# Modeling of Aerodynamic Separation of Preliminarily Stratified Grain Mixture in Vertical Pneumatic Separation Duct

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{−1}; universal air-sieve machines, 0.86–1.61 kWh·Mg

^{−1}; vibro-pneumatic separators, 1.88–3 kWh·Mg

^{−1}; and triers, 0.22–0.29 kWh·Mg

^{−1}[10].

## 2. Materials and Methods

_{g}is the density of air; U is the air velocity relative to the movement of the grain mixture particles; and d is the equivalent particle diameter of the grain mixture defined for wheat and barley.

_{p}∙ρ is the mass of the grain mixture particles; F is the force acting on a particle of the grain mixture from the side of the air stream, determined according to formula (1); F·cosγ is the vertical component of the force acting on the grain mixture; γ is the angle between the direction of the force F and the vertical axis of the coordinate system, V

_{p}; ρ is the particle volume and density of grain mixtures.

_{0}cos θ, vy = U

_{0}·sinθ, where U

_{0}is the velocity at which the grain mixture particle enters the pneumatic separation duct, θ is the angle of entry of the particles into the pneumo-separation duct (Figure 1b). The expression for the relative velocity of the grain mixture particles is as follows:

_{p}ϑ, k

_{p}≈ 1.06 [24].

_{0}we define the distance from the particle of the mixture to the inclined scaly airtight surface at the initial time.

_{0}= H, taking into account the averaged velocity, is:

_{0}is the distance of the impurity particle from the scaly surface at the moment of entering the duct; W is the velocity of the impurity particles upwards (due to the short relaxation time it is close to constant). This velocity is determined by the equilibrium of the forces acting on the impurity particle. The main ones are the force of motion resistance, and the force from the influence on the impurity particle of the air stream, which are determined by Equation (4), and the gravitational force. Thus, the velocity of the impurity particles up is equal to:

_{p}, ρ

_{p}are equivalent diameter and average particle density of impurities, respectively; ρ0 is the bulk density of grain; ε is the porosity of the layer at the moment of entering the pneumatic separation duct.

_{i}is the equivalent particle diameter i—faction; f

_{i}is the weight fraction in the mixture.

_{g}, ρ

_{g}are the kinematic viscosity and density of the air.

_{2}, where k

_{2}is the stratification coefficient of the grain mixture on the inclined scaly surface, will be free of impurity particles. In order to confirm the results of mathematical modeling, experimental studies (shown schematically in Figure 2) were carried out at the established laboratory stand (Figure 3).

^{−1}; probe type—impeller; error ±1.5%; divisions 0.1 m·s

^{−1}. The airflow velocity was regulated by means of a damper (Figure 2, position 7).

_{p}is the path traveled by the particle of the mixture in time t; k is the number of frames responsible for moving a particle over a given distance; t

_{frames}= 1·n

^{−1}is the time of one frame, where n is the frame rate per second.

^{−2}, weight of 1000 grains—41 g) grains of the main crop, of which beaten grains—4%, lean grains—5%; mineral impurities—0.5%; organic weeds (grain films, straw, etc.)—6%; weed seeds—4.8%; dust particles (grain and mineral)—0.3%.

## 3. Results

^{−3}, calculated value of flow viscosity μ

_{0}= 0.1 Pa·s, equivalent impurity diameter d

_{p}= 0.002 m, average impurity particle density ρ

_{p}= 400 kg·m

^{−3}. The selected values of density ρ at numerical miscalculations were accepted under the condition of basic humidity of grain mix of wheat of 14%. It was not difficult to take into account the change in moisture content of the grain mixture and grain density of the main crop and impurities, conducting additional experiments.

^{°}, its length 0.5 m, the airflow velocity on the scaly surface 3 m·s

^{−1}, the airflow velocity in the vertical ducts V= 6 m·s

^{−1}, duct width 0.05 m. The results of mathematical modeling of the dynamics of components of grain mixtures in the vertical duct in the form of trajectories of impurity particles are presented in Figure 6.

## 4. Conclusions

- The positive effect of the previously stratification on the intensity of redistribution of light impurity particles in the grain mixture layer and their separation in the working zone of the vertical pneumatic separator duct is proved.
- The result of mathematical modeling was to determine the final equations of motion of particles of lightweight impurities in the vertical duct, taking into account the preliminary stratification of the mixture, which allowed us to determine the dependence of the motion of particles of impurities on the properties of grain mixtures and parameters of the pneumatic separation duct. The trajectories of light impurity particles in the working zone of the pneumatic duct, depending on their initial coordinate according to the thickness of the grain mixture layer, are established.
- Studies have shown that increasing the separation of the bulk medium is able to increase the discrepancy between the trajectories of grain and lightweight impurities, to intensify the process of cleaning grain mixtures in pneumatic separation ducts and to improve the productivity of grain cleaning machines and separators.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematic block of (

**a**) vertical pneumatic separation duct with stratification device, and (

**b**) schematic block of vertical pneumatic separation duct with stratification device showing forces acting on a particle of the grain mixture and the angle of entry of the particles into the pneumo-separation duct. u is relative speed to the airflow; U is absolute speed of the seed; U

_{0}is absolute speed at the exit.

**Figure 2.**Scheme of unit for research of purification process of preliminarily stratified grain mixture: 1—fan; 2—the pneumo-separation duct; d—loading hopper; 4—the adjustable damper; 5—the scaled air surface; 6—the receiver of the main grain (purified); 7—airflow rate controller; 8—lightweight impurity filter-receiver.

**Figure 3.**Laboratory unit for research of purification process of preliminarily stratified grain mixture: (

**a**) general appearance; (

**b**) grain receiver; (

**c**,

**d**) breathable scaly surface.

**Figure 4.**Videography of the dynamics of the components of the grain mixture and photographic images: (

**a**) general appearance; (

**b**) close-up on a moving layer of grain and impurities; (

**c**) markings used for frame-by-frame analysis of photographic images.

**Figure 5.**The trajectory of motion of the particles of the components of the grain mixture in the vertical pneumatic separation duct: 1—ρ

_{p}=150 kg·m

^{−3}; 2—ρ

_{p}=200 kg·m

^{−3}; 3—ρ

_{p}=600 kg·m

^{−3}; 4—ρ

_{p}=700 kg·m

^{−3}(U = 7 m·s

^{−1}; d

_{p}= 0.0015 m; θ = 40

^{°}, V = 6 m·s

^{−1}).

**Figure 6.**The trajectories of impurity particles in the vertical duct (d

_{p}= 0.001 m; ρ

_{p}= 600 kg·m

^{−3}): 1—trajectories of impurity; 2—the upper boundary of the grain layer; 3—the impurity trajectory without considering the effect of the grain layer.

**Figure 7.**The trajectories of particles of lightweight impurities in the vertical duct: 1—ρ

_{p}=400 kg·m

^{3}; 2—ρ

_{p}= 500 kg·m

^{−3}; 3—ρ

_{p}= 600 kg·m

^{−3}; (H = 0.05 m; y

_{0}= 0.025 m; i = 7 m·s

^{−1}; d

_{p}= 0.002 m); —the upper boundary of the grain layer; —trajectories of impurities.

**Figure 8.**The trajectories of the grain mixture particles in the vertical duct at the initial coordinate: 1—y

_{0}= 0.05 m; 2—y

_{0}= 0.04 m; 3—y

_{0}= 0.03 m; 4—y

_{0}= 0.02 m; 5—y

_{0}= 0.01 m; 6—y

_{0}= 0 m; (H = 0.05 m; i = 7 m·s

^{−1}; d

_{p}= 0.002 m; ρ

_{p}= 700 kg·m

^{−3}); —the upper boundary of the grain layer; —trajectories of impurities.

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**MDPI and ACS Style**

Kharchenko, S.; Borshch, Y.; Kovalyshyn, S.; Piven, M.; Abduev, M.; Miernik, A.; Popardowski, E.; Kiełbasa, P.
Modeling of Aerodynamic Separation of Preliminarily Stratified Grain Mixture in Vertical Pneumatic Separation Duct. *Appl. Sci.* **2021**, *11*, 4383.
https://doi.org/10.3390/app11104383

**AMA Style**

Kharchenko S, Borshch Y, Kovalyshyn S, Piven M, Abduev M, Miernik A, Popardowski E, Kiełbasa P.
Modeling of Aerodynamic Separation of Preliminarily Stratified Grain Mixture in Vertical Pneumatic Separation Duct. *Applied Sciences*. 2021; 11(10):4383.
https://doi.org/10.3390/app11104383

**Chicago/Turabian Style**

Kharchenko, Serhii, Yurii Borshch, Stepan Kovalyshyn, Mykhailo Piven, Magomed Abduev, Anna Miernik, Ernest Popardowski, and Paweł Kiełbasa.
2021. "Modeling of Aerodynamic Separation of Preliminarily Stratified Grain Mixture in Vertical Pneumatic Separation Duct" *Applied Sciences* 11, no. 10: 4383.
https://doi.org/10.3390/app11104383