Modeling of Peat Mass Process Formation Based on 3D Analysis of the Screw Machine by the Code YADE

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2. Computer Model

On the basis of peat briquetting investigations of Russian scientists ^{[2, 3]}, as well as on the basis of investigations of foreign authors on flow of slip bodies ^[4], we propose to make the entrance part of the die (bookel) in the way of a catenary line. Profile calculation is performed upon the following formula:

(1)

(2)

where h₁ – distance between symmetry axis of the curved part of the die profile and entrance end of the channel; b – height of the curved part of the channel profile; b₁ – half of channel height along the symmetry axis of cambered die (Figure 3).

Figure 2. A die which entrance part is made in the way of a catenary line

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According to theoretical calculations of the Russian scientist Professor B.A. Bogatov ^[2] perform narrowing inlet nozzle portion by a chain line can significantly decrease the costs for the extruder while forming peat as compared with straight cone of narrowing and cylindrical transition. In order to check the data of theoretical investigations, we’ve conducted virtual tests of the model created in the open-source software YADE for modeling particle movement with discrete elements method and using ParaView visualization program based on the laboratory of 3D-modelling of the Institute of mineral dressing in the TU Freiberg Bergakademie, Germany ^[5]. YADE software has been created for the calculation with discrete elements method on the basis of developments of scientists from , and scientists from other leading universities of . YADE has proved its applicability in many fields: processing and destruction of rocky materials, analysis of module unit operation and separate machines on extruding free-flowing substances.

3. Numerical Results

While conducting calculation, we’ve considered three forms of narrowing of the die entrance part (Figure 3).

Figure 3. Form of narrowing of the die entrance part: а – cylindrical transition; b – conical; c- in the way of a catenary line

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Calculation modules of YADE software (Figure 4) allowed obtaining data about such values as: particle angular velocity ω, rad/s; particle linear speed ν, m/s; normal stress in material particles in case of the interaction with processing screw Q stand, Pa; torque on screw shaft М, Nm; resultant of forces applied to the flight screw F cut, N.

Figure 4. Modeling scheme: а) cylindrical passage; b) narrowing in the way of a catenary line; c) conical narrowing

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Angular and linear velocity of the particles are determined by the average of the readings recorded by the analysis YADE all particles, being in the case of screw machine. Tension on normal Q different standards (Figure 4 a, b, c) depending on the proximity of the particles to the die, and it shows different color particles corresponding scale.

Table 1 shows the results of an experiment in the virtual software module YADE. Productivity in even feed process is 3 tons of pellets/hour.

Table 1. Results of tests of different narrowing forms of dies

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Tables index

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Peat mass compressed in the forming part is protruded into its calibrating part, which length defines the time of relaxation of inner stresses and calibrates the piece surface. In order to determine the ratio of these parameters we used a semi-empiric model of Benbow-Bridgwater ^[6]. The scientists who have developed this model used the conclusion that total pressure during formation is a sum of pressure in the pressure area P1 and extrusion area pressure P2 (Figure 5). Model Benbow-Bridgewater - is the sum of the pressures (P1 + P2), changing in the transition from one particle diameter in the other. This expression has been expanded and refined for each diameter die.

Pressure Р1 reflects the effect of the shape at the entrance to dies, σ 0, α are evaluated as material constants featuring material resistance, and as supposed, they are not dependent from the die geometry. A mass flow goes in the die as a solid plug surrounded by the shallow moisture layer, which separates it from the wall. Thus, shearing stress is a function of mass speed, and β is a material constant featuring speed effect while decreasing pressure Р2 along the die length. When evaluating indicators of stress decrease in the material during the tests of a die with narrowing in the way of a catenary line, the equation (3) gets shape ratio sr = 0,72 (standard stress decrease by 18%) for the die entrance part made in the way of a catenary line.

(3)

Here Р1is a pressure in the pressure area, Pa; Р2 is an extrusion area pressure, Pa; σ0 is one-axis stress of fluctuation at the entrance to the die, Pa; average rate of mass flow in the forming part, m/s; α is a rate development factor at the entrance to the die; S0 is a cross-sectional area of the screw housing, m; ΣS is the total area of section of die forming and calibrating parts, m; τ0 is a shear stress at the forming part wall, Pa; β–a share of near-wall sliding from the average mass flow rate; L is the length of the die forming part, m; d is the diameter of the die forming part, m; kf is an experimental ratio considering the influence of the die entrance part form.

It should be mentioned that in order to determine the interaction forces between the particles, a linear contract model was used. Rigidity of particles imitating peat particles has been selected without considering their physical parameters.

The obtained absolute values of torques and stresses can be used only for illustration of quality picture of screw extruder operation. In order to determine the geometrical parameters of the calibrating part of the matrix die, the ratio of length of forming part h 1 and calibrating part h 2 of the die, experiments were conducted on 8 dies with different parameters (Figure 5) on the extruder «Autоgraph - Shimadzu». While manufacturing agglomerate peat fuel on the machine with set geometrical parameters at the stage of peat material preparation, it’s necessary to conduct botanical analysis, decomposition level, ash-content, dispersity and degree of contamination.

Figure 5. Pressure in the pressure area and extrusion area in the die

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