^{1}

^{1}

^{1}

^{2}

^{1}

^{2}

A three-dimensional numerical simulation combining discrete phase method (DPM) and porous media based on the theory of Euler-Lagrange has been employed to investigate particles distribution in a separator. The DPM model is applied to monitor the movement of individual particles and calculate the contact force between them in the separator. The simulation results display the migration feature of dust particles over time and the distribution of particles on the surface element in porous region and reveal that the flow field influences the distribution uniformity of the particles in porous area directly. Based on the analysis, the structure of separator is optimized by the Taguchi method. An orthogonal relation motion has been established. The optimal solution is achieved by the calculation of the weight relationship. The calculated optimal structure is evaluated by the signal to noise (SNR). The result reveals that the values of SNR in case are eligible. As a result, the research of the separator points out a useful and improvable method for the parameter optimization of structure design.

Coal, as the primal fossil fuel, has played an important role in national economy, such as the areas of electricity, heating, and transportation. Coal resource can be divided into high rank coal and low rank coal. Among them, low rank coal is not only characterized by the high moisture content but also the high volatility which can cause an explosion easily [

In this paper, multiphase flow model is chosen for simulation analysis of the model combined with computational fluid dynamics (CFD). The commonly used mathematical models that have been raised so far can be grouped into two categories: one is the continuum-continuum approach, as represented by Euler-Euler model [

Many scholars have studied the porous media model in the different structure. Wu [

However, minimum studies considered the more uniformity of particles in porous media by optimizing the structural parameters. Optimization design methods have used various metaheuristics such as nonlinear search optimization [

The Taguchi method has been proposed by Genichi Taguchi [

In summary, the paper is organized as follows: Section

Computational fluid dynamics method is used in this study. Its basic approach is dividing the continuous physics region into discrete. Based on the Navier-Stokes equations, the fluid domain is calculated to obtain the key physical parameters of heated air such as speed, temperature, pressure, and flow positions.

The flow condition can be judged from the Reynolds number. The turbulence model is selected which includes the conversation laws of mass, momentum, and energy. The turbulence equation should be considered. Thus k-_{M} is the contribution in the turbulent pulsating pressure expansion.

The filter area in separator needs to be calculated with model of porous media which is defined as laminar. A flow resistance value is introduced. The porous medium model based on superficial velocity can simulate pressure loss. The flow resistance of porous material in the fluid domain is calculated by adding a feature in momentum equation. The feature is composed of two parts, Darcy viscous resistance terms and inertial loss terms, which is expressed as

Here_{ij} and_{ij} is the viscous resistance and inertia loss coefficient matrix, respectively. This negative result leads to a pressure drop in the unit of porous medium.

where_{p} is the particle diameter,

The particles trajectory is tracked using the DPM model. The particle motion formula is on a Lagrange coordinate system. The particles motion formula of discrete phase is shown in (

Here up is the velocity of particle. _{D}_{p}_{D} represents the resistance impacting on particles in unit-mass:

_{ e } is the relative Reynolds number and_{D} is the product ratio of fluid dynamic pressure._{D} has impact on the projection which is the movement direction of the particles, namely, the drag force coefficient._{p} is the particle diameter here. The control equations of coupling model in the continuous phase, discrete phase, and porous media [

Adsorption balance equations [

The computational domain and grid arrangements of the separator are shown in Figure

Calculation domain and grid arrangement.

The semi-implicit method for pressure-link equation (SIMPLE) algorithm is used as the numerical method. In computational fluid dynamics, the SIMPLE algorithm is widely used to solve the Navier-Stokes equations, and it has been extensively used to solve fluid flow and heat transfer problems [

Calculation domain is meshed by Gambit. The total number of meshes is 6,197,815; therefore, the time of calculation of the meshed model needs about 48 hours on a workstation (System is Windows 8. The processor is Xeon 1231v3. The memory is 16G). The calculation is done in Fluent 14.0 and the result is extracted by Tecplot 360 21013R1. The type of grid is chosen as tetrahedron structure. The grid density is increased appropriately in the six filter parts. The Jacobian value is positive.

In this study, we set medium volatile coal (Coal-Mv) as the particles of discrete phase in calculation. Compared with highly volatile coal (Coal-Hv) and low volatile coal (Coal-Lv), Coal-Mv is suitable for simulating most coal powders in working conditions [

The parameter settings of calculation.

Gas phase | Density(kg/m3) | 1.225 |

Viscosity(kg/m-s) | 1.7894e-05 | |

Reference Temperature(k) | 298.15 | |

Velocity Magnitude(m/s) | 20 | |

Turbulent Intensity(%) | 10 | |

Hydraulic Diameter(m) | 0.4 | |

| ||

Particles phase | Cp(Specific Heat )(j/kg-k) | 1550 |

Molecular Weight (kg/kg-mol) | 17.237 | |

Standard State Enthalpy(j/kg-mol) | -5.601e+07 | |

Reference Temperature(k) | 298.15 | |

Velocity (m/s) | 20 | |

Turbulent Kinetic Energy | 0.8 | |

Momentum | 0.2 | |

| ||

Porous area | Porosity | 0.4 |

face permeability(m2) | 1.19e-11 | |

Porous permeability | 0.5 | |

Viscous Resistance | 8.4e+10 | |

Inertial Resistance | 5.1e+04 |

The Rosin-Rammler model is used to describe the distribution of particle diameters in this work. The Rosin-Rammler model was first applied by Rosin-Rammler to describe a particle size distribution. The expression function of the Rosin-Rammler is described as

where F is the distribution function of particles with a diameter of d. c is the characteristic diameter which is always the average diameter of particles. The exponent m is uniformity constant [

Inlet and outlet of the mode are mentioned in Figure

In order to make result closer to reality, other options are set based on the real actual working conditions.

This section discusses the results of the simulation. The result positions of the three cross-sectional in porous region in Figure

Particle distribution at different times.

position | Simulation result | |||
---|---|---|---|---|

T:126s | T:162s | T:198s | T:234s | |

Y=-1100mm | | | | |

| ||||

Y=-1500mm | | | | |

| ||||

Y=-1900mm | | | | |

Three-dimensional particle distribution (t=286s).

Table

The image of velocity distribution.

position | | |||
---|---|---|---|---|

T:126s | T:162s | T:198s | T:234s | |

Y=-1100mm | | | | |

| ||||

Y=-1500mm | | | | |

| ||||

Y=-1900mm | | | | |

The results of mean square error.

Position of section | 126s | 162s | 198s | 234s |

-1100mm | 10.877 | 9.957 | 9.073 | 8.838 |

-1500mm | 7.886 | 7.852 | 8.083 | 5.441 |

-1900mm | 6.777 | 6.777 | 5.685 | 6.230 |

N is the number of data point and xi is the value of each point.

In engineering, the replacement of filter has a high cost and complicated operation. Therefore, we hope that most particles will not penetrate filter. A large number of particles accumulated in the middle area will cause filter to be partially stressed resulting in the aging rate of the filter, so particle should distribute uniformly in the filter to reduce the accumulation of particles partially in the filter. The particles are mainly affected by the continuous phase. Therefore, the goal of the separator structure optimization is to get a more homogeneous flow field in porous media zone. In our paper, the uniformity of flow field is evaluated by velocity and pressure.

A separator model is given by an enterprise in China. Our purpose is to improve parameters about inlet and filters based on CFD. As to a separator, performance is always decided by the distribution of velocity and pressure. In ideal status, a uniform distribution of flow field means that the particle will contact the filters equivalently; therefore, all the filters paly the same role. Otherwise, particles will focus on some parts of few filters which will be damaged easily. These filters may be blocked by too much concentrated particles, while an unfair distribution also means that some area of filters does not work at all. For these reasons, mean square errors of velocity and pressure are used to evaluate the result of optimization, and a smaller value means a better performance.

As to a given separator in specific working conditions, the mainframe cannot be changed, and the filter is already made according to standard; therefore, their sizes always cannot be changed. Inlet is a key part to decide the distribution of fluid filed; thus both the position and inclination angle of inlet are chosen to optimize. In the inner of separator, the utilization rate of filters is decided by the installation site directly, since it is so, it cannot be neglected that the distance between two filters in the direction-Z in Figure

Based on the reasons above, three parameters are selected to optimize the model according to the mean square error from distribution of both velocity and pressure. Taguchi method is used to realize the target.

The basic principle of the Taguchi method, avoiding the blindness of traverse type analysis, is the inspection of the effectiveness from the experimental variables which is the synthesis procedure conducted by orthogonal array with minimum number of experiments [

In the study based on Taguchi method, to represent three parameters, we take the angle between the inlet axis and the horizontal direction as factor A, the distance between the inlet and bottom of filter as factor B, and the distance of two filters in direction-Z as factor C. Control factors and its levels are designed and shown in Table

The statistics of element.

Factor | Level 1 | Level 2 | Level 3 |
---|---|---|---|

A (degree) | 45 | 22.5 | 0 |

B (m) | 1.267 | 0.725 | 0.200 |

C (m) | 1.220 | 1.020 | 0.820 |

Factor A is often between 0° to 45° in actual equipment, thus 0°, 45°, and 22.5° are chosen. As to factor B and factor C, the extreme values and their medium value are taken into consideration, ranging from the highest and lowest position. Different values are noted as different levels in Taguchi method as shown in Table

Table

The proof of the orthogonal.

case | A | B | C | AB | BC | CA |
---|---|---|---|---|---|---|

1 | + | + | + | + | + | + |

2 | + | - | - | - | + | - |

3 | + | 0 | 0 | 0 | 0 | 0 |

4 | - | + | - | - | - | + |

5 | - | - | 0 | + | 0 | 0 |

6 | - | 0 | + | 0 | 0 | - |

7 | 0 | + | 0 | 0 | 0 | 0 |

8 | 0 | - | + | 0 | - | 0 |

9 | 0 | 0 | - | 0 | 0 | 0 |

Total | 0 | 0 | 0 | 0 | 0 | 0 |

L_{9} orthogonal array is used here; it contains nine tests, three levels, and three variables (L means Latin square and 9 means the number of cases). The orthogonal table is recorded in Table

The orthogonal table of separator.

case | A | B | C |
---|---|---|---|

1 | A1 | B1 | C1 |

2 | A1 | B2 | C2 |

3 | A1 | B3 | C3 |

4 | A2 | B1 | C2 |

5 | A2 | B2 | C3 |

6 | A2 | B3 | C1 |

7 | A3 | B1 | C3 |

8 | A3 | B2 | C2 |

9 | A3 | B3 | C1 |

For example, A1 stands for factor A with Level 1.

In Taguchi method, the ratio of signal to noise (SNR) is always used as the key value to evaluate the performance of each experiment in Taguchi analysis. In this study, the target is to find smaller mean square errors; thus SNR can be expressed as (

The SNR, a function of noise, is a good performance measure for robustness, is a good performance measure for robustness. Thus, it is expected that the results of statistically significant should represent the optimal combination of kinematic parameters [

Values of

The results about velocity.

case | A(degree) | B(m) | C(m) | Y | |
---|---|---|---|---|---|

1 | 45 | 1.267 | 1.220 | 3.000 | -9.542 |

2 | 45 | 0.725 | 1.020 | 1.052 | -0.440 |

3 | 45 | 0.200 | 0.820 | 1.895 | -5.552 |

4 | 22.5 | 1.267 | 1.020 | 1.338 | -2.529 |

5 | 22.5 | 0.725 | 0.820 | 0.677 | 3.388 |

6 | 22.5 | 0.200 | 1.220 | 0.121 | 18.344 |

7 | 0 | 1.267 | 0.820 | 1.687 | -4.542 |

8 | 0 | 0.725 | 1.020 | 0.181 | 14.846 |

9 | 0 | 0.200 | 1.220 | 0.790 | 2.047 |

The results about pressure.

case | A(degree) | B(m) | C(m) | Y | |
---|---|---|---|---|---|

1 | 45 | 1.267 | 1.220 | 38.132 | -31.626 |

2 | 45 | 0.725 | 1.020 | 16.057 | -24.113 |

3 | 45 | 0.200 | 0.820 | 43.186 | -32.707 |

4 | 22.5 | 1.267 | 1.020 | 3.895 | -11.810 |

5 | 22.5 | 0.725 | 0.820 | 40.566 | -32.163 |

6 | 22.5 | 0.200 | 1.220 | 2.042 | -6.201 |

7 | 0 | 1.267 | 0.820 | 55.801 | -34.933 |

8 | 0 | 0.725 | 1.020 | 3.405 | -10.642 |

9 | 0 | 0.200 | 1.220 | 31.813 | -30.052 |

Then the contribution rate is expressed as (

The contribution of factors based on velocity.

A | B | C | ||
---|---|---|---|---|

SNR | 1 | -5.178 | -5.528 | 3.616 |

2 | 6.401 | 5.931 | 3.959 | |

3 | 4.117 | 4.947 | -2.235 | |

| ||||

Range | 11.579 | 11.459 | 6.194 | |

| ||||

Contribution Rate | 39.611% | 39.200% | 21.189% |

The contribution of factors based on pressure.

A | B | C | ||
---|---|---|---|---|

SNR | 1 | -29.482 | -26.123 | -22.626 |

2 | -16.725 | -22.306 | -15.522 | |

3 | -25.209 | -22.987 | -33.267 | |

| ||||

Range | -12.757 | -0.681 | -17.745 | |

| ||||

Contribution Rate | 40.910% | 2.184% | 56.906% |

From Table

In order to obtain better parameters of the separator, both distributions are considered. The values of

SNR according to velocity.

SNR according to pressure.

It can be seen that there is a positive correlation between the distribution of velocity and pressure. A better scheme can be obtained with Taguchi method to get a uniform distribution of fluid filed in inner part.

From the result above, A2B2C2 is considered as the best scheme. The mean square errors of velocity and pressure are shown in Figures

The mean square error of velocity in all cases.

The mean square error of pressure in all cases.

The mean square error of the 10th scheme is close to the optimal, as well as the case of 6th scheme and the case of 8th scheme. The most obvious characteristic of the three cases is the smaller angle between import and horizontal. Therefore, control factor A has great influence for the flow field uniformity in the filter sections. We can draw the conclusion that the Taguchi method can also evaluate the importance of a single factor.

The Taguchi methods can not only evaluate the importance of elements and also evaluate the rate of contribution of the single factor. This method applied in structure design can be refined and extended in a follow-up study such as increasing the number of parameters and the degree of level factors. A better scheme can be got to reduce the cost of design and manufacture through the analysis and calculation.

In this paper, a separator is simulated with CFD, and key parameters of a separator are optimized with Taguchi method. The results in this paper are as follows:

In this paper a theoretical foundation and effective means has been provided and help in extending the knowledge on the research of optimization design in separator.

The data used to support the findings of this study are included in the supplementary material file.

The authors declare that they have no conflicts of interest.

This work was supported by the National Natural Science Foundation of China (Grant 51876175), the Innovative Talents Promotion Project of Shaanxi, China (Grant 2018KJXX-067), and the Tianjin Municipal Science and Technology Foundation (no. 14JCYBJC43200).

The data is extracted from the postprocessing software Tecplot. There are a total of 9 cases with 120 speed values for each case. The mean square error is obtained by the 120 data of each case. SNR is obtained from the formula in Table