Chapter 3 Verifications and Parallel Performance of the Gas Flow Model
3.5. Summary
In this chapter, the validations of the gas flow model and parallel performance were presented. The validation is found to be very good agreement with previous simulations. Parallel efficiency is reasonably good up to 64 processors with parallel efficiency of ~70%.
Chapter 4
Applications in Low-Temperature Plasma Discharge
This chapter presents the gas flow model coupling with the plasma fluid modeling applied in low-temperature plasma discharge. Figure 4-1 to 4-4 exhibit the plasma properties include electron number density, electron temperature, and ion number densities in an atmospheric-pressure plasma jet w/ and w/o considering the neutral gas flow model. These results demonstrate that influence of gas flow model in the low-temperature plasma discharge should not be underestimated.
4.1. Simulation of Silane/Hydrogen Gas Discharge in a Plasma Enhanced Chemical Vapor Deposition (PECVD) Chamber
This phase demonstrates a large-scale realistic PECVD using the mixture Silane/Hydrogen gas. In order to get a uniform thickness of coating, optimization of the flow streamlines with respect to the influence of deposition parameters by using numerical simulation is necessary. Figure 4-5 show the schematic diagram of the PECVD chamber. Due to the symmetry of the plasma chamber, only half domain is considered in this simulation.
4.1.1. Simulation Conditions
Simulation conditions in this study include: (1) chamber pressure (600 mtorr); (2) a square glass plate (20 Å ~ 20 cm); (3) substrate temperature (250C); (4) gap distance between shower-head and substrate (14 mm) and (5) inflow rate ratio of silane to hydrogen (50 : 80 sccm).
The boundary conditions used in the gas flow model are defined as At the gas inlet:
0, i, i, extrapolation, i
u v v T T P Y Y (4-1)
where v is calculated depending on the gas flow rate, the cross section of the shower i head, and background pressure using a temperature of 300 K.
At the outlet:
The schematic of the computational cells used in this simulation is shown in Figure 4-6.
4.1.2. Results and Discussion
The steady-state neutral flow field including the distributions of species number density, temperature and mass-averaged velocities are simulated by using the developed gas flow model. The applied frequency was 25 kHz and the total gas pressure was 600 mTorr. These properties were then used in the plasma fluid modeling as the background gas properties. Figure 4-7 to 4-8 show the distributions of H2 and SiH4, and gas temperature. In this case, the Reynolds number is small with inflow velocity of silane/hydrogen and gap distance as the characteristic velocity and length, respectively. A small Reynolds number leads to a small Peclet number (Pe Re Pr ), which means that the conduction is dominated. This phenomenon is clearly seen in
Figure 4-7, where the temperature distribution between the electrode and subtract is almost linear. In addition, the density near the substrate surface decreases greatly because of the heated substrate at elevated temperature (250C). Non-uniform background density is important in determining the ionization rate during the simulation. The detailed flow structure is given by the streamlines in Figure 4-9.
4.2. Simulation of a Helium Micro-Cell Plasma
4.2.1. Simulation Conditions
Figure 4-10 shows the schematic diagram of a micro-cell plasma investigated in this study. The micro-cell consists of two ring-shaped electrodes made of aluminum separated by an insulator. The powered electrode is connected to an RF power source (f=13.56 MHz) with amplitude of 300 Volt, and the other one is grounded. Helium gas is applied as the working gas under the atmospheric-pressure condition. This study is numerically solved in a cylindrical coordinate in the right region in Figure 4-10.
40 60 uniform computational cells is used in x- and y-direction, respectively. Table 4 lists the substance properties used in this study. A gravitational field g is considered in the negative y-direction.
The boundary conditions for helium micro-cell plasma include:
At domain boundaries:
4.2.2. Results and Discussion
The present study numerically investigates the characteristics of flow field and heat transfer in a helium micro-cell plasma at atmospheric pressure. Figure 4-11 and 4-12 show the force due to ion-molecule collisions generated by the plasma fluid model for x- and y-momentum equations, respectively. And the energy source duo to ion Joule heating and electron elastic collision is shown in Figure 4-13.
Figure 4-14 shows the temperature distribution without considering the plasma momentum sources. The helium gas is heated and the maximum temperature in the plasma region is about 307 K. The increasing temperature produces an increase in the flow field due to the buoyancy effect. As expected, the buoyancy effect leads a weak clockwise flow field shown in Figure 4-15. However, the situation is totally different when the plasma momentum sources are considered. The clockwise flow field is reversed into a counter-clockwise field shown in Figure 4-16. There is a large component of the force (Fplasma SU2 SV2 ) directed toward the powered electrode 1 2 shown in Figure 4-17. The intensity of the force per unit volume is extremely larger than the buoyancy force, which leads an opposite flow field. The flow is accelerated to a speed of 0.8 m/s. Figure 4-18 shows the distributions of temperature with considering the plasma momentum sources. two-dimensional parallelized plasma fluid modeling code developed by another group
member [Lin, 2010]. The converged steady-state results of flow field, temperature, and other neutral gas properties are present.
4.3.1. Simulation Conditions
The schematic of the helium dielectric barrier discharge atmospheric-pressure plasma jet used in this study is illustrated in Figure 4-20. This system consists of two parallel electrodes made of copper and each of the electrodes is cuboid of 25 50 8 mm3. The lower electrode is connected to an AC power source (f=25 kHz) with amplitude of 250 Volt, and the upper one is grounded. Each electrode is covered with a 35 70 1 mm3 ceramic plate as the dielectric. The gap spacing between the two dielectric plates is kept at 1 mm throughout the study. Helium gas with nitrogen impurity (100ppm) is applied under the atmospheric-pressure condition. The total gas flow rate passing with a cross section of 1 50 mm2 is fixed at 20 slm.
In addition, the initial background gas temperature is assumed to be 300 K, and the surroundings are filled with air (78% N2 and 22% O2). The substrate surface is specified under two kinds of boundary conditions: a) an adiabatic wall (Neumann boundary) and b) an isothermal wall (dirichlet boundary).
The boundary conditions for the helium dielectric barrier atmospheric-pressure plasma jet include:
At the gas inlet:
, 0, , extrapolation,
i i i
u u v T T P Y Y (4-7)
where u is calculated depending on the gas flow rate, the cross section of inlet, and i background pressure using a temperature of 300 K.
At the outlet:
If the gas flows out of the domain,
, , ,
where the subscript “amb” means the state of the surrounding environment.
At the substrate surface:
4.3.2. Results and Discussion
A two-dimensional helium dielectric barrier discharge atmospheric-pressure plasma jet is investigated by solving the governing conservation equations with the boundary conditions. According to the gap between the two dielectric layers, the Reynolds number is estimated to be about 60. The gas flow is assumed to be laminar.
The Knudsen number related to the Mach number and the Reynolds number is less than 0.001, and the gas is treated as continuum. For this reason, the no-slip condition is imposed at the boundary. The 160 160 non-uniform computational cells shown in the Figure 4-21 are employed in the simulation. The parallelized neutral gas flow model uses 8 processors in x-direction and 5 processors in y-direction, respectively.
Figure 4-22 shows the time-history of the velocity and temperature profiles at the export of helium dielectric barrier discharge at atmospheric-pressure with gas flow rate of 20 slm under two kinds of boundary conditions of substrate surface. The computations are continued until it is obtained that the fluid properties have reached a statistically stationary state. It is seen the gas velocity at the exit of the plasma jet increase achieved a maximum velocity of about 14 m/s. The result in an adiabatic substrate surface is quite similar to that in an isothermal substrate surface. The steady-state solutions of the maximum temperatures at the exit of the plasma jet are 321 K and 322.5 K for the adiabatic and isothermal substrate surfaces, respectively.
The two-dimensional spatial distributions of pressure and over-all density are shown in Figure 4-23. The inlet pressure is approximately 760.5 torrs. In Figure 4-24, the spatial distributions of temperature for d 1 mm, H d 10, Re 60 and gas flow rate of 20 slmare shown for two different thermal boundaries. The gas is heating due to ion Joule heating and electron-neutral elastic collision. The maximum shown temperature in the plasma channel is about 323 K.
The velocity components in x- and y-direction are presented in Figure 4-25. Figure 4-26 shows the spatial distributions of the mean-speed, stream lines, and velocity vector.
In the stagnation region, the fluid velocity is zero and the surrounding flow is turning into the wall direction. Results illustrate that there are several pairs of vortices formed in the region between the jet exit and substrate and shown almost symmetric pattern.
Figure 1 shows the steady-state velocity vectors and streamlines at Re 60 , 10
H d , and gas flow rate of 20 slm. The locations of primary and secondary vortexes are depicted in Figure 4-27. A counter-clockwise primary vortex is formed near to the jet exit owing to low-pressure formation near the jet exit. When the momentum of the jet is unable to overcome retarding effect of the primary vortex and
the opposing frictional force of the impingement plate, the clockwise secondary vortex is formed. Figure 4-28 show the numerical simulated stream lines at different time level for d 1 mm, H d 10, Re 60 and gas flow rate of 20 slm. The results denote that the primary and secondary vortices glow and move toward the outlet as time increases. Finally, the flow converges to its steady state.
Figure 4-29 shows the horizontal velocity profiles in the plasma channel at different x position. The entrance length, a length in the channel until the flow velocity profile is fully developed, correlation with the Reynolds Number for laminar flow can be expressed as 0.06Re. It is clear that the flow is nearly fully developed with a parabolic velocity profile. The temperature profile in the plasma channel at various x positions is illustrated in Figure 4-30. The temperature difference between an adiabatic and an isothermal substrate surface is about 3 K.
Figure 4-31 shows the horizontal velocity and temperature profiles along the center line of the plasma jet. The gas flow velocity increases with increasing the distance from the inlet, and reaches a nearly constant value about 11.8 m/s in the plasma channel. A pronounced reduction in the velocity of the helium gas can be observed out of the plasma channel. The gas temperature in the plasma region is continuously increasing due to the electron-neutral elastic collision and ion Joule heating. The maximum values in the plasma channel, respectively, are about 324.5 K and 322.8 K for adiabatic and for isothermal boundaries. The gas temperature outside the plasma region decreases with the distance, as expected. Vertical velocity and 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 are shown in Figure 4-32 and 4-33.
The local Nusselt number distribution along the isothermal substrate surface for
1 mm
d , H d 10, Re 60 and gas flow rate of 20 slm is obtained in Figure.
4-34. The local Nusselt number, a ratio of convective to conductive heat transfer normal to the surface, is defined as:
bulk i
shd d dT
Nu k T T dx
(4-13)
where h is local heat transfer coefficient, and Tbulk is the bulk temperature. The bulk temperature Tbulk in this study is defined as follows:
p bulk i FM
m C T T Q (4-14)
where m is the helium mass flow rate, and Q is the heat source generated from the FM plasma fluid modeling. The local Nusselt number would not change significantly if the substrate surface treated as an adiabatic wall. A typical bell-shaped profile is obtained near the stagnation point while the substrate surface is kept at 300 K. The local Nusselt number variation in the substrate surface presents a peak of 2.37 at the stationary point for d 1 mm, H d 10, Re 60 and gas flow rate of 20 slm. Thereafter, the Nu decreases monotonically.
Chapter 5
Parametric Study of a Helium Dielectric Barrier Discharge Atmospheric-Pressure Plasma Jet
The purpose of this parameter study is to determine the influences of the system configurations, and the flow conditions on the flow and heat transfer characteristics of a helium dielectric-barrier discharge atmospheric-pressure plasma jet. The parameters varied in this study are the electrode lengths (5 mm and 25 mm ), gas flow rates( 10 30 slm ), and dimensionless jet-to-substrate spacing rates, H d (5, 7.5, 10, 12.5, and 15). The simulations are performed using helium with nitrogen impurity (100ppm) as the working gas. The neutral flow properties including velocity, pressure, total enthalpy, and species concentrations et al., are calculated by using the co-located cell finite volume method. The results are presented in the following sections.
5.1 The Effect of Electrode Length
5.1.1 Simulation Conditions
The two systems consist of two parallel electrodes made of copper. The electrodes of two systems are cuboid of 25 50 8 mm3 and of 5 50 8 mm3, respectively. The powered electrode is connected to an AC power source (f=25 kHz) with amplitude of 250 Volt. The electrodes of two systems are respectively covered with 35 70 1 mm 3 and 15 70 1 mm 3 ceramic plates. The gap spacing between the two dielectric plates is kept at 1 mm throughout the two systems. Helium gas with nitrogen impurity (100ppm) is applied under the atmospheric-pressure
condition. The total gas flow rate is fixed at 20 slm.
5.1.2 Results and Discussion
In this study, the value of velocity, pressure, total enthalpy, and species concentration are calculated numerically for two different electrode lengths. Figure 5-1 to 5-3 show the steady-state solutions of flow properties including pressure, over-all density, temperature, and velocity components. The heating source generated by plasma will decrease due to reduce the electrode length. Short electrode length leads to small plasma region, which results in decreased power source generated by plasma. The temperature in short electrode length rises from 300 K to 305.5 K. However, the flow field and the distributions of species mole fraction are no significant different between two different electrode lengths.
5.2 The Effect of Jet-to-Substrate Spacing Rate
5.2.1 Simulation Conditions
In order to determinate the effect of the dimensionless jet-to-substrate spacing rats on the flow and temperature fields in a simulation of helium dielectric barrier discharge atmospheric-pressure plasma jet, the numerical simulations are performed for five different H d
5, 7.5, 10, 12.5, and 15
.The number of computational cells used in the present calculations for various
jet-to-substrate spacing rates is list Table 5. The simulations are advanced in time until the flow properties reach to the steady-state solutions.
5.2.2 Results and Discussion
The influence of the jet-to-substrate spacing rate on the flow and temperature is determined. Simulations of flow properties are done by setting the dimensionless jet-to-substrate spacing rates H d from 5 to 15.
The temperature distributions, respectively, for an adiabatic boundary and for an isothermal boundary for the effect of various jet-to-substrate spacing rates are plotted in Figure 5-4 and 5-5. It can be seen that the jet-to-substrate spacing rate has an important effect on the heat transfer performances. The temperature distribution for an adiabatic boundary is relatively high to that for an isothermal boundary. Figure 5-6 shows the comparison of the mean speed distributions for various jet-to-substrate spacing rates.
The predicted streamlines for the jet-to-substrate spacing rates of
5, 7.5, 10, 12.5, and 15
H d at the plasma jet exit region are shown in Figure 5-7.
It is observed that the size of the primary vortex increases with increasing the jet-to-substrate spacing ratio. With increasing jet-to-substrate spacing rate, the turning acceleration and the velocity in the flow transverse direction will decrease. Figure 5-8 to 5-10 show the distributions of species mole fraction.
Variation in the local Nusselt number distribution with dimensionless jet-to-substrate spacing (H d ) can be seen in Figure 5-11. It is clear that the relative decrease in the local Nusselt number with increasing the dimensionless jet-to-substrate spacing. This is due to the convection effect. The local Nusselt number at the stationary point decreases from 3.7 to 1.8 with the dimensionless jet-to-substrate spacing increasing from 5 to 15.The smallest dimensionless jet-to-substrate spacing rate
(H d ) yielded the largest Nusselt number at the stagnation point for gas flow rate 5 of 20slm.
5.3 The Effect of Gas Flow Rate
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
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