OLAS Axexo2 Teoria Flujos

Computational

analysis of

viscous effects

on submerged

bodies

Julen García Ibáñez

1. INTRODUCTION

2. STATE OF ART

3. CONCEPTUAL OVERVIEW

1. INTRODUCTION

Aim of work

Objectives

AIM OF WORK

“The aim of this work is the

development of methodologies for

an efficient simulation of flow

around bodies with different

turbulence models, applying

comparative studies between

numerical and experimental

results.”

OBJECTIVES

Analyze the flow around a circular cylinder, and the effect

of variations of the Reynolds number on it

Obtain force coefficients and velocity vector fields of the

flow

Simulate vortex shedding phenomenon in turbulent

situations: von Kármán Vortex street

Study and compare the different turbulence models

Apply grid convergence theory to validate computational

results

Objectives

2. STATE OF ART

Overview Navier-Stokes equations

Computational Fluid Dynamics

Discretisation

Direct Numerical Simulation

Turbulence models Reynolds Averaged Navier-Stokes

Large Eddy Simulations (LES)

Dettached Eddy Simulations (DES)

OVERVIEW

Navier-Stokes equations


Discretisation



Set of partial differential equations (PDE)

Conservation of mass:

A) Continuity equation

Newton’s Second Law of Motion:

B) Momentum equation

First law of Thermodynamics:

C) Conservation of energy

Allow obtaining the pressure and velocity of the fluid

throughout the flow


A) Continuity equation:

B) Momentum equation


C) Conservation of energy


Solves Navier-Stokes equations numerically

Three main elements:

A) Pre-processor

B) Solver

C) Post-processor

CFD allows the study of complex flow fluid and has

become a key part of nowadays engineering

researching projects


A) Pre-processor

The real problem is defined in a suitable form for

the use of the software

The computational domain is created as a big

number of discrete elements that set up the mesh

Properties of the fluid and boundary conditions

need to be defined


B) Solver

The governing equations are solved using the

information given in the pre-processing stage

By succesive iterations the solution is derived

Convergence is a key part to ensure the wellness

of the solutions

Residuals need to be as small as possible


C) Post-processor

It is used to analyze the results given by the

solver

Actual CFD packages provide vector and contour

plots to display the properties of the flow as

velocity, pressure, vorticity, viscosity…

Furthermore, specific reports can be presented by

mixing data like force & lift coefficients in specific

places

Discretisation

The real surface cannot be analyzed by the CFD

Thus, a set of some regularly and irregularly spaced

nodes needs to be generated: the mesh

The mesh breaks up the domain, in order to allow

time dependant calculations to be made

The discretisation is divided into:

A) Equation discretisation

B) Spatial discretisation

C) Temporal discretisation

Discretisation


The translation of the governing equations into a

numerical modelisation that can be solved by the

computer

Can be achieved by Finite Difference Method

(FDM), Finite Element Method (FEM), Finite

Volume Method (FVM)

The analysis of this document uses FVM

Discretisation


In FVM, the domain is separated into a finite

number of elements: control volumes

The Navier-Stokes equations are solved

iteratively on each control volume

The integration of the results of the algebraic

equations for each control volume derive the flow

It’s efficiency makes FVM standard in CFD codes

Discretisation

B) Spatial discretisation

The division of the computational domain into

small sub-domains that put together the mesh

Structured, unstructured and multi-block

structured mesh can be created

Unstructuration and multi-blocking allow a more

efficient use of the elements and higher

adaptability to complex geometries

Discretisation

C) Temporal discretisation

The splitting of the time in the continuous flow into

discrete time steps

In time-dependent situations, the PDE need

either an implicit or explicit solving method

Explicit methods are straight forward, but small

time-steps are needed to obtain convergence.

Implicit ones, even if require more computational

time, have a bigger range of stability


DNS involves the direct solving of Navier-Stokes

equations, without any approximation

All scales of motion are solved, even down to

Kolmogorv scales, where energy dissipation

happens

It’s computational cost is unaffordable

Spalart estimates that nearly a century would be

needed for DNS to be interesting for enegineering

TURBULENCE MODELS

Reynolds Averaged Navier-Stokes

Large Eddy Simulations

Dettached Eddy Simulations


In RANS, the flow is separated into mean and

fluctuating components

Time-averaged Navier-Stokes equations are obtained


Reynolds stress: correlation between the fluctuating

velocity components

RANS models have been developed based on the

concept that a velocity scale and a length scale is

sufficient to describe the effects of turbulence in a flow


A) k-ε TURBULENCE MODEL

Solves the flow assuming that the rate of

production and dissipation of turbulence are in

near-balance in energy transfer

The dissipation rate, ε of the energy, is:

where k is the kinetic energy of the flow and

L is the length scale involved


A) k-ε TURBULENCE MODEL

Advantages:

• Robustness of the formulation

• A very used and proven model

• Low computational cost

Disadvantages:

• Turbulence over-prediction at the stagnation

point

• Too large length scales

• Fails in the solving of flows with large strains


B) k-ω TURBULENCE MODEL (Reynolds Stress Model)

Uses similar mathematics to the k-ε turbulence

model

Substitutes the energy dissipation rate, ε,

by the energy dissipation rate per unit of kinetic energy, ω


B) k-ω TURBULENCE MODEL (Reynolds Stress Model)

Advantages:

• Simple and robust sub layer analysis

• No need of additional damping functions to

solve ω equation

Disadvantages:

• Inaccurate prediction of eddy viscosity values

• Higher computational power than k-ε


C) Shear Stress Transport (SST) TURBULENCE MODEL

Tries to overcome the problems of k-ε and k-ω

turbulence models

Uses k-ω near the wall to reduce the over-

prediction of length scales

Uses near the boundary layer edge to overcome

the problem of free-stream dependancy

The application is restricted to periodical flows

Large Eddy Simulation (LES)

Computes directly the large-scale turbulent structures

responsible for the transfer of energy and momentum

in a flow (large scale eddies)

Models the smaller scale of dissipative and isotropic

structures (small scale eddies)

A filter function is used to dictate which eddies are of

large scale and which ones are of small scale


The most used filter function in LES is the top hat

filter:

The filtered equations governing the flow in LES are:


An unknown stress term needs to be obtained

For that purpose the following equation has been derived:

Subgrid Scale (SGS) Reynolds Stress: Represents the

large scale momentum flux due to turbulence motion


To obtain the SGS Reynolds Stress , a subgrid scale

model has to be used

The most used model is the Smagorinsky model

Basically, the Smagorinsky SGS model simulates the

tranference of energy between the large and the

subgrid-scale eddies

It takes into account the SGS eddy viscosity νSGS, and

the backscattering (reverse of cascade process)


Advantages:

• The influence of turbulence is very well

captured in LES

Disadvantages:

• Too disipative in laminar regions

• Special near wall treatment

• Backscatter of flow is uncertain

• High computational cost o Re1.8 near to the viscous sublayer

o Re0.4 away from the wall

Dettached Eddy Simulation (DES)

DES uses the RANS models (generally SST) close to

the wall and LES in the wake region of a flow where

flow unsteadiness appear

Basically, DES employs a turbulent length scale, Lt, to

determinate which approach to use during a simulation

The activation of LES or the switching to RANS models

is controlled by a blending factor F

where CDES constant

Dettached Eddy Simulation (DES)

The blending factor is defined as:

where CDES is a constant

SST-DES model offers great potential in the application

of simulations for a large class of flows at high Reynolds

numbers

DES is the more practical, computationally efficient and

widely used turbulence model nowadays

3. CONCEPTUAL OVERVIEW

Reynolds number

Vortex shedding

Drag and Lift coefficients

REYNOLDS NUMBER

Reynolds number (Re)

The flow varies with the Reynolds number around a

circular cylinder

In small Reynolds numbers, small vicous flows

where frictional forces are dominant take place

With the increase of Reynolds number, flows have

rapid regions with velocity changes, thus generating

vortices and turbulence


Matematically:

where u is the inlet velocity, D the diameter of the cylinder and ν the kinematic viscosity of the flow

From Roshko’s experiment was obtained:

Stable range: 40 – 150

Transitional range: 150 – 300

Irregular range: 300 – 200,000

VORTEX SHEDDING

Vortex shedding

The separation of the flow around a circular cylinder

creates pairs of eddies to form alternately on the bottom

and top part of the cylinder

This eddies travel into the wake region thus generating

vortex shedding

Vortex shedding

Strouhal number is a dimensionless number that

describes the shedding of the vortices in the wake

region

where fs is the shedding frecuency of the vortices (1/T),

u is the inlet velocity and D cylinders diameter

Vortex shedding is very usual in engineering

Vortex shedding

The frecuency at which vortices are shed remains

constant within Re=250 and Re=10,000 frecuencies

DRAG AND LIFT COEFFICIENTS


A dimensionless quantity that is used to quantify the

resistance of an object in a fluid environment such as

air or water

where A is the projected are in the flow and F is the sum

of the pressure force and the viscous force components

on the cylinder surface (in the along-flux direction)


Drag coefficient is made up of three components:

• Viscous force Ff

• Pressure force Fp

Wave force Fo

The figure shows the evolution of CD with Re

!!!


Roshko stated that Strouhal number and the Drag

Coefficient of the flow are related in the sub-critical

range (Re<10,000), where an increase in the Strouhal

number is accompained by a decrease in CD

Lift coefficient is defined similarly but vertical force is

considered


Theoretically, in a vortex shedding situation, the drag

force is changing at twice the frecuency of the lift force

in a flow involving separation

It is important that any turbulence model can simulate

this accordingly and should be measured

Julen García Ibáñez

Contact: [email protected]

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