Meccanica dei Fluidi
Alessandro Bottaro
Dipartimento di Ingegneria Civile,
Chimica e Ambientale (DICCA)
Secondo Semestre 2014/2015
Textbook
Fluid Mechanics. Fundamentals and
Applications, McGraw-Hill, 2006
Yunus A. Çengal (UNV Reno) and John M. Cimbala
(Penn State)
Includes DVD with movies created at PSU by Prof.
Gary Settles
Available at
Amazon.com, ~ $90.00 (paperback)
Libreria Frasconi, Corso Gastaldi 193r
A version in Italian exists …
Check the following web site for movies of fluid
motion, simulations, exercises, sample exams, etc.:
http://highered.mcgrawhill.com/sites/0072472367/information_center_view0/
(Online Learning Center, Student Edition)
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CD-ROM
MultiMedia Fluid Mechanics,
by G.M. Homsy et al., Cambridge U., 2004
Available at
Amazon.com, $21.00
Can be loaned at the DICCA library
(Villa Cambiaso, Mrs. Tina D’Agostino)
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Web site
All class material and announcements will be posted on
the course web site: www.dicat.unige.it/bottaro/fmnew.html
Syllabus
Schedule/Calendar
Lecture notes
Message boards
Past mid terms and finals
Exam rules
Grades
Other interesting links can be found at
www.dicat.unige.it/bottaro/teaching.html
Roberto Verzicco
Jean Pierre Petit
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IL VOLO, Jean Pierre Petit
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Grading
Mid-term exam:
50%
Strongly encouraged!!!!
Final exam:
50%
For those doing “mid-term + final” the oral exam is
optional (to be done in June/July, 2015)
The grade of the oral exam (required for those with a
grade G with 15  G < 18) averages out with the written
tests. Cut-off grade: 15.
For those not doing a “mid-term+final”:
Comprehensive written exam
compulsory oral exam
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Dates for the “mid-term + final” exams
mid term: April 3, 2015; 14h00 - 17h00, B2
final:
June 3, 2015; 9h00 - 12h00, B2
Optional oral exam for those under this option
is in June/July 2015.
The grade is registered one week after having being
posted on the instructor’s web site. If you do not accept
the grade send an email to: [email protected]
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Future indicative exam periods
July 2015
September 2015
EXACT DATES WILL BE POSTED ON THE
INSTRUCTOR’S WEB SITE
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Exam policies
Philosophy
One of the best ways to learn something is
through practice and repetition
Therefore, exercises are extremely important
in this class!
If you study and understand the exercises in
the book and elsewhere, you should not have
to struggle with the exams
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BONUS!!
The UNIGE-ME class photo competition
Keep an eye on fluid flow phenomena, and
take pictures!
Send me your best original shots, with
indications of date/location/brief description
(about 100 words) of phenomenon you are
displaying.
The three best photographs will gain 3/2/1
points to be added to your final grade.
Only one entry per student. No group entries.
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BONUS!!
The UNIGE-ME class photo competition
All photos will be judged by the instructor (with
the possible help of two colleagues) on three
criteria: aesthetic appeal, uniqueness of the
phenomenon, and quality of explanation of the
observed phenomenon.
All photos will be published in a special section
of the instructor’s web site.
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EXAMPLES
Dye Droplets at an Oil-Water Interface
This image shows the portion of a glass filled with water (bottom, higher density) and coconut oil
(top, lower density), and the droplets of food dye that rest on the interface between the oil and the
water. It illustrates the effects of surface tension, both at the oil-water interface and at the surface
of the droplets. The droplets are supported by the surface tension at the oil-water interface (they
are on the oil side of the interface and thus they will not mix with the water just yet). Interfacial
tension at the droplet surfaces means that they take on a spherical shape that minimizes their
surface area. When the droplets diffuse through the interface and enter the water (with which they
are miscible), they burst. Just below the oil interface, the different colors have not diffused into
each other yet, but they have on the bottom of the water layer (as indicated by the darker color).
1st prize MIT photo contest 2014
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EXAMPLES
Smoke Ring
Smoke rings are possible through the use of toroidal vortices. A toroidal vortex occurs when a
fast-moving parcel of fluid is injected into a stationary fluid. Different parameters, such as
temperature, relative speed, and size of the moving fluid all affect the “crispness” of a smoke ring.
Normally, a vortex is a parcel of fluid spinning around a linear axis, like a tornado or hurricane. In
a toroidal vortex, the axis is still there, but it loops and closes on itself so that the vortex forms a
donut shape. Thus the spinning air traps the smoke inside the vortex, forming a barrier with the
surrounding, stationary fluid. This spinning flow decreases the friction between this parcel of air
and the stationary air around it. Thus the ring can travel for long distances and remain intact, while
other smoke trails blown out with it dissipate.
2nd prize MIT photo contest 2014
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EXAMPLES
1st prize UWA photo contest 2013
Paint on a speaker
2nd prize UWA photo contest 2013
Dye flowing into a syphon
3rd prize UWA photo contest 2013
Water balloon to the face
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Motivation for Studying Fluid Mechanics
Fluid Mechanics is present almost everywhere
Aerodynamics
Bioengineering and biological systems
Combustion
Energy generation
Geology
Hydraulics and Hydrology
Hydrodynamics
Meteorology
Ocean and Coastal Engineering
Water Resources
…numerous other examples…
Fluid Mechanics is beautiful
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Aerodynamics
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Bioengineering
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Energy generation
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Geology
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River Hydraulics
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Hydraulic Structures
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Hydrodynamics
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Meteorology
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Water Resources
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Fluid Mechanics is Beautiful
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Tsunamis
Tsunami: Japanese for “Harbour Wave”
Created by earthquakes, land slides, volcanoes,
asteroids/meteors
Pose infrequent but high risk for coastal regions.
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Tsunamis: role in religion, evolution, and
apocalyptic events?
Most cultures have deep at
their core a flood myth in which
the great bulk of humanity is
destroyed and a few are left to
repopulate and repurify the
human race. In most of these
stories, God is meting out
retribution, punishing those
who have strayed from his path
Were these “local” floods due
to a tsunami instead of global
events?
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Tsunamis: role in religion, evolution, and
apocalyptic events?
Scientists now widely accept that the
worldwide sequence of mass extinctions at
the Cretaceous-Tertiary (K/T) boundary 65.5
million years ago was directly caused by the
collision of an asteroid or comet with Earth.
Evidence for this, all dated to the same
epoch as the extinction event, includes:
the large (200-km diameter) buried
impact structure at Chicxulub in Mexico's
Yucatan Peninsula,
the worldwide iridium-enriched layer at
the K/T boundary,
and the tsunamic deposits well inland in
North America, all dated to the same
epoch as the extinction event.
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Tsunamis: role in religion, evolution, and
apocalyptic events?
La Palma Mega-Tsunami = geologic time bomb?
Cumbre Vieja volcano eruption could cause
western half of La Palma (Canary islands) to
collapse into the Atlantic and send a 100 m
tsunami crashing into Eastern coast of U.S.
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Methods for Solving Fluid Dynamics
Problems
Analytical Fluid Dynamics (AFD)
Mathematical analysis of governing
equations, including exact and
approximate solutions. This is the primary
focus of this course
Computational Fluid Dynamics (CFD)
Numerical solution of the governing
equations
Experimental Fluid Dynamics (EFD)
Observation and data acquisition.
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Analytical Fluid Dynamics
How fast do tsunamis travel in the deep ocean?
Incompressible Navier-Stokes equations
Linearized wave equation for inviscid, irrotational flow
Shallow-water approximation, l/h >> 1 (also kh << 1)
For g = 9.8 m/s2 and h = 3000 m, c = 171 m/s = 617 km/h
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Computational Fluid Dynamics
In comparison to analytical
methods, which are good
for providing solutions for
simple geometries or
behavior for limiting
conditions (such as
linearized shallow water
waves), CFD provides a
tool for solving problems
with nonlinear physics and
complex geometry.
Animation by Vasily V. Titov, Tsunami
Inundation Mapping Efforts, NOAA/PMEL
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Experimental Fluid Dynamics
Oregon State University
Wave Research
Laboratory
Model-scale experimental
facilities
Tsunami Wave Basin
Large Wave Flume
Dimensional analysis
(Chapter 7 of C&C) is
very important in
designing a model
experiment which
represents physics of
actual problem
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Experimental Fluid Dynamics
Experiments are sometimes
conducted in the field or at full
scale
For tsunamis, data acquisition is
used for warning
DART: Deep-ocean Assessment
and Reporting of Tsunamis
(U.S. National Tsunami Hazard
Mitigation Program)
Primary sensor: Bourdon tube for
measuring hydrostatic pressure
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THE FLUID DYNAMICS GROUP AT DICAT
Dipartimento di Ingegneria delle Costruzioni, dell’Ambiente e del Territorio,
Università degli Studi di Genova.
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BRIEF OVERVIEW OF RECENT ACTIVITIES
1. FUNDAMENTAL STUDIES ON STABILITY AND TRANSITION
- LINEAR STABILITY ANALYSES IN DUCTS, BOUNDARY
LAYERS, FLOWS PAST COMPLIANT WALLS, ETC.
- DIRECT NUMERICAL SIMULATIONS
2. SIMULATION OF 2D AND 3D COMPLEX MOVING GEOMETRIES
- CONVENTIONAL AND CHIMERA GRID APPROACHES
WITH AMR
- FLAPPING FOILS AND WINGS, OPTIMISATION
- BEATING CILIA (ACTIVELY AND PASSIVELY)
3. DETONATION AND SHOCK WAVES
NOTE:
ALL CODES DEVELOPED AND SHOWN HERE ARE HOME-MADE
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1.
FUNDAMENTAL STUDIES ON
STABILITY AND TRANSITION
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EFFECT OF WALL COMPLIANCE
Study of the effect of compliant walls on the onset of hydrodynamic
instability modes, and on the creation of hydroelastic modes
Wall: shell (or plate) theory
Disturbance field behaves like exp(iax + ibz + st)
Eigensolver: QZ-global or Arnoldi approaches
Initial value solver to treat the initial transient stages
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BY-PASS TRANSITION IN A SQUARE DUCT
secondary mean
cross-flow
link with optimal
pertubations?
• Always linearly stable …
• DNS shows a mean
cross-flow motion
• Link with optimal perturbations?
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2.
SIMULATION OF 2D AND 3D
COMPLEX MOVING GEOMETRIES
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PROPULSION BY BEATING CILIA: THE PLEUROBRACHIA
“Planar” beat patterns of combplates of this small marine invertebrate generate surface waves:
Antiplectic metachronal wave
Propulsion of
the organism
Propulsion
NUMERICAL TECHNIQUE: IMMERSED BOUNDARIES
9 combplates beating at 15Hz
Velocity vectors (arrows) together with velocity magnitude (contours)
3D EFFECTS
The horizontal velocity vectors are magnified 10 times compared to vectors in the vertical plane
3D EFFECTS
Advection of a passive scalar
PASSIVE CILIA: TWO-WAY COUPLING
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STRUCTURAL MODELING
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Testing the model in the fluid (a vortex pair in a periodic box)
Amplitude of the velocity
Testing the model in the fluid (flow in a channel with one hairy wall)
Amplitude of the velocity
AN ALTERNATIVE TO THE IMMERSED BOUNDARY TECHNIQUE:
THE OVERLAPPING (or CHIMERA) GRIDS METHOD
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OVERVIEW OF THE OVERLAPPING GRIDS METHOD
MOVING BOUNDARIES
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OVERVIEW OF THE OVERLAPPING GRIDS METHOD
EASILY EXTENDABLE TO MULTIPLE MOVING BODIES
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FLAPPING FOILS, i.e. ICARUS DREAM
July 8, 2006
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heaving:
pitching:
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SIMPLE ENOUGH: CAN USE SINGLE GRID APPROACH
Coarse grid: 64*64 nodes and and domain radius equal to 10 chord lengths
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… OR
STILL USE 2 OVERLAPPING GRIDS
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HEAVING AIRFOIL, VALIDATION OF START UP
Heathcote, S., Gursul. I., Jet Switching phenomena for a
Plunging Airfoil, 34th Fluid Dynamics Conference and
Exhibit, Portland, Oregon, AIAA-2004-2150, 2004.
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HEAVING AIRFOIL, THRUST PRODUCING CASE
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HEAVING AIRFOIL, REVERSED VON KARMAN STREET
Heathcote, S., Gursul. I., Jet Switching phenomena for a
Plunging Airfoil, 34th Fluid Dynamics Conference and
Exhibit, Portland, Oregon, AIAA-2004-2150, 2004.
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HEAVING AIRFOIL, neutral wake at reduced frequency
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THE DRAGONFLY
Vorticity contours on different planes
Instantaneous streamlines
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3.
SHOCK AND DETONATION WAVES
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SOME NUMERICAL EXAMPLES
COMPRESSIBLE FLOW PAST A CYLINDER WITH AMR
(AUTOMATIC MESH REFINEMENT)
GRID SUMMARY
ITER 1
NG = 5
NP = 11433
IP = 233
ITER 30
NG = 43
NP = 40443
IP = 691
INITIAL CONDITIONS
BEHIND THE SHOCK
r = 2.6
U = 1.250
V=0
P = 3.214
MACH = 0.962
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INITIAL CONDITIONS
IN FRONT THE SHOCK
r =1
U=0
V=0
P = 0.714
MACH = 0
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SOME NUMERICAL EXAMPLES
COMPRESSIBLE FLOW PAST A CYLINDER WITH AMR
Density
contours
AMR levels
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SOME NUMERICAL EXAMPLES
SHOCK/BUBBLE INTERACTION WITH AMR
GRID SUMMARY
ITER 1
NG = 12
NP = 24520
IP = 0
ITER 3000
NG = 12
NP = 27282
IP = 0
INITIAL CONDITIONS
BEHIND THE SHOCK
r = 3.81
U = 2.85
V=0
P = 10
MACH = 0.1485
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INITIAL CONDITIONS
IN FRONT THE SHOCK
r =1
U=0
V=0
P=1
MACH = 0
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INITIAL CONDITIONS
WITHIN THE BUBBLE
r = 0.1
U=0
V=0
P=1
MACH = 0
Information and Introduction
SOME NUMERICAL EXAMPLES
SHOCK/BUBBLE INTERACTION WITH AMR
Schlieren countours
Density contours and AMR levels
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SOME NUMERICAL EXAMPLES
EXPLOSION IN A CLOSED BOX
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Contents of the Fluid Mechanics course
1.
2.
3.
4.
5.
6.
Introductions and basic concepts
Properties of fluids
Pressure and fluid statics
Fluid kinematics
Mass, Bernoulli and energy equation
Momentum analysis of flow systems
7.
8.
9.
10.
11.
Dimensional analysis and p theorem
Internal flows and Moody chart …
(TECH. PHYSICS ?!)
Differential analysis of fluid flows
Approximate solutions of the Navier-Stokes equations
External flows: drag and lift
(IF TIME PERMITS …)
Everybody, including “old” students can take mid-term and final …
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