Tordella, Daniela

English

TORDELLA, Daniela

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

05 August 2020POLITECNICO DI TORINORepository ISTITUZIONALEDetermination of Density and concentration from fluorescent images of a gas flow, Ludwig Prandtl – Fluid DynamicsSeminar (chair E.Bodenschatz), July 2, 2008, Max Plank Institute for Dynamics and Self-Organization, Gottingen,Germany. / TORDELLA D.. - (2008). ((Intervento presentato al convegno Seminar tenutosi a Max Planck Institute,Goettingen nel July 1 - 2, 2008.OriginalDetermination of Density and concentration from fluorescent images of a gas flow, Ludwig Prandtl –Fluid Dynamics Seminar (chair E.Bodenschatz), July 2, 2008, Max Plank InstitutePublisher:PublishedDOI:Terms of use:openAccessPublisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/2367702 since:DETERMINATION OF DENSITY ANDCONCENTRATION FROM FLUORESCENT IMAGESOF A GAS FLOWApplications to laboratory hypersonic jetsD. TordellaDipartimento di Ingegneria Aerospaziale - Politecnico di TorinoM. BelanDipartimento di Ingegneria Aerospaziale - Politecnico di MilanoS. de PonteDipartimento di Ingegneria Aerospaziale - Politecnico di Milano1 Facilitieselectron gun andsecondary pumps     primary vacuum pump     vacuum vesselcamera    auxiliary windows/portstruncated nozzlesfitting  ambient gas inletde Laval nozzles       fitting  •Vacuum vessel •Nozzles •Electron gun •High-sensitivity camera22 Capability of the system / tested flows(ICIASF meeting 2001, Astrophysics and Space Science 2004)• Long-scale jet visualization (up to 100 initial diameters)• 2D-visualizations of 3D-flows (slices)• Density measurements• Concentration measurements, jet gas 6= environment gas•Mixing layer thickness, shock thickness measurements3 Physical conditions• Rarefied gases (n < 1022m−3, p < 100 Pa and ρ < 1 g/m3 for air)• Stagnation/ambient pressure ratio: p0/pamb up to 105•Mach number M up to 50 (or more, v ∼ vlimit).• Density ratio 0.04 < ρjet/ρamb < 45 (0.01 to 100 is possible).• ReD up to 2000 (diameter), Rex > 105 (axial length)34 Density and concentration (mixing) measurements4.1 Fluorescent emission of rarefied gasesRadiant intensity I vs numerical density n (Gru¨n, 1954):I =k1 n1 +2nσ2Pij−1√√√√4pimkT =k1 n1 + k2(T )nTypical fluorescent emission at constant T:0 2 4 6 8 10 12 14 16numerical density n [x 1023 m-3]0246810Photoemission        I(n,T)[relative units]I ~ k1 nI ~ k1/k2(T)(gas mixtures: I~Σi Ii)44.2 Image analysis: concentration450 500 550 600 650 7000.20.40.60.81wavelength [nm]B G R20406080100fluorescence  spectrum   CCDresponserelativeintensityrelative outputX5Algorithm: (Exp Fluids 2008)I = k n total emission ∝ numerical density nR = kR nG = kG nB = kB nCCD output colors (partial emission) ∝ nC = aR + bG+ cB = kC n weighted spectral superposition ∝ nFor different gases:jet gasR jet = kRjn jetG jet = kGjn jetB jet = kBjn jetambient gasR amb = kRan ambG amb = kGan ambB amb = kBan ambExample: He jet in Ar ambient (IHe < IAr).Decoupled emission gives R = RHe +RAr , G = GHe +GAr=⇒ rpure Ar ≤GR≤ rpure HeIn general, for a mixture of 2 gases,rmin ≤C1C2≡ a1R + b1G + c1Ba2R + b2G + c2B≤ rmax6Decoupled emission for a given color combination C:Cmix = C amb + C jetkC n = kan amb + kjn jetIntroducing zgas = ngas/n:kC = kaz amb + kjz jet = ka(1− z jet) + k jetz jetColor combinations setup (choice of a1, b1, c1, a2, b2, c2):C1 = a1R + b1G + c1B ; C2 = a2R + b2G + c2BDefinition of the color ratio:r ≡ C1C2=kC1kC2=ka1z amb + kj1z jetka2z amb + kj2z jetConcentration (solving for z jet):z jet(r) =ka1 − ka2 r(ka1 − kj1)+(kj2 − ka2)r(k-constants are obtained by experimental calibration)74.3 Image analysis: densityRadiant intensity of gases (decoupled emissions):I jet = kj n jetI amb = ka n ambRadiant intensity of the gas mixture gives the total numerical density:I = I jet + I amb = (kj z jet + ka z amb)n=⇒ n = I/(kj z jet + ka z amb)Density (m: molar masses):ρ = n(z ambm amb + z jetm jet)Remarks:On the image domain r(x, y) 7→ z jet(x, y), z amb(x, y) 7→ ρmix(x, y)• C1, C2 should be chosen to get the widest range for r = C1/C2• results may be strongly noise-sensitive• if (jet gas)=(ambient gas) the density is much easier to calculate84.4 Calibration (example)(* 2008).75  1.5 2.25  3.0 3.75 4.510002000300040005000600070008000Ar calibration @ 16 kVIntensity [pixel values]RBGn [x1021 m-3]95 Underexpanded jetspressure gauge vacuum vesselnozzle section (particular)D internal reservoirjet gas  inletjetsolenoid  valvevalvesolenoid valveambient gas inlet valve• Small jet radius: rjet < 0.1 rvessel• Quasi-stationary jet: ∆tvalve tjetAdjustable parameters:• (stagnation/ambient) pressure ratio p0/p amb: Mmax = f(p0/p amb)• density ratio ρjet/ρamb (selection of light or heavy gases)10Jet structure:Mach diskbarrel shockmixing layerρjet/ρamb >1 ρjet/ρamb<<1 0.04 < ρjet/ρamb <105<M<50, K~1M>1 M< 3Reδ fluctuations zoneReD 5000 < Rex<105~ ~~ ~~ ~Jets similarity:• Short range (barrel zone): ρjet/ρamb similarity,(the jet properties depend on the pressure ratio p0/p amb)• Long range: Mach similarity,(the jet properties depend on the density ratio ρjet/ρamb)116 ResultsExample: Argon jet in Helium medium127 ResultsHelium jets in Argon medium: jets at several pressure ratios p0/p ambMmax ' 36 Mmax ' 25 Mmax ' 17Argon jets in Helium medium: jets at several pressure ratios p0/p ambMmax ' 36 Mmax ' 29 Mmax ' 25(other gases in use: air, xenon)137.1 Light jet in heavy medium, same γ (monoatomic gases)Example: Helium jet in Argon medium.x axisA Bunbalanced RGB image, long exposure time (80ms  time scale)p0/p amb ' 840 ; Mmax ' 26 ; ρ jet/ρ amb ' 0.14weak gradients, density/pressure fluctuations after the shock14Helium jet in argon medium: axial density and concentrationx/dρ0 10 20 30 40 50 60 70 80 90 100020406080100120140[ m3]mgzHe0.000.250.500.751.0015Helium jet in argon medium: radial density10 20 30 40 500100200300400500y/djet axisρ[mg/m3]•: section (A), before the Mach disk. 2: section (B), after the Mach disk.16Helium jet in argon medium: radial concentration10 20 30 40 500.00.10.20.30.40.50.60.70.80.91.0zHejet axis y/d•: section (A), before the Mach disk. 2: section (B), after the Mach disk.177.2 Heavy jets in light mediums, same γ (monoatomic gases)Example: Argon jet in Helium medium.A Bx axisunbalanced RGB image, long exposure time (80ms  time scale)p0/p amb ' 1200 ; Mmax = 29 ; ρ jet/ρ amb ' 11sharp gradients, no fluctuations after the normal shock18Argon jet in helium medium: axial density and concentrationρx/d0 10 20 30 40 50 60 70 80 9005001000150020000.000.250.500.751.00[ m3]mg zAr19Argon jet in helium medium: radial density10 20 30 40 5001002003004005006007008009001000y/djet axisρ[mg/m3]•: section (A), before the Mach disk. 2: section (B), after the Mach disk.20Argon jet in helium medium: radial concentrationzArjet axis y/d10 20 30 40 500.50.60.70.80.91.0•: section (A), before the Mach disk. 2: section (B), after the Mach disk.217.3 Comparison with literature data0.5 1.0 1.5 2.0x/L1234  5  6  7008ρ/ρfpresent experiment (He jet)present experiment (Ar jet)LI experiment, Kobayashi et al, 1984 Euler method, Nishida et al, 1985 DSMC method, D'Ambrosio et al, 19991/r 2 expansion 9227.4 z-measurements: collected dataNear jet: Mixing layer (plume) spreading angle α vs Mmax. (* 2008)15 20 30 40Mmax  αAr/HeXe/HeHe/ArHe/Xe51015[o]25 35 45Barrel zone, before the Mach disk. Cross-section at x = 0.8 barrel lengths23Far jet: jet spreading angle α vs ρjet/ρamb (* 2007, unpublished [Msc thesis])0 1 2 3 4-1001020[o]Ar/HeXe/HeHe/Ar ρjet /ρamb  αPapamoschou & Roshko model (1988)long range, Cross-section at 2.5 barrel lengths248 Underexpanded jet: results outlineJet morphology in the range 500 < p0/p amb < 105, 0.1 < ρ jet/ρ amb < 15heavy jets, e.g.: He in air, Ar, Xemixing layercorebright zonecore}}mixing layerbright zonelight jets, e.g:Ar, Xe in He, air fluctuations for p0/pamb<1000259 Isoentropic jetsvacuum vesselde Laval nozzle jet gas  inletjetsolenoid valveambient gas inletvalvedrive gas    inletpiston• Small jet radius: rjet < 0.1 rvessel• Fast (single pulse) jets: ∆tpiston ' tjetAdjustable parameters:• jet Mach number M jet• density ratio ρjet/ρamb (selection of light or heavy gases)26Expected jet structure:cocoonbow shockcoreterminal	  shockworking surfacenozzle27Interchangeable de Laval nozzlesMach 5Mach 10Mach 15Mach 2028Working principle of the annular piston:29System timingintensifiercamerapiston/nozzleservertimer 131 2timer 25 64ambient gas valvemagnet controljet gas loadingpiston control jet30Piston view (connected to the vacuum vessel):31Camera / triggered intensifier view32Working tests: a M=15 Argon jet38.5 mx1x1x1x1025 mm 20 mm 20 mm 70 mm 70 mm 70 mm 20 mm3310 BibliographyBelan M., De Ponte S., Tordella D., Determination of density and concentration from fluorescent imagesof a gas flow. Exp Fluids 2008 - online firstBelan M., De Ponte S., Tordella D., Simultaneous density and concentration measurements on hyper-sonic jets. Abstract, EFMC6 KTH, Euromech Fluid Mechanics Conference 6, Royal Institute oftechnology, Stockholm, 2006.Belan M., De Ponte S., Massaglia S., Tordella D., Experiments and numerical simulations on the mid-term evolution of hypersonic jets. Astrophysics and Space Science 293 (1-2): 225-232, 2004Belan M., De Ponte S., Tordella D., Cross density variations and vorticity generation in compressibleshears. Abstract, 57th APS-DFD, Annual Meeting of the American Physical Society, Division ofFluid Dynamics, 2004, Seattle, Washington, University of WashingtonBelan M., Tordella D., De Ponte S., A system of fast acceleration of a mass of gas for the laboratorysimulation of stellar jets. Proceedings of the ICIASF meeting, Cleveland 2001, 409-416Belan M., De Ponte S., D’Ambrosio D., Tordella D., Design of an experiment on the spatial evolutionof hypersonic jets. Atti XVI Conferenza AIDAA, Palermo, 200134

Determination of Density and concentration from fluorescent images of a gas flow, Ludwig Prandtl – Fluid Dynamics Seminar (chair E.Bodenschatz), July 2, 2008, Max Plank Institute for Dynamics and Self-Organization, Gottingen, Germany.

PORTO Publications Open Repository TOrino

DETERMINATION OF DENSITY AND
CONCENTRATION FROM FLUORESCENT IMAGES
OF A GAS FLOW
Applications to laboratory hypersonic jets
D. Tordella
Dipartimento di Ingegneria Aerospaziale - Politecnico di Torino
M. Belan
Dipartimento di Ingegneria Aerospaziale - Politecnico di Milano
S. de Ponte
Dipartimento di Ingegneria Aerospaziale - Politecnico di Milano
1 Facilities
electron gun and
secondary pumps
     primary 
vacuum pump
     vacuum vessel
camera
    auxiliary 
windows/ports
truncated nozzles
fitting 
 
ambient 
gas inlet
de Laval nozzles
       fitting 
 
•Vacuum vessel •Nozzles •Electron gun •High-sensitivity camera
2
2 Capability of the system / tested flows
(ICIASF meeting 2001, Astrophysics and Space Science 2004)
• Long-scale jet visualization (up to 100 initial diameters)
• 2D-visualizations of 3D-flows (slices)
• Density measurements
• Concentration measurements, jet gas 6= environment gas
•Mixing layer thickness, shock thickness measurements
3 Physical conditions
• Rarefied gases (n < 1022m−3, p < 100 Pa and ρ < 1 g/m3 for air)
• Stagnation/ambient pressure ratio: p0/pamb up to 105
•Mach number M up to 50 (or more, v ∼ vlimit).
• Density ratio 0.04 < ρjet/ρamb < 45 (0.01 to 100 is possible).
• ReD up to 2000 (diameter), Rex > 105 (axial length)
3
4 Density and concentration (mixing) measurements
4.1 Fluorescent emission of rarefied gases
Radiant intensity I vs numerical density n (Gru¨n, 1954):
I =
k1 n
1 +
2nσ2Pij−1
√√√√4pi
mkT
 =
k1 n
1 + k2(T )n
Typical fluorescent emission at constant T:
0 2 4 6 8 10 12 14 16
numerical density n [x 1023 m-3]
0
2
4
6
8
10
Photoemission 
       I(n,T)
[relative units]
I ~ k1 n
I ~ k1/k2(T)
(gas mixtures: I~Σi Ii)
4
4.2 Image analysis: concentration
450 500 550 600 650 700
0.2
0.4
0.6
0.8
1
wavelength [nm]
B G R
20
40
60
80
100
fluorescence
  spectrum
   CCD
response
relative
intensity
relative 
output
X
5
Algorithm: (Exp Fluids 2008)
I = k n total emission ∝ numerical density n
R = kR n
G = kG n
B = kB n
CCD output colors (partial emission) ∝ n
C = aR + bG+ cB = kC n weighted spectral superposition ∝ n
For different gases:
jet gas

R jet = kRjn jet
G jet = kGjn jet
B jet = kBjn jet
ambient gas

R amb = kRan amb
G amb = kGan amb
B amb = kBan amb
Example: He jet in Ar ambient (IHe < IAr).
Decoupled emission gives R = RHe +RAr , G = GHe +GAr
=⇒ rpure Ar ≤
G
R
≤ rpure He
In general, for a mixture of 2 gases,
rmin ≤
C1
C2
≡ a1R + b1G + c1B
a2R + b2G + c2B
≤ rmax
6
Decoupled emission for a given color combination C:
Cmix = C amb + C jet
kC n = kan amb + kjn jet
Introducing zgas = ngas/n:
kC = kaz amb + kjz jet = ka(1− z jet) + k jetz jet
Color combinations setup (choice of a1, b1, c1, a2, b2, c2):
C1 = a1R + b1G + c1B ; C2 = a2R + b2G + c2B
Definition of the color ratio:
r ≡ C1
C2
=
kC1
kC2
=
ka1z amb + kj1z jet
ka2z amb + kj2z jet
Concentration (solving for z jet):
z jet(r) =
ka1 − ka2 r(
ka1 − kj1
)
+
(
kj2 − ka2
)
r
(k-constants are obtained by experimental calibration)
7
4.3 Image analysis: density
Radiant intensity of gases (decoupled emissions):
I jet = kj n jet
I amb = ka n amb
Radiant intensity of the gas mixture gives the total numerical density:
I = I jet + I amb = (kj z jet + ka z amb)n
=⇒ n = I/(kj z jet + ka z amb)
Density (m: molar masses):
ρ = n(z ambm amb + z jetm jet)
Remarks:
On the image domain r(x, y) 7→ z jet(x, y), z amb(x, y) 7→ ρmix(x, y)
• C1, C2 should be chosen to get the widest range for r = C1/C2
• results may be strongly noise-sensitive
• if (jet gas)=(ambient gas) the density is much easier to calculate
8
4.4 Calibration (example)
(* 2008)
.75  1.5 2.25  3.0 3.75 4.5
1000
2000
3000
4000
5000
6000
7000
8000
Ar calibration @ 16 kV
In
te
ns
ity
 [p
ixe
l v
al
ue
s]
R
B
G
n [x1021 m-3]
9
5 Underexpanded jets
pressure gauge vacuum vessel
nozzle section (particular)
D
 internal 
reservoir
jet gas
  inlet
jetsolenoid
  valve
valve
solenoid valve
ambient 
gas inlet 

valve
• Small jet radius: rjet < 0.1 rvessel
• Quasi-stationary jet: ∆tvalve tjet
Adjustable parameters:
• (stagnation/ambient) pressure ratio p0/p amb: Mmax = f(p0/p amb)
• density ratio ρjet/ρamb (selection of light or heavy gases)
10
Jet structure:
Mach
 disk
barrel shock
mixing layer
ρjet/ρamb >1 ρjet/ρamb<<1 0.04 < ρjet/ρamb <10
5<M<50, K~1M>1 M< 3
Reδ 
fluctuations zone
ReD 
5000 < Rex<105
~ ~
~ ~
~ ~
Jets similarity:
• Short range (barrel zone): ρjet/ρamb similarity,
(the jet properties depend on the pressure ratio p0/p amb)
• Long range: Mach similarity,
(the jet properties depend on the density ratio ρjet/ρamb)
11
6 Results
Example: Argon jet in Helium medium
12
7 Results
Helium jets in Argon medium: jets at several pressure ratios p0/p amb
Mmax ' 36 Mmax ' 25 Mmax ' 17
Argon jets in Helium medium: jets at several pressure ratios p0/p amb
Mmax ' 36 Mmax ' 29 Mmax ' 25
(other gases in use: air, xenon)
13
7.1 Light jet in heavy medium, same γ (monoatomic gases)
Example: Helium jet in Argon medium.
x axis
A B
unbalanced RGB image, long exposure time (80ms  time scale)
p0/p amb ' 840 ; Mmax ' 26 ; ρ jet/ρ amb ' 0.14
weak gradients, density/pressure fluctuations after the shock
14
Helium jet in argon medium: axial density and concentration
x/d
ρ
0 10 20 30 40 50 60 70 80 90 1000
20
40
60
80
100
120
140
[
 m3]mg
zHe
0.00
0.25
0.50
0.75
1.00
15
Helium jet in argon medium: radial density
10 20 30 40 500
100
200
300
400
500
y/djet axis
ρ
[mg/m3]
•: section (A), before the Mach disk. 2: section (B), after the Mach disk.
16
Helium jet in argon medium: radial concentration
10 20 30 40 500.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
zHe
jet axis y/d

•: section (A), before the Mach disk. 2: section (B), after the Mach disk.
17
7.2 Heavy jets in light mediums, same γ (monoatomic gases)
Example: Argon jet in Helium medium.
A B
x axis
unbalanced RGB image, long exposure time (80ms  time scale)
p0/p amb ' 1200 ; Mmax = 29 ; ρ jet/ρ amb ' 11
sharp gradients, no fluctuations after the normal shock
18
Argon jet in helium medium: axial density and concentration
ρ
x/d
0 10 20 30 40 50 60 70 80 90
0
500
1000
1500
2000
0.00
0.25
0.50
0.75
1.00
[
 m3]mg zAr
19
Argon jet in helium medium: radial density
10 20 30 40 500
100
200
300
400
500
600
700
800
900
1000
y/djet axis
ρ
[mg/m3]
•: section (A), before the Mach disk. 2: section (B), after the Mach disk.
20
Argon jet in helium medium: radial concentration
zAr
jet axis y/d
10 20 30 40 50
0.5
0.6
0.7
0.8
0.9
1.0
•: section (A), before the Mach disk. 2: section (B), after the Mach disk.
21
7.3 Comparison with literature data
0.5 1.0 1.5 2.0
x/L
1
2
3
4
  5
  6
  7
00
8
ρ/ρf
present experiment (He jet)
present experiment (Ar jet)
LI experiment, Kobayashi et al, 1984 
Euler method, Nishida et al, 1985 
DSMC method, D'Ambrosio et al, 1999
1/r 2 expansion 
9
22
7.4 z-measurements: collected data
Near jet: Mixing layer (plume) spreading angle α vs Mmax. (* 2008)
15 20 30 40
Mmax
  α
Ar/He
Xe/He
He/Ar
He/Xe
5
10
15
[o]
25 35 45
Barrel zone, before the Mach disk. Cross-section at x = 0.8 barrel lengths
23
Far jet: jet spreading angle α vs ρjet/ρamb (* 2007, unpublished [Msc thesis])
0 1 2 3 4
-10
0
10
20
[o]
Ar/He
Xe/He
He/Ar
 ρjet /ρamb
  α
Papamoschou & Roshko model (1988)
long range, Cross-section at 2.5 barrel lengths
24
8 Underexpanded jet: results outline
Jet morphology in the range 500 < p0/p amb < 10
5, 0.1 < ρ jet/ρ amb < 15
heavy jets, e.g.: 
He in air, Ar, Xe
mixing
 layer
core
bright zone
core
}
}mixing layerbright zone
light jets, e.g:

Ar, Xe in He, air 
fluctuations for p0/pamb<1000
25
9 Isoentropic jets
vacuum vessel
de Laval
 nozzle 
jet gas
  inlet
jet
solenoid valve
ambient 
gas inlet
valve
drive gas 
   inlet
piston
• Small jet radius: rjet < 0.1 rvessel
• Fast (single pulse) jets: ∆tpiston ' tjet
Adjustable parameters:
• jet Mach number M jet
• density ratio ρjet/ρamb (selection of light or heavy gases)
26
Expected jet structure:
cocoon
bow shock
core
terminal	 
 shock
working
 surface
nozzle
27
Interchangeable de Laval nozzles
Mach 5
Mach 10
Mach 15
Mach 20
28
Working principle of the annular piston:
29
System timing
intensifier
camera
piston/nozzle
server
timer 1
31 2
timer 2
5 64
ambient gas 
valve
magnet control
jet gas loading
piston control 
jet
30
Piston view (connected to the vacuum vessel):
31
Camera / triggered intensifier view
32
Working tests: a M=15 Argon jet
38.5 mx1
x1
x1
x10
25 mm 20 mm 20 mm 70 mm 70 mm 70 mm 20 mm
33
10 Bibliography
Belan M., De Ponte S., Tordella D., Determination of density and concentration from fluorescent images
of a gas flow. Exp Fluids 2008 - online first
Belan M., De Ponte S., Tordella D., Simultaneous density and concentration measurements on hyper-
sonic jets. Abstract, EFMC6 KTH, Euromech Fluid Mechanics Conference 6, Royal Institute of
technology, Stockholm, 2006.
Belan M., De Ponte S., Massaglia S., Tordella D., Experiments and numerical simulations on the mid-
term evolution of hypersonic jets. Astrophysics and Space Science 293 (1-2): 225-232, 2004
Belan M., De Ponte S., Tordella D., Cross density variations and vorticity generation in compressible
shears. Abstract, 57th APS-DFD, Annual Meeting of the American Physical Society, Division of
Fluid Dynamics, 2004, Seattle, Washington, University of Washington
Belan M., Tordella D., De Ponte S., A system of fast acceleration of a mass of gas for the laboratory
simulation of stellar jets. Proceedings of the ICIASF meeting, Cleveland 2001, 409-416
Belan M., De Ponte S., D’Ambrosio D., Tordella D., Design of an experiment on the spatial evolution
of hypersonic jets. Atti XVI Conferenza AIDAA, Palermo, 2001
34


Determination of density and concentration from ﬂuorescent images of a gas ﬂow. Exp Fluids

Experiments and numerical simulations on the midterm evolution of hypersonic jets.

Determination of Density and concentration from fluorescent images of a gas flow, Ludwig Prandtl - Fluid Dynamics Seminar (chair E.Bodenschatz), July 2, 2008, Max Plank Institute for Dynamics and Self-Organization, Gottingen, Germany

https://iris.polito.it/retrieve/handle/11583/2367702/52871/slidesgot08.pdf

Determination of Density and concentration from fluorescent images of a gas flow, Ludwig Prandtl - Fluid Dynamics Seminar (chair E.Bodenschatz), July 2, 2008, Max Plank Institute for Dynamics and Self-Organization, Gottingen, Germany

Abstract

Similar works

Full text

Available Versions

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

PORTO Publications Open Repository TOrino