CUBIT University of Pisa The Group of Applied Fluid Dynamics€¦ · Compressor Diffuser rotating...

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CUBIT-UNIPI Applied Fluid Dynamics Group 1 CUBIT – University of Pisa The Group of Applied Fluid Dynamics March 2018

Transcript of CUBIT University of Pisa The Group of Applied Fluid Dynamics€¦ · Compressor Diffuser rotating...

Page 1: CUBIT University of Pisa The Group of Applied Fluid Dynamics€¦ · Compressor Diffuser rotating stall (General Electric) 17 Non-steady CFD evaluation Time step 0.5 ms Centrifugal

CUBIT-UNIPI Applied Fluid Dynamics Group 1

CUBIT – University of Pisa

The Group of Applied Fluid Dynamics

March 2018

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CUBIT-UNIPI Applied Fluid Dynamics Group

The Group of Applied Fluid Dynamics

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Prof. Giovanni Lombardi (Director)

• 3 Senior Engineering

• 6 Junior Engineering

At present the team is composed of:

Several Theses in Aerospace Engineering, Vehicles Engineering and Wind Turbine are supported by the group

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CUBIT-UNIPI Applied Fluid Dynamics Group

Prof. Giovanni Lombardi (career)

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• 1982 Master Degree in Aeronautical Engineering• 1983 Researcher at the Dep. of Aerospace Engineering

• 1990 Professor of "Aircraft Aerodynamics”• 2005 Professor of ”Vehicle Aerodynamics”• 2005 Director of the Master in “Yacht Engineering”• 1999 to 2008 Professor of ”Experimental Aerodynamics” in the Module of “Fluid

Dynamics” of the Masters in “Yacht Engineering” and “Planning and Management of Renewable Energy Systems”

• Module of “Aerodynamics” at the Training Program Maserati-Alfa Romeo

• Since 1989 person in charge of the cooperation with CSIR (Council for Scientific and Industrial Research, South Africa).

• Since 2000 person in charge of the cooperation between the University of Pisa and FERRARI (Aerodynamics researches).

• Person in charge of the cooperation between the University of Pisa and “Clan Des Team Challenger” for the scientific support to the America’s Cup 2007.

• Technical Coordinator of the AC Team “Green Comm Racing”.

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CUBIT-UNIPI Applied Fluid Dynamics Group

Prof. Giovanni Lombardi (scientifical)

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Author of more than 120 scientific publications and 90 technical reports.• 40 papers are published in Journals (26 as principal author). • 6 articles in books.• More than 80 papers presented at conferences.

In general, he has always used both the experimental and the numericaldevelopment in research, thus taking advantage of both methodologies toobtain results unachievable by one approach only.The attention has been posed on the physical aspects of research and theindustrial applications, using, from time to time, the techniques, numericaland/or experimental, that best suited to the analysis of the fundamentalissues involved in the particular investigation.

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CUBIT-UNIPI Applied Fluid Dynamics Group

FUNDAMENTAL ACTIVITIES

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• WIND TUNNEL EXPERIMENTS

• CFD EVALUATIONS

Analysis of fluid dynamics problems by using the most appropriate techniques

• NUMERICAL AERODYNAMICS OPTIMISATION

• DATA ANALYSIS

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CUBIT-UNIPI Applied Fluid Dynamics Group

Cooperation(Aerospace)

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•Alenia Aeronautica

•Aermacchi

•Augusta

•MBDA

•Oto Melara

• Selex-Galileo

• SNIA BPD

•CSIR (South Africa)

• IDS (unmanned airplanes)

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CUBIT-UNIPI Applied Fluid Dynamics Group

Cooperation(Naval)

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•WASS

•Fincantieri

• Intermarine

•Econboard

•Vallicelli yacht design

•America’s Cup 1987 (Azzurra)

•America’s Cup 2007 (Team +39)

•America’s Cup 2013 (Green Comm Racing)

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CUBIT-UNIPI Applied Fluid Dynamics Group

Cooperation(Green Energy-wind turbine)

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• General Electric (Nuovo Pignone)

• XEMC DARWIND (Netherland)

• ENEL Green Power

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CUBIT-UNIPI Applied Fluid Dynamics Group

Cooperation (Road Vehicles)

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•Ferrari

•Minardi F1

•Dallara

•Maserati-Alfa Romeo

•Tatuus

•Continental

•Centro Ricerche Fiat

•Piaggio

•Cicli Pinarello

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CUBIT-UNIPI Applied Fluid Dynamics Group

The Wind Tunnel (University of Pisa)

Closed circuit Open Test Section Subsonic

Test Section: diameter = 1.1m length = 1.5m

Velocity: up to 35m/s Turbulence level: 0.9%

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CUBIT-UNIPI Applied Fluid Dynamics Group

Experimental experiences

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• Several Campaigns in the subsonic wind tunnel of University of Pisa

• Organization of experimental campaign in Subsonic, Transonic and Supersonic wind tunnel in:

• FFA (Sweden)

• CSIR (South Africa)

• ONERA (France)

• Data analysis of the experimental data

• Data correction for the real conditions

• Data analysis of flight tests

• POLITECNICO of TORINO

• FERRARI

• MINARDI F1

• Calibrations of the test section (Dallara wind tunnels)

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CUBIT-UNIPI Applied Fluid Dynamics Group

CFD – HARDWARE (at present)

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3 Dedicated parallel Cluster for the CFD evaluations

• 96 cores 192 Gb RAM

• Intel based 1024 cores cluster (~16 Tflops)

2 GB Ram/Core

Infiniband DDR fast network (20 Gb/sec)

• Intel based 1216 cores cluster (~24Tflops)

3 GB Ram/Core

Infiniband DDR fast network (40 Gb/sec)

• 2 Workstations with 96 and 256 Gb of RAM for the grids generation• Several PC

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CUBIT-UNIPI Applied Fluid Dynamics Group

CFD – HARDWARE (in the month)

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2 Dedicated parallel Cluster for the CFD evaluations

• 96 cores 192 Gb RAM

• AMD based 9216 cores cluster (~100 Tflops)

2 GB Ram/Core

Infiniband DDR fast network (60 Gb/sec)

• 2 Workstations with 96 and 256 Gb of RAM for the grids generation• Several PC

Note: the hardware can be used as “external service”

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CUBIT-UNIPI Applied Fluid Dynamics Group

Evolution of Computational Capabilities

40 mill. cells

≈ 1 min.

≈ 20 Bil.

1216 cores

9200 cores

About one order of magnitude every4 years !

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CUBIT-UNIPI Applied Fluid Dynamics Group

CFD - Software

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The following solver are utilized:

• ANSYS FLUENT• STAR CCM+ (SIEMENS)• OpenFoam

For the geometries management:

• CATIA• ANSA• Pro-Engineering• Rhino

Optimization procedures:

• ModeFrontier

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CUBIT-UNIPI Applied Fluid Dynamics Group

CFD Experiences (Aerospace)

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• External flow on complete configurations

• Flow in the intakes

• Helicopter rotors flow analysis

• Wing optimisation

• Aeroelastic analysis

• Transonic Flow

• Mini UAV development

• Flow for carbon lamination cooling system

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CUBIT-UNIPI Applied Fluid Dynamics Group

Compressor Diffuser rotating stall(General Electric)

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Non-steady CFD evaluationTime step 0.5 ms

Centrifugal Compressor Diffuser RotatingStall: Vanless Vs. Vaned.Proceedings of 12th European Conference on Turbomachinery Fluid dynamics & Thermodynamics ETC12, April 2017; Stockholm

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CUBIT-UNIPI Applied Fluid Dynamics Group

Wind Turbines

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• Flow around the rotor of different size• Vertical axle• Horizontal axle

• Design optimization

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CUBIT-UNIPI Applied Fluid Dynamics Group

ALENIA

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CUBIT-UNIPI Applied Fluid Dynamics Group 20

(m/s)

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CUBIT-UNIPI Applied Fluid Dynamics Group

CFD Experiences (Naval)

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• Flow around the hull with free surface

• Flow on the sails

• 6 DOF motion with rough sea

• Torpedos

• Hull optimization

• Sail shape optimization

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CUBIT-UNIPI Applied Fluid Dynamics Group

6 DOF High Speed Catamaran in rough sea

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➢ The sea wave dynamics is represented by the 5° order Stokes theory.

➢ The following characteristics are assigned:

➢ Wave height, H

➢ Wave Length, L

➢ Sea depth, d

➢ Direction and velociy of the sea tide, cE

H

dcE

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CUBIT-UNIPI Applied Fluid Dynamics Group

6 DOF Motion set-up

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• Total mass

• C.G. position

• Inertial Moments

•The applied power is kept constant

ARE ASSIGNED

Time step: 0.005 s

Iterations per step 10

Starting Speed: 5 m/s

• The thrust is evaluated as a function of the speed

and it is applied in the direction of the propeller axle

• Propulsion efficiency = 0.92

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CUBIT-UNIPI Applied Fluid Dynamics Group 24

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CUBIT-UNIPI Applied Fluid Dynamics Group

Max. Boat Speed, Flat sea (1900 HP)

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Regime (oscillating)

No

oscillations

≈ 22 sec≈ 7 sec

Oscill.

transient

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CUBIT-UNIPI Applied Fluid Dynamics Group

Boat Motion, Flat sea (1900 HP)

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CUBIT-UNIPI Applied Fluid Dynamics Group

CFD Experiences (Automotive)

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• Flow around the entire car (external and internal)

• Flow in the radiator ducts

• Thermal Comfort

• Aero-acoustic analysis

• Brake cooling

• Thermal aspects in the vanes

• Flow in the injectors

• Optimization of the car shape

• Optimization of the geometrical details

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CUBIT-UNIPI Applied Fluid Dynamics Group

Tatuus

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CUBIT-UNIPI Applied Fluid Dynamics Group

FLOW IN THE RADIATOR DUCTS

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CUBIT-UNIPI Applied Fluid Dynamics Group

Condotti radiatori – velocità di attraversamento

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CUBIT-UNIPI Applied Fluid Dynamics Group

Exhaust Gas

Analysis of the exhausts trajectory of a high-performance car during an acceleration and a following braking phase

The goal is to improve the comfort inside the cockpit, preventingdiseases linked to unexpected exhausts paths due to a particular

driving condition

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CUBIT-UNIPI Applied Fluid Dynamics Group

The Physics of the problem can be reproduced by means of different analyticalmodels, each presenting its peculiarities and its drawbacks.

Sliding/Dynamic Mesh

VOF Model

Mixture Model

Eulerian Model

Static Mesh

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CUBIT-UNIPI Applied Fluid Dynamics Group

Physics Model

Considerations of various nature should lead to a compromise choice betweentime and accuracy

The model must be able to catch the nature of the phenomenon that we are interested in, introducing as many simplifying hypotheses as possible

Eulerian Discrete Phase Model with Particle Tracking

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CUBIT-UNIPI Applied Fluid Dynamics Group

Volume Grid ~ 60 Million of Tetrahedral Cells

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CUBIT-UNIPI Applied Fluid Dynamics Group

CFD Analysis

• Initialisation: Steady-State Simulation

• Unsteady Simulation: Inlet Velocity Profile and Exhausts Mass Flow Rate expressed in function of time (Ferrari Experimental Data)

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CUBIT-UNIPI Applied Fluid Dynamics Group

CFD Analysis

• Inlet Velocity Profile and Exhausts Mass Flow Rate described by means of User-Defined Functions

• Total time = 20 seconds

• Δt = 0,01 s – 10 Inner Iterations for each Time Step• Particle Tracking – Injections coincident with the exhausts surfaces

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CUBIT-UNIPI Applied Fluid Dynamics Group

Post-Processing of Results

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CUBIT-UNIPI Applied Fluid Dynamics Group

Post-Processing of Results

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CUBIT-UNIPI Applied Fluid Dynamics Group

Post-Processing of Results

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CUBIT-UNIPI Applied Fluid Dynamics Group

Post-Processing of Results

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CUBIT-UNIPI Applied Fluid Dynamics Group

THERMAL CONFORT

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CUBIT-UNIPI Applied Fluid Dynamics Group

THE COMFORT IN THE COCKPIT

The thermal comfort is a result of the physiological behaviour, even ifthe thermo-aerodynamics aspects are preponderant for a quantitativeevaluation.

Essentially related to

thermo-aerodynamicsof the flow in the cockpit

Problem: TO CORRELATE THE THERMO-FLUID DYNAMICS VARIABLES TO

COMFORT/DISCOMFORT FEELINGS

AERODYNAMICS

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CUBIT-UNIPI Applied Fluid Dynamics Group

The COMFORT “FLUX”

Environment Man Judgment

Stimuli

PhysiologyCOMFORT

INDEX

IT IS NECESSARY TO SPECIALIZE THESE ASPECTS TO THE ANALYSIS OF A CAR COCKPIT

➢ UNI e ASHRAE Rules

➢ Rules to estimate the localdiscomfort

➢ Indices for environment

➢ Thermal sensitivity

➢ Thermal balance

➢ Thermoregulation

Aerodynamics

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CUBIT-UNIPI Applied Fluid Dynamics Group

OBJECTS

• TO DEFINE ONE (or MORE) COMFORT INDICES SUITABLE FOR

THE CAR COCKPIT CONDITIONS

• TO DEFINE THE PROCEDURES FOR THE EVALUATION OF THE

THERMO-AERODYNAMICS ASPECTS OF THE COMFORT

(The aspects of thermal comfort related to the physiological answers to the

environmental situation were analysed with the Department of Physiology of

the University of Pisa)

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CUBIT-UNIPI Applied Fluid Dynamics Group

THE COMFORT INDEX: STRUCTURE

The index is assumed to derive from the following

fundamental factors:

➢ The global thermal equilibrium of the body (IE)

➢ The discomfort related to the gusts (IG)

➢ The vertical gradient of temperature (IVT)

➢ The horizontal gradient of temperature (ILT)

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CUBIT-UNIPI Applied Fluid Dynamics Group

AERODYNAMIC

From the aerodynamic point of view it is necessary to evaluate the

flow characteristics in the cockpit, in terms of:

• Analysis of the car thermal comfort

• Air Velocity

• Air Temperature

• Radiation Temperature

COMFORT INDEX

• Effects of the relevant parameters

• Indications about modifications to increase the comfort

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CUBIT-UNIPI Applied Fluid Dynamics Group

CFD SET-UP

the material properties are assigned as:• alloy for the car faces• glass for the window• plastic for the dashboard• leather for the seats

Activated on the windows

RADIATION DO Radiation Modelcoupled with DO Irradiation Solar Load Model for the solar load

CONDUCTION

CONVECTION

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CUBIT-UNIPI Applied Fluid Dynamics Group 48

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CUBIT-UNIPI Applied Fluid Dynamics Group

THERMAL COMFORT INDEX

at this stage of the activity, it is assumed K1= K2= K3= K4=1

THE CORRELATION BETWEEN EXPERIMENTAL AND NUMERICAL DATA APPEARS SATISFACTORY

with more significant differences in the local indices, probably related to the difficulty in the gradient evaluation, especially in the experiments

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CUBIT-UNIPI Applied Fluid Dynamics Group 50

NUMERICAL OPTIMISATION

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CUBIT-UNIPI Applied Fluid Dynamics Group

Ex. : Fairing on a 2D cylinder – step 1

C

Object Function: Drag

Reference solution: NACA 0012

NACA 0012

t/c 0,12

c 0,830

Re 1,1 * 106

CD 0,0052

DRAG 1,085 N/m

t

Optim. Step 1: same section family

Numerical solver: X-Foil 1 Design Parameter: chord

NACA 00169

0,169

0,590

8,1 * 105

0,0070

1,04 N/m

Results:

• t/c 16.88 %

Alghoritm: Conjugate Gradient

• DRAG - 4%

Clearly, Drag is a function of c

Time on PC: about 1/2 hour

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CUBIT-UNIPI Applied Fluid Dynamics Group

Fairing on a 2D cylinder – step 2

C

Object Function: Dragt Optim. Step 2: wing sect. defined

by Bezier points

8 Design Parameter: chord + 7 Bezer points

Time on PC: about 6 hours

Results:

•t/c 17.1% + Bezier points

Alghoritm: Genetic

• DRAG - 25%

NACA 0012

t/c 0,12

c 0,830

Re 1,1 * 106

CD 0,0052

DRAG 1,085 N/m

NACA 00169

0,169

0,590

8,1 * 105

0,0070

1,04 N/m

ID 75593

0,171

0,594

8,1 * 105

0,0054

0,811 N/m

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CUBIT-UNIPI Applied Fluid Dynamics Group

Optimisation of a car rear diffuser

As the interest is focused on the rear diffuser, only a part of the geometry will be varied during the optimisation procedure

the CAD geometry is divided in two parts

• the “fixed” part (red) • the “detail” part (yellow)

Only the “detail” part is parametric, and its geometry will change during the optimisation process

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CUBIT-UNIPI Applied Fluid Dynamics Group

Impact on the GRID

FixedParametric

Also the grid volume is subdivided in two parts:

• the fixed part, representing the geometry of the car not

changing in the optimisation

• the parametric part (yellow), defining the rear diffuser, and

changing during the optimisation, following its parameters

variations

At any step of the optimisation, the grid volume is obtained by merging the fixed part with the parametric one

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CUBIT-UNIPI Applied Fluid Dynamics Group

Advantages

• Reduced time for the CAD phase

• Reduced time for the grid generation

• Smaller dimensions of the file to manage

• Better representation of the geometry with respects to a global parametric scheme

• REDUCED TIME

• REDUCED COMPUTATIONAL REQUIREMENTS

• BETTER RESULTS

• REDUCED COST

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CUBIT-UNIPI Applied Fluid Dynamics Group

The Optimisation Procedure

Genetic ALGORITHM Moga-II

The optimisation procedure was driven by ModeFrontier

The OBJECT FUNCTION was related to both the total drag and the vertical download of the car

CONSTRAINTS:• minimum volume of the gearbox • Maximum span of the lateral side of the diffuser• The vertical download cannot be reduced (CZ ≤ CZref)

• 42 initial base data (DOE, Design Of Experiments) were used, with 16 new populations

• 570 different geometries were evaluated

STRATEGY:

TOTAL TIME for the entire procedure:

2 month (with 400 cpu hours)

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CUBIT-UNIPI Applied Fluid Dynamics Group

Results

Two interesting configurations can be identified:

• “Low Drag”, characterised by a drag as lower as possible (without increase in vertical down-load)

• “High Load”, characterised by a high value of the vertical download, with a low increase in drag

Pareto

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CUBIT-UNIPI Applied Fluid Dynamics Group

Bicycle - Chassis Section

Lateral wind: LIFT, it is possible a DRAG reduction!

a = 0°

a = 10°

a = 20°

8 Geometrical parameters:

•Position of maximum thickness (1)

Airfoil forebody:

•1 Beziers point (2)

Airfoil afterbody:

•2 Beziers points (4)

•Base height (1)

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CUBIT-UNIPI Applied Fluid Dynamics Group

Objective Function and Results

0,28

0,28

0,27

0,12

0,05

• Computational time for each simulation about 30 minutes on 24 processors

• Total time about 170 hours

Obj = a0 Fax0 + a5 Fax5 + a10 Fax10 + a15 Fax15 + a20 Fax2

Obj Fax_0 Fax_5 Fax_10 Fax_15Fax_20

4199 0,080 0,343 0,261 -0,105 -0,322 -0,437

Base 0,448 0.241 0.389 0.582 0.634 0.770

Winner at Tour de France

Clearly, for the athlete ability!

Results

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CUBIT-UNIPI Applied Fluid Dynamics Group

A particular application of optimisation

COMPARISON BETWEEN “OPTIMIZED CONFIGURATIONS”

The comparison between different solutions is usually not“conclusive”, because they are not at the same level of“possible performance”

POSSIBLE APPROACH:

TO OPTIMISE EACH CONFIGURATION IN ORDER TO MAKE A

In this way, it is possible to make a comparison between thedifferent solutions, because

THEY ARE AT THE SAME LEVEL OF PERFORMANCE

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CUBIT-UNIPI Applied Fluid Dynamics Group

Ex.: Different Blowing Configurations

First blowing type (1)

Original

Second blowing type (2)

Internal view

(in green the blowing area)

Additional parameters: • Blowing area• Flow velocity from the area

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CUBIT-UNIPI Applied Fluid Dynamics Group

Scatter Charts

ReferenceScheme 1

Scheme 2

del

ta_C

z (p

oin

ts)

delta_Cx (points)

Blowing effect

Example of modification without optimisation:Divergent conclusions!

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NUMERICAL OPTIMISATION

MORPHING and ADJOINT

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Passenger Area Geometry

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Aiming to obtain a target to evaluate

efficiency improvements, an ideal

duct is optimised.

THIS DUCT DOES NOT COPE WITH SPACE

CONSTRAINTS !

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MORPHING BOXES

Morphing boxes allow three-

dimensional geometry modifications

and have been already used in previous

works.

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13 morphing parameters are

chosen in the optimisation process.

ANSA Morphing Tools

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Opt. Control

0,902

0,904

0,906

0,908

0,910

0,912

0,914

0,916

12 17 22

Uniform

ity

Δptot [Pa]

More efficient configurations

Initial design

• Object functions:

• Pressure drop

• Flow uniformity

• Space constraints were

known and shape

modifications limited

The analysis of 1000

configurations requires 1

week on 512 cores.

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RESULTS

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CUBIT-UNIPI Applied Fluid Dynamics Group

Morphed

configurationOriginal

configuration

Ideal

configuration20,54

12,35

2,61

05

10152025

Δptot [Pa]

-40% loss

-87% loss

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RESULTS (Δptot)

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A CFD simulation and an adjoint solution give a normal

optimal displacement map for the duct, with respects

to the total pressure drop reduction.

This map steers shape change on the entire duct

avoiding geometry parametrisation.

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Adjoint optimisation

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Morphing

Adjoint

-75% loss

20,54

12,35

5,19

0

5

10

15

20

25

Originalconfig.

Morphedconfig.

Adjointconfig.

Δptot [Pa]

-40% loss

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Adjoint optimisation Results (Δptot)

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• Optimisation results depend

on the choice of the control

parameter

• High computational time

Morphing

• It allows local modifications

and their magnitude can be

limited to cope with space

constraints

Disadvantages

• Effectiveness and lower

computational power

• Modified shape regularity

• Adjoint solver is sensible to

mesh quality and shows

convergence problems

• Shape modifications are global

and might not cope with

space constraints

Disadvantages

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AdvantagesAdvantages

Adjoint

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• The Adjoint method appears very effective, but

there are problems in setting the costraints

• In case of strict space constraints it is more

appropriate to use box morphing optimisation

• Adjoint sensitivity map allows to establish the

problematic zones and to speed up the optimisation

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Coupled Approach

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Adjoint sensitivity analysis

allows to set up an

optimisation process that

converges in 100 simulations

instead of 1000.

(less than 1 day vs 1 week).

More efficient

configurations

Initial

design

0,902

0,904

0,906

0,908

0,910

0,912

0,914

0,916

0,918

0,920

0,922

9 10111213141515161718192021U

niform

ity

Δptot [Pa]

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Adjoint Driven optimisation

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Coupled approach

configuration

20,54

12,359,31

2,61

05

10152025

Δptot [Pa]

-40% loss -52% loss

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Results (Δptot)

Morphed configuration

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Original

configuration

Morphed

configuration

Coupled approach

configuration

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Results (Uniformity)

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CUBIT-UNIPI Applied Fluid Dynamics Group

WIPER ANALYSIS

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Obiettivi :

Elaborazione di una procedura di calcolo che:

• Riproduca la dinamica della pioggia sulla vettura;

• Verifichi l’adeguato smaltimento dell’acqua piovana senza

il danneggiamento degli impianti interni.

• Tergicristalli in movimento;

• Deformazione dei tergicristalli durante il moto;

• Presenza di fluido multifase nel dominio.

Problematiche :

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Impostazione del moto dei tergicristalli

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• Overset mesh Definizione dei Motion Controllers:• Morphing

• Rotation

Definizione del vincolo di ‘‘Slide-on-surface’’

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Solutore

Modelli per il Flusso:

• Implicit unsteady

• Realizable k-ε

Modelli per fluido multifase:

• Eulerian Multiphase

• Volume of Fluid

• Lagrangian Multiphase

• Fluid Film

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Condizioni al bordo

Condizioni al bordo sul dominio:

• Velocità del flusso 20 m/s;

• Aspirazione dell’aria al setto poroso è di 0,150 kg/s.

Condizioni per la pioggia:

• Dimensione particelle 0,5 mm di diametro;

• Mass flow rate 0,2 kg/s.

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Tempi di calcolo

Time-Step: 0,005 s Tempo fisico: 20 s

È stata scelta la griglia n°2 per avere tempi di calcoloragionevoli.

N° CelleN°

ProcessoriTime-step

Time-

step/Tempo

Tempo

totale

Griglia 1 90 mln 512 0.001 s 1 / 30 min.500 giorni

(stima)

Griglia 2 12,5 mln 256 0.005 s 1 / 3 min. 10 giorni

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RISULTATI - Evoluzione film d’acqua

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Analisi dei Risultati

Mass flow rate attraverso il setto poroso

Massa: 0,054 g in 20 s9,73 g in 1 h

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Conclusioni

• La procedura consente di

• Riprodurre adeguatamente la dinamica del fluido al di sopra dellavettura;

• Prevedere la dinamica dell’acqua in prossimità degli impiantivitali.

• Permette di conseguire risultati affidabili

Possibilità di utilizzare la procedura come unostrumento di progettazione intervenendo sullageometria della vettura, dove necessario, prima diavere il modello reale.

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Thank you for your attention

85

For more detailed information:Prof. Giovanni LombardiTel. +39 050 2217293 e-mail: [email protected]