Numerical Study of DC Electric Field Effects on the Turbulent Swirl Flame in Tube Burner

2.1 Physical description

The chemical basis describes the extent to which the electric field affects the behavior of fire within the combustion process due to the presence of ionic species. Much literature has dealt with the effect of the electric field on the flame in order to improve the flame properties, starting with flame speed and stability, flame front brightness, flame composition, and pollutant emissions. Moreover, it verified the possibility of electric fields being considered one of the flame control triggers. As a result of the electron transfer or ionization accompanying the collision process or chemical ionization, ions are formed in the flame. Schmidt [27] reported that the reaction in hydrocarbon's combustion process was a reason for the production of H₃O⁺ ion. While the reaction produces CHO⁺ ion [27]:

$\mathrm{CH}+\mathrm{O} \rightarrow \mathrm{CHO}^{+}+e^{-}$                      (1)

$\mathrm{CHO}^{+}+\mathrm{H}_2 \mathrm{O} \rightarrow \mathrm{CO}+\mathrm{H}_3 \mathrm{O}^{+}$                        (2)

While H₃O⁺ is involved in another reaction [27];

$\mathrm{H}_3 \mathrm{O}^{+}+e^{-} \rightarrow \mathrm{H}_2 \mathrm{O}+\mathrm{H}$                    (3)

Figure 1 demonstrates the effect of the electric field applied to the flame; firstly, the Coulomb force generated by an electric field is the force affecting electric charges placed within the range of this field. As shown in the figure, the electric field affected by the combustion region moves electrons from the reaction region to the positive electrode. In contrast, the positive ions move in the opposite direction. When positive ions collide with the natural species, part of the ions' momentum is transferred to the natural species, thereby generating a hydrodynamic pressure on the flame front. It is called the ionic wind.

Figure 1. The schematic of the ionic wind generated in the flame front

2.2 Computational methodology

A model of Turbulent Flame Speed Closure (TFSC) was adopted to simulate the swirl combustion for turbulent flame in a vertical burner under the effect of a DC electric field. Modeling was also completed within an environment of the commercial Computational Fluid Dynamics (CFD) software ANSYS 17.0 FLUENT, for premixed combustion. The combustion of swirl turbulent flame under the effect of an electric field, including the low swirl formation premixed in the lean side, was simulated by Fluent. The electric field equation was applied in Fluent by User Defined Function (UDF) and contacted with the simulation by UDFs, which were prepared in C++. Several steps were used for performing the simulations, as shown in Figure 2. This simulation investigates the influence of DC electric fields on the low swirl flame through an edge burner.

Figure 2. Flow chart of simulation steps

The 3D model of a vertical burner was prepared in SolidWorks 10.0 software and adapted to analyze the swirl flame structure and stability for a premixed turbulent swirl flame under a range of DC electric fields at LPG/air flame. The turbulent swirl flame model comprises two zones. The dimensions of the first zone, the vertical burner, were received from the experimental setup for Abdul Wahhab [4]. A vertical burner includes a pipe of 42 mm in inner diameter and 500 mm in length, 30 mm from the external edge of the burner. As shown in Table 1, four strips were fixed inside the burner. These strips were welded in a helical path to generate a swirl flow pattern for the premixed gases while identifying the angle between the plate's axes at 90°, as shown in Figure 3. The second zone includes a reaction region, or swirl flame zone, meaning that the flame speed possesses a tangential and axial component. The tangential component of velocity is generated by inter-burner strips (having an outlet angle of 90°) to the axial direction. The second zone includes the electrode ring with a diameter of 90 mm located at 110 mm above the burner edge, and a high electric potential was applied to the ring electrode as the positive electrode, while the burner edge represents the negative electrode.

Figure 3. Sketch of swirl burner domain geometry

Table 1. Swirl burner geometric dimensions

The computational grid is a critical component of the simulation process. It's a discretization of the geometric domain of the problem into smaller, manageable elements or cells. This grid forms the basis on which numerical methods solve the combustion equations. Meshing is a crucial step for defining the computational domain and ensuring accurate and efficient simulation results. Types of meshing can be broadly categorized based on element shape, structure, and method. In this research, air-fuel mixture flow and combustion domain are meshed with adopting tetrahedral, structure-based, and path-conforming meshing because they generally provide higher accuracy and efficiency for certain simulations, have a regular grid structure with well-defined layers, are suitable for complex geometries with multiple faces and regions, and maintain the integrity of the original geometry. Computational processes have been carried out for four selected grid sizes: 145620, 280630, 415630, 623451, and 788467. A summary of the grid-independent test results is shown in Table 2. Observed that the 623451 and 788467 nodes produced almost identical results. Hence, a domain with 788467 nodes was chosen to increase computational accuracy and reduce the time of computation. Figure 4 shows the variation of average time with the total element number. Results for the selected grid sizes show very good agreement with each other.

Table 2. Grid independence test result

Figure 4. Variation of average time with total element number

The mesh of the geometry appears in Figure 5. The number of nodes and elements is 788467 and 697833, respectively. The ANSYS Design Modeler was used to make the geometry model, while the fine meshing tool was used to prepare the mesh body. A grid independent test was performed to ensure that the mesh sizes are considered to produce identical results. The mesh size is refined at the fuel-air mixture inlet to get the most accurate numerical results. The important parameters of simulations are demonstrated in Table 3.

Figure 5. Computational domain and geometrical mesh model of a vertical tube burner

Table 3. Important parameters of the computational model

The electric potential is generated between the burner outlet and the ring electrode. To get a clear idea of the electric field effects, the simulation without combustion was done first to verify the effect of electric field dissuasion in the reaction region by ANSYS 17.0, as shown in Figure 6. The electric field gradient points are generated from the ring electrode to the burner edge.

Figure 6. Distribution of electric field intensity without flame

2.3 Governing equations

The CFD model was controlled by a number of assumptions.

• Unsteady, two dimensions, premixed swirl flame in the external region.
• Low swirl rate of mixed gases in the internal region, also the homogeneously assumed that LPG/air together, that the LPG to air ratio is of the order of limitation, and evaporation, initial reaction phenomena can be neglected.
• Assume a steady DC electric field. An important process that happens in addition to ionization is the recombination process.
• Assume no reactions between LPG gas and air in the internal burner region. Furthermore, assuming that gases (LPG and air) are adopted as two reactants and their properties remain constant.

The dynamic fluid equations for fuel mixtures, multi-vector, compressible fluid, and dynamic flows with the influence of electric forces control the subject. Where ρ is a mixture of density v_i is the mixture of velocity components, and F_i is the external electric force, the mass continuity and momentum equations read [5]:

$\frac{\partial \rho}{\partial t}+\frac{\partial \rho v_i}{\partial x_i}=0$                        (4)

$\frac{\partial \rho v_i}{\partial t}+\frac{\partial \rho v_i v_j}{\partial x_i}=-\frac{\partial p}{\partial x_i}+\frac{\partial \tau_{i j}}{\partial x_i}+F_i$                     (5)

where, t is time, and x_i is the typical coordinates. p is total pressure, and τ_ij is the viscous tensor [5]:

$\tau_{i j}=-\frac{2}{3} \mu \frac{\partial \rho v_k}{\partial x_k} \delta_{i j}+\mu\left(\frac{\partial v_i}{\partial x_i}+\frac{\partial v_j}{\partial x_i}\right)$                           (6)

where, μ is the dynamic viscosity and δ_i,j is the Kronecker factor.

The vectors of the electric force $F_i$ that is generated from charge boosters when a DC electric field is affected by applied electric field intensity $E_i$ and charge boosters' types n⁺, n^- [5]:

$F_i=e E_i\left(n^{+}-n^{-}\right)$                       (7)

where, the n^- and n⁺ are negative and positive charge boosters, also, e represents the transported electron. At the same time, the intensity of the electric field is calculated from the electric potential V by the simple equation [5].

$E_i=-\frac{\partial V}{\partial x_i}$                   (8)

The electric potential is divided as described by the Poisson equation, which changes in time with active species concentrations, and ε_o represents the permittivity of the free region.

$\nabla^2 V=-e \frac{\left(n^{+}-n^{-}\right)}{\varepsilon_0}$                 (9)

Chemical species equations (neutral or charged) could be presented by Eq. (10) [5]:

$\frac{\partial \rho Y^k}{\partial t}+\frac{\partial \rho v_j Y^k}{\partial x_i}=-\frac{\partial \rho Y^k V_j^k}{\partial x_i}+\dot{\omega}^k$                             (10)

The energy equation can present:

$\frac{\partial \rho E}{\partial t}+\frac{\partial \rho v_i E}{\partial x_i}=-\frac{\partial q_i}{\partial x_i}+\frac{\partial\left(\tau_{i j}-p \delta_{i j}\right)}{\partial x_i}+\dot{Q}+f$                        (11)

where, f, the energy transport equation by contribution to the electric force, is known as:

$f=\sum_{k=1}^{N c} e n^k S^k E_j\left(v_j+V_j^k\right)$                       (12)

The turbulent swirl flame from a tube burner using LPG as fuel with air at an equivalent ratio of 0.7 (lean fuel side) under a DC electric field was studied numerically. The effects of a DC electric field on swirl flame stability and flame temperature were investigated. The main conclusions are summarized as follows: The distance between the swirl flame root and burner edge decreased with increasing applied DC electric field due to the ionic wind effect, which in turn increases the flame temperature and the diffusivity. Numerical results were represented by the increasing swirl flame temperature at 4.6% and 13.4% at the effect of electric fields 2KV and 5 kV, respectively. The application of DC electric fields can reduce the emission of soot particles, and the effect of the small distance between DC electrodes is better. Particle diagnosis technology needs to be further developed to obtain more accurate values and observe more subtle changes. Future works by the researchers must include studying a wide range of electric potential with flame properties and more stable combustion rates. A numerical study on the influence of DC electric field on the flame front in swirl flame should be performed to describe the combustion mechanism quantitatively.