Tubo di Pitot
Tubo di Pitot
Flussi laminari e flussi turbolenti
C.1.1 TURBOLENZA
• Turbolenza presente in molti campi dell’ingegneria (aerodinamica,
diluizione di inquinanti, studio della scia a valle di un corpo in movimento,
miscelazione e combustione in reattori chimici, moto dell’aria nell’apparato
respiratorio e del sangue a valle di valvole cardiache, ecc.).
• Turbolenza: fenomeno non totalmente compreso ma non casuale:
le statistiche della separazione di coppie di particelle (~t3) sono diverse da
quelle dei random walks (~t1) (Ottino 1990).
• Approccio
topologico:
punti
critici
iperbolici
ed
ellittici,
geometria frattale e strutture ad
“8 in 8” (es.: Antonia et al. 1986,
Davila & Vassilicos 2003).
PUNTO CRITICO IPERBOLICO
PUNTO CRITICO ELLITTICO
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C.1.2 TURBOLENZA 2D in oceano
C.1.2 TURBOLENZA 2D in oceano
C.1.2 TURBOLENZA 2D in atmosfera
• Turbolenza quasi-bidimensionale (Q2D): importanza teorica
(semplificazione della 3D ma anche peculiarità: conservazione lagrangiana
della vorticità, cascata inversa dell’energia, ecc.) e pratica (es. previsioni
atmosferiche, moto delle masse d’acqua negli oceani e nell’atmosfera).
VORTICE E PUNTO
CRITICO ELLITTICO
GETTO 2D
PUNTI CRITICI
IPERBOLICI
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Measurement via PTVA of the acceleration on
quasi-two-dimensional turbulent-like flows
controlled by multi-scale electromagnetic forces
Simone Ferrari(1)(2), Lionel Rossi(2) and John Christos Vassilicos(2)
(1)
(2)
1.2. Q2D EM controlled multi-scale flows
• Experimental set-up: a shallow layer of brine EM forced.
• Topology and forcing time-dependency are known and controlled.
• Power-law shaped energy spectrum and Richardson-like pair
dispersion properties (Rossi et al., JFM 2006) in a laminar steady flow.
• Experiments: constant and time-dependent forcing.
Electrodes
Electrodes
Magnets
Magnets’ size:
160 mm,
40 mm,
10 mm
Tank size: 1700x1700 mm²
Brine layer’s thickness: 5 mm
a
b
Flow visualizations
with constant forcing;
(a, b, c: whole field;
d: SW quarter)
Stirring on the SW
quarter (same
flow on the
left)
c
d
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Diluizione e turbolenza
Constant forcing
Time-dependent forcing
3.5 Time dependent flows
• Time dependent forcing with different frequencies, mean intensities
and magnitudes, to excite different flow scales.
• A further step towards fully controlled turbulent-like flows.
Mass exchange
between small
and medium
scales is
enhanced.
Mass exchange
between large
and medium
scales is
enhanced.
Expected time scales of the three scales of forcing t versus current I; M160,
M40 and M10 refers to the magnets’ size; the black straight line identifies
the current value over which the bottom friction is no more negligible.
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3.1 Results: measured trajectories
• Trajectories are measured at all the scales of the flow (stagnation
points with three different length scales).
Example of measured trajectories (8 runs): on the left the whole investigation field, on the right a
zoom on the SW quarter
MAGNETS’
POSITION
= hyperbolic stagnation point
= elliptical stagnation point
large scales medium scales
small scales
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Dal Lagrangiano all’Euleriano
3.2 Results: Eulerian fields
VELOCIY:
hyperbolic stagnation point;
ACCELERATION:
“source”;
elliptical stagnation point
“sink”;
“spreader”
The mesh has 600x600 points with a mesh’s size of 3x3 pixels (resolution 4 times higher than PIV)
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Accelerazione
• Flusso con accelerazione locale nulla.
Deformazione
• L’accelerazione è alta dove sia la
velocità che la deformazione sono alte.
Accelerazione
Velocità
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3.3 Results: Navier-Stokes equations’ terms
• A zoom on the SW quarter to highlight
the
physical
coherence
of
the
measures.
• Acceleration is much larger than
viscous term everywhere but at the
small scales (like in turbulent flows).
Viscous term
Acceleration
Velocity
This allows an
indirect
measure of the
pressure
gradient over
all the
investigation
field.
Acceleration and viscous term in
pixel/s2, velocity in pixel/s; 1 pixel
= 0.495 mm
12b/ 17
3.4 Results: towards efficient mixing
u·a
·a
MAGNETS’ POSITION
Power input and output, in pixel2/s3;
1 pixel = 0.495 mm
Stirring intensity, in s-2;
1 pixel = 0.495 mm
•
The power input-output is closely related to the pressure term.
•
•
Experimental measure of a over the whole investigation field.
Local maxima of a correspond to acceleration sources, local minima of a
correspond to acceleration sinks.
Stirring is stronger where a large and positive (Vassilicos, 2002):
the points of highest stirring are not the ones connected to the largest power
input.
Tools to optimize the power input according to the required mixing =>
efficient mixing.
•
•
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[email protected]