The structure of the swirling flow in the counterflow vortex reactor

Full Text

Introduction

The quest for environmentally friendly energy sources continues and requires development of new solutions and apparatuses. In [1], a group from JIHT proposed vortex-based approach and described plasma-vortex reactor (PVR) – the promising technology capable of simultaneous generation of heat and hydrogen. Such machine exploits swirling flow to hold away hot gas from the walls of the system inside the active area. Experimental and theoretical research into PVR provided several insights about performance of device [2–4]. It can be anticipated that the efficiency depends not distinguishably on the parameters of electric discharge or the structure of the swirling flow but on their complex interaction [5; 6]. From the geometrical point of view there are several factors which can crucially affect the final outcome: the configuration of the working mixture input and output and the design of the electrode system. This statement was tested in [7], which confirmed using numerical simulation of the turbulent vortex flow for an experimental setup that formation of recirculation zone, which eventually determines the direction and intensity of the energy stream, strongly depend on the shape of the electrodes and their location relative to the swirler and the outlet.

The key feature of described system is that products from zone of active plasma-chemical reactions are carried away with the direct flow. However, that is not the only possible conception. In present paper, we propose results of numerical investigation into structure of the flow in alternative vortex reactor which utilizes reverse flow to withdraw thermal energy and desired products.

1. Mathematical modelling

1.1. Numerical model geometry and governing equations

The geometries of the principal part of the device (swirler, tube, and electrodes) is sketched in figure 1 for two cases. The common features both variants share are the following. The swirler has 4 tangential inlets (visible ones are colored in blue) of size in axial direction equal to 10 mm. The system of electrodes consists of coaxial cylindrical cathode (colored in light blue) of 85 mm length and 23 mm diameter and anode (yellow surface and orange base) – 112 mm and 12 mm respectively. There are 2 possible outlets. The primary one is the red annular area at the tube face near the swirler with inner diameter equal to 23 mm and outer one to 30 mm. The secondary optional one is the base of anode (orange). The heat source, which emulates heating in the discharge area, is located between electrodes. The length of the whole system is 267 mm and diameter of the tube 56 mm. Uncolored surfaces are the walls. The difference between two realizations lies in presence or absence of additional coaxial tube with inner diameter of 30 mm and wall thickness of 1 mm which contours are depicted in green color.

 

Рис. 1. Геометрия главной части устройства, использованная для численного моделирования: а – без ограничивающей трубки, б – с ограничивающей трубкой

 

Standard unsteady Reynolds averaged Navier-Stokes equations along with SST $k-\omega$ turbulence model, which is well suited for similar system [5], were used to describe the water-vapor flow:

$\frac{\partial \rho }{\partial t}+\frac{\partial \left(\rho {\nu }_i\right)}{\partial x_i}=0,$

$\frac{\partial \left(\rho {\nu }_i\right)}{\partial x_i}+\frac{\partial \left(\rho {\nu }_i{\nu }_j\right)}{\partial x_i}=-\frac{\partial P}{\partial x_i}+\frac{\partial }{\partial x_i}\left[\mu \left(\frac{\partial {\nu }_j}{\partial x_i}+\frac{\partial {\nu }_i}{\partial x_i}-\frac{2}{3}{\delta }_{ij}\frac{\partial {\nu }_k}{\partial x_k}\right)\right]+\frac{\partial }{\partial x_i}\left[-\rho \overline{{{\nu }_i}^{\text{'}}{{\nu }_j}^{\text{'}}}\right]\mathrm{,}$

$\frac{\partial \left(\rho E\right)}{\partial t}+\frac{\partial \left[{\nu }_i\left(\rho E+P\right)\right]}{\partial x_i}=\frac{\partial }{\partial x_j}\left[\left(\kappa +\frac{c_p{\mu }_t}{P{r}_t}\right)\frac{\partial T}{\partial x_j}+{\nu }_i{\left({\tau }_{ij}\right)}_{eff}\right]+N\left(\overrightarrow{x}\right)\mathrm{,}$

$E=h-\frac{P}{\rho }+\frac{{\upsilon }^2}{2}\mathrm{,}$

$P=\frac{\rho T}{M}$

where ${\left({\tau }_{ij}\right)}_{eff}={\mu }_{ij}\left(\frac{\partial {\nu }_j}{\partial x_i}+\frac{\partial {\nu }_i}{\partial x_j}\right)-\frac{2}{3}{\mu }_{ij}\frac{\partial {\nu }_k}{\partial x_k}{\delta }_{ij}$ is the deviatoric stress tensor, $\left[-\rho \overline{{{\nu }_i}^{\text{'}}{{\nu }_j}^{\text{'}}}\right]$ are the Reynolds stresses which must be modeled using chosen turbulence approach to close the set of equations, ${\nu }_i\mathrm{,}{{\nu }_i}^{\text{'}}\mathrm{,}\rho \mathrm{,}T\mathrm{,}P\mathrm{,}E$ and $h$ are the mean and fluctuating velocity components, density, temperature, pressure, total energy, and enthalpy, respectively; $N$ is the energy source which total power was set to 0 or 500 W, $\mu \mathrm{,}{\mu }_t\mathrm{,}{\mu }_{eff}$ are the molecular, turbulent, and effective viscosity coefficients, respectively; $c_p$ is the molar specific heat capacity at constant pressure; $\kappa$ is the thermal conductivity coefficient and $P{r}_t$ is the turbulent Prandtl number.

The no-slip velocity and fixed temperature boundary conditions were used for solid surfaces. Mass flow rate was set equal to 1 g/sec at every tangential inlet with gas temperature of 300 K. At the outlets, pressure equal to standard atmosphere was set. Temperature at the walls was constant equal to 300 K.

1.2. Numerical procedure

The whole system of equations for the non-stationary 3D turbulent swirling flow was solved using the ANSYS FLUENT 15.0 program package. A second-order upwind scheme was used for spatial discretization of density, momentum, energy and turbulent variables. The higher-order scheme does not provide any considerable change. The diffusion terms are central-differenced and second-order accurate. The pressure values at the faces were interpolated using the PRESTO! scheme developed for the flows of strong swirl behavior.

Transient terms were discretized using the fully implicit scheme of the second-order accuracy. Different pressure-velocity coupling schemes were tested and gave equal results. So, the SIMPLE scheme was chosen as the least resource consuming. The convergence was obtained when the residual reached ${10}^{-6}$ for the energy equation and ${10}^{-4}$ for the continuity equation, the momentum equation, and the equations for turbulent quantities.

The computational grid consisted of about $2.6\oplus {10}^6$ hexahedral cells. The skewness metric has an average value of 0.15, the minimum value of orthogonal quality metric – 0.10, the mean one – 0.9. The time step was fixed and set equal to $5\oplus {10}^{-5}$ sec in order to achieve convergence at every time step in recommended by ANSYS manufacturer iterations.

2. Results of numerical simulation

Axial velocity profiles of interest are shown in Fig. 2 and 3. Limited velocity ranges are used in order to make pictures more contrast and highlight areas of negative values. For both realizations, with (b) and without (a) additional bounding tube, there is pronounced counterflow which can suck out hot gas and reaction products from the interelectrode zone. However, absolute values of axial velocity in that area when only primary outlet is open are relatively low which could lead to overheating and exceeding limits or the used model. In the case of open secondary outlet (Fig. 2), there is direct flow sufficient to keep temperatures in computationally allowed range (Fig. 3).

 

Рис. 2. Распределения осевых скоростей с (b) и без ( a) ограничивающей трубы. Вторичный выход закрыт

 

Рис. 3. Распределения осевых скоростей с (b) и без ( a) ограничивающей трубы. Дополнительный выход открыт

 

Presence of the bounding tube results in two changes of the flow characteristics. The first one, visible from the axial velocity profiles, is narrowing of the stagnation area between electrodes, which in the case of one outlet leads even to two almost splitted zones. The second one is intensification of reverse flow squeezed between the cathode and the bounding tube. When the secondary outlet is open, it leads to shift of heat flux distribution in favor of primary outlet: from $~42$% of thermal energy being carried away through it to $~67$%. Moreover, there is significant decrease in maximum temperature (Fig. 4) which seems to be result of both aforementioned effects.

 

Рис. 4. Распределения температуры с (b) и без ( a) ограничивающей трубки. Дополнительный выход открыт

 

Conclusion

Results of modelling demonstrate viability of vortex reactor with reverse flow. Hot gas from interelectrode area is carried away in both examined cases: closed and open outlet at the base of cylindrical anode. Additional coaxial bounding tube which encircles the cathode significantly affects the flow characteristics. Its presence leads to narrower interelectrode stagnation zone, redistribution of energy fluxes in favor of primary outlet in the face of the whole cylindrical system and lower maximum temperature in the active zone between electrodes. Still, there is a room for optimization. Possible parameters to explore include length of both electrodes, radius and length of bounding tube. However, more experimental data are needed to select criteria and range of search.

About the authors

Denis P. Porfiriev

Samara National Research University; Samara branch of the Lebedev Physical Institute of the Russian Academy of Sciences

Author for correspondence.
Email: ipzav63@mail.ru
ORCID iD: 0000-0003-2203-8133

Candidate of Physical and Mathematical Sciences, associate professor of the Department of Physics; research associate of the Theoretical Department

Russian Federation, Samara; Samara

Igor P. Zavershinskii

Samara National Research University

Email: ipzav63@mail.ru
ORCID iD: 0000-0002-2391-1881

Doctor of Physical and Mathematical Sciences, professor of the Department of Physics

Russian Federation, Samara

Daria V. Agapova

Samara National Research University; Samara branch of the Lebedev Physical Institute of the Russian Academy of Sciences

Email: agapovadaria2019@gmail.com
ORCID iD: 0000-0002-3957-7339

Master Degree Student of the Physical Department; junior researcher of the Theoretical Department

Russian Federation, Samara; Samara

References

Supplementary files