Figure
1.
Schematic diagram of the thermal plasma reactor with a counterflow jet.
| Citation: |
Xu ZHOU, Xianhui CHEN, Taohong YE, Minming ZHU, Weidong XIA. Quasi-direct numerical simulations of the flow characteristics of a thermal plasma reactor with counterflow jet[J]. Plasma Science and Technology, 2023, 25(7): 075403. DOI: 10.1088/2058-6272/acb9d8
|
Three-dimensional quasi-direct numerical simulations have been performed to investigate a thermal plasma reactor with a counterflow jet. The effects of the momentum flux ratio and distance between the counterflow jet and the thermal plasma jet on the flow characteristics are addressed. The numerical results show that the dimensionless location of the stagnation layer is significantly affected by the momentum flux ratio, but it is not dependent on the distance. Specifically, the stagnation layer is closer to the plasma torch outlet with the increase of the momentum flux ratio. Furthermore, the flow regimes of the stagnation layer and the flow characteristics of the thermal plasma jet are closely related to the momentum flux ratio. The characteristic frequencies associated with the different regimes are identified. The deflecting oscillation flow regimes are found when the momentum flux ratio is low, which provokes axial velocity fluctuations inside the thermal plasma jet. By contrast, for cases with a high momentum flux ratio, flapping flow regimes are distinguished. The thermal plasma jets are very stable and the axial velocity fluctuations mainly exist in the stagnation layer.
Thermal plasma, characterized by its high temperature and high enthalpy, has been widely applied in the spraying, cutting and synthesis of nanoparticles [1, 2]. High requirements for thermal plasma reactors are put forward in the synthesis of nanoparticles; for example, sufficient heating time and high quenching rates [3]. A novel plasma reactor with a counterflow jet was developed by the University of Minnesota [4, 5]. Figure 1 shows a schematic diagram of the thermal plasma reactor with the counterflow jet. Compared with a traditional reactor, the novel reactor not only increases the heating time of the raw materials, but also promotes the mixing characteristics between the raw material and the thermal plasma, and higher quenching rates are provided in the reactor with the counterflow jet, so that the nanoparticle sizes are smaller and the uniformities are improved [6]. At present, the plasma reactor with the counterflow jet is used in the production process of high-quality and high-performance nanoparticles.
The flow rate of the quench gas, the distance between the outlet of the plasma torch and the nozzle of the counterflow jet, and the power of the plasma torch, are the key parameters affecting the synthesis of nanoparticles in reactors with a counterflow jet. Research results [7, 8] show that the increase of the distance and flow rate of the quench gas is favorable to enhance the quenching rates and heating time of raw materials, which contribute to synthesizing nanoparticles with a small size. In addition, numerical studies [9] found that the stagnation layer moves to the side of the counterflow jet with the increase in the input power of the plasma torch. The effect is more obvious when the power of the plasma torch is small.
Although some progress has been made in the impingement between the thermal plasma and the quench gas, the mass, momentum and energy transfer characteristics in the reactor are unclear due to the limitation of the experimental diagnostic methods [6, 8–10]. Moreover, the steady-state assumption, two-dimensional axisymmetric computational domain, laminar and k - ε turbulence model were employed to study the mean flow field in the reactor by numerical simulations [5, 6, 11–17], in which the characteristics of three-dimensional asymmetry and unsteady state in the reactor cannot be resolved.
The flow regimes have been identified due to the impingement of two fluids at room temperature [18–26]. Linear stability analysis was used to reveal the impingement of the laminar isothermal flows at a finite Reynolds number [24]. According to the Reynolds number and geometric aspect ratio, the flow regimes are classified as follows: (a) symmetric single steady state, (b) three steady states, (c) deflecting oscillation flow, and (d) chaotic flow. The flapping flow and transition from the flapping flow to the deflecting oscillation flow were reported in experiments [26]. However, the flow regimes in the thermal plasma reactor with the counterflow jet are unclear because of the impingement process with high velocity and temperature ratio. Therefore, it is necessary to carry out high-resolution numerical simulations to investigate the flow characteristics in the reactor.
Quasi-direct numerical simulations (q-DNS) methods in OpenFOAM [27] have been widely applied to turbulent channel flow, pipe flow, flow past a bluff body, interfacial flow, turbulent combustion and so on [28–37]. It is worth noting that the differences between q-DNS and direct numerical simulation (DNS) lie in the order of the discretization schemes. In general, high-order discretization schemes are employed in the DNS, while the order of the discretization schemes in the q-DNS is only second. However, many numerical studies [28, 31–33, 36] have proved that the physics can be mapped and DNS quality can be achieved by q-DNS when appropriate mesh resolutions are used. Therefore, based on our previous work [38, 39], q-DNS methods are employed for the first time to study the influence of the momentum flux ratio and distance between the counterflow jet and the thermal plasma jet on the flow and mixing characteristics in the reactors in this work, which can provide guidelines for the design of plasma reactors.
A geometrical schematic of a thermal plasma reactor with a counterflow jet is shown in figure 2. The inlet of the argon thermal plasma jet (or the outlet of the thermal plasma torch) is located at the bottom of the reactor, while the nozzle of the counterflow argon jet is at the top of the reactor. The inlet diameter of the plasma jet is the same as that of the counterflow jet, which is D = 8 mm The length of the counterflow pipe is LEF = 5 mm and the wall thickness is 0.5 mm. The distance L between the thermal plasma jet inlet and the counterflow jet outlet is variable in our simulations. In addition, the radius of the thermal plasma reactor is rAC = 40 mm
In this work, the effects of the flow configurations of the counterflow jet on the flow and mixing characteristics in the thermal plasma reactor are studied. The maximum velocity Uj and maximum temperature Tj of the thermal plasma jet inlet are 600 m s-1 and 13 000 K, respectively. In addition, the temperature T∞ and pressure P∞ of the stationary ambient air are 300 K and 1 atm, respectively. The detailed flow parameters of the counterflow argon jet are listed in table 1, where Ucounter and Tcounter represent the bulk velocity and temperature of the counterflow jet inlet, respectively. The momentum flux ratio between the counterflow jet and the thermal plasma jet is defined as M=∫rGH0(ρ2u22)2πrdr/∫rAB0(ρ1u21)2πrdr, where the subscripts 1 and 2 represent the jet inlet of the plasma and counterflow, respectively. The effects of the momentum flux ratio on the flow and mixing characteristics in the reactor are investigated in cases 1–4, in which the momentum flux of the thermal plasma jet is constant, and the distance between the thermal plasma jet inlet and the counterflow jet outlet is L/D = 5.625 Meanwhile, case 5 reveals the influence of the distance L on the flow fields.
| Case | Ucounter (m s-1) | Tcounter (K) | M | L/D |
| Case 1 | 60 | 300 | 1.015 | 5.625 |
| Case 2 | 80 | 300 | 1.805 | 5.625 |
| Case 3 | 100 | 300 | 2.82 | 5.625 |
| Case 4 | 80 | 537 | 1.015 | 5.625 |
| Case 5 | 80 | 300 | 1.805 | 2.5 |
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The q-DNS methods are used to investigate the effect of the counterflow jet on the flow characteristics in the thermal plasma reactor. Compared with our previous work [38, 39], the differences in the numerical methods are that the sub-grid terms marked by the superscript 'SGS' in the governing equations are zero. In other words, three-dimensional, high-resolution simulations with no turbulence model are employed. In addition, studies [5, 6] have shown that there is almost no interaction between the nanoparticles with small sizes and the fluids, and the velocity and temperature of the nanoparticles are the same as those of the fluids. Therefore, the governing equations of the particles are not considered in this paper.
The following assumptions are made: (1) the plasma is in the local thermodynamic equilibrium and local chemical equilibrium state; (2) the plasma is assumed to be optically thin; (3) the buoyancy effects are negligible because of their small size [38, 39]. Based on the preceding assumptions, the compressible governing equations can be written as follows:
| ∂ρ∂t+∂ρui∂xi=0 | (1) |
| ∂ρuj∂t+∂ρuiuj∂xi=−∂p∂xj+∂τij∂xi | (2) |
| ∂ρh∂t+∂ρuih∂xi=∂∂xi(kcp∂h∂xi)−Q−∂∂xi[(hA−hB)(μSc∂YA∂xi+kcp∂YA∂xi)] | (3) |
| ∂ρYA∂t+∂ρuiYA∂xi=∂∂xi(μSc∂YA∂xi) | (4) |
where t, xi(i=1,2,3),ui(i=1,2,3)( or uj(j=1,2,3)), p, h and YA are the time, spatial coordinate components, velocity components, pressure, specific enthalpy and mass fraction of argon in the argon–air mixture, respectively. The viscous stress τij is defined as
| τij=2μSij−23μSkkδij | (5) |
where Sij=12(∂ui∂xj+∂uj∂xi) is the strain rate tensor and δij is the Kronecker operator. μ, k, cp and Q are the dynamic viscosity, thermal conductivity, specific heat at constant pressure and radiative heat loss. The physical parameters related to the temperature and mass fraction of argon are provided by Murphy [40].
The last term on the right-hand side of the energy conservation equation (3) represents the energy transport caused by species diffusion [41], where the subscripts 'A' and 'B' correspond to pure air and pure argon, respectively. In order to consider the mixing of the argon with the cold air, the species conservation equation (4) is employed, and the mass fraction of air is obtained by (1 - YA).
The distributions of mean velocity and temperature in the thermal plasma jet inlet are specified as in [42–44]:
| U=Uj[1−(rrAB)nU] | (6) |
| T=(Tj−Tw)[1−(rrAB)nT]+Tw | (7) |
where the fitting parameters nU and nT are 1.4 and 2.3, respectively, and the plasma torch wall temperature is Tw = 300 K. The radial distribution of mean velocity in the counterflow jet inlet is satisfied [45, 46]:
| U=1.218Ucounter(1−r1.01rGH)1/7. | (8) |
In addition, 5% turbulence intensities are applied in equation (8) to achieve the turbulence inlet boundary. The temperatures in the counterflow jet inlet are uniformly distributed and the values are shown in table 1, and the adiabatic and no-slip boundary conditions are employed in the counterflow pipe wall. The mass fraction of argon YA is assumed to be 1.0 in the inlet of the thermal plasma jet and counterflow jet. Open boundary conditions [17] are applied in the lateral face C-D in figure 2. A detailed description of the code development and numerical validation can be observed in our previous studies [38, 39].
Three sets of hexahedral meshes with different resolutions (coarse, medium and fine) are employed to implement the mesh sensitivity analysis. The whole computational meshes are divided into 64 × 89 × 173, 96 × 132 × 336 and 128 × 164 × 364 cells in the circumferential, radial and axial directions, respectively, and the total number of cells is 1.05, 4.50 and 8.09 million, respectively. Figure 3 shows the distributions of mean axial velocity and temperature obtained by the three sets of meshes. It can be seen that the velocity and temperature predicted by the coarse mesh are slightly higher, while good convergences are achieved with the results obtained with the medium mesh and fine mesh. In order to save computing cost, all results presented in the following numerical study are obtained based on the medium mesh.
It is worth noting that the locations of the stagnation layer are uncertain for different cases. In order to perform mesh refinement near the stagnation layer with the large spatial gradients of velocity and temperature, the approximate locations of the stagnation layers are obtained under the uniform and rough hexahedral mesh. Then, the mesh refinements are carried out, and the numerical results obtained with the rough hexahedral mesh are mapped to the refined mesh. Finally, the main numerical simulations are performed with the refined mesh. These operations can not only reduce the computing cost, but also ensure that the mesh resolution near the stagnation layer meets the requirements of calculation accuracy.
In this section, the flow characteristics in the thermal plasma reactor with the counterflow jet are revealed under different momentum flux ratios and distances.
Figures 4–6 compare the distributions of the mean flow fields in cases 1–5. The radial and axial coordinates are normalized with the inlet diameter (D) of the thermal plasma jet and the distance (L) between the plasma jet inlet and the counterflow jet outlet, respectively. It can be shown that the effects of the flow configurations of the counterflow jet on the flow, temperature and composition field in the reactor are significant. The stagnation layer with large velocity and temperature gradient is formed due to the impingement between the thermal plasma jet and the counterflow jet [9]. The fast quenching effect can be achieved near the stagnation layer, which is conducive to the synthesis of nanoparticles [6].
As the velocity or momentum flux of the counterflow jet inlet increases, the counterflow jet length extends, the thermal plasma jet length reduces, and the stagnation layer gradually moves towards the thermal plasma jet inlet. Although the velocities and temperatures of the counterflow jet inlet in case 1 and case 4 are different, the mean flow fields are similar. It is indicated that the momentum flux ratios play dominant roles in the flow fields. By comparing case 2 and case 5, it can be seen that the distance L has little influence on the dimensionless location of the stagnation layer. However, the region with an argon mass fraction above 0.9 expands wider with the decrease in the distance. In addition, more air is entrained into the stagnation layer in case 3 with a high momentum flux ratio, which may lead to the oxidation of pure metal nanoparticles in the synthesis processes.
The distributions of mean flow fields along the jet axis in cases 1–5 are shown in figure 7. The stagnation point is defined as the location with an axial velocity of 0 m s-1 in the jet axis, namely the intersection of the solid line and dotted line in figure 7(a). Although the distributions of mean flow fields are greatly different due to the movement of the stagnation layer caused by the change in the momentum flux ratio, the largest gradients of the velocity and temperature and the highest air content are usually found near the stagnation point. In addition, narrowing the distance between the plasma jet inlet and counterflow jet outlet will produce a pure argon environment in the jet axis.
The instantaneous flow fields in the reactor under different cases are analyzed to investigate the flow regimes. Figure 8 compares the instantaneous contour plots of axial velocity after the flow fields have reached stability in case 2. The cold argon flows from the counterflow jet outlet are dominated by the turbulent transport mechanism due to the Kelvin–Helmholtz instability caused by the velocity shear. However, the thermal plasma flows from the plasma torch outlet are still stable and dominated by the molecular transport mechanism due to the high viscosity. The behavior near the stagnation layer z/L = 0.389 is characterized by the flapping flow regime because of the impingement of two flows [24, 26], and the periodic time is about 3.6 ms.
The power spectral density (PSD) is a probabilistic statistical method, which represents the frequency domain characteristic of a time series and is appropriate for the detection of frequency composition in a stochastic process [47]. PSD is employed to analyze the characteristic frequencies of shear layers in the simulations. Figure 9 shows the PSD of velocity at different locations along the shear layer of case 2. The corresponding locations are shown in figure 8(a) with the white squares. An obvious characteristic frequency can be observed in the reactor. The frequency of the vortex shedding near the counterflow jet outlet is 7814 Hz. Then, the characteristic frequency is about half of that near the counterflow jet outlet due to the vortex pairing and merger. A characteristic frequency of f = 297 Hz is observed near the stagnation layer z/L = 0.389, corresponding to the frequency of the flapping flow regime.
The instantaneous flow fields in case 3 and case 5 are similar to those of case 2, which are dominated by the flapping flow regime. As shown in figure 10, the characteristic frequencies in the stagnation layer of case 3 and case 5 are 359 Hz and 107 Hz, respectively. With the increase in the momentum flux ratio and distance between the counterflow jet and the thermal plasma jet, the turbulent effect in the stagnation layer is enhanced, resulting in an improvement of the characteristic frequency.
The deflecting oscillation flow regimes are distinguished in case 4 with a low momentum flux ratio [24, 26]. Figure 11 shows the time evolution of the instantaneous flow field in case 4. It can be seen from the figure that the period of the deflecting oscillation is about 5.0 ms, and the deflecting amplitude is smaller than that of the impingement of two fluids at normal temperature, which may be due to the strong robustness of the thermal plasma. The instability of the thermal plasma jet is observed under the deflecting oscillation flow regimes.
In order to further investigate the deflecting oscillation of the stagnation layer and the vortex fluctuation characteristic of the thermal plasma jet, probes are set in the shear layer to detect the axial velocity signal. The results are shown in figure 12. The vortex shedding frequency in the counterflow jet outlet is 8011 Hz, which is close to the result in case 2. The characteristic frequency f = 192 Hz is observed in the stagnation layer z/L = 0.889, representing the frequency of the deflection oscillation. In addition, the characteristic frequency f = 8121 Hz is detected in the shear layer of the thermal plasma jet, which is the vortex shedding frequency of the thermal plasma jet. The value of the vortex shedding frequency is close to that in the counterflow jet outlet. It is indicated that the instability of the thermal plasma jet may be caused by the counterflow jet.
The flow fields in case 1 are also dominated by the deflecting oscillation flow regimes. Figure 13 shows the PSD of velocity at different positions along the shear layer in case 1. It can be seen that the frequency of the deflection oscillation in the stagnation layer and the vortex shedding frequency in the shear layer of the thermal plasma jet are 221 Hz and 7685 Hz, respectively. Moreover, the flow fields under the deflecting oscillation flow regimes are asymmetric about the jet axis, so the real physical results may be not obtained under the steady-state and two-dimensional axisymmetric assumptions.
The vorticity in the x-direction in the reactor is shown in figure 14. The vortex structures on both sides of the stagnation layer are obviously different. Vortex roll-up with opposite signs can be found in the shear layer of the counterflow jet due to the Kelvin–Helmholtz instability. With the development of flow, the vortex cores become larger, and more ambient air is entrained into the jet. Therefore, the air content near the stagnation layer is the highest. Finally, the orderly vortex structures are broken by the impingement of the thermal plasma jet, enhancing the mixing characteristics between the cold argon and the thermal plasma. The vortex structures on the thermal plasma side are greatly affected by the momentum flux ratio. For case 1 and case 4 with low momentum flux ratio, the phenomenon of vortex roll-up can be observed in the shear layer. However, there is no vortex structure for other cases with high momentum flux ratio.
The root-mean-squared (rms) fluctuation contour plots of axial velocity, temperature and argon mass fraction in the reactor are shown in figures 15–17. The flow regimes of the stagnation layer play important roles in the turbulence statistical characteristics. For case 1 and case 4 with low momentum flux ratio, the temperature fluctuations mainly exist in the stagnation layer and shear layer of the thermal plasma jet, and the large fluctuations in axial velocity are distinguished inside the thermal plasma jet due to the deflecting oscillation flow regimes. However, for other cases with high momentum flux ratio, the axial velocity fluctuations appear in the stagnation layer due to the flapping flow regimes. Meanwhile, the peaks of the fluctuations increase with the increase in the momentum flux ratio. By comparing case 2 and case 5, it can be seen that decreasing the distance L is beneficial to reducing the fluctuations of axial velocity and temperature. In addition, strong fluctuations of argon mass fraction are found in the shear layer of the thermal plasma jet and counterflow jet.
The effects of the momentum flux ratio and distance between the counterflow jet and thermal plasma jet on the flow and mixing characteristics in plasma reactors have been studied by q-DNS methods. The main conclusions are drawn as follows.
Large gradients of axial velocity and temperature as well as a high air content are found near the stagnation layer. With the increase in the momentum flux ratio, the stagnation layer gradually moves from the counterflow jet outlet to the plasma torch outlet. However, the dimensionless location of the stagnation layer is independent of the distance. For cases with a high momentum flux ratio, more air is entrained into the stagnation layer by the turbulent transport mechanism of the counterflow jet.
Two flow regimes are identified in the thermal plasma reactor with the counterflow jet, which depend on the momentum flux ratio. The deflecting oscillation flow regimes are distinguished in the case with low momentum flux ratio. Vortex shedding in the shear layer of the thermal plasma jet is observed, and the characteristic frequency is close to that in the counterflow jet outlet. As a result, axial velocity fluctuations appear inside the thermal plasma jet. However, the flow regimes transform into the flapping of the stagnation layer with the increase in the momentum flux ratio. The vortex shedding in the shear layer of the thermal plasma jet is suppressed. The thermal plasma jets are very stable and the axial velocity fluctuations mainly exist in the stagnation layer. Meanwhile, the peaks of the fluctuations and the flapping characteristic frequency increase with the increase in the momentum flux ratio and distance.
This work is supported by National Natural Science Foundation of China (Nos. 12035015 and 12105282). The numerical simulations in this paper have been performed on the supercomputers in the Supercomputing Center, University of Science and Technology of China.
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| 1. | Wang, S., Kong, D., Chen, X. et al. Numerical Simulation Study on Plasma Rapid Heater of Methane. Plasma Chemistry and Plasma Processing, 2023. DOI:10.1007/s11090-023-10433-9 |
| 1. | Wang, S., Kong, D., Chen, X. et al. Numerical Simulation Study on Plasma Rapid Heater of Methane. Plasma Chemistry and Plasma Processing, 2024, 44(1): 95-114. DOI:10.1007/s11090-023-10433-9 |
Figures(17) / Tables(1)
Supported by: Beijing Renhe Information Technology Co., Ltd. 
| Case | Ucounter (m s-1) | Tcounter (K) | M | L/D |
| Case 1 | 60 | 300 | 1.015 | 5.625 |
| Case 2 | 80 | 300 | 1.805 | 5.625 |
| Case 3 | 100 | 300 | 2.82 | 5.625 |
| Case 4 | 80 | 537 | 1.015 | 5.625 |
| Case 5 | 80 | 300 | 1.805 | 2.5 |
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