Project Topic. Simulation of turbulent flow laden with finite-size particles using LBM. Leila Jahanshaloo

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1 Project Topic Simulation of turbulent flow laden with finite-size particles using LBM Leila Jahanshaloo

2 Project Details Turbulent flow modeling Lattice Boltzmann Method All I know about my project Solid-liquid Interaction Write code in Matlab

3 Gantt Chart Goals Oct- 11 Nov- 11 Dec- 11 Jan- 12 Feb- 12 Mar- 12 Apr- 12 May- 12 Jun- 12 Jul- 12 Aug- 12 Sep Primary Study Turbulent Flow Turbulent Modelling Topic Selection Secondary study Literature Review Objectives Definition Topic Finalization Methodology Development Proposal Writing

4 Everyday Life,Turbulence observation Turbulence

5 Osborn Reynolds Experiment The term turbulence was introduced by Reynolds and denotes the irregular stochastic motion of all fluid elements. critical Reynolds number for the transition from laminar to turbulent flow was

6 Types of Fluid Flow Laminar Flow Layers of water flow over one another at different speeds with virtually no mixing between layers. Turbulent Flow The flow is characterized by the irregular movement of particles of the fluid.

7 Why study turbulence? Almost all natural flows are turbulent to some extent but turbulence is difficult to define Engineering Physic Studying turbulence provide engineering solutions to real problems nature of turbulence must be explored airplanes must fly, weather must be forecast, sewage and water management systems must be built, society needs ever more energyefficient hardware and gadgets

8 Why Turbulence Happen? Tiny disturbance in laminar flow +viscous forces can no longer dampen Instabilities breakdown in stability of a fluid flow In large Reynolds number inertial forces associated with fluid mass try to amplify it Flow paths of the particles are chaotic and change rapidly Turbulence The magnitude and direction of movement seemingly inexpressible The motion of a single particle is meaningless from the point of view of the whole flow The velocity of a single particle changes at random and it moves chaotically

9 Unpredictability or Randomness Turbulent fluctuations occur over a wide range of excited length and time scales Even though turbulence is chaotic it is described by the Navier-Stokes equations. Turbulent flow is irregular, random and chaotic Turbulence problems are always treated statistically rather than deterministically. Deterministic description of the motion as a function of time and space impossible.

10 Diffusivity The diffusivity is one of the most important properties as far as engineering application are concerned To accelerate the homogenization of any non-uniform fluid mixture Diffusivity Increased rates of momentum, heat, and mass transfer Increases the resistance (wall friction)

11 Rotationality and Dissipation of Energy Turbulent flow is always three-dimensional. Existence of eddies implies rotation or vorticity. The stretching of three-dimensional vortices play a key role in turbulence As end points of a vortex line move randomly further apart, the vortex line increases in length but decreases in diameter. Vorticity increases because angular momentum is nearly conserved. As a result, the radial length scale of the vortices decreases and the larger flow structures break down into smaller structures. The process continues until the small scale structures are small enough to the extent where their kinetic energy is overwhelmed by the fluid's molecular viscosity and dissipated into heat.

12 Vortex stretching

13 Turbulence Scales Turbulent Fluctuation accrue over a wide range of length and time scales Serious problem for Navier-Stokes solving, fluctuation term add new unknowns In other word turbulence is a multi scales problem with a highly non-linear coupling between these scales We should define very fine resolutions to capture the smallest eddies A complete description of a turbulent flow field at any instance in time requires specification of flow values

14 A time record of one component of velocity measured at a point in a flow field Any fluid properties can be expressed as consisting of a mean, time-averaged component and a fluctuation component u is defined as the time average of u T is the averaging period Turbulent kinetic energy k (per unit mass) is defined as

15 Time scales Due to our assumption of flow, one needs to be careful in defining the time scales of turbulent fluctuation. Turbulence time scales are defined by the length of time over which the mean of the fluctuating part goes to zero and at the same time the mean of the base flow remains unchanged. The variability of the process must be very small over this much smaller time period and the process could be considered as being approximately steady.

16 Averaging Due to the random nature of turbulent motions, it is usually more convenient to deal with statistical or averaged properties of the flow field: Averaging Methods Ensemble Averaging Defined as the arithmetic average of a number of measurements of a random process Time Averaging Defined as average of the quantities over a large time interval

17 Time averaged Navier-Stokes equation Continuity Navier-stoke Equation According to averaging laws

18 Reynolds stresses Therefore:

19 Turbulent Stress

20 Important Definitions Stationary A process is stationary if the statistics describing the process are independent of time. It is common to assume stationary for the analysis of turbulent fluctuations. For stationary processes, the ensemble average is the same as time average. Isotropic A turbulent field is said to be isotropic if its statistics are independent of direction or orientation( For example if the individual velocity fluctuation are equal in all three(x,y,z) direction) Homogeneous A process is homogeneous when the statistics are independent of position. so turbulence level do not change from one point to another.

21 Length Scales Turbulence consisting of a wide range of length scales can be described by the energy spectrum based on this approach the length scales be categorized Integral length scales Kolmogrov length scales Teylor length scales

22 Integral Length Scales Largest scales in the energy spectrum These are the energy production eddies which contain the most of the energy Integral scales are highly anisotropic Integral Length Scales The large velocity fluctuation and low in frequency The max. length of these scales is restricted by the characteristic length of the system

23 Teylor Length Scales not dissipative scale but passes down the energy from the largest to the smallest without dissipation Play a dominant role in energy and momentum transfer Intermediate scales between the largest and the smallest scales Teylor Length Scales Make the inertial subrange Taylor is often used in describing the term turbulence more conveniently

24 Kolmogorov Length Scales Smallest scales in the spectrum Form the viscous sublayer range The small scales are in high frequency Kolmogorov Length Scales Energy input from nonlinear interactions and the energy drain from viscous dissipation are in exact balance Turbulence is locally isotropic and homogeneous

25 Length Scales Definition

26 Next Presentation Kolmogorov Theory Length Scales formulation Turbulence modeling

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