Analysis of A Thermal Transpiration Flow:

Transcription

1 1 / 28 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 Graur and J. Gilbert Meolans Université de Provence Aix-Marseille I, IUSTI, UMR 6595 CNRS, Marseille, France IUVSTA Leinsweiler Hof, Leinsweiler May 16th - 19th 2011

2 Outline 2 / 28 1 Introduction: Thermal Transpiration 2 The Experimental Apparatus 3 The Experimental Methodology 3.1 The Stages of the Experiment 3.2 The Mass flow rate 4 Results 5 Conclusions

3 Introduction 3 / 28 Thermal transpiration is the Macroscopic movement of particles due only to an imposed Temperature Gradient. Objective: Measure the Mass Flow Rate along a tube induced by thermal transpiration.

4 Thermal Transpiration 4 / 28 p outlet = p inlet T outlet T inlet Infinit Volume inlet Temperature micro-tube Infinit Volume outlet Density

5 Thermal Transpiration 5 / 28 Macroscopic movement of gas particles: T inlet < T outlet Infinit Volume inlet micro-tube N inlet N outlet Infinit Volume outlet

6 Where are we? 6 / 28 1 Introduction: Thermal Transpiration 2 The Experimental Apparatus 3 The Experimental Methodology 3.1 The Stages of the Experiment 3.2 The Mass flow rate 4 Results 5 Conclusions

7 Experimental apparatus 7 / 28 experimental system Ar N2 He Vacuum pump CDG valve A micro valve valve B test section C O L D microtube thermocouples H O T D.A.Q. CDG infrared camera CDG Heater

8 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 8 / 28

9 Temperature gradient 9 / Infrared camera caption of the temperature distribution along the external surface of the micro-tube.

10 Temperature gradient 10 / Temperature Celsius degrees Infrared Camera Thot-Tcold= 37 Infrared Camera Thot-Tcold= 53 Infrared Camera Thot-Tcold= 71 analytical fitting x/l The temperature distribution along the external surface of the micro-tube.

11 Where are we? 11 / 28 1 Introduction: Thermal Transpiration 2 The Experimental Apparatus 3 The Experimental Methodology 3.1 The Stages of the Experiment 3.2 The Mass flow rate 4 Results 5 Conclusions

12 The experimental methodology 12 / 28 Initial conditions: Inlet Volume T1<T2 p1=p2 Outlet Volume micro-tube 1 2 big diameter

13 The experimental methodology 13 / 28 Inlet Volume T1<T2 Outlet Volume p1 micro-tube 1 2 p2 Close big diameter

14 The experimental methodology 14 / 28 Inlet Volume T1<T2 Outlet Volume p1 micro-tube 1 2 p2 Close big diameter

15 The experimental methodology 15 / 28 Thermal Transpiration = Mass flow imposed by a Temperature Gradient Poiseille Flow = Mass flow imposed by a Pressure Gradient Thermal Transpiration Poiseuille Flow 1.5 Pressure [torr] Pressure variation inside cold-side reservoir Pressure variation inside hot-side reservoir Helium: T -T = 40 K Time [s]

16 Stages of the experiment 16 / 28 1 Thermal Transpiration Poiseuille Flow Thermal Transpiration = Mass flow imposed by a Temperature Gradient Poiseille Flow = Mass flow imposed by a Pressure Gradient 1.5 Pressure [torr] Initial equilibrium p outlet =p inlet 1 inlet p inlet = p outlet T inlet < T outlet micro-tube outlet thermal creep flow generated by temperature difference Time [s]

17 Stages of the experiment 16 / 28 2 Thermal Transpiration Poiseuille Flow Thermal Transpiration = Mass flow imposed by a Temperature Gradient Poiseille Flow = Mass flow imposed by a Pressure Gradient 1.5 Pressure [torr] Stationary pressure variation p t is linear 2 inlet p inlet < p outlet T inlet < T outlet micro-tube outlet thermal creep flow generated by temperature difference poiseuille flow generated by pressure difference Time [s]

18 Stages of the experiment 16 / 28 Thermal Transpiration 3 Poiseuille Flow Thermal Transpiration = Mass flow imposed by a Temperature Gradient Poiseille Flow = Mass flow imposed by a Pressure Gradient 1.5 Pressure [torr] Non - Stationary pressure variation p t is not linear 3 inlet p inlet < p outlet T inlet < T outlet micro-tube thermal creep flow generated by temperature difference outlet poiseuille flow generated by pressure difference Time [s]

19 Stages of the experiment 16 / 28 Thermal Transpiration 4 Poiseuille Flow Thermal Transpiration = Mass flow imposed by a Temperature Gradient Poiseille Flow = Mass flow imposed by a Pressure Gradient 1.5 Pressure [torr] Final equilibrium p outlet p inlet 4 4 inlet p inlet < p outlet T inlet < T outlet micro-tube outlet thermal creep flow generated by temperature difference = poiseuille flow generated by pressure difference Time [s]

20 Pressure [torr] Exponential Behavior 17 / Experimental data Helium T 2-T 1 = 40 K Time [sec]

21 Exponential Behavior 17 / Pressure [torr] Exponential fit to experimental data Helium T 2-T 1= 40 K Time [sec]

22 Exponential Behavior 17 / Pressure [torr] Exponential fit to the experimental data Helium T 2-T 1= 40 K p (t)=a [1- e h p (t)=b [e c (-t/tau ) h (-t/tau c ) ] + c - 1 ] + d Time [sec]

23 Where are we? 18 / 28 1 Introduction: Thermal Transpiration 2 The Experimental Apparatus 3 The Experimental Methodology 3.1 The Stages of the Experiment 3.2 The Mass flow rate 4 Results 5 Conclusions

24 Stationary flow at t=0+ 19 / Exponential fit to the experimental data Pressure [torr] Pressure variation in time: p(t)=a [1- e h (-t/tau ) h ] + c Stationary flow limit Pressure variation speed e-05 6e-05 Stationary t= Non Sationary Pressure variation speed: (-t/tau ) dp h(t) = A [e ] h dt Tau h 4e-05 2e Time [sec]

25 Stationary flow at t=0+ Mass flow rate PV = mrt dp P = dm m + dt T Dividing by the experimental time length when the phenomenon is still stationary (Stage 2). dm t = V dp RT t (1 ǫ) ǫ = dt/t dp/p 1 20 / 28

26 Stationary flow at t=0+ 20 / 28 Mass flow rate Ṁ = V RT dp t t < 1[s] dp t is linear

27 Stationary flow at t=0+ 21 / Stationary, not-perturbed flow Pressure variation speed e-05 6e-05 4e-05 Stationary t= Non Sationary Pressure variation speed: (-t/tau ) dp h(t) = A [e ] h dt Tau h 2e Time [sec] M = V h dp h(t) dt RTh t=0

28 Where are we? 22 / 28 1 Introduction: Thermal Transpiration 2 The Experimental Apparatus 3 The Experimental Methodology 3.1 The Stages of the Experiment 3.2 The Mass flow rate 4 Results 5 Conclusions

29 Working regimes 23 / 28 δ = p (D tube/2) µ 2 T R Hydro-dynamic continuum regime Slip regime Rarefied Gas Transitional regime Free molecular regime Knudsen number δ = π 2 1 Kn 15

30 Working regimes 23 / 28 δ = p (D tube/2) µ 2 T R Hydro-dynamic continuum regime Slip regime Rarefied Gas Transitional regime Free molecular regime Knudsen number δ = π 2 1 Kn 15

31 Mass Flow Rate 24 / e-11 2e-11 Mass flow rate : Helium MFR T h - T c = 30 C MFR T h - T c = 40 C MFR T h - T c = 50 C 2.2e e-11 MFR T h - T c = 30 C MFR T h - T c = 40 C MFR T h - T c = 50 C Mass flow rate : Nitrogen M.F.R. [kgs -1 ] 1.5e-11 1e-11 M.F.R. [kgs -1 ] 1.4e-11 1e-11 5e-12 6e a) b) 2e Rarefaction parameter delta Rarefaction parameter delta

32 Where are we? 25 / 28 1 Introduction: Thermal Transpiration 2 The Experimental Apparatus 3 The Experimental Methodology 3.1 The Stages of the Experiment 3.2 The Mass flow rate 4 Results 5 Conclusions

33 Conclusions 26 / 28 Conclusions: Still no efforts have been done to describe and analyze experimentally a mass flow rate induced by thermal transpiration: Here an original method is proposed. Thermal Transpiration can be introduced for high precision rarefied gas flow control systems.

34 Perspectives 27 / 28 Perspectives: The physics behind the exponential pressure variation in time will be explored: Divergences in function of the gas rarefaction, the temperature imposed gradient and the gas nature will be investigated. A new experimental setup will be installed, different geometries of the channel will be investigated. The experimental system will be equipped with interchangeable reservoir volumes in order to investigate the influence of the reservoirs in the system s time reaction.

35 Acknowledgments 28 / 28 The research leading to these results has received funding from the European Community s Seventh Framework Programme (FP7/ under grant agreement n ).