Studies of flow in confluence channel ...........................................35 Experimental studies of flow in confluence channel ..........................39 3.1.1
Turbulence properties of flow in confluence channel..............39
3.1.2 Vertical non-uniformity of velocity distribution of flow in confluence channel .............................................................................45 3.2
3.3 Chapter 4 4.1
Numerical simulations of flow in confluence channel .......................53 3.2.1
Two-dimensional simulations of flow in confluence channel .. 53
3.2.2
LBM based LES of flow in confluence channel......................62
3.2.3
Three-dimensional simulations of flow in confluence channel 65
Conclusion .......................................................................................73 Studies of flow in bend channel.....................................................74 Experimental studies of flow in bend channel ...................................77 4.1.1 Vertical non-uniformity of velocity distribution of flow in bend channel 77
4.2
4.3 Chapter 5
4.1.2
Section circulation of bend flow .............................................79
4.1.3
Tangent velocity distribution ..................................................81
Numerical simulations of flow in bend channel.................................83 4.2.1
Two dimensional simulation of bend flow ..............................83
4.2.2
Three dimensional simulation of bend flow ............................87
Conclusion .......................................................................................94 Studies of flow in channel with width expansion and contraction ..95
5.1 Experimental studies of flow in channel with expansion and contraction..................................................................................................97 5.1.1
The velocity and water level variation ....................................99
5.1.2
Vertical non-uniformity of velocity distribution .....................99
5.1.3
Distribution of longitude velocity and section circulation ..... 101
VIII 5.2 Numerical simulations of flow in channel with expansion and contraction................................................................................................ 103 5.2.1 Two-dimensional numerical simulation of flow in channel with expansion and contraction ................................................................. 103 5.2.2 Three-dimensional numerical simulation of flow in channel with expansion and contraction ......................................................... 107 5.3 Chapter 6
Conclusion ..................................................................................... 111 Summary and future work ........................................................... 112
6.1
Summary ........................................................................................ 112
6.2
Future work .................................................................................... 114
List of publications ........................................................................................... 115 References........................................................................................................ 117
