Physical and Computation Modelling of Turbidity Currents

Preparing to load PDF file. please wait...

0 of 0
100%
Physical and Computation Modelling of Turbidity Currents

Transcript Of Physical and Computation Modelling of Turbidity Currents

Physical and Computation Modelling of Turbidity Currents: The Role of
Turbulence-Particles Interactions and Interfacial Forces
Ke San Yam
Submitted in accordance with the requirements for the degree of Doctor of Philosophy
The University of Leeds School of Earth & Environment,
December 2012

The candidate confirms that the work submitted is his own, except where work which has formed part of jointly-authored publications has been included. The contribution of the candidate and the other authors to this work has been explicitly indicated below. The candidate confirms that appropriate credit has been given within the thesis where reference has been made to the work of others. Chapter 3 is based on the following paper: Yam, K; McCaffrey, WD; Ingham, DB; Burns, AD CFD modelling of selected laboratory turbidity currents. Journal of Hydraulic Research, vol. 49, pp. 657-666. The candidate is the primary author of the paper. This copy has been supplied on the understanding that it is copyright material and that no quotation from the thesis may be published without paper acknowledgement.
© 2012 The University of Leeds and Ke San Yam

i
Abstract
Experimental and numerical investigations have been conducted in order to evaluate the accuracy of the Mixture Model, a depth-resolved and time-averaged multiphase numerical model, in predicting the behaviour of dilute surge-type turbidity currents. The effects of turbulent dispersion and turbulence modulation upon sediment transport within turbidity currents are directly modelled via their incorporation into the Mixture Model. Modelled predictions of flow front propagation and deposit density are compared against both experimental data and refined two-fluids model from previous studies. When modelled using the formulation of Chen & Wood (1985), turbulence modulation does not affect on the propagation of dilute turbidity currents significantly. Turbulent dispersion can be modelled by incorporating the formulation of Simonin (1991) into the slip equation of the Mixture Model. Its effect is strongest in dilute flows carrying fine particles and diminishes when either grain size or flow concentration increases. Modelled turbulent dispersion effects are too strong in simulations of flows carrying silicon carbide particles; Mixture Model simulations agree poorly with both experimental data or refined two-fluids model results of the deposit mass profile. Yet turbulent dispersion is essential to ensure that model predictions of flows carrying glass beads compare well with experimental data. The reasons for the discrepancy between modelling approaches best suited to each of these flow types remains poorly understood.
A new analytical approach is developed to evaluate the effect of the lift force on particles of small, intermediate and large particle Reynolds number immersed in two-dimensional shear flows. The lift force always reduces the magnitude of the particle settling velocity and may push particles forward or backward, depending on the sign of both the lift coefficient and the flow vorticity. Given plausible velocity profiles within natural turbidity currents, the effect of lift force on the sand-like particles immersed in such turbidity currents is negligible. It may become significant when the ratio of the particle density to the flow density approaches unity.
New experiments are presented for flows over the flow concentration range 0.25 – 5% and grain size range 58 - 115µm. The data are used to facilitate a more complete validation of the Mixture Model, based on flow front propagation rates, deposit mass density and deposit grain characteristics. Modelling results for first two variables are in good agreement with the experimental data, when turbulent dispersion effects are incorporated. For reasons which remain unclear, the model cannot simulate the unexpected experimental result that deposit grain size is largely unfractionated if the standard deviation of the source material is less than 11 but significantly fractionated if it exceeds 18. This discrepancy requires further work.

ii
Acknowledgements
I would like to express my gratitude to my supervisors, Profs. Bill McCaffrey, Derek Ingham and Dr. Alan Burns for the guidance and support they have given during the progress of this project. Without their constant encouragement and sound advice, I would have never been able to complete this work. Their diligent proof reading has significantly improved the text of this thesis, and the prompt return of chapters was much appreciated.
I also would like to thank Turbidite Research Group (TRG) for sponsoring this project. Without the financial supports from TRG, I would never had the opportunity to undertake this research.
Thanks to Gareth, Russ and Kat in assisting me in setting-up and develop a proper methodology for the lock-release experiments.
Thanks to my office mates Nic Yin, Ya Dong, Tao Wei, Andy, Chris, Kieran, and Lindsey.
Finally, I would like to thank my families for their unwavering love and supports throughout my life.

iii
Table of Contents
Abstract....................................................................................................................... i Acknowledgements.................................................................................................... ii Table of Contents .....................................................................................................iii List of Tables ............................................................................................................ vi List of Figures.......................................................................................................... vii Nomenclature .......................................................................................................... xv Chapter 1 Introduction............................................................................................. 1
1.1 Research Rationale...................................................................................... 1 1.2 Aims of Thesis ............................................................................................ 2 1.3 Thesis Structure............................................................................................ 3 Chapter 2 Literature Review ................................................................................... 4 2.1 Introduction................................................................................................. 4 2.2 Origins of Turbidity Currents ..................................................................... 4 2.3 Laboratory Turbidity Currents .................................................................... 5 2.4 Dynamics of Turbidity Currents ................................................................. 8
2.4.1 General Description ......................................................................... 8 2.4.2 Front Propagation........................................................................... 10 2.4.3 Velocity Profiles ............................................................................ 10 2.4.4 Concentration Profiles.................................................................... 12 2.4.5 Flow Turbulence ............................................................................ 15 2.4.6 Deposit Characteristics .................................................................. 16 2.5 Physics Within Turbidity Currents ........................................................... 17 2.5.1 Particle Interfacial Forces .............................................................. 20
2.5.1.1 Drag Force......................................................................... 20 2.5.1.2 Lift Force........................................................................... 21 2.5.2 Turbulence ..................................................................................... 22 2.5.2.1 Single-phase flow.............................................................. 22 2.5.2.2 Multiphase flow ................................................................ 24 2.5.3 Turbulent Dispersion...................................................................... 29 2.5.4 Mixture Model and Slip Equation.................................................. 32 2.5.5 Near Wall Dynamics ...................................................................... 34 2.6 Theoretical Model For Turbidity Currents................................................ 39 2.6.1 Integral Box Models....................................................................... 39

iv
2.6.2 Shallow Water Models................................................................... 40 2.6.3 Depth Resolved Models ................................................................. 42 2.7 Conclusion ................................................................................................ 44 Chapter 3 Modelling 2D Particle Laden Lock-Release Flows ............................ 45 3.1 Introduction............................................................................................... 45 3.2 Mixture Model .......................................................................................... 47 3.3 Validation Data ......................................................................................... 48 3.4 Numerical Approach ................................................................................. 51 3.5 Boundary Conditions ................................................................................ 52 3.6 Simulation Setup ....................................................................................... 54 3.7 Numerical Accuracy ................................................................................. 55 3.8 Simulation Results and Discussion ........................................................... 57 3.8.1 Temporal Flow Evoluation ............................................................ 57 3.8.2 Rate of Propagation and Total Mass in Suspension....................... 61 3.8.3 Depositional Patterns ..................................................................... 64 3.8.4 Vertical Structure ........................................................................... 76 3.9 Conclusions............................................................................................... 80 Chapter 4 The Influence of Lift Force On the Settling Velocities of Rotating Particles In 2D Flows ..................................................................... 82 4.1 Introduction............................................................................................... 82 4.2 Literature Review...................................................................................... 83 4.3 Balance of the Drag and Lift Forces With Gravity ................................... 90 4.3.1 Drag Force Analysis....................................................................... 90 4.3.2 Combined Drag and Lift Force Analysis ....................................... 93 4.3.3 Small Particle Reynolds Number Limit ......................................... 98 4.3.4 High Particle Reynolds Number Limit .......................................... 99 4.3.5 Intermediate Particle Reynolds Number (Semi Analytical) ........ 102 4.3.6 Intermediate Particle Reynolds Number (Numerical) ................. 105 4.4 Implications............................................................................................. 108 4.4.1 General Considerations ................................................................ 109 4.4.2 Turbidity Currents........................................................................ 109 4.4.3 Particle Entrainment..................................................................... 112 4.5 Conclusions ............................................................................................ 114 Chapter 5 Physical and Numerical Modelling of Lock-Release Turbidity Currents ........................................................................................................ 115 5.1 Introduction............................................................................................. 115

v
5.2 Objectives................................................................................................ 116 5.3 Experimental Techniques........................................................................ 116
5.3.1 Material Size ................................................................................ 118 5.3.2 Experimental Procedure ............................................................... 122 5.3.3 Measurement Techniques Verification ........................................ 125 5.4 Experimental Programme ....................................................................... 128 5.5 Experimental Results and Discussions ................................................... 130 5.5.1 Flow Images ................................................................................. 130 5.5.2 Front Propagation......................................................................... 133 5.5.3 Deposit Mass Density .................................................................. 136 5.5.4 Deposit Grain size Distribution.................................................... 140 5.6 Numerical Modelling .............................................................................. 144 5.7 Model Details and Assumptions ............................................................. 145 5.8 Simulation Validation ............................................................................. 145 5.9 Simulation Result.................................................................................... 149 5.9.1 Deposit Total Mass Density......................................................... 150 5.9.2 Individual Grain Size Deposit Mass Density ............................... 159 5.9.3 Front Propagation and Total Mass in Suspension........................ 164 5.9.4 Concentration Field...................................................................... 169 5.9.5 TD Distribution ............................................................................ 174 5.10 Conclusions............................................................................................ 177 Chapter 6 Concluding Remarks .......................................................................... 180 6.1 Thesis Summary...................................................................................... 180 6.2 Key Conclusions ..................................................................................... 183 6.3 Future Work ............................................................................................ 185 References .............................................................................................................. 188 Appendix ................................................................................................................ 201 A1. Turbulence Modulation ........................................................................... 201 A2. Simulation Detail .................................................................................... 206 A3. Flows Carrying Non-Spherical Particles................................................. 210

vi
List of Tables
2.1 Measurements performed on the ‘sustained’ surged-typed particulate density currents conducted in the past ............................................................... 7
2.2 Measurements performed on the ‘lock-release’ surge-typed saline or particulate density currents conducted in the past ............................................. 8
3.1 Experiments on the lock-release generated turbidity currents ........................... 49 3.2 Experimental flows used in this thesis for validating the Mixture Model .......... 50 3.3 Formulae for parameters used in this thesis ........................................................ 51 3.4 Details of the mesh used to simulate the flows of (a) Gladstone et al.
(1998) (Domain length = 8m, domain height = 0.4m), and (b) Gladstone & Pritchard (2009) (Domain length = 6m, domain height = 0.2) ................... 55 4.1 Previous investigations on the lift force on a particle immersed in a linear shear or parabolic flow .................................................................................... 89 5.1 The size and hydraulic characteristics of each material investigated................. 120 5.2 Series A Experiments ........................................................................................ 129 5.3 Series B Experiments. Each flow used Grade 0-100(2)), but in differing initial concentrations...................................................................................... 129 5.4 Series C Experiments ........................................................................................ 129 5.5 Detail of different mesh used in this study........................................................ 146 5.6 The value of λ of flows of Experiments A, B and C for the Mixture Model both with and without TD.............................................................................. 157 5.7 Size ranges and the mean size of the particle in the flows for Experiment A. The mean size is listed in the brackets...................................................... 162 A2.1 Numerical schemes employed for each simulation .......................................... 206 A2.2 Convergence criteria......................................................................................... 206 A2.3 Simulations on flows investigated in Chapter 3 ............................................... 208 A2.4 Simulations on flows investigated in Chapter 5 ............................................. 209

vii
List of Figures
2.1 Schematic diagram showing (a) a lock box configuration for producing a fixed volume turbidity currents employed in Gladstone et al. (1998), (b) a configuration for producing a quasi-steady turbidity current employed in Garcia (1994), and (c) a configuration for producing a stationary head of a turbidity current employed in Simpson & Britter (1979)........................... 7
2.2 Photograph showing (a) the structure of a compositional gravity current, reproduced from Simpson and Britter (1979), and (b) a turbidity currents, reproduced from Gladstone & Woods (2000). Both flows are produced using the lock-release configuration .................................................. 9
2.3 A Direct Numerical Simulation of a lock-release generated saline gravity current showing the structure of lobe breakdown and cleft formation at an advancing gravity current head, reproduced from Haartel et al. (2000)....... 9
2.4 Schematic diagram on the definitions of a typical turbidity current velocity profile of the Ellison & Turner (1959) ............................................. 11
2.5 Dimensionless velocity profile of a turbidity currents flowing on different beds (reproduced from Sequeiros et al., 2010) ................................ 12
2.6 Experimental predictions on the concentration profile of a turbidity current flow in (a) flat bed, reproduced from Garcia (1994), and (b) different bed roughness, reproduced from Sequeiros et al. (2010) ................ 14
2.7 A measurement on the concentration distribution within a turbidity current at five different downstream locations, for flows with a 14% initial concentration, reproduced from Choux et al. (2004) ........................... 14
2.8 Numerical predictions on the concentration distribution on gravity currents carrying (a) salt, (b) silt, (c) fine sand, and (d) coarse sand, reproduced from Felix (2002) ......................................................................... 14
2.9 (a) Measurements on the time-series downstream and vertical velocities of a lock-release saline gravity currents at downstream 800mm and height 7mm. (b) Streamwise and vertical components of the turbulent kinetic energy per unit mass as a function of height within the current, reproduced from Kneller et al. (1997) ............................................................ 15
2.10 Percentage change in turbulent intensity of flows carrying particles as function of the ratio o the particle size to eddy length scale, reproduced from Gore & Crowe (1989) ............................................................................ 28
2.11 Plot of ௅ as a function of (reproduced from Tanaka & Eaton, 2008) ......................................................................................................................... 28

viii
2.12 Plot of ∗ as a function of the particle Reynolds number ௣ with experimental data (circle) and the criteria proposed by Shields (1936), Van Rijn (1984), and Bagnold (1966), reproduced from Niño et al. (2003) .............................................................................................................. 39
3.1 Mixture Model prediction on the final deposit mass density as a function of the downstream distance of flows (a) G69, and (b) G37 based on different mesh sizes. See Table 3.1 & 3.2 for the detail of the mesh. The employed time step is 0.01s............................................................................. 56
3.2 Mixture Model prediction on the final deposit mass density as a function of the downstream distance of flows (a) G69, and (b) G37 based on different time steps (0.05s, 0.02s, 0.01s, 0.005s). .......................................... 56
3.3 Prediction from the Mixture Model without TD (left), and the Mixture Model with TD (right), on the concentration field of flows G69 at t = 0, 5, 10, 15, and 20s............................................................................................. 59
3.4 Prediction from the Mixture Model without TD (top), and (b) the Mixture Model with TD (bottom), on the concentration field of flows G25 at t = 0, 20, 40, 60, and 80s...................................................................... 59
3.5 Prediction from the (a) the Mixture Model without TD, and (b) the Mixture Model with TD, on the concentration field of flows G37 at t = 0, 5, 10, 15, and 20s. ....................................................................................... 60
3.6 Prediction from the (a) the Mixture Model without TD, and (b) the Mixture Model with TD, on the concentration field of flows G13at t = 0, 10, 20, 30, and 40s. ......................................................................................... 60
3.7 Prediction from the Mixture Model without TD (top), and (b) the Mixture Model with TD (bottom), on the concentration field of flows D37 at t = 0, 5.5, 10.5, 15.5, and 20.5s............................................................ 61
3.8 Prediction from the Mixture Model without () and with TD () on the total percentage mass in the suspension (left axis) and the rate of propagation of the front (right axis) of the flows (a) G69, (b) G25, (c) G37, (d) G13, and (e) D37. The symbols in (a – b) refer to data from Gladstone et al. (1998) .................................................................................... 63
3.9 The difference between the prediction of the Mixture Model without and that with TD on the total for flows G69 (black), G25 (red), G37 (blue), G13 (green) and D37 (purple) ........................................................................ 64
3.10 Combined plot of the prediction of the Mixture Model without TD on the front of propagation of flows G69 (black), G25 (red), G37 (blue), G13 (green) and D37 (purple) ................................................................................ 64
Mixture ModelFlowsTurbidity CurrentsDataFunction