Frontiers in Computing and Intelligent Systems ISSN: 2832-6024 | Vol. 3, No. 2, 2023 96 Experimental research and numerical simulation based on granary effect Linda Fan Energy and Power Engineering, North China Electric Power University, Baoding 071003, China Abstract: Based on Janssen model and discrete element model, experiment and numerical simulation are used to verify the granary effect of coal storage silo in power plant. In the experiment, the bottom pressure of two different particles in a variable- diameter cylinder is measured. The type of particles and the diameter of the cylinder are used as the research objects to explore the function relationship between the bottom pressure of the cylinder and the particle filling quality. In the experiment with soybeans as filling particles, the granary effect is more obvious, and the smaller the cylinder diameter is, the more obvious the granary effect is. At the same time, establish a mathematical model of particles, simulation of particle accumulation process, solve the force information of particles. Through numerical simulation, it is found that the data is more in line with the Janssen model, and the granary effect is more obvious. Keywords: Granary effect; Coal storage silo; Numerical simulation; DEM. 1. Introduction Generally speaking, the containers for storing particulate matter are generally cylindrical silos, conical silos and other silo structures. The types and sizes of silos are various: sugar cans containing several grams of sugar and coal silos storing tens of thousands of tons of coal [1]. However, in the actual construction and use of silos, we often see the dangerous accidents of silo wall cracking and even overall collapse [2]. Therefore, it is very important to study the pressure distribution in the silo and the internal stress distribution of particulate matter, which will be of great help to the design of the silo. In addition, it is of great significance to reduce the cracks often found in the side wall of the silo and the overall collapse accident of the silo [3,4]. This paper mainly studies a famous static mechanical property in granular matter physics: granary effect [5]. The granary effect means that the pressure on the bottom of the silo will not increase significantly when the height of the filled particles in the silo exceeds twice the diameter of the bottom of the silo, that is, when the filled particles in the silo accumulate to a certain height, the bottom pressure of the silo will approximately reach a saturated stable value and will not increase significantly with the increase of the height of the filled particles. 2. Discrete element method Discrete element method is to discretize the target into a finite number of elements, analyze and solve each element according to the classical mechanical theory, so as to obtain the state of the whole system of the target [6]. This method is widely used in the study of particle physics [7]. According to the characteristics of particle movement in silo, a particle calculation model of free settlement and accumulation process is established based on discrete element method, which realizes the real-time update of micro information such as force, acceleration, velocity and displacement of particle. The collision force between particles is: �⃗�𝑝 = βˆ‘ οΌˆπ‘“π‘›οΌŒπ‘–π‘— + π‘“π‘‘οΌŒπ‘–π‘—οΌ‰ π‘˜ 𝑗=0 (1) In the formula: k is the number of particles colliding with particle j; π‘“π‘›οΌŒπ‘–π‘— is the normal force between particle i and particle j; π‘“π‘‘οΌŒπ‘–π‘— is the tangential force between particle i and particle j. The normal force on the particles is: π‘“π‘›οΌŒπ‘–π‘— = π‘“π‘π‘›οΌŒπ‘–π‘— + π‘“π‘‘π‘›οΌŒπ‘–π‘— (2) π‘“π‘π‘›οΌŒπ‘–π‘— = βˆ’π‘˜π‘› βˆ— π›₯𝛿𝑛 (3) π‘“π‘‘π‘›οΌŒπ‘–π‘— = πœ‚π‘› βˆ— ¡⃗⃗𝑛 (4) In the formula: π‘“π‘π‘›οΌŒπ‘–π‘— represents the elastic force generated by the collision of two particles; π‘˜π‘› represents the elastic coefficient of particles in the normal direction; π›₯𝛿𝑛 represents the normal upward relative displacement of particle i and particle j after impact; π‘“π‘‘π‘›οΌŒπ‘–π‘— represents the viscous damping force of two particles in the normal direction; πœ‚π‘› represents the normal damping coefficient; ¡⃗⃗𝑛 = Β΅βƒ—βƒ—π‘Ÿ βˆ— οΏ½βƒ—βƒ—οΏ½ represents the relative velocity of a particle in the normal direction at the point of impact. π›₯𝛿𝑛 = (Β΅βƒ—βƒ—π‘Ÿ βˆ— π›₯𝑑) βˆ— οΏ½βƒ—βƒ—οΏ½ (5) In the formula: Β΅βƒ—βƒ—π‘Ÿ represents the velocity vector of two particles; οΏ½βƒ—βƒ—οΏ½ represents the unit vector of particulate matter in the normal direction. π‘“π‘‘οΌŒπ‘–π‘— = βˆ’οΌˆπ‘˜π‘‘ βˆ— π›₯𝛿𝑑 + πœ‚π‘‘ βˆ— ¡⃗⃗𝑑） (6) In the formula: π‘˜π‘‘ represents the elastic coefficient of particulate matter in the tangential direction; πœ‚π‘‘ represents the damping coefficient of particulate matter in the tangential direction; π›₯𝛿𝑑 represents the relative displacement in the tangential direction when particle i and particle j collide; ¡⃗⃗𝑑 is the relative velocity of two particles in the tangential direction at the impact point. when |π‘“π‘‘οΌŒπ‘–π‘—| ≀ ΞΌ |π‘“π‘›οΌŒπ‘–π‘—| π›₯ π‘“π‘‘οΌŒπ‘–π‘— = π‘“π‘π‘‘οΌŒπ‘–π‘— + π‘“π‘‘π‘‘οΌŒπ‘–π‘— (7) when|π‘“π‘‘οΌŒπ‘–π‘—| > ΞΌ |π‘“π‘›οΌŒπ‘–π‘—| |π‘“π‘‘οΌŒπ‘–π‘—| = ΞΌ |π‘“π‘›οΌŒπ‘–π‘—| (8) In the formula: Β΅ is the sliding friction coefficient of particles. 97 According to Newton's second law, the motion equation of granular material is: π‘šπ‘– 𝑑𝑒𝑖⃗⃗ βƒ—βƒ— βƒ—βƒ— βƒ—βƒ— 𝑑𝑑 = �⃗�𝑝 + π‘šπ‘–π‘” (9) In the formula: �⃗�𝑝 is the resultant force of all collision forces on the particle; π‘šπ‘–π‘” is the gravity of the particle itself. After a time step βˆ†t, the velocity of particle j at t +βˆ†t: �⃗�𝑗 t+Ξ”t = �⃗�𝑗 t + �⃗�𝑖 βˆ— βˆ†t (10) The position of particle j at t + βˆ† t is: �⃗�𝑗 t+Ξ”t = �⃗�𝑗 t + οΏ½βƒ—οΏ½π‘₯ βˆ— βˆ†t (11) �⃗�𝑗 t+Ξ”t = �⃗�𝑗 t + �⃗�𝑦 βˆ— βˆ†t (12) 𝑧𝑗 t+Ξ”t = 𝑧𝑗 t + �⃗�𝑧 βˆ— βˆ†t (13) In the formula, �⃗�𝑗 、 �⃗�𝑗 、𝑧𝑗 are the coordinates of particulate matter j in the rectangular coordinate system; οΏ½βƒ—οΏ½π‘₯ 、 �⃗�𝑦 、�⃗�𝑧 are the velocities of particulate matter j in the X, Y and Z directions in the rectangular coordinate system. 3. Experimental and numerical simulation methods 3.1. Experimental method The experimental design is shown in Figure 1. Fix the rigid and non-deformable acrylic transparent round tube on the stainless-steel support, place the electronic balance horizontally under the cylinder, adjust the height of the cylinder to ensure that the cylinder and the electronic balance do not contact each other, so as to ensure that there is no interaction between them. At the same time, the size of the gap shall not be greater than the radius of the particles to avoid the leakage of particles from the gap. Put a smooth glass plate with a thickness not greater than the size of the gap into the gap [8]. Figure 1. Flow chart of target tracking process 3.2. Numerical Simulation The simulation object is shown in figure 2. Figure 2. Simulation object The discrete element method is used to simulate the settlement and accumulation process of particles in a three- dimensional cylindrical silo under the action of gravity. The relevant simulation parameters are set as shown in table 1. Table 1. Simulation parameters and values Simulation parameters Analog parameter value time step(s) 1*10-5 Particle recovery coefficient 0.9 Particle friction coefficient Β΅ 0.3 Particle density(kg/m3) 2700 Young's modulus 1.04*106 Particle diameter(mm) 4 4. Results and discussion 4.1. Experimental results and discussion The functional relationship between the apparent mass Ma of mung bean under four different cylinder diameters and the corresponding filling mass Mt is shown in figure 3. From the diagram, it can be seen that in the function curves of four different cylinder diameters, the apparent mass Ma of mung bean increases with the increase of the filling mass Mt, and finally tends to be saturated. The whole trend shows a nonlinear relationship, and the apparent mass Ma that finally reaches the saturation value is obviously smaller than the actual filling mass Mt. In addition, when the cylinder diameter is 50 mm, the granary effect of mung bean is the most obvious, and when the cylinder diameter is 65 mm, the granary effect of mung bean is the least obvious. Figure 3. The relationship between Ma and Mt of mung bean under different diameters The functional relationship between the apparent mass Ma of soybean and the corresponding filling mass Mt under four different cylinder diameters is shown in figure 4. From the diagram, it can be seen that in the function curves of four different cylinder diameters, the apparent mass Ma of soybean increases with the increase of the filling mass Mt, and finally tends to saturation. The whole trend shows a nonlinear relationship, and the apparent mass Ma that finally reaches the saturation value is obviously smaller than the actual filling mass Mt. In addition, when the cylinder diameter is 50 mm, the granary effect of soybean is the most obvious, and when the cylinder diameter is 65 mm, the granary effect of soybean is the least obvious. 98 Figure 4. The relationship between Ma and Mt of soy bean under different diameters 4.2. Numerical simulation results and discussion Figure 5 is the functional relationship between the apparent mass ma of soybeans and the corresponding filling mass Mt obtained by simulating the free settlement and accumulation of soybeans in a three-dimensional cylindrical silo with a barrel diameter of 50mm by using the discrete element method. The apparent mass Ma of the particulate matter increased with the increase of the filling mass Mt, and finally tended to be saturated. The whole trend showed a nonlinear relationship, and the apparent mass Ma that eventually reached the saturation value was significantly smaller than the actual filling mass Mt. In addition, compared with the experimental data, the granary effect is more obvious in the data reflected by the numerical simulation. Figure 5. The relationship between Ma and Mt under numerical simulation 5. Conclusion Based on the granary effect phenomenon and Jason model, this paper studies the functional relationship between the pressure at the bottom of the cylindrical silo and the actual filling quality of particulate matter from the macro scale and micro scale by using the methods of physical experimental research and numerical simulation, respectively, to verify the granary effect phenomenon and explore its causes. In the bottom pressure measurement experiment of three- dimensional cylindrical silo, by measuring the bottom pressure of soybean and mung bean in three-dimensional cylindrical silo with different diameters, taking the particle type and silo diameter as the research object, the functional relationship between the bottom pressure of silo and the actual filling quality of particles in silo is explored, which basically conforms to Jason model, And the phenomenon of granary effect appears. It is found that the granary effect is more obvious in the experiment with soybean as filling particles, and the smaller the silo diameter is, the more obvious the granary effect is. In the numerical simulation of discrete element method, a three-dimensional DEM particle motion mathematical model is established to simulate the free settlement and accumulation process of particulate matter in the three-dimensional cylindrical silo, analyze the stress of particulate matter in the cylindrical silo, verify the phenomenon of granary effect and explore the causes of granary effect in combination with physical experimental data and numerical simulation data. Through numerical simulation, it is found that the data reflected by numerical simulation is more in line with Jason model, and the phenomenon of granary effect is more obvious. References [1] Smart Ashley G,Ottino Julio M. Evolving loop structure in gradually tilted two-dimensional granular packings.[J]. Physical review. E, Statistical, nonlinear, and soft matter physics,2008,77(4 Pt 1). [2] Vivanco Francisco,Mercado JosΓ©,SantibÑñez Francisco,Melo Francisco. Stress profile in a two-dimensional silo: Effects induced by friction mobilization. [J]. Physical review. E, 2016,94(2-1). [3] Nedderman R M. Statics and Kinematics of Granular Materials[M]. 1992, Cambridge University Press, Cambridge, England. [4] Alex C Barnett. The Silo Effect: The Peril of Expertise and the Promise of Breaking Down Barriers 1[J]. The Army Lawyer,2017. [5] Janssen H A. Versuche ΓΌber getreidedruck in siloz-ellen [J]. Zeit. Ver. Deutsch. Ing., 1895, 39:1045~1049. [6] P. A. Cundall, O. D. L. Strack. A discrete numerical model for granular assemblies[J]. GΓ©otechnique, 1979, 29(1):47-65. [7] Zhang Xinggang, Dai Dan. Lattice system model of pressure problem in two-dimensional particle accumulation [J]. Journal of physics, 2017,66 (20): 154-162. [8] Han Zhiqiang, Shen Zhongchi, Tang Mingjun. Experimental verification of bottom and side wall pressure of granary effect [J]. Physical experiment, 2021,41 (01): 50-54.