Analysis of A Thermal Transpiration Flow · IUVSTA 2011 Leinsweiler 16th 19th of May Stages of the experiment Thermal Transpiration Poiseuille Flow Poiseille Flow = Mass flow imposed

IUVSTA 2011Leinsweiler 16th - 19th of May

Analysis of A Thermal Transpiration Flow:A Circular Cross Section Micro-tube Submitted

to a Temperature Gradient Along its Axis

Marcos Rojas, Pierre Perrier, Irina Graurand J. Gilbert Meolans

Universite de Provence Aix-Marseille I, IUSTI, UMR 6595 CNRS,Marseille, France

IUVSTALeinsweiler Hof, Leinsweiler

May 16th - 19th 2011

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Outline

1 Introduction: Thermal Transpiration

2 The Experimental Apparatus

3 The Experimental Methodology

3.1 The Stages of the Experiment3.2 The Mass flow rate

4 Results

5 Conclusions

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Introduction

Thermal transpiration is the Macroscopic movement of particlesdue only to an imposed Temperature Gradient.

Objective: Measure the Mass Flow Rate along a tube inducedby thermal transpiration.

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Thermal Transpiration

poutlet = pinlet

Toutlet > Tinlet

Infinit Volume inlet

Infinit Volume outlet

Tempera

ture

Density

micro-tube

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Macroscopic movement of gas particles:

Infinit Volume inlet

Infinit Volume outlet

micro-tube

N inlet > N outlet

>

>

>

>

T inlet < T outlet

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Where are we?





4 Results

5 Conclusions

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Experimental apparatus

N2 He

micro valve

Vacuum pump

microtube HOT

COLD

CDG

Heater

thermocouples

CDG

1 2 3

D.A.Q.>>

valve A valve B

Ar

infrared camera

CDG

test section

experimental system

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Micro-tube

The circular cross-section glass micro-tube.

dtube = 485µm ± 1.2% ; dext = 6.5mm ± 0.1mm

Ltube = 5.27cm ± 0.01cm ; Λ = 1.14W/m◦C

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Temperature gradient

10030.5

Infrared camera caption of the temperature distribution alongthe external surface of the micro-tube.

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Temperature gradient

20

30

40

50

60

70

80

90

100

110

0 0.2 0.4 0.6 0.8 1

Infrared Camera Thot-Tcold= 37 Infrared Camera Thot-Tcold= 53 Infrared Camera Thot-Tcold= 71

analytical fitting

x/L

Tem

pera

ture

Cels

ius d

egre

es

The temperature distribution along the external surface of themicro-tube.

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Where are we?





4 Results

5 Conclusions

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The experimental methodology

Initial conditions:

Inlet Volume

Outlet Volume

1 2

p1=p2

T1<T2

micro-tube

big diameter

>

>

>

> >

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>

>

>

Close

p1 > p2

>

Inlet Volume

Outlet Volume

1 2

T1<T2

micro-tube

big diameter

> >

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>

>

>

Close

p1 > p2

>

Inlet Volume

Outlet Volume

1 2

T1<T2

micro-tube

big diameter

> >

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Poiseuille Flow

Poiseille Flow = Mass flow imposed by a Pressure Gradient

Thermal Transpiration = Mass flow imposed by a Temperature Gradient

1.45

1.46

1.47

1.48

1.49

1.5

0 10 20 30 40 50 60

Pre

ssu

re [

torr

]

Time [s]

Pressure variation inside cold-side reservoirPressure variation inside hot-side reservoir

Helium: T -T = 40 K 2 1

21 3 4

21 3 4

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Stages of the experiment


Poiseuille Flow



1.45

1.46

1.47

1.48

1.49

1.5

0 10 20 30 40 50 60

Pre

ssu

re [

torr

]

Time [s]

1

1

1 Initial equilibrium

poutlet

= pinlet

micro-tube

>

T inlet < T outlet

p inlet = p outlet

thermal creep flow generatedby temperature difference

>

1inlet outlet

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Poiseuille Flow



1.45

1.46

1.47

1.48

1.49

1.5

0 10 20 30 40 50 60

Pre

ssu

re [

torr

]

Time [s]

2

2

2 Stationary pressure variation

∆p

∆tis linear

micro-tube

>

T inlet < T outlet

p inlet < p outlet

poiseuille flow generatedby pressure difference


>>

>

2inlet outlet

>

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Poiseuille Flow



1.45

1.46

1.47

1.48

1.49

1.5

0 10 20 30 40 50 60

Pre

ssu

re [

torr

]

Time [s]

3

3

3 Non - Stationary pressure variation

∆p

∆tis not linear

micro-tube

>

T inlet < T outlet

>

p inlet < p outlet



>

>

3inlet outlet

>

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Poiseuille Flow



1.45

1.46

1.47

1.48

1.49

1.5

0 10 20 30 40 50 60

Pre

ssure

[to

rr]

Time [s]

4

4

4 Final equilibrium

poutlet

> pinlet

micro-tube

>

T inlet < T outlet

>

p inlet < p outlet



=

>

>

4inlet outlet

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Exponential Behavior

1.38

1.39

1.4

1.41

1.42

1.43

1.44

1.45

200 220 240 260 280

Pre

ssu

re [

torr

]

Time [sec]

Experimental data

Helium T -T = 40 K12

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1.38

1.39

1.4

1.41

1.42

1.43

1.44

1.45

200 220 240 260 280

Pre

ssu

re [

torr

]

Time [sec]

Exponential fit to experimental data


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1.38

1.39

1.4

1.41

1.42

1.43

1.44

1.45

200 220 240 260 280

Pre

ssu

re [

torr

]

Time [sec]

Exponential fit to the experimental data


p (t)=A [1- e ] + c(-t/Tau )

>

p (t)=B [e - 1 ] + d(-t/Tau )

>

c

h

h

c

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Where are we?





4 Results

5 Conclusions

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Stationary flow at t=0+

1.38

1.39

1.4

1.41

1.42

1.43

1.44

1.45

200 220 240 260 280

Pre

ssu

re [to

rr]

Time [sec]

Exponential fit to the experimental data

p(t)=A [1- e ] + c(-t/Tau )h

0

2e-05

4e-05

6e-05

8e-05

0.0001

0.00012

0.00014

0.00016

0.00018

0.0002

0.00022

0.01 0.1 1 10 100

Pre

ssu

re v

aria

tio

n s

pe

ed

12

Stationary

t=0+

Non

Sationary

Stationary flow limit

Pressure variation in time:

h

dp (t) A [e ](-t/Tau )h

Pressure variation speed:

h

Tauhdt=

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Mass flow rate

→ PV = mRT → dPP =

dmm +

dTT

Dividing by the experimental time length when the phenomenon isstill stationary (Stage 2).

dm∆t =

VRT

dP∆t (1 − ǫ)

→ ǫ = dT/TdP/P ≪ 1

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Mass flow rate

M =V

RTdP∆t

∆t < 1[s] → dP∆t is linear

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Time [sec]

0

2e-05

4e-05

6e-05

8e-05

0.0001

0.00012

0.00014

0.00016

0.00018

0.0002

0.00022

0.01 0.1 1 10 100

Pre

ssu

re v

aria

tio

n s

pe

ed

12

Stationary

t=0+

Non

Sationary

Stationary, not-perturbed flow

dp (t) A [e ](-t/Tau )h

Pressure variation speed:

V dp (t)

RT t=0

M =dt

>

h

h

Tauh

h

h

dt=

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Where are we?





4 Results

5 Conclusions

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Working regimes

δ =p·(Dtube/2)µ·√

2·T ·R

δ =

√π

2 · 1Kn 15

Hydro-dynamiccontinuumregime

Slip regime

Transitionalregime

Free molecularregime

0.01 0.1 10Knudsen number

>

Rarefied Gas

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Working regimes

δ =p·(Dtube/2)µ·√

2·T ·R

δ =

√π

2 · 1Kn 15

Hydro-dynamiccontinuumregime

Slip regime

Transitionalregime

Free molecularregime

0.01 0.1 10Knudsen number

>

Rarefied Gas

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Mass Flow Rate

2e-12

6e-12

1e-11

1.4e-11

1.8e-11

2.2e-11

1 10 0

5e-12

1e-11

1.5e-11

2e-11

2.5e-11

0.1 1 10

M.F

.R. [k

gs-

1 ]

Rarefaction parameter delta

Mass flow rate : HeliumMFR Th - Tc= 30 CMFR Th - Tc= 40 CMFR Th - Tc= 50 C

Mass flow rate : Nitrogen

Rarefaction parameter delta

a) b)M

.F.R

. [k

gs-

1 ]

MFR Th - Tc= 30 CMFR Th - Tc= 40 CMFR Th - Tc= 50 C

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Where are we?





4 Results

5 Conclusions

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Conclusions

Conclusions:

◮ Still no efforts have been done to describe and analyzeexperimentally a mass flow rate induced by thermaltranspiration: Here an original method is proposed.

◮ Thermal Transpiration can be introduced for high precisionrarefied gas flow control systems.

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Perspectives

Perspectives:

◮ The physics behind the exponential pressure variation intime will be explored: Divergences in function of the gasrarefaction, the temperature imposed gradient and the gasnature will be investigated.

◮ A new experimental setup will be installed, differentgeometries of the channel will be investigated.

◮ The experimental system will be equipped withinterchangeable reservoir volumes in order to investigatethe influence of the reservoirs in the system’s time reaction.

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Acknowledgments

The research leading to these results has received funding fromthe European Community’s Seventh Framework Programme(FP7/2007-2013 under grant agreement n 215504).

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Documents

Analysis of A Thermal Transpiration Flow · IUVSTA 2011 Leinsweiler 16th 19th of May Stages of the experiment Thermal Transpiration Poiseuille Flow Poiseille Flow = Mass flow imposed