DINAMICA FLUIDELOR COMPUTATIONALA APLICATA ... -...

RENAULT TECHNOLOGIE ROUMANIEDr. Ioan TELEAGA Brasov, june 2011

DINAMICA FLUIDELOR COMPUTATIONALA APLICATA LA VEHICULE: DE LA TEORIE LA PRACTICA

Profesionalism şi exemplaritate

Respect şi solidaritate

Dezvoltare personală

Satisfacţia clientului

Valorile RTR

RENAULT TECHNOLOGIE ROUMANIEDr. Ioan TELEAGA Brasov, june 2011 2

Overview

INTRODUCTION

01FROM THEORY TO

NUMERICS

02AERODYNAMICS

03THERMODYNAMICS

04


01 INTRODUCTION


CUSTOMER SPECIFICATIONS: Activities

Numerical simulations

NVH

Performance and fuel consumption

CFD: aero/heat transfer

Vehicle dynamics

Measurements

NVH

Thermal

Customer usage analysis

Statistics of the usage of our/competitor car

Subjective evaluations/bench

NVH noise levels

Driving pleasure

Competition benchmark


02 FROM THEORY TO NUMERICS


Modelling a phenomenon

REAL PHENOMENON

MATHEMATICAL MODEL

NUMERICAL MODEL

ANALYTICAL SOLUTION

NUMERICAL SOLUTION

DOMAIN

MESH

BORDER INFORMATION

BOUNDARY CONDITIONS

ERROR

SOLVER

ERROR


BACKGROUND (1)

IC are important in order to have good starting points (according to the physical modeled phenomena)

IC are very useful to speed up the numerical convergence

BC are the most important data to be added

BC need to add NEW information to the model

0

forcesextrastressconvection

u

fupuutu

Initial Conditions (IC)Boundary Conditions (BC)


BACKGROUND (2)

Types of grids:

structured

unstructured

Elements:

triangles, rectangles, hexagons in 2D

prisms/tetrahedra, parallelepipeds, etc in 3D

Meshes/Grids

Different grids have different impact on the numerical solution → We will talk later about!


BACKGROUND: NUMERICAL SCHEMES (1)

Properties of all numerical schemes:

Consistency: means that the discretized version of the equation must fit the analytical one if one goes with the grid size to zero and the truncation error (i.e. the difference between the exact and numerical (discrete) equation) must be small and bounded

Stability: assures that the errors made at each time step/iteration will not grow in time

Convergence: numerical solution tends to the exact one as the grid size tends to zero

LAX equivalence theorem: consistency + stability convergence

Quality


BACKGROUND: NUMERICAL SCHEMES (2)

Based on FEM method

Try to approximate the solution

Remark: Not often used for NS equations because forces the div-free condition only globally!

Based on FV method

Try to approximate the NS system and NOT the solution

My opinion: the most used in CFD computations!

Codes: FLUENT

Based on FD method

Try to approximate the NS system and NOT the solution

The most ancient and simple method!

Based on LBM method

Based on Boltzmann equation approach

Relatively new on the market

Based on Spectral approximation (based on Fourier transform)

Diversity


NUMERICAL SCHEMES (2)

The above integration is exact!

There is not explicit integration of the remaining integrals!

To completely get the exact u we need to integrate “exact” in space too!

fin

finfin

T

TT

fin

dtu

dtfupdtuuuTu

0

00

0

)()0()(

Dummy Unsteady Approach

Final time = finT

Integrating in time

First concept of global error is needed!!!


NUMERICAL SCHEMES (3)

In software engineering (and not only) numerical error bears all (d)effects which may disturb the final solution/result

In the numerical error is included first of all the incapability of the computer to store an rational/irrational number

Sources of errors

accumspacetimeroundtot eeeee Total error

rounde - round-off errors

spacee - spatial errors

accume - accumulation error

timee - temporal errors

To define in a rigorous general way the concept of error it is an impossible task!


SPATIAL ERRORS

Definition: The function u has a derivative at the point x0 if the following limit exists:

)()()(0

'

0

0lim0

xuxx

xuxu not

xx

What is happening in numerical case?

Here begins the crowd world of numerical “definitions”, and let researchers to write many papers in this field

Each numerical definition is strictly connected/adapted to the problem to be solved


SPATIAL ERRORS

Consider the following 2D example:

x

tyxutyxxutyxxu

),,(),,(,, 0000

00

could be an approximation (forward) of the exact derivative

xtyxutyxxu

x

),,(),,(lim 0000

0

The error between the exact and approximate derivative is called truncation error

How this error can be evaluated?

mesh size

x

y

x0

y0

x0 +Δx

y0 -Δy

Δx

Δy

Dummy grid


TEMPORAL ERRORS

When is necessary to numerically integrate a function?

Answer:

when an analytical result is unavailable

when the function is too complicated

only few values of the function is given

0 x

f (x)

a b

b

a

dxf

Looking geometrically at the right picture, first idea to approximate an integral would be to approximated as good as we can the hashed area! → “Split big area in a sum of small areas” !

n

iii

b

a

xfadxxf0

)()( index i counts the nodes number between a and b.


NUMERICAL SCHEMES

From theory to numerics…

0

forcesextrastressconvection

u

fupuutu

bAx

Discretization procedure

Linear system (LS) →

In this case we treat only this way, and not other nonlinear approaches based on Newton iterations!!!

A = matrix (SPARSE) coefficients

x = unknown variables (u,v,w,p,etc)

b = known data (data at previous time, BC, IC, f)


SOLVING LS

Behind linear systems…

bAx

Direct Methods

Iterative Methods

bAx 1+Preconditioning

Multigrid

Generalities:

if x has N entries then A has the dimension N2!

# of arithmetic operations needed to obtain the solution x is proportional usually with N3! → How to decrease the computational time?

Computational demand today: Solve the linear system within N iterations!!!


NUMERICAL SCHEMES FACTS

Overview:

Usually in CFD the matrix A is sparse (e.g. more zero entries than non-zero)!

A is always quadratic. For a 1.000.000 grid points the dimension of A is (1.000.000)2!

The non-zero entries are only the coefficients of the unknown values and the connections to their neighbors! So, A is never stored as a full matrix. A is stored as a three vectors:

1st vector: position in x dir in A

2nd vector: position in y dir in A

3th vector: non-zero value of A

Important to have symmetric matrices… easier to solve the LS

The type of discretization operators, or in the grid elements together with the overall numerical scheme chosen have direct impact to the coefficients of the A matrix → more tuning needed to solve LS! That’s why

Do not use angles too small

Discretization lengths in all directions in the same range, and smooth transition of the layers!


FINAL REMARKS

Numerical scheme

For our purposes use ALWAYS a second-order scheme both in time and space

A first-order scheme is producing in excess numerical diffusion which will spoil the solution

A higher-order scheme will produce more accurate results, but the price paid is that needs more computational time and finer tuning of the start-up!

It is also a must when dealing with turbulence. Each turbulence model is producing a turbulent viscosity ~ O(h2)!!! Indeed, if using a first-order scheme, it does not mater which turbulence model is taken the effect on the final solution will be ~0! WHY?

Accuracy RAM demand CPU time

1st-order scheme

~ mesh size / time step

2nd-order scheme

~ with O(mesh size2, timestep2) exponentially exponentially

higher-order schemes

third-order or higherexponentially exponentially


MODELLING: Turbulence?

Turbulence modelling

“Definition”: a turbulent flow is characterized by a non regular/chaotic movement!

Models (just few…)

No model: DNS – usually for small Re numbers…

Zero-order models (algebraic): ex. Baldwin-Lomax Model

1 equation models: Spalart-Allmaras model (implemented FLUENT)

2 equations models: k-ε and variants (well accepted in industry)

Reynolds Stress Models (RSM)

LES, VLES

DES – to treat near boundaries in a RANS view and in other parts as LES. etc

Turbulent solutions give you only mean values instead of point wise

There are NO exact turbulence models, only approximations

Always playing/changing the overall viscosity

Need a lot of coefficients to be tuned

LES/VLES/DES new on the market


03 AERODYNAMICS


Basic Aerodynamics (1)

Fx : Drag forceFx : Drag force

Fy : Lateral Fy : Lateral forceforce

Fz : Lift forceFz : Lift force

L : RollL : Roll

M : PitchM : Pitch

N : LaceN : Lace


Fx = ½

S.Cx V² Fuel Consumption

Fx : Drag

Sphère : Cx = 0,47

Disque : Cx = 1,17 Cube : Cx = 1,05

Aile : Cx = 0,04

Clio 3 : Cx = 0,34 F1 : Cx = 1.0 Cz=-3

Cooling

Tires

Mirror

Under bodyWheel covers

Global design

6

1ixix SCSC




Cx0,25 0,30 0,35 0,4

A2

JXsara Break

K

BPrius

C220

L

Cx represents the aero performance, and do not take into account the frontal surface

Some superstructures are more suitable to be aerodynamic


Aerodynamic results: Different visualizations


Car with a little rear spoiler

S*Cx wake = 0,073

Initial car

S*Cx wake = 0,105

Aerodynamic result: SCx improvement


04 HEAT TRANSFER


WHAT DOES MEAN VEHICLE HEAT TRANSFER?

Validation of the cooling systems

Water

Oil

Heat exchangers

Underbody/underhood validation

Material choice

Component position

Thermal shields

Thermal comfort

Air diffusion

Heat and AC system

Defrost windshield


Coupling PWF-PWT-AmeSim (1)

PowerFlow (PF)

FINAL STRATEGY: Coupling between PF - PT - Ame !

airflow

T_conv

T_diff

T_cond

T_rad

( DES as turbulence model )

T (Heat exchangers backflow)

Amesim

PowerTherm (PT)


Coupling PWF-PWT-AmeSim (2)

T

HTC, T

PF mesh PT mesh


Unsteady coupling PF-PT strategy

Numerical Strategy

t=0 t=T_fin

time

coupling time

Period

PF run

PT run

ΔtPT

ΔtPF

ΔtPF

ΔtPT

time step size PF

time step size PT

Exchange/Update BC


Duster Condensation analysis

Airflow is taken from the engine compartment

The suction side to the beam implies recirculation of hot air on the COND

Temperature [degC]

Recirculation zonesRecirculation zone


Megane: Underhood/Underbody thermal simulation

Temperature field and airflow for hillTemperature field and airflow at 165km/h

Aero and thermal analysis


Megane: Underhood/Underbody part positioning

Surface temperature field at 165 km/h Stagnation zone behind EGR

Aero and thermal analysis


Thermocouples Test (oC) Simulation (oC)

1 61 61

2 82 84

4 81 80

11 253 268

Thermocouples1

Calcul H2S Trap

Sens de l’écoulement

160 mmMegane: Tests/simulations “V165km/h” correlation


Thermocouples Test(oC) Simulation (oC)

1 91 88

2 143 133

4 133 139

11 406 388

Thermocouples1

Calcul H2S Trap

Sens de l’écoulement

160 mmMegane: Tests/simulations “Hill” correlation


Duster: Defrosting


Conclusions

Scientific computation is used with success within Renault

Nowadays experiments and theory are supplemented in many cases by numerical computation that is an equally important component

Within scientific computing one can treat more complex and less simplified problems through massive amounts of numerical calculations and thanks to the increased computer facilities in short time

RENAULT TECHNOLOGIE ROUMANIEDr. Ioan TELEAGA Brasov, june 2011 39

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