5.3.1 Simulation Conditions
The influence on the flow and heat transfer characteristics of a helium dielectric-barrier discharge atmospheric-pressure plasma jet is investigated for various gas flow rates. The parameters used in this study are the same as the Chapter 4, except the gas flow rate.
5.3.2 Results and Discussion
The fluid flow and heat transfer for a helium dielectric barrier discharge atmospheric-pressure jet tested for different helium gas flow rates are presented. Figure 5-12 shows the comparisons of the temperature distributions for an adiabatic substrate for gas flow rates between 10 and 30 slm. It is observed that a higher gas flow rate brings a lower temperature distribution. This phenomenon can also been discovered at the temperature distributions for an isothermal substrate shown in Figure 5-13. A higher gas flow rate is corresponding to a higher gas velocity shown in Figure 5-14. A constant thermal source provided by the plasma fluid model resisting a higher gas velocity leads a lower temperature distribution. The predicted streamlines for various gas flow rates with H d 10 are presented in Figure 5-15. It is observed that there is a slight change in position and size of the vortexes as the gas flow rate changes. Figure 5-16 to 5-18 show the comparison of the distributions of species mole fraction for various gas flow rates.
Figure 5-19 shows the time-histories of velocity at the export of the helium
dielectric barrier discharge atmospheric-pressure jet for various helium gas flow rates and for different thermal boundaries. The jet exit velocity increases from 6 to 17 m/s with increasing the helium gas flow rate from 10 slm to 30 slm for d 1 mm and
10
H d . The jet exit temperature as a function of time for different helium gas flow rates for two different thermal boundaries is shown in Figure 5-20. At the plasma jet exit, the temperatures decrease, respectively, from 342 to 317 K for an adiabatic boundary and from 329 to 314 K for an isothermal boundary with increasing the gas flow rate from 10 to 30 slm. Figure 5-21 and 5-22 show the horizontal velocity and temperature profiles along the center line of the helium DBD APPJ for various gas flow rates.
The approximated Reynolds numbers based on plasma jet gap distance and inflow conditions increase from 30 to 90 with increasing the helium gas flow rate from 10 slm to 30slm. The bulk temperatures for various gas flow rates are list in Table 6.The bulk temperature decreases significantly with increasing the gas flow rate. A strong dependence of heat transfer on gas flow rate is shown. Figure 5-23 shows the local Nusselt number distributions along the substrate surface for various gas flow rates. The local Nusselt numbers at the stationary point show a maximum value of 38.4 for gas flow rate of 30 slm, and a minimum value of 10.2 for gas flow rate of 10slm. Higher gas flow rate generates strong convection effects, which results in higher Nu.
5.4 Summary
Numerical simulations to investigate the flow and heat transfer characteristics in a helium dielectric barrier discharge atmospheric-pressure jet are carried out for different electrode lengths, jet-to-substrate spacing rates, and helium gas flow rates.
Chapter 6
Conclusion and Recommendations for Future Study
6.1 Summaries of This Thesis
In this thesis, a parallelized 2D/2D-axisymmetric pressure-based, finite-volume gas flow model has been reported. Implementation and validations against earlier simulations data are described in detail. Developed code is then applied to simulate two-dimensional silane/hydrogen gas discharge in a PECVD chamber, helium micro-cell plasma and helium dielectric barrier discharge atmospheric-pressure plasma jet.
The main conclusions of this study can be briefly summarized as follows:
1. Parallelized 2D gas flow model using finite-volume method for simulating compressible, viscous, heat conductive and rarefied gas flows at all speeds with conjugate heat transfer was developed and validated against previous simulations.
2. Parallel efficiency of a micro-scale supersonic channel gas flow simulation with 800,000 computational cells using 64 processors maintained about 70%.
3. In the silane/hydrogen gas discharge in a low-pressure PECVD chamber driven by a RF power source (27.12 MHz), the conduction is dominated.
4. Helium micro-cell plasma is simulation coupling with a parallelized fluid modeling code, and a reverse flow field is found with considering the plasma momentum source.
5. A non-equilibrium atmospheric-pressure helium dielectric barrier discharge driven by a realistic distorted-sinusoidal voltage power source (25 kHz) is investigated by using the developed gas flow model coupling with a parallelized fluid modeling code. Electrode lengths, jet-to-substrate spacing rates, and gas flow
rates have a remarkable influence on the flow and heat transfer characteristics.
6.2 Recommendations for Future Work
There are several recommendations for further work:
1. To further reduce the computational time in large-scale gas flow problem.
2. To solve the gas flow model in the curvilinear coordinate frame for complex geometry problem.
3. To involve the turbulent model for complex flows.
4. To add chemical reaction and electrochemistry module
5. To extend the gas flow model into three-dimensional version for realistic applications
References
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1029-1050
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“Heat and Mass Transfer in Recirculating Flow.” Academic Press, 1980
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[14] Harlow, F.H. and Amsden, A.A., “The SMAC Method: A Numerical Technique for Calculating Incompressible Fluid Flows.” Los Alamos Scientific Laboratory Rept, LA-4370, 1970.
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197-213.
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[22] Karki, K.C. and Patankar, S.V., “Pressure Based Calculation Procedure for Viscous Flows at all Speeds in Arbitrary Configurations,” AIAA J., Vol. 27, pp.
1167-1174,1989.
[23] Lin, K.M., “Development of Parallel Hybrid Simulation of Gas Discharge and Gas Flow and Its Application in the Modeling of Atmospheric-Pressure Helium Dielectric Barrier Discharge Jet Considering Impurities”, Ph.D. thesis, National Chiao Tung University, Taiwan, 2012.
[24] Merkle, C.L. and Athavale, M., 1987, AIAA Technical Paper, 87-1137.
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[26] Patankar, S.V. and Spalding, D.B., 1972, Int. J. Heat & Mass Transfer, Vol. 15, No.
1787-1806
[27] Rahman, Md. M., Alim, M. A., Saha, S.and Chowdhury, M. K., “A Numerical study of mixed convection in a square cavity with q heat conducting square cylinder at different locations”, J. Mech. Eng, 39, pp.78, 2008.
[28] Rhie, C.M., 1989, AIAA Journal, Vol. 27, No. 8, pp. 1017-1018.
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[35] Shterev, K.S., Stefanov, S.K., “Pressure based finite volume method for calculation of compressible viscous gas flows”, J. Comp. Phys. n.229, pp 461-480, 2010.
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Table 1. Lennard-Jones potential parameters. [Bird et al., 2002]
Table 2. Constant-pressure specific heats and heat of formation of various ideal gases.
[Borgnakke & Sonntag, 2008]
†Chase, M. W. et al., JANAF Thermochemical Tables, Third Edition, J. Phys. Chem. Ref. Data, Vol. 14, Suppl.1, 1985
Table 3. Scaling parameters used in gas flow model.
Scaling Parameter Description Unit
L Characteristic length m
U Characteristic speed m s
Characteristic density kg m 3
T Characteristic temperature K
Characteristic viscosity kg m s
k Characteristic conductivity W m s
R Characteristic gas constant J mol K
,
Cp Characteristic specific heat capacity J kg K
Table 4. Substance parameters in helium micro-cell plasma.
Material [kg m3] Cp [J kg K ] k W m K [ ]
Electrode Al 2750 900 228
Insulator SiO2 2200 703 1.4
Plasma He 0.16 5194 0.15
Table 5. Test cases and results of a helium dielectric barrier discharge atmospheric-pressure plasma jet for various H d for d 1 mm, and gas flow rate of 20slm.
Case H d Nx Ny Pstag [Torr] Nustag
a 5 140 160 760.033 3.5
b 7.5 150 160 760.027 2.8
c 10 160 160 750.023 2.4
d 12.5 170 160 760.02 2.1
e 15 180 160 760.018 1.8
Table 6. The approximated Reynolds numbers and bulk temperatures for various gas flow rates.
Gas flow rate [slm] 10 15 20 25 30
Re 30 45 60 75 90
Tbulk (K) 346.3 330.9 323.2 318.5 315.4
Figure 2-1: Two-dimensional control volume.
Figure 2-2: Flowchart of the extended SIMPLE algorithm.
Figure 3-1: Schematic of the computational grid a in two-dimensional lid-driven cavity.
Figure 3-2: Streamlines for driven cavity flow with Reynolds numbers of 100, 400 and 1,000 (top to bottom). Note: Ghia et al. [1982] (left); present (right).
Figure 3-3: Streamlines for driven cavity flow with Reynolds numbers of 3200, 5000, and 10000 (top to bottom). Note: Ghia et al. [1982] (left); present (right).
Figure 3-4: Schematic of the flow in a square cavity with a square block.
Figure 3-5: Streamlines for Different Locations of Cylinder at Ri = 0. Note: Rahman et al. [2008] (left); present (right).
Figure 3-6: Isotherms for Different Locations of Cylinder at Ri = 0. Note: Rahman et al. [2008] (left); present (right).
Figure 3-7: Streamlines for Different Locations of Cylinder at Ri = 1. Note: Rahman et al. [2008] (left); present (right).
Figure 3-8: Isotherms for Different Locations of Cylinder at Ri = 1. Note: Rahman et al. [2008] (left); present (right).
Figure 3-9: Streamlines for Different Locations of Cylinder at Ri = 5. Note: Rahman et al. [2008] (left); present (right).
Figure 3-10: Isotherms for Different Locations of Cylinder at Ri = 5. Note: Rahman et al. [2008] (left); present (right).
(a) (b)
Figure 3-11: Distributions of (a) streamlines and (b) isotherms at Ri = 5, Lx=0.25 and Ly=0.5. Note: T=50 K (top), 100 K (middle), and 200 K (bottom).
(a) (b)
Figure 3-12: Distributions of (a) streamlines and (b) isotherms at Ri = 5, Lx=0.75 and Ly=0.5. Note: T=50 K (top), 100 K (middle), and 200 K (bottom).
Figure 3-13: Schematic of the two-dimensional micro-scale channel flow
Figure 3-14: Normalization Distributions of Pressure, Density, Temperature, Velocity in x- and y-direction in the channel at Ma=2.4261 and Kn=0.05.
Figure 3-15: Normalization Distribution of horizontal velocity. Note: Shterev and Stefanov [2010] (upper); present (lower).
Figure 3-16: Normalization Distribution of temperature. Note: Shterev and Stefanov [2010] (upper); present (lower).
Figure 3-17: Profiles of the horizontal velocity along the center line of the channel (y=Hch/2) for different spatial steps in front of the square.
Figure 3-18: Profiles of the horizontal velocity along the center line of the channel (y=Hch/2) for different spatial steps behind of the square.
Figure 3-19: Temperature profiles along the center line of the channel (y=Hch/2) for different spatial steps in front of the square.
Figure 3-20: Temperature profiles along the center line of the channel (y=Hch/2) for different spatial steps behind of the square.
Figure 3-21: Parallel Performance and runtime per time step of a 2D micro-scale supersonic flow with 2000x400 computational cells.
Figure 4-1: Simulated cycle average of electron number density (a) with and (b) without heating flow field.
Figure 4-2: Simulated cycle averaged distributions of electron temperature (a) with and (b) without heating flow field.
Figure 4-3: Simulated cycle averaged distributions of N4+ (a) with and (b) without considering neutral flow field.
Figure 4-4: Simulated cycle averaged distributions of electron Hemeta (a) with and (b) without heating flow field.
Figure 4-5: Sketch of a H2/SiF4 PECVD chamber.
Figure 4-6: Schematic of the computational grid in the H2/SiF4 PECVD chamber.
(a)
(b)
(c)
Figure 4-7: Distribution of (a) pressure, (b) density (c) and gas temperature in a PECVD chamber.
(a)
(b)
(c)
Figure 4-8: Distribution of (a) total enthalpy, (b) density of H2 and (c) SiH4 in a PECVD chamber.
(a)
(b)
(c)
(d)
Figure 4-9: Distribution of (a) velocity in x-direction, (b) Velocity in y-direction, (c) Mean velocity and (d) streamline in a PECVD chamber.
Figure 4-10: Sketch of helium micro-cell plasma.
Figure 4-11: Distribution of plasma u-momentum source in the He micro-cell plasma.
Figure 4-12: Distribution of plasma v-momentum source in the He micro-cell plasma
Figure 4-13: Distribution of plasma energy source in the He micro-cell plasma.
Figure 4-14: Temperature distribution of a He micro-cell plasma without considering plasma momentum source.
Figure 4-15: Mean speed distribution of a He micro-cell plasma without considering plasma momentum source.
Figure 4-16: Mean speed distribution of a He micro-cell plasma with considering plasma momentum source.
Figure 4-17: Force field distribution of a He micro-cell plasma.
Figure 4-18: Temperature distribution of a He micro-cell plasma with considering plasma momentum source.
Figure 4-19: Schematic sketch of a planar dielectric barrier discharge atmospheric-pressure plasma jet.
Figure 4-20. Sketch of two-dimensional dielectric barrier discharge atmospheric-pressure plasma jet.
Figure 4-21. Schematic of the computational grid in the two-dimensional dielectric barrier discharge atmospheric-pressure plasma jet.
Figure 4-22. Time history of velocity and temperature profiles at the export of helium DBD APPJ for d 1 mm, H d 10, Re 60 and gas flow rate of 20 slm.
(a)
(b)
Figure 4-23: Steady-steady distribution of (a) pressure and (b) density of helium DBD APPJ for d 1 mm, H d 10, Re 60 and gas flow rate of 20 slm.
(a)
(b)
Figure 4-24: Spatial distribution of temperature with (a) a adiabatic substrate surface;
(b) an isothermal substrate surface of a helium DBD APPJ for d 1 mm, H d 10, Re 60 and gas flow rate of 20 slm.
(a)
(b)
Figure 4-25: Spatial distribution of velocity (a) in x-direction and (b) in y-direction of helium DBD APPJ for d 1 mm, H d 10, Re 60 and gas flow rate of
20 slm.
(a)
(b)
Figure 4-26: Steady-steady distributions of (a) mean speed, (b) streamlines and velocity vector of helium DBD APPJ for d 1 mm, H d 10, Re 60 and gas
flow rate of 20 slm.
Figure 4-27: streamlines and velocity vector patterns of helium DBD APPJ for 1 mm
d , H d 10, Re 60 and gas flow rate of 20 slm.
Figure 4-28: Time history of streamlines and velocity vector patterns of helium DBD APPJ for d 1 mm, H d 10, Re 60 and gas flow rate of 20 slm.
Figure 4-29. Horizontal velocity profiles in the helium DBD APPJ channel at different x positions for d 1 mm, H d 10, Re 60 and gas flow rate of 20 slm.
Figure 4-30. Temperature profiles in the helium DBD APPJ channel at different x positions for d 1 mm, H d 10, Re 60 and gas flow rate of 20 slm.
Figure 4-31. Horizontal velocity and temperature profiles along the center line of the helium DBD APPJ channel for d 1 mm, H d 10, Re 60 and gas flow rate of
20 slm.
Figure 4-32. Vertical velocity profiles between helium DBD APPJ and substrate at different y positions for d 1 mm, H d 10, Re 60 and gas flow rate of
20 slm.
Figure 4-33. Temperature profiles between helium DBD APPJ and substrate at different y positions for d 1 mm, H d 10, Re 60 and gas flow rate of
20 slm.
Figure 4-34. Local Nusselt number along a isothermal substrate surface for d 1 mm, 10
H d , Re 60 and gas flow rate of 20 slm.
(a) (e)
(b) (f)
(c) (g)
(d) (h)
Figure 5-1. Comparison of the distributions of (a, e) pressure, (b, f) over-all density, (c, g) temperature for an adiabatic wall, and (d, h) temperature for an adiabatic wall for
electrode lengths of 5 mm and 25 mm, respectively.
(a) (e)
(b) (f)
(c) (g)
(d) (h)
Figure 5-2. Comparison of the distributions of velocity components for electrode lengths of (a-d) 5 mm and of (e-h) 25 mm, respectively.
(a) (e)
(b) (f)
(c) (g)
(d) (h)
Figure 5-3. Comparison of the distributions of species mole fraction for electrode lengths of (a-d) 5 mm and of (e-h) 25 mm, respectively.
(a) (b)
(c) (d) (e)
Figure 5-4. Comparison of the temperature distributions for an adiabatic substrate for H d (a) 5, (b) 7.5, (c) 10, (d) 12.5, (e) and 15, respectively.
(a) (b)
(c) (d) (e)
Figure 5-5. Comparison of the temperature distributions of an isothermal substrate for H d (a) 5, (b) 7.5, (c) 10, (d) 12.5, (e) and 15, respectively.
(b)
(c) (d) (e)
Figure 5-6. Comparison of the mean speed distributions for H d (a) 5, (b) 7.5, (c) 10, (d) 12.5, (e) and 15, respectively.
(a) (b) (c) (d) (e)
Figure 5-7. Comparison of the streamline profiles for H d (a) 5, (b) 7.5, (c) 10, (d) 12.5, (e) and 15, respectively.
(b)
(c) (d) (e)
Figure 5-8. Comparison of the distributions of XHe for various H d (a) 5, (b) 7.5, (c) 10, (d) 12.5, (e) and 15, respectively.
(a) (b)
(c) (d) (e)
Figure 5-9. Comparison of the distributions of XN2 for various H d (a) 5, (b) 7.5, (c) 10, (d) 12.5, (e) and 15, respectively.
(a) (b)
(c) (d) (e)
Figure 5-10. Comparison of the distributions of XO2 for various H d (a) 5, (b) 7.5, (c) 10, (d) 12.5, (e) and 15, respectively.
Figure 5-11. Local Nusselt number along a isothermal substrate surface for various H d .
(a) (b)
(c) (d) (e)
Figure 5-12. Comparison of the temperature distributions for an adiabatic substrate for various gas flow rates of (a) 10 slm, (b) 15 slm, (c) 20 slm, (d) 25 slm, (e) and 30 slm, respectively.
(a) (b)
(c) (d) (e)
Figure 5-13. Comparison of the temperature distributions for an isothermal wall for various gas flow rates of (a) 10 slm, (b) 15 slm, (c) 20 slm, (d) 25 slm, (e) and 30 slm, respectively.
(a) (b)
(c) (d) (e)
Figure 5-14. Comparison of the mean speed distributions for gas flow rates of (a) 10 slm, (b) 15 slm, (c) 20 slm, (d) 25 slm, (e) and 30 slm, respectively.
(a) (b) (c) (d) (e)
Figure 5-15. Comparison of the streamline profiles for various gas flow rates of (a) 10 slm, (b) 15 slm, (c) 20 slm, (d) 25 slm, (e) and 30 slm, respectively.
(b) (b)
(c) (d) (e)
Figure 5-16. Comparison of the distributions of XHe for various gas flow rates of (a) 10 slm, (b) 15 slm, (c) 20 slm, (d) 25 slm, (e) and 30 slm, respectively.
(c) (b)
(c) (d) (e)
Figure 5-17. Comparison of the distributions of XN2 for various gas flow rates of (a) 10 slm, (b) 15 slm, (c) 20 slm, (d) 25 slm, (e) and 30 slm, respectively.
(d) (b)
(c) (d) (e)
Figure 5-18. Comparison of the distributions of XO2 for various gas flow rates of (a) 10 slm, (b) 15 slm, (c) 20 slm, (d) 25 slm, (e) and 30 slm, respectively.
Figure 5-19. Horizontal velocity profiles at export of helium DBD APPJ as a function of times for various gas flow rates.
Figure 5-20. Temperature profiles at export of helium DBD APPJ as a function of times for various gas flow rates.
Figure 5-21. Horizontal velocity profiles along the center line of the helium DBD APPJ for various gas flow rates.
Figure 5-22. Temperature profiles along the center line of the helium DBD APPJ for various gas flow rates.
Figure 5-23. Local Nusselt number profiles along the substrate surface for various gas flow rates.
Publication List of Meng-Hua Hu
Journal Papers:
1. C.-T. Hung, M.-H. Hu, J.-S. Wu* and F.-N. Hwang, “A New Paradigm for Solving Plasma Fluid Modeling Equations,” Computer Physics Communications, Vol. 177, pp. 138-139, 2007.
2. M.-H. Hu, J.-S. Wu* and Y.-S. Chen, ”Development of a Parallelized 2D/2D-Axisymmetric Navier-Stokes Equation Solver for All-Speed Gas Flows,”
Computers & Fluids, Vol. 45, pp. 241–248, 2011.
3. K.-M. Lin, M.-H. Hu, C.-T. Hung and J.-S. Wu*, “Development of a Parallel 2-D Hybrid Modeling Algorithm for Gas Flow and Discharge,” Computer Physics Communications, 2012(submitted).
4. M.-H. Hu, K.-M. Lin, J.-S. Wu* and Y.-S. Chen, “Flow Simulation of a Cold Planar Atmospheric-Pressure Plasma Jet Considering Gas Heating,” International Journal of Heat and Mass Transfer (preparing, 2012).
International Conference Papers:
Hwang, “Non-Thermal Plasma Simulation Using Parallel 2D Fluid Modeling
Code,” Workshop on High Performance Simulation of Physical Systems, HPSPS’09, March 2-5 (2009), Kaohsiung, Taiwan.
3. Meng-Hua Hu, J.-S. Wu*, Y. -S. Chen, “Development of a Parallelized 2D/2D-Axisymmetric Navier-Stokes Solver for Conjugate Heat Transfer at All-Speed Gas Flows, The 22nd International Conference on Parallel Computational Fluid Dynamics, Kaohsiung, Taiwan, May 17-21, 2010.
4. J.-S. Wu*, K.-M. Lin, M.-H. Hu, C.-T. Hung and Y.M. Chiu, “Progress in Developing Fluid Modeling and Gas Flow Simulation Codes for General Gas-Discharge Application,” American Vacuum Society International Plasma Workshop, Taipei, Taiwan, March 22-25, 2011.
5. K.-M. Lin, M.-H. Hu, C.-T. Hung and J.-S. Wu*, “Numerical Investigation of Atmospheric Pressure Plasma Jet Using Helium Discharge Driven a Radio-Frequency Power Source,” American Vacuum Society International Plasma Workshop, Taipei, Taiwan, March 22-25, 2011.
6. K.-M. Lin, M.-H. Hu, C.-T. Hung and J.-S. Wu*, “Development of Parallel Hybrid Simulation Tools for Modeling Atmospheric-Pressure Gas Discharges,”
8th EU-Japan Joint Symposium on Plasma Processing (JSPP2012), Nara, Japan, January 16-18, 2012.
7. K.-M. Lin, M.-H. Hu, C.-T. Hung and J.-S. Wu*, “Development of a Parallel 2-D Hybrid Gas Flow and Plasma Fluid Modeling Algorithm and Its Application in Simulating Atmospheric-Pressure Plasma Jet,” The 7th Asia-Pacific International Symposium on the Basics and Applications of Plasma Technology, Taipei, Taiwan, April 14-16, 2012.
Domestic Conference Papers:
1. M.-H. Hu, J.-S. Wu* and Y.-S. Chen, “Development of a Pressured-Based Finite Volume Compressible Flow Solver at All Speeds with Conjugate Heat Transfer,”
2010 CFD Conference Taiwan, Chungli, Taiwan, July 29-July 31, 2010.
2. A. Aliat, K.-M Lin, J.-S. Wu*, and M.-H. Hu, “Numerical Investigation of an Anode Supported Intermediate Temperature Solid Oxide Button Fuel Cell by considering Feed Tubes Positioning,” 2010 CFD Conference Taiwan, Chungli, Taiwan, July 29-July 31, 2010.
3. M.-H. Hu, J.-S. Wu*, Y.-S. Chen, and J.-P. Yu, “A Pressure-based All-speed Navier-Stokes Equation Solver and Its Parallel Implementation,” 18th Computational Fluid Dynamics Conference in Taiwan, Yilan, Taiwan, August 3-5, 2011