TOWARDS A THEORETICAL MODEL OF LOCALIZED TURBULENT SCOUR TOWARDS A THEORETICAL MODEL OF LOCALIZED TURBULENT SCOUR by 1 Fabián A. Bombardelli and 2 Gustavo.

Slides:

Advertisements

Similar presentations

A mathematical model of steady-state cavitation in Diesel injectors S. Martynov, D. Mason, M. Heikal, S. Sazhin Internal Engine Combustion Group School.

Advertisements

Subgrid-Scale Models – an Overview

Fractal dimension of particle clusters in isotropic turbulence using Kinematic Simulation Dr. F. Nicolleau, Dr. A. El-Maihy and A. Abo El-Azm Contact address:

11 th International Conference on Pressure Surges Lisbon, Portugal, 24 – 26 October 2012 Evaluation of flow resistance in unsteady pipe.

ON WIDTH VARIATIONS IN RIVER MEANDERS Luca Solari 1 & Giovanni Seminara 2 1 Department of Civil Engineering, University of Firenze 2 Department of Environmental.

MODELLING OF CAVITATION FLOW IN A DIESEL INJECTION NOZZLE S. Martynov 1, D. Mason 2, M. Heikal 2 1 Department of Mechanical Engineering, University College.

Boundary Layer Flow Describes the transport phenomena near the surface for the case of fluid flowing past a solid object.

Lecture 9 - Kolmogorov’s Theory Applied Computational Fluid Dynamics

LES of Turbulent Flows: Lecture 10 (ME EN )

Sediment Movement after Dam Removal

Equations of Continuity

1 MECH 221 FLUID MECHANICS (Fall 06/07) Tutorial 7.

MECH 221 FLUID MECHANICS (Fall 06/07) Chapter 9: FLOWS IN PIPE

1 B. Frohnapfel, Jordanian German Winter Academy 2006 Turbulence modeling II: Anisotropy Considerations Bettina Frohnapfel LSTM - Chair of Fluid Dynamics.

CE 1501 CE 150 Fluid Mechanics G.A. Kallio Dept. of Mechanical Engineering, Mechatronic Engineering & Manufacturing Technology California State University,

Lecture 7 Exact solutions

Estimation of Prandtls Mixing Length

Dr. Xia Wang Assistant Professor Department of Mechanical Engineering Tel: Fax: Contact.

FUNDAMENTAL EQUATIONS, CONCEPTS AND IMPLEMENTATION

Similitude and Dimensional Analysis

Torino, October 27, 2009 CNRS – UNIVERSITE et INSA de Rouen Axisymmetric description of the scale-by-scale scalar transport Luminita Danaila Context: ANR.

Dynamic Characteristics of Break Debris Flow and its Numerical Simulation State Key Laboratory of Geohazard Prevention and Geoenvironment Protection Chengdu.

© Arturo S. Leon, BSU, Spring 2010

Nondimensionalization of the Wall Shear Formula John Grady BIEN 301 2/15/07.

Xin Xi. 1946: Obukhov Length, as a universal length scale for exchange processes in surface layer. 1954: Monin-Obukhov Similarity Theory, as a starting.

Turbomachinery Lecture 4a Pi Theorem Pipe Flow Similarity

Governing equations: Navier-Stokes equations, Two-dimensional shallow-water equations, Saint-Venant equations, compressible water hammer flow equations.

Reynolds-Averaged Navier-Stokes Equations -- RANS

1 LES of Turbulent Flows: Lecture 6 (ME EN ) Prof. Rob Stoll Department of Mechanical Engineering University of Utah Spring 2011.

Turbulent properties: - vary chaotically in time around a mean value - exhibit a wide, continuous range of scale variations - cascade energy from large.

Fluid Flow in Rivers Outline 1.Flow uniformity and steadiness 2.Newtonian fluids 3.Laminar and turbulent flow 4.Mixing-length concept 5.Turbulent boundary.

CHAPTER 3 EXACT ONE-DIMENSIONAL SOLUTIONS 3.1 Introduction  Temperature solution depends on velocity  Velocity is governed by non-linear Navier-Stokes.

Unit 1: Fluid Dynamics An Introduction to Mechanical Engineering: Part Two Fluid dynamics Learning summary By the end of this chapter you should have learnt.

Dynamic subgrid-scale modeling in large- eddy simulation of turbulent flows with a stabilized finite element method Andrés E. Tejada-Martínez Thesis advisor:

Title: SHAPE OPTIMIZATION OF AXISYMMETRIC CAVITATOR IN PARTIALY CAVITATING FLOW Department of Mechanical Engineering Ferdowsi University of Mashhad Presented.

WALL FREE SHEAR FLOW Turbulent flows free of solid boundaries JET Two-dimensional image of an axisymmetric water jet, obtained by the laser-induced fluorescence.

Dr. Jason Roney Mechanical and Aerospace Engineering

On Describing Mean Flow Dynamics in Wall Turbulence J. Klewicki Department of Mechanical Engineering University of New Hampshire Durham, NH

CEE 262A H YDRODYNAMICS Lecture 13 Wind-driven flow in a lake.

ITP 2008 MRI Driven turbulence and dynamo action Fausto Cattaneo University of Chicago Argonne National Laboratory.

Convection in Flat Plate Boundary Layers P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi A Universal Similarity Law ……

Compressible Frictional Flow Past Wings P M V Subbarao Professor Mechanical Engineering Department I I T Delhi A Small and Significant Region of Curse.

Dimensional Analysis.

DIMENSIONAL ANALYSIS SECTION 5.

Reynolds Stress Constrained Multiscale Large Eddy Simulation for Wall-Bounded Turbulence Shiyi Chen Yipeng Shi, Zuoli Xiao, Suyang Pei, Jianchun Wang,

Turbulence Models Validation in a Ventilated Room by a Wall Jet Guangyu Cao Laboratory of Heating, Ventilating and Air-Conditioning,

Boundary Layer on a Flat Plate: Blasius Solution H z from Kundu’s book Assuming displacement of streamlines is negligible →u = U = constant everywhere,

1 GMUWCollaborative Research Lab Advanced Turbulence Modeling for engine applications Chan Hee Son University of Wisconsin, Engine Research Center Advisor:

Convergence Studies of Turbulent Channel Flows Using a Stabilized Finite Element Method Andrés E. Tejada-Martínez Department of Civil & Environmental Engineering.

Formulations of Longitudinal Dispersion Coefficient A Review:

The Standard, RNG, and Realizable k- Models. The major differences in the models are as follows: the method of calculating turbulent viscosity the turbulent.

Advanced Numerical Techniques Mccormack Technique CFD Dr. Ugur GUVEN.

Introduction to the Turbulence Models

Titolo presentazione sottotitolo

Coastal Ocean Dynamics Baltic Sea Research Warnemünde

Reynolds-Averaged Navier-Stokes Equations -- RANS

Introduction to Symmetry Analysis

The k-ε model The k-ε model focuses on the mechanisms that affect the turbulent kinetic energy (per unit mass) k. The instantaneous kinetic energy k(t)

On the Hierarchical Scaling Behavior of Turbulent Wall-Flows

Dimensional Analysis.

Fluid flow in an open channel

Sunny Ri Li, Nasser Ashgriz

9th Lecture : Turbulence (II)

Bed material transport

Turbulent Kinetic Energy (TKE)

Turbulent properties:

L.V. Stepanova Samara State University

CN2122 / CN2122E Fluid Mechanics

Presentation transcript:

TOWARDS A THEORETICAL MODEL OF LOCALIZED TURBULENT SCOUR TOWARDS A THEORETICAL MODEL OF LOCALIZED TURBULENT SCOUR by 1 Fabián A. Bombardelli and 2 Gustavo Gioia 1 Assistant Professor Department of Civil and Environmental Engineering, University of California, Davis 2 Department of Theoretical and Applied Mechanics, University of Illinois, Urbana- Champaign

Motivation Motivation Intermediate asymptotics. Dimensional analysis Intermediate asymptotics. Dimensional analysis Methodology for the case of jet-induced erosion: Methodology for the case of jet-induced erosion: Application of dimensional analysis Application of dimensional analysis Imposing of the incomplete similarity Imposing of the incomplete similarity Derivation of an expression for the turbulent shear stress on the bed using the phenomenological theory of turbulence Derivation of an expression for the turbulent shear stress on the bed using the phenomenological theory of turbulence Derivation of the equation and the similarity exponent Derivation of the equation and the similarity exponent Validation of results with available measurements Validation of results with available measurements Outline

Motivation I

Motivation II Applications Applications Erosion below dams Erosion below dams Scour below flip buckets Scour below flip buckets Scour downstream pipe outlets Scour downstream pipe outlets

Motivation III Notably large number of experimental evidence from last century: Notably large number of experimental evidence from last century: Schoklitsch (1932) Schoklitsch (1932) Veronese (1937) Veronese (1937) Eggenberger and Muller (1944) Eggenberger and Muller (1944) Hartung (1959) Hartung (1959) Franke (1960) Franke (1960) Kotoulas (1967) Kotoulas (1967) Chee and Padiyar (1969) Chee and Padiyar (1969) Chee and Kung (1974) Chee and Kung (1974) Machado (1980) Machado (1980) Mason and Arumugam (1985) Mason and Arumugam (1985) Yuen (1984) Yuen (1984) Bormann and Julien (1991) Bormann and Julien (1991) Stein et al. (1993) Stein et al. (1993) Chen and Lu (1995) Chen and Lu (1995) D’Agostino and Ferro (2004) D’Agostino and Ferro (2004) Drawbacks of some of the formulas: 1)They often lack dimensional homogeneity. 2)They often have been the result of mangled attempts at dimensional analyses. 3)They are often predicated on limited experimental data. 4)They sometimes disregard the importance of the bed particle size.

Motivation IV Questions: Questions: Can we improve existing dimensional analyses? Can we improve existing dimensional analyses? Can we obtain a completely theoretical expression for the maximum scour depth? Can we obtain a completely theoretical expression for the maximum scour depth? Can we interpret physically the exponents of the equation through the theory of turbulence? Can we interpret physically the exponents of the equation through the theory of turbulence?

Motivation Motivation Intermediate asymptotics. Dimensional analysis Intermediate asymptotics. Dimensional analysis Methodology for the case of jet-induced erosion: Methodology for the case of jet-induced erosion: Application of dimensional analysis Application of dimensional analysis Imposing of the incomplete similarity Imposing of the incomplete similarity Derivation of an expression for the turbulent shear stress on the bed using the phenomenological theory of turbulence Derivation of an expression for the turbulent shear stress on the bed using the phenomenological theory of turbulence Derivation of the equation and the similarity exponent Derivation of the equation and the similarity exponent Validation of results with available measurements Validation of results with available measurements Outline

Intermediate asymptotics I Barenblatt analysis Dimensional analysis (Buckingham Pi Theorem)

Intermediate asymptotics II Barenblatt analysis n Question: What happens with the function when the variable is very small or very large? Cases: n There is a limit, it is finite and non-zero: C n The limit is NOT finite COMPLETE SIMILARITY

Intermediate asymptotics III Barenblatt analysis n Third case: INCOMPLETE SIMILARITY – POWER LAWS!!! INTERMEDIATE LIMIT

Intermediate asymptotics III Barenblatt analysis n Example: velocity distribution in a turbulent flow in an open channel COMPLETE SIMILARITY – LAW OF THE WALL!!! INCOMPLETE SIMILARITY – POWER LAW!!!

Motivation Motivation Intermediate asymptotics. Dimensional analysis Intermediate asymptotics. Dimensional analysis Methodology for the case of jet-induced erosion: Methodology for the case of jet-induced erosion: Application of dimensional analysis Application of dimensional analysis Imposing of the incomplete similarity Imposing of the incomplete similarity Derivation of an expression for the turbulent shear stress on the bed using the phenomenological theory of turbulence Derivation of an expression for the turbulent shear stress on the bed using the phenomenological theory of turbulence Derivation of the equation and the similarity exponent Derivation of the equation and the similarity exponent Validation of results with available measurements Validation of results with available measurements Outline

Dimensional analysis and similarity Partial result. It depends only on one exponent What happens with P when d/R tends to 0? We assume INCOMPLETE SIMILARITY on d/R !!

Motivation Motivation Intermediate asymptotics. Dimensional analysis Intermediate asymptotics. Dimensional analysis Methodology for the case of jet-induced erosion: Methodology for the case of jet-induced erosion: Application of dimensional analysis Application of dimensional analysis Imposing of the incomplete similarity Imposing of the incomplete similarity Derivation of an expression for the turbulent shear stress on the bed using the phenomenological theory of turbulence Derivation of an expression for the turbulent shear stress on the bed using the phenomenological theory of turbulence Derivation of the equation and the similarity exponent Derivation of the equation and the similarity exponent Validation of results with available measurements Validation of results with available measurements Outline

Phenomenological theory of turbulence and bed shear stress Based on two tenets: a) The production of TKE occurs at large scales b) The rate of production of TKE is independent of viscosity Large scales Small scales

Phenomenological theory of turbulence and bed shear stress We surmise that the excess of energy of the jet converts to TKE The eddy close to the wall belongs to the inertial sub-range

Phenomenological theory of turbulence and bed shear stress Predicts nicely the scalings of Strickler, Manning and Blasius (Gioia and Bombardelli, 2002)

Phenomenological theory of turbulence and scour equation Kolmogorov-Taylor scaling Final result: α = 1 Shields stress

Motivation Motivation Intermediate asymptotics. Dimensional analysis Intermediate asymptotics. Dimensional analysis Methodology for the case of jet-induced erosion: Methodology for the case of jet-induced erosion: Application of dimensional analysis Application of dimensional analysis Imposing of the incomplete similarity Imposing of the incomplete similarity Derivation of an expression for the turbulent shear stress on the bed using the phenomenological theory of turbulence Derivation of an expression for the turbulent shear stress on the bed using the phenomenological theory of turbulence Derivation of the equation and the similarity exponent Derivation of the equation and the similarity exponent Validation of results with available measurements Validation of results with available measurements Outline

Validation with experiments 3D, axisymmetric case: Bombardelli and Gioia, 2005, submitted

Validation with experiments R measured (m) R computed (m)

Conclusions Dimensional analysis is a powerful technique but it does not provide the values of the exponents. The phenomenological theory of turbulence is the key to address the dynamics. Dimensional analysis is a powerful technique but it does not provide the values of the exponents. The phenomenological theory of turbulence is the key to address the dynamics. The exponents are driven by the Kolmogorov- Taylor scaling, signaling the effect of momentum transfer (clear physical meaning). The exponents are driven by the Kolmogorov- Taylor scaling, signaling the effect of momentum transfer (clear physical meaning). The dimensional analysis in terms of the power of the jet is crucial in exposing the correct factors that govern the scour problem. The dimensional analysis in terms of the power of the jet is crucial in exposing the correct factors that govern the scour problem. The final expression for scour is purely theoretical and agrees with data and existing formulas. The final expression for scour is purely theoretical and agrees with data and existing formulas.