Alma Mater Studiorum - Università di Bologna FACOLTÀ DI SCIENZE MATEMATICHE, FISICHE E NATURALI Corso di Laurea specialistica in Fisica Dipartimento di Fisica UNDULAR JUMP NUMERICAL MODEL AND SENSITIVITY ANALYSIS Tesi di laurea di: Relatore: MICHELE RAMAZZA Prof. RAMBALDI SANDRO Correlatori: Prof. MANSERVISI SANDRO Dott. CERVONE ANTONIO Sessione III Anno Accademico 2007-2008 2 CONTENTS Abstract................................................................................................................................................5 Sommario.............................................................................................................................................5 List of symbol ....................................................................................................................................6 1.Introduction ....................................................................................................................................8 1.1.Open channel flow.................................................................................................................8 1.1.1.Introduction....................................................................................................................8 1.1.2.Classification of open channel flows.........................................................................8 1.1.3.Complexity ....................................................................................................................8 1.2.Bases of open channel hydraulics ...................................................................................10 1.2.1.Supercritical and subcritical flows..........................................................................10 1.2.2.Momentum equation..................................................................................................11 1.2.3.Momentum function...................................................................................................11 1.2.4.Critical Flow ...............................................................................................................12 1.3.Hydraulic jump ....................................................................................................................12 1.3.1.Definition of hydraulic jump....................................................................................12 1.3.2.Undular jump...............................................................................................................13 1.3.3.Undular bore................................................................................................................14 1.3.4.Morning Glory............................................................................................................15 1.3.5.Two dimensional Approach.....................................................................................16 1.3.6.Momentum function balance...................................................................................16 1.3.7.Undular surge, state of art ......................................................................................17 2.Open channel numerical modelling.........................................................................................18 2.1.Fluent......................................................................................................................................18 2.1.1.Introduction for open channel simulations with Fluent...................................18 2.1.2.User steps for open channel flow simulations ....................................................18 2.2.Generic fluid flow equations ............................................................................................19 2.2.1.Variables........................................................................................................................19 2.2.2.Continuity and momentum equations ..................................................................19 2.2.3.Transport equation discretization..........................................................................19 2.2.4.Time evolution ............................................................................................................20 2.2.5.Evaluation of gradients and derivatives ...............................................................21 2.3.Volume of fluid, VOF..........................................................................................................21 2.3.1.Overview ......................................................................................................................21 2.3.2.Geo-reconstruction method.....................................................................................21 2.4.Pressure based solver ........................................................................................................22 2.4.1.Overview of pressure based solver.........................................................................22 2.4.2.Discretization of continuity and momentum equations....................................22 2.4.3.Coupled solver ............................................................................................................23 2.4.4.Multigrid method.......................................................................................................23 2.5.Grid ........................................................................................................................................23 2.6.Standard turbulence model...............................................................................................24 2.7.Wall functions ......................................................................................................................25 3.Undular jump simulation............................................................................................................27 3.1.Numerical modelling ........................................................................................................27 3.1.1.Introduction to undular jump simulation.............................................................27 3.1.2.Operating conditions..................................................................................................27 3.1.3.Boundary: velocity inlet ...........................................................................................28 3 3.1.4.Boundary: turbulent inlet quantities ....................................................................28 3.1.5.Boundary: pressure outlet.........................................................................................29 3.1.6.Standard channel.........................................................................................................29 3.2.Model validation .................................................................................................................30 3.2.1.Grid sensitivity ...........................................................................................................30 3.2.2.Outlet sensitivity .......................................................................................................33 3.2.3.Turbulent inlet sensitivity........................................................................................33 3.2.4.Undular jump experiment .......................................................................................36 3.2.5.Free surface data comparison .................................................................................37 3.3.Undular jump fields.............................................................................................................38 3.3.1.Velocity fields ..............................................................................................................38 3.3.2.Static pressure profiles...............................................................................................38 3.3.3.Vorticity field...............................................................................................................40 3.4.Undular jump sensitivity analysis...................................................................................41 3.4.1.Velocity inlet profile ..................................................................................................41 3.4.2.Turbulent kinetic energy .........................................................................................44 3.4.3.Froude number ...........................................................................................................45 3.4.4.Instability for critical waves.....................................................................................49 4.Conclusions....................................................................................................................................51 4.1.Undular jump ......................................................................................................................51 4.1.1.General considerations..............................................................................................51 4.1.2.Necessary parametrized models..............................................................................51 4.1.3.Sensitivity.....................................................................................................................52 4.1.4.Essential physical conditions...................................................................................52 4.1.5.Wave characteristic, dependencies from Froude number.................................52 4.2.Applicability of the model