Research and Development of an Industrial Denitration-Used Burner with Multiple Ejectors via Computational Fluid Dynamics Analysis

Abstract

Nowadays, since the air pollution problem is becoming global and denitrification is efficient to control nitrogen oxides, research and development of burners with low pollutant emissions in industries are urgent and necessary due to the increasingly severe environmental requirements. Based on the advanced CFD (computational fluid dynamics) numerical analysis technique, this work focuses on developing an industrial denitration-used burner, aiming to decrease the emission of nitrogen oxides. A burner with multiple ejectors is proposed, and the gas premixing and combustion process in the burner are systematically studied. Firstly, for the ejector, the well-known orthogonal experiment method is adopted to reveal the premixing performance under different structural parameters. Results show that the angle and number of swirl blades have significant effects on the $CO$ mixing uniformity. The $CO$ mixing uniformity first decreases and then increases with thr rising swirl blade angle, and it enhances with more swirl blades. Through comparison, a preferred ejector is determined with optimal structure parameters including the nozzle diameter of 75 mm, the ejector suction chamber diameter of 290 mm, the blade swirl angle of ${45}^{\circ }$, and the swirl blade number 16. And then, the burners installed with the confirmed ejector and two types of flues, i.e., a cylindrical and a rectangular one, are simulated and compared. The effects of ejector arrangements on the temperature distributions at the burner outlet are analyzed qualitatively and quantitatively. It is found that the temperature variances at the outlets of $R2$ and $C1$ are the smallest, respectively, $13.12$ and $23.69$, representing the optimal temperature uniformity under each type. Finally, the burner of the R2 arrangement is verified with a satisfied premixing performance and combustion temperature uniformity, meeting the denitration demands in the industry.

1. Introduction

Currently, air pollution caused by the emission of nitrogen oxides ($N{O}_x$) is becoming increasingly serious [1,2,3,4]. Normally, there are many nitrogen oxides in the industry flue gas. Catalytic oxidation reactions could happen on the nitrogen oxides in the air. Then, nitric acid, nitrite and nitrate could easily form, which would exacerbate the fine particle pollution in the atmosphere and haze phenomenon. It may produce acid rain as well, which is harmful to crops and human survival. In addition, NO can react with the ozone and destroy the ozone layer. A significant amount of damage could occur. Consequently, the low-pollutant emission technology has attracted worldwide attention [5,6].

In the field of industry combustion, enhancing the premixing in burners is important to achieve low nitrogen emission levels. $N{O}_x$ is mainly produced during combustion [7], and the mixing degree between the fuel and supporting gas affects this process. It has been reported that premixed combustion compared with non-premixed and partially premixed combustion could reduce $N{O}_x$ emissions significantly because it does not produce Fuel $NO$ (F-NO) and Prompt $NO$ (P-NO) [5,8], which decrease the chance of Thermal $NO$ (T-NO) generation [9]. Correspondingly, there are types of burners that exist in various industries. And, as a typically premixed combustion, the ejector burner type is commonly applied. As Figure 1 and Figure 2 demonstrate, in the ejector burners, gas flow with a high speed injects from a nozzle into a mixing chamber, which could produce relatively negative pressure and suck other low-speed gases around the flow. And then, the gases could mix in the mixing chamber before the combustion start point. The premixing uniformity at the outlet of an ejector has been experimentally proved to have strong influence on pollutant emission [10].

The temperature control of a burner outlet is also of significance. Specific temperature distributions may be vital to subsequent process. We take, for instance, the denitrification process of flue gas using the SCR method [11]. The reductant $N{H}_3$ is used to reduce $NO$ and $N{O}_2$ in the flue gas to friendly $N_2$ and $H_{2}O$ [12,13], in which keeping the flue gas temperature 563–693 K is necessary [14]. If there is space inside the burner flue, especially in a large-power burner, the heated flue gas may not complete heat exchange when it moves to the denitration position. It would result in the flue gas temperature distribution for denitrification not fully reaching the reaction conditions, thus leading to low denitrification efficiency [15,16]. Therefore, it is of great importance to improve the gas premixing effect and flue gas temperature uniformity for subsequent denitrification.

Since the ejectors in burners play significant roles in the mixing and flowing behaviors, they attracted much attention and caused numerous investigations. Many studies improve the premixing performance of ejectors by optimizing structural parameters such as nozzle size and position, suction tube diameter and shape. André et al. [17] studied the influence of mixing tube diameter, jet tube diameter and the type of mixing tube inlet on premixing; increase in the diameter of the mixing tube increases primary burner air entrainment, also increasing the diameter of the injector decreases primary burner air entrainment. Szabolcs Varga et al. [18] and other researchers found that the nozzle-to-mixing zone cross-section ratio and the nozzle protrusion position of an induced combustor have a significant effect on the induced coefficient and back pressure of the induced combustor, while the mixing zone length has a minimal or even negligible effect on the induced coefficient. Mafalda et al. [19] improved the premixing of the ejector by changing the length and shape of the injection port and the influence of the fuel flow rate on the air entrainment ratio. The use of sharp fuel nozzle inlets (rather than round inlets) is more conducive to improving the equivalence ratio. Ran et al. [20] improved the premixing effect by changing the back pressure and the operating pressure of the ejector burner, the length of the ejector suction chamber and the ejector fuel nozzle exit locations. Operation pressure has little impact on the entrainment ratio of the two fuels, but the rise of back pressure leads to rapid decrease in the entrainment ratio for the two fuels. Kamil et al. [21] studied the effect of geometric parameters of gas ejector burner on the performance of the ejector burner, investigating it using a combination of numerical simulation and experiments, and the comparison revealed that the error of the results for temperature and static pressure was less than 10%. He et al. [22] studied the combustion characteristics of blast furnace gas in the porous medium burner. The gas temperature and flame length increased and then decreased as the distance between the porous body and the burner inlet increased. Gong et al. [23] discussed the influence of different nozzle shapes on $N{O}_x$ emissions.

On the other hand, some studies improved the premixing effect by adding auxiliary structures such as deflectors. Zhao et al. [6] improved the uniformity of methane concentration by applying the distribution orifice plates. Zhang et al. [10] introduced a distribution orifice and a deflector. The quantitative analysis showed that the gas mixing outlet is significantly improved and the uniformity of velocity and the fuel–gas mixing of a single ejector increased by 234.2% and 2.9%, respectively. Liu et al. [5] proposed the distribution chamber which was applied to balance the pressure and improve the mixing process of methane and air in front of the fire hole. A distribution plate with seven orifices was introduced at the outlet of the ejector to improve the flow organization, and it improved the flow distribution and premixed combustion for the designed ejector.

Even though many efforts have been made in previous studies, there is still a lack of developing new structures. In order to further enhance the premixing performance and improve the temperature distributions, here, in this work, we propose an ejector structure combined with multiple swirl blades and a blunt body (see Figure 2 for details). When the high-speed gas passes through the mixing chamber guided by the swirl blades and the blunt body, the exit velocity may be reduced, and meanwhile, the mixing effect between the gases may be enhanced. Compared with other burners, this structure may make the combustion flame shorter, avoid the flame stripping phenomenon, have better premixing performance, high flame stability, and can meet the industrial demands for greater thermal power. Under these considerations, the CFD (computational fluid dynamics) combined with multiple models like turbulence and combustion is employed to numerically investigate the premixing behaviors in the ejector as well as the combustion processes. Firstly, an ejector, an important component of the burner, is designed and developed based on the orthogonal experiment method. Then, the multi-ejector burner installed with the ejector is numerically explored and compared for the combustion process. Finally, the determined ejector burner is verified with well premixing and combustion performance, satisfying the denitration requirements.

The arrangement of the rest of this paper is as follows. Firstly, the numerical model including the geometry, controlling equations and simulation conditions employed in this work is described in Section 2. Then, the computational experiment designing strategy as well as the indicators for performance evaluation are given in Section 3. Section 4 demonstrates the promising experimental results, followed by conclusions in Section 5.

2. Model Description

2.1. Geometry Model

In this work, a large-scale burner with two initial setups, namely cylindrical and rectangular flues, is considered and shown in Figure 1. The diameter of the left cylindrical flue is $\Phi =4.8$ m, and the right rectangular flue has a $4.5\times 4.0$ m${}^2$ cross-section. The cross-section areas of the flues are the same at 18 m${}^2$. Both the cylindrical flue and the rectangular flue are designed with a 10 m height for the sake of comparison.

The ejector shown in Figure 2 has several zones, including the fuel inlet, the suction chamber, the mixing chamber and a diffuser. To enhance the mixing process for the ejector, a set of swirling blades is installed at the outlet of the mixing chamber. The geometry parameters initially settled of the ejector are listed in

Table 1. The initial parameters of the ejector.

Parameter	Value	Unit
$d_1$	290	mm
$d_2$	68	mm
$d_3$	90	mm
$d_4$	420	mm
$L_1$	100	mm
$L_2$	250	mm
$L_3$	191	mm
Swirl blade number, $N_b$	16	pcs
Blade thickness, $T_k$	5	mm
Blade swirl angle, $A_s$	55	${}^{\circ }$

.

2.2. The Combustion Coupled CFD Model Description

2.2.1. Base Governing Equations

The CFD technique was used for the flowing, mixing and combustion. The basic governing equations [24] for calculating the mass, momentum and energy [25] in fluids are, respectively, given by

$$\frac{\partial \rho }{\partial t}+\nabla ·\rho \overrightarrow{\mathit{v}}=0,$$

(1)

$$\frac{\partial }{\partial t}\left(\rho \overrightarrow{\mathit{v}}\right)+\nabla ·\left(\rho \overrightarrow{\mathit{v}}\overrightarrow{\mathit{v}}\right)=\nabla ·(\mu \nabla \overrightarrow{\mathit{v}})-\nabla p+\rho \overrightarrow{\mathit{g}}+\overrightarrow{F},$$

(2)

$$\begin{array}{c}\hfill \frac{\partial }{\partial t}\left[\rho \left(e+\frac{{\overrightarrow{v}}^2}{2}\right)\right]+\nabla ·\left(\sum _j{h}_j{J}_j\right)=S_h-\nabla ·\left[\overrightarrow{\mathit{v}}\left(\rho \left(e+\frac{{\overrightarrow{v}}^2}{2}\right)+p\right)\right],\end{array}$$

(3)

where $\mu$ denotes the molecular viscosity of the fluid; p is the static pressure on the fluid microelement; $\rho \overrightarrow{g}$ denotes the gravity of the micro element; $\overrightarrow{F}$ is the external force acting on the micro element; e is the internal energy of the microelement; $J_j$ is the diffusion flux of component j; and $S_h$ is the source term of various heat sources.

2.2.2. Turbulence Model

The standard k-$\epsilon$ model was adopted to calculate the velocity field of the gas phase for the consideration of the effect of turbulence fluctuation on the flow in the burner. Similar to references [26,27,28], the flow inside is assumed as a fully turbulent flow, and the effect of molecular viscosity is negligible. The transport equations for kinetic energy (k) and dissipation rate ($\epsilon$) are, respectively, described as

$$\begin{array}{c}\hfill \frac{\partial }{\partial t}\left(\rho k\right)+\frac{\partial }{x_i}\left(\rho k{u}_i\right)=\frac{\partial }{\partial x_i}\left[\left(\mu +\frac{{\mu }_t}{{\sigma }_k}\right)\frac{\partial k}{\partial x_j}\right]+G_k+G_b-\rho \epsilon ,\end{array}$$

(4)

$$\begin{array}{c}\hfill \frac{\partial }{\partial t}\left(\rho \epsilon \right)+\frac{\partial }{x_i}\left(\rho \epsilon u_i\right)=\frac{\partial }{\partial x_i}\left[\left(\mu +\frac{{\mu }_t}{{\sigma }_{\epsilon }}\right)\frac{\partial k}{\partial x_j}\right]+C_{1\epsilon }\frac{\epsilon }{k}{G}_k-C_{2\epsilon }\rho \frac{\epsilon }{k}+S_{\epsilon },\end{array}$$

(5)

and the turbulent eddy viscosity ${\mu }_t$ is computed with

$${\mu }_t=\rho C_{\mu }\frac{k^2}{\epsilon },$$

(6)

where $G_k$ and $G_b$ represent the generation of turbulence kinetic energy due to the mean velocity gradients and buoyancy, respectively. The constants $C_{1ϵ}=1.44$, $C_{2ϵ}=1.92$, ${\sigma }_k=1.0$, ${\sigma }_{ϵ}=1.3$, $C_{\mu }=0.09$ refer to previous investigations [28].

2.2.3. Species Transport Equation

The flow inside the ejector includes homogeneous and heterogeneous chemical reactions. The species transport model modified by the addition of volume fraction, a mass transfer source term and the reaction rates of homogeneous and heterogeneous reactions [25,29,30] could be given by

$$\begin{array}{c}\hfill \frac{\partial }{\partial \mathrm{t}}\left(\rho \alpha Y_i\right)+\nabla ·\left(\rho \alpha u{Y}_i\right)=-\nabla ·\alpha {\overrightarrow{J}}_i+\alpha R_i,\end{array}$$

(7)

where $Y_i$ is the mass fraction of species i, $R_i$ is the homogeneous reaction rate for generating species i, ${\overrightarrow{J}}_i$ is the diffusion flux of species i caused by concentration gradients, which in turbulent flow is given by

$${\overrightarrow{J}}_i=-\left(\rho D_i+\frac{{\mu }_t}{S{c}_t}\right)\nabla Y_i.$$

(8)

Here, $D_i$ denotes the diffusion coefficient for species i, ${\mu }_t$ is turbulent viscosity and $S{c}_t$ is the turbulent Schmidt number.

2.2.4. Radiation Model

The P1 model [28] was used to calculate the radiative heat transfer between gases. Reflections on all surfaces were assumed to diffuse, which is the same as in the case of another commonly used discrete transfer radiation model (DTRM) [22]. The exaggerated radiation heat transfer effect caused by local heat source was also ignored. Then, the radiant heat flow was computed with [31]

$$q_r=\frac{1}{3\left(a+{\sigma }_{\zeta }\right)-C{\sigma }_{\zeta }}\nabla G,$$

(9)

where a is the absorption coefficient, $\sigma$ is the scattering coefficient, G is the incident radiation, C is the line aranisotropic phase function. Given $\Gamma =\frac{1}{3\left(a+{\sigma }_{\varsigma }\right)-C{\sigma }_{\varsigma }}$, the above Equation (9) could be changed into

$$q_r=-\Gamma \nabla G.$$

(10)

Thus, the transport equation of G is

$$\nabla (\Gamma \nabla G)-aG+4a\sigma T^4=S_a,$$

(11)

where $S_a$ is the user-defined radiation source phase. Combining equations Equations (10) and (11), the following equation can be obtained:

$$-\nabla q_r=aG-4a\sigma T^4.$$

(12)

The left side term $(-\nabla q_r)$ can be used for the energy equation to obtain the radiation heat.

2.2.5. Combustion Model

Blast-furnace gases are considered to be fuel in this work, in which the combustible components are $CO$, $H_2$ and other alkanes. As a consequence, the chemical reaction equations of combustion could be described by

$$2CO+O_2\to 2C{O}_2,$$

(13)

$$2H_2+O_2\to 2H_{2}O,$$

(14)

$$C_x{H}_y+\left(x+\frac{1}{4}y\right)O_2\to xC{O}_2+\frac{y}{2}{H}_{2}O.$$

(15)

All the above controlling equations would be computed, which could enable the numerical simulation of the whole burner combustion.

2.3. Simulated Conditions

The combustion process is described as follows. Firstly, the recycled flue gas illustrated in Figure 1 enters into the flue. Then the fuels, i.e., blast furnace gases applied in this work as stated before, are be pumped in. After the premixing, and when the flows become stable, ignition is started and then the burning process begins. Therefore, like in the simulations for the premixing processes between the fuel gas and flue gas accelerant, a two-step solution strategy is employed. The cold state for premixing and flowing before ignition is calculated first and then the hot state with combustion is computed. The cold state field solution provides a good initial condition for the chemical reaction calculation. After the fields become stable, the flow, energy and component equations of the chemical reaction are initiated once the ignition until the final hot state field solution is reached.

The ANSYS FLUENT software package 2020 [10] is used in this work, and steady calculations are carried out in these simulations. The flue gas entrance and the fuel entrance are set as the mass flow inlet boundary condition, and the burner exit is set as the pressure outlet. Other key boundary conditions are listed in

Table 2. The simulated boundary conditions of the ejector model.

Boundary Name	Value	Unit
Fuel gas flow	0.2452	kg/s
Fuel gas temperature	300	K
Flue gas flow	2.4	kg/s
Flue gas temperature	373	K
Negative pressure at outlet	−1500	Pa

.

The grid independence check is required in the simulations. The polyhedral mesh generation method of the whole ejector region is adopted, which is shown in Figure 3 below. Five meshes with 93,000, 221,000, 363,000, 598,000, 1,132,000 grids are generated. The gas mass flow, flue gas mass flow and injection coefficient of each setting are computed. The ejection coefficient is defined as the mass flow ratio of the entrained flow to the fuel operating fluid. Figure 4 provides the simulated results. It is found that the calculation results are not significantly affected when the grid number is more than 221,000, in which the gas mass flow, flue gas mass flow and injection coefficient could keep stable. Therefore, the mesh with 363,000 grids is applied, which meets the grid independence demand.

3. Computational Experiment Design and Performance Evaluation

3.1. Orthogonal Experimental Design for Ejector

The orthogonal table is the main tool of orthogonal experimental design [32]. It is generally expressed as $L_n\left(m^k\right)$, where n is the number of tests, k is the number of factors, and m is the level number of each factor. The ejector suction chamber diameter ($d_1$), the nozzle diameter ($d_2$), the blade swirl angle ($A_s$) and the swirl blade number ($N_b$) are considered since they have a strong impact on the ejector [6,10,17]. Each factor is considered with four levels as listed in

Table 3. Test factor levels for ejector experiment.

Level Index	${\mathit{d}}_1$ (mm)	${\mathit{d}}_2$ (mm)	${\mathit{A}}_{\mathit{s}}\left({}^{\circ }\right)$	${\mathit{N}}_{\mathit{b}}$ (pcs)
1	280	60	25	8
2	290	65	35	12
3	300	70	45	16
4	310	75	60	20

. The scheme of this orthogonal experiment can be obtained from the standard protocol. As a result, their four-level orthogonal experiment table $L_{16}\left(4^4\right)$ is given in

Table 4. Design of orthogonal table $L_{16}\left(4^4\right)$.

Exp. No.	${\mathit{d}}_1$ (mm)	${\mathit{d}}_2$ (mm)	${\mathit{A}}_{\mathit{s}}\left({}^{\circ }\right)$	${\mathit{N}}_{\mathit{b}}$ (pcs)
1	280	60	25	8
2	290	60	35	12
3	300	60	45	16
4	310	60	60	20
5	280	65	35	16
6	290	65	25	20
7	300	65	60	8
8	310	65	45	12
9	280	70	45	20
10	290	70	60	16
11	300	70	25	12
12	310	70	35	8
13	280	75	60	12
14	290	75	45	8
15	300	75	35	20
16	310	75	25	16

, which illustrates the fact that the best design out of 64 plans is likely to be found just with 16 experiments.

3.2. Ejector Layout Designs for the Burner

After the preferred ejector is designed, it has to be integrated into the flue to form a burner. Multiple ejectors are needed due to the large burner scale. Thus, it is important to analyze the ejector layout distributions. Considering both the cylindrical flue and the rectangular flue, 8 different layouts are initially designed for evaluation and comparison, as shown in Figure 5. C1 to C4 refer to cylindrical flue, and R1 to R4 stand for rectangular type. The ejectors are arranged axially in the left four layouts in which most ejectors are located at the half radius of the cylindrical flue. C1 and R1 are circular arrangement while C2 and R2 are linear arrangement, and the ejectors are installed in the radial direction in the right four arrangements. In C4 and R4, all the axes of installed ejectors are equally tangent with a locating circle inside the flues. The size of the circle diameter, i.e., $d_{in}$ in the schematic diagram is $1/3$ times that of the cylindrical flue diameter.

3.3. The Premixing Degree of the Ejector

To evaluate the premixing performance for fuel and flue gases under each design, it is necessary to compare the $CO$ concentration at different points of the ejector outlet. In this case, 8 sampling positions are adopted to measure the $CO$ mixing non-uniformity, i.e., $COMNU$ for short, at the outlet section of the ejector as illustrated in Figure 6. The location diameters of the inner 4 and the outer 4 points are, respectively, $1/3$ and $2/3$ times those of the ejector diffuser diameter. Like in the work of [33,34], the $COMNU$ could be calculated by

$$COMNU=\sqrt{\frac{{\sum }_{i=1}^n{\left(w_i-\overline{w}\right)}^2}{(n-1)}}/\overline{w},$$

(16)

where $w_i$ represents the $CO$ concentration at the ith sampling point, $\overline{w}$ represents the average value, and $n=8$ denotes the total sampling number. The ejector has a better premixing effect when the $COMNU$ metric is smaller.

3.4. The Temperature Uniformity of the Burner

To evaluate the combustion performance of burner, the temperature cloud picture is used for visual inspection and qualitative analysis. In addition, temperature values from 9 different points are sampled to quantitatively compute the average statistic ($mean$) and temperature variance ($var$) at the burner outlet. Likewise, the sampling points are located uniformly at the radial direction, which is demonstrated in (Figure 7). For example, the outer and middle 4 points are situated, respectively, at distances $2/3$ and $1/3$ times that of the flue diameter. They are all arranged with symmetric distributions as the sampling positions in the rectangular flue. Obviously, a lower variance value indicates a more uniform temperature for the flue gas after combustion.

4. Results and Discussions

4.1. Model Verification

In order to verify the model used in this study, a comparative analysis for the ejector premixing characteristics between the present work and reference [7] is carried out. Since the structure sizes and boundary conditions of the ejectors are not quite the same, dimensionless parameters are selected and compared. Two important indexes, i.e., the molar entrainment ratio (MER) and the combustion efficiency [7], are selected as the evaluation indicators. The MER is the ratio between the molar amount of the ejected air and the molar amount of fuel. The comparison results are shown in Figure 8 and Figure 9.

The ratio of the mixing chamber diameter to the nozzle diameter has great influence on MER. The larger the ratio, the greater the MER value [19,20]. It can be seen in Figure 8 that the distribution of MER in the reference ranges from 8 to 10. Under each load, the MER fluctuates by less than one. In the present work, the ejector MER is distributed between five and six, and the fluctuation value of MER is less than one. The changing trend is consistent with the reference results. However, there is an almost unchanged gap of about three in MER under each load. This may be caused by the nozzle diameter, the mixing tube diameter, and the nozzle position [7,20]. It was found that the MER rises as the ratio of the mixing tube diameter to the nozzle diameter increases [7]. The ratio in the reference is 5.3, larger than 1.2 in this study, implying that the MER values are reasonable. Consequently, the MERs fit the conclusions in reference [7]. On the other hand, according to the definition of combustion efficiency in reference [7], the burnout rate of the ejector in this study under different loads is calculated and compared as shown in Figure 9. It can be found that the results stay very close and they show the same changing trend. The relative difference is within 0.75%, indicating that the combustion simulation in our work is feasible. To sum up, the model employed in this work is verified, proved to be sound and reasonable.

4.2. Premixing Degree on the Orthogonal Designs

4.2.1. Qualitative Analysis of the Premixing Uniformity at the Ejector Outlet

At the ejector outlet, the $CO$ concentration distributions based on the orthogonal experiments from Table 4 are compared in Figure 10. For the cases with $N_b=8$ (Figure 10a,l,n), the patterns are like flowers with eight petals. This means that the eight swirl blades are not enough to achieve a sufficient premixing of fuel gas and flue air. For the cases with $A_s={60}^{\circ }$ (Figure 10d,g,j,m), the patterns are like tree rings with several layers. This means that the large $A_s$ is bad for gas–air mixture due to the over whirl.

4.2.2. Range Analysis of the Premixing Uniformity at the Ejector Outlet

The $COMNU$ results calculated in Equation (16) for the 16 cases are listed in

Table 5. The simulation results (COMMU) based on different parameters in the orthogonal table.

Exp. No.	1	2	3	4	5	6	7	8
COMNU	0.0934	0.1069	0.0563	0.2334	0.0794	0.0584	0.2973	0.0586
Exp. No.	9	10	11	12	13	14	15	16
COMNU	0.0599	0.1872	0.1200	0.1092	0.2217	0.0739	0.0235	0.0773

. It could be found that the ejector designed with Setting 15 exhibits the best premixing performance ($COMNU=0.0235$) among the 16 tests.

$K_i$ is used to represent the average value of $COMNU$ of a factor at a certain level (four decimal places) to obtain the relationship between $COMNU$ and various factors. For example, for the second level of factor $d_1$, $K_2$ is the average value of $COMNU$ of the second, sixth, tenth and fourteenth groups of orthogonal tests. The calculation process is ${\mathrm{K}}_2=(0.1069+0.0584+0.1872+0.0739)/4=0.1066$. In addition, the orthogonal experiment can determine the best level for each design factor by computing its average $COMNU$ as shown in Figure 11. The results signify that the best choices for each factor are $d_1=290$ mm, $d_2=75$ mm, $A_s={45}^{\circ }$ and $N_b=20$, and $COMNU=0.0153$ could be obtained. Obviously, this combination is not one of the 16 cases in Table 4. Therefore, a simulation case with $COMNU=0.0153$ was carried out again. The results demonstrate a significant premixing performance improvement, verifying this optimization design with $COMNU=0.0153$.

The distribution trend of the K value at each factor level can also be found in Figure 11. The $COMNU$ decreases first and then increases with the increase in the $A_s$ value. This is because the swirl blades have little effect on the change in the airflow direction when $A_s$ is too small, resulting in a poor premixing effect. Most of the high-speed gas hits the swirl blades and quickly passes through the swirl blades in the radial direction when the $A_s$ is too large, resulting in a large $CO$ concentration in the outer ring and a small $CO$ concentration in the inner ring, leading to uneven $CO$ mixing. It is agreed in study [10] that suitable $A_s$ can significantly improve premix performance. The $CO$ concentration uniformity is better with the increase in the $N_b$ value. This is because the swirling strength of the gas becomes greater with the increase in $N_b$, thus enhancing the premixing degree between the gases. Similar results could be found in [6].

The range of $COMNU$ of any factor is the difference between the maximum and the minimum of $k_i$ under this factor, and the calculation is

$$R=max\left(k_1,k_2,k_3,k_4\right)-min\left(k_1,k_2,k_3,k_4\right).$$

(17)

The range of each factor and the variance analysis are used for factor sensitivity evaluation. Figure 12 shows the influence of the four factors on the premixing effect of the fuel–flue gas of the ejector. The range value is in the order of $A_s$, $N_b$, $d_1$ and $d_2$. The $A_s$ has the greatest influence on the premixing effect, because the blade angle directly determines the mixing swirl direction of fuel and flue gas, and the flow direction of the two gases affects the composition exchange between gases. The range value of $d_1$ and $d_2$ is small, indicating that these two factors have relatively weak influence on premixing performance.

4.2.3. Variance Analysis of the Premixing Uniformity

The variance and the F value of each factor were calculated to judge the influence of each factor on the premixing effect, and the calculation formulas are

$$S_j=\sum _{i=1}^n{\left(k_i\right)}^2,$$

(18)

$$F_j=\frac{S_j/f_j}{S_e/f_e}\sim F\left(f_j,f_e\right),$$

(19)

where $S_j$ is the sum of squares of factor $k_i$ values, n is the total number of tests, $k_i$ is the K value at the corresponding level of each factor, j is $d_1$, $d_2$, $A_s$, or $N_b$, $F_j$ is the F value of factor j, $f_j$ is the degree of freedom of factor j, $S_e$ is the sum of squares of errors, $f_e$ is the degree of freedom of errors.

The calculation results are shown in

Table 6. Analysis of variance of orthogonal test. (* means average significance).

Source	Sum of Squares	Freedom	Mean Square Sum	F Value	Significance
$d_1$	0.0542	3	0.0181	0.9862	Not significant
$d_2$	0.0540	3	0.0180	0.9823	Not significant
$A_s$	0.7302	3	0.2434	13.2767	*
$N_b$	0.5547	3	0.1849	10.0850	*
error	0.0550	3	0.0183

. It can be judged that for the influence on ejector premixing performance, $A_s$ and $N_b$ are significant factors while $d_1$ and $d_2$ are not that important.

In conclusion, the ejector with $d_1=290$ mm, $d_2=75$ mm, $A_s={45}^{\circ }$ and $N_b=20$ is selected, and $COMNU=0.0153$ indicates good premixing capability.

4.3. Temperature Uniformity Based on the Ejector Layout Designs

4.3.1. Qualitative Comparison for the Temperature Uniformity at the Burner Outlet

Using the selected ejector, the eight burner layouts (Figure 5) are evaluated to obtain a better design. The temperature distributions of all layouts are shown in Figure 13. The results show that the outlet temperature distribution of layouts $C1,C2,R1,R2$ is more uniform because the flow direction is axial. The hot flue gas of the circular layout and the linear layout is consistent with that of the gases to be heated. Heat exchange could happen over a long time, leading to a uniform temperature distribution. However, for layouts $C3,C4,R3,$ and $R4$, the flow direction of the hot gas and the cooling gas is vertical, and the space for heat exchange between them is small, resulting in uneven temperature distribution of the outlet section.

Examining Figure 13d,h, it can be seen that the high temperature is distributed around the outlet section and the temperature in the central area is low in a tangential arrangement, while the opposite is true for the opposing arrangement. The temperature distribution cloud diagram of the profile of the ejector with the opposing arrangement and the tangential arrangement is shown in Figure 14. For the tangential arrangement, the high-temperature hot flue gas generated by the burner combustion flows in a spiral form around the flue towards the flue outlet. Meanwhile, there is only a small amount of hot flue gas in the central area for heat exchange, so the outlet section is high around it and low in the center. For the offset arrangement, the high-temperature hot flue gas generated by the burner combustion flows to the geometric center of the section. Therefore, there is more central hot flue gas than the surrounding hot flue gas during the heat exchange of the cold and hot flue gas, resulting in a high temperature in the center of the outlet section and a low temperature in the surroundings.

4.3.2. Quantitative Analysis for the Temperature Uniformity at the Burner Outlet

In addition to visual display, the temperatures are recorded according to a sampling scheme (Figure 7). The recorded data (Figure 15) are provided with standard statistics ($mean$ and $var$) in

Table 7. The temperature statistics for different layouts.

	C1	C2	C3	C4	R1	R2	R3	R4
$mean$ (K)	676.0	679.8	574.5	615.1	676.9	682.3	575.5	602.0
$var$ (K${}^2$)	25.1	91.4	271.4	178.7	35.3	15.5	288.1	187.0

. All the layouts demonstrate a satisfactory mean temperature. However, the layouts C2, C3, R1, and R3 have some unwanted points whose temperature is out of the SCR denitration range. Regarding the variance, the layouts C1 and R2 have the minimum values for the cylindrical flue and rectangular flue, respectively, resulting in the best temperature uniformity of the flue gas at the outlet.

Overall, the C1 and R2 layouts with seven optimized ejectors are expected to satisfy the challenging requirement of large-scale denitration burners. And the R2 arrangement shows a more uniform temperature distribution. A final selection would depend on the flue type employed.

4.4. The Combustion Stability in the Designed Burner

To further investigate the combustion stability of the large-scale burner, layout R2 with the most uniform temperature distribution is examined further with varying levels of fuel gas flow. Four working conditions in a great range are considered with 50%, 75%, 100%, and 125% gas flow, respectively. The 100% fuel gas flow equals to 0.2452 kg/s. As shown in Figure 16, the temperature distributions in and at the outlet of the burner are consistent between different working conditions with a ∼0.5 m flame length and well flame patterns. The highest temperature for each working condition is about 1420–1430 K, indicating that the designed burner could work in stable and adapt to complex combustion conditions.

Consequently, the large industrial burner with seven ejectors distributed in the R2 layout could be selected and determined for denitration applications.

5. Conclusions

Based on CFD simulations and analysis, an industry-scale multi-ejector burner with good performance including sufficient premixing capability, outstanding temperature uniformity, short flames and stable combustion, is developed. The burner satisfies different thermal power requirements and makes contributions to other related industrial applications. Main conclusions in this work are drawn as follows.

(1) The influencing degree on the ejector premixing performance of the studied parameters ranks in the following order: blade swirl angle ($A_s$) > swirl blade number ($N_b$) > ejector suction chamber diameter ($d_1$) > nozzle diameter ($d_2$). The first two are dominant. The optimized premixing non-uniformity of the ejector could be reached, indicating the best premixing performance. The specific parameters of the ejector include the nozzle diameter of 75 mm, the suction chamber diameter of 290 mm, the blade swirl angle of 45° and the swirl blade number of 16.

(2) For the burners installed with the selected ejector and flues, the minimum values of the temperature variances at the burner outlets with linear and circular arrangements were obtained, respectively, indicating the two most uniform temperature distributions.

(3) The outlet temperature uniformity, the averaged outlet temperature, the combustion efficiency and the flame pattern of the determined burner could remain stable under different loads, and they could be adjusted in a large range, which verifies the reasonable quality of the developed industrial denitration-used burner.