A backpressure filling system is a kind of air type filling system which could be applied to power type, fine or coarse grain, or mixtures with fine and coarse components. The working principle of backpressure filling system was discussed based on fundamental hydromechanics. The research limit values of backpressure were achieved via mechanical analysis. Comparing with the exit velocity of material by theoretical analysis and numerical simulation, the CFD simulation model was confirmed and its related parameters were determined. The CFD numerical simulation shows the relationship between production capacity of packaging machine and backpressure, and the results matched actual operation of the equipment well. Combining with the demand of device capacity, the range of backpressure could be controlled at 8 kPa~11 kPa.
The key packaging technology of bulk material is the design of filling system. The typical filling system in industry includes screw type and impeller type. These two kinds of filling systems push the bulk material to filling spouts with high speed via screw blade and impeller blade, respectively. Their construction is simple and obtained material flow is stabilized. The weakness of two-type filling systems is that motors have to start and pause frequently, and power consumption is high. Moreover, abrasion of blade is faster, and the filling system is easy to be blocked, especially filling bulk material with particle, such as dry mortar.
Mortar is a kind of cementing building material and is composed of sand and cementing material (such as cement, lime putty, and clay). More customers want to buy matched dry mortar for their convenience. Adapting to the requirement of packaging filling for particle mixture material, reducing the abrasion of filling system and the incidence rate of industrial accident, the research group developed the backpressure filling system as shown in Figure
The backpressure filling system.
Backpressure filling system also can be named as fluidization filling system. It sets aeration pads on the wall of filling box near the filling spout. It provides fixed pressure on the bulk material which is in the filling bin, to prevent arched material and accelerate its flow. The advantages of backpressure filling system are that there are no mechanical vulnerable parts and there is less mechanical failure. Even so, if the pressure of backpressure cannot be controlled very well, a series of problems will take place. When the pressure is too high, air will break through the bulk material and go into the packing bag to bulge the bag. When the pressure is too low, the capacity of packaging machine will be insufficient.
The speed of bulk material near the exit of packaging machine could directly affect the capacity of the machine. Therefore, improving the flow velocity of exit could effectively increase the machine capacity. The impact coefficients on flow velocity include material properties, geometrical shape of filling box, and pressure of backpressure. The pressure of backpressure is one of the principal coefficients.
The value range of backpressure will affect regular work of the packaging machine, and it is crucial coefficient for the capacity of the equipment. The relationship between backpressure and equipment capacity is the fundamental mechanism research for industry application. The research work started at the limiting value of the backpressure.
The force of bulk material to filling bin wall and the force of filling bin to bulk material are a pair of action and reaction. The pressure value which aeration pads provided should be between the dynamic pressure
The real filling bin was simplified to a cylinder bin as shown in Figure
Filling bin and its force analysis.
Assume that the flow of bulk material is in a constant state; that is, the bulk material is flowing into filling bin unceasingly and is flowing out from the exit. The outflow volume is equal to inflow volume. In this case, the dynamic pressure of bulk material to bulkhead has nothing to do with the time [
To find the equilibrium condition on dynamic pressure of bulk material to bin wall, researcher picks the infinitesimal element of filling bin to study as shown in Figure
In the above formula,
Equation (
Due to the different deformation state when the bulk material flows in the filling bin, the stress state is different. When the bulk material is in the top of filling bin, the material is in the outward deformation state away from the vertical axis, which is also called the active stress state. The lateral pressure coefficient should be given as follows:
In the end of filling bin, the material is in the inward deformation state which is forward to vertical axis, and thus the material here is accordingly in a passive stress state. Therefore, the lateral pressure coefficient should be taken as follows:
That is, when the material is flowing, its deformation state and stress state should be different due to the height of material. The stress state of material from top to bottom gradually varies from the active state to the passive state. As the Bert test said, the lateral pressure coefficient
Thus, the lateral pressure coefficient of material in a certain depth could be decided by the following equation:
Substituting formula (
When the bulk material flows in the filling bin, the dynamic pressure against bulkhead at different depth could be calculated by (
In the construction, the most commonly used cement mortar is mixed by the volume ratio of 1 : 3, and its density is about 2100 kg/m3; its mixture friction angle is about 29°, and the friction coefficient between bulk material and steel is 0.5.
According to the geometry of backpressure filling system, the inlet hopper radius
Considering the cement mortar is in a relatively dense state in the filling bin, it can be assumed incompressible. When the material suffers the backpressure that is greater than its own weight, the material will break down. Therefore, the maximum backpressure of the depth
Thus, when the depth of material exit
Cement mortar material can be regarded as incompressible viscous fluid when it flows with free flowing under gravity in filling bin. When backpressure is not provided, material flowing can be considered as laminar flow due to its slow flow rate. The motion equations (Navier-Stokes equations) of incompressible viscous fluid under
Backpressure filling system model.
Because the material flowing is laminar and symmetry flow
When the flowing is constant, the unit mass force
By using boundary conditions
It indicates that for incompressible viscous flow the velocity distribution on any fracture surface is a revolving paraboloid whose mean flow velocity is a half of the maximum flow velocity (
When
Substituting relevant parameters into (
mean flow velocity of exit surface
maximum velocity of exit surface
Computational fluid dynamics (CFD) method by FLUENT software is used to simulate the exit velocity of bulk material in the backpressure filling system. FLUENT provides a flexible grid feature, and a variety of complex meshes can be classified easily via the structured grid and unstructured mesh area. For the three-dimensional problem, it can provide many grid units including tetrahedron, hexahedron, pyramid, wedge, and mixed grids. Besides, FLUENT also allows users to refine or roughen partial meshes according to their own solving scale, accuracy, and efficiency. For a flow area with the large gradient, FLUENT with adaptive characteristic of grid can give the solution with high accuracy [
Unstructured tetrahedral meshes with excellent adaptability could be selected when simulating the exit velocity of materials in the free flow process. According to the actual flow ability of mortar, the 3D separator implicit solver will be selected. And the operating environment includes two parts; one is the selection of the reference pressure, and the other is the option of gravity. According to the operating environment of the cement mortar packaging machine, the atmosphere pressure, which is 101,325 Pa, should be selected as the reference pressure, due to the direct contact with atmosphere at the inlet and outlet of the machine. Besides, standard pressure uses a discrete format. Momentum equation, turbulent kinetic energy equation, and turbulent kinetic energy dissipation rate equations use the second-order discrete format, calculation of the pressure and velocity fields uses SIMPLEC algorithm, and the convergence criteria are set as 10−3. As the material flows by gravity, the gravity acceleration, which is
After dividing the mesh and setting computing model, material, and boundary conditions, the following settings should be clear in order to better control the solution process: select a discrete format, set underrelaxation factor, and initialize field variables and activate the monitoring variables. According to the flow characteristics of materials and the requirements of solution accuracy, the residual error of fluid computation shows that the convergence effect is good after more than two thousand iterations.
The velocity change near the exit could be as shown in Figure
The velocity change near the exit.
As shown in Figure
Figure
Velocity vector graph at exit.
Figure
Velocity contour graph at exit surface.
According to the result of analog computation, the average velocity of exit
When the backpressure filling mechanism works, backpressure would have a huge impact on the velocity of material flow. Quantitative analysis on the effect of backpressure change to material flow velocity and finding the relationship between capacity of equipment and backpressure value will be beneficial to the equipment testing and working. This part of the study will be based on the previous research.
According to the real working conditions and the requirements of simple model principal, the following assumptions about materials and flow conditions are assumed. The flow of material is stable, which is steady-state flow. The density of cement mortar mixture does not change with time. The temperature and the energy of the flow would be ignored.
For flow of mortar mixture inside the hopper, single-phase flow analysis, which worked on numerical simulation on gravity free flow, can be taken when the backpressure is zero; on the contrary, when considering the effect of backpressure, the Euler two-phase model on Euler-Euler numerical method can be selected because it is impossible to apply the pressure to the inlet part without inflow of materials in the FLUENT. In practice, the air inside the filling bin would never flow forward with the materials as the entrance of backpressure could only provide the pressure. Thus, the Euler model that worked in this case could be simplified as the air loss ratio is zero [
When analyzing the impact of multiple backpressures on the bulk material flow, the mesh generation could be meshed according to the result above. Figure
Geometric modeling and meshing with multiple backpressures coexisting.
3D implicit segregated solver is selected after the two-phase model of Euler developing and boundary settings. During the simulating, standard discrete format is used to provide the pressure. The momentum equation, turbulent kinetic energy equation, and turbulent kinetic energy dissipation rate equations use second-order discrete format, the solving of pressure and velocity fields uses SIMPLEC algorithm, and the convergence criteria are set as 10−4.
To simulate the real working conditions of the filling mechanism, the situation when eight backpressures work together is simulated. Figure
The distribution and contours of exit velocity when the backpressures are 12 kPa.
As shown in Figure
In order to acquire the specific simulating results under different backpressures, the data processing software MATLAB is used to display the statistics shown in Table
The specific simulating results under different backpressures.
Backpressure (kPa) | Average velocity of exit (m/s) | Mass flow rate of exit (kg/s) | Production capacity of machine (t/h) |
---|---|---|---|
4 | 0.112 | 1.473 | 42.42 |
5 | 0.120 | 1.603 | 46.17 |
6 | 0.155 | 2.058 | 59.27 |
7 | 0.208 | 2.759 | 79.46 |
8 | 0.237 | 3.130 | 90.14 |
9 | 0.252 | 3.342 | 96.25 |
10 | 0.260 | 3.445 | 99.22 |
11 | 0.268 | 3.555 | 102.38 |
12 | 0.273 | 3.622 | 104.31 |
The fitting curve on average velocity of exit.
The fitting curve on production capacity of packaging machine.
The relationship between average velocity of exit and backpressure is as shown in the following equation:
The relationship between production capacity of packaging machine and backpressure is as shown in the following equation:
In the practical work of rotary packaging machine, provided backpressure by backpressure filling mechanism should meet the requirements of packaging capacity. At the same time, it cannot break down material or let gases get into the cement bags or burst bags. Thus, the balance between the two requirements should be found to ensure production efficiency and the safety of production process.
As shown in Table
According to the theoretic calculation and CFD numerical analysis above, when rotary cement mortar packing machine adopts backpressure filling system, the backpressure should be controlled at 8 kPa~11 kPa. In this way, the production capacity of equipment could be 90 t/h~102 t/h.
To verify the results of CFD simulation, the research set up an actual test on a rotary cement mortar packaging machine with backpressure filling system and recorded its actual production capacity under different backpressures. Table
The comparison on the simulation results and actual production capacity of machine.
Backpressure (kPa) | Production capacity of machine (t/h) | |
---|---|---|
Simulating result | Actual result | |
|
||
6 | 59.27 | |
8 | 90.14 | |
10 | 99.22 | |
11 | 102.38 | |
12 | 104.31 |
Figure
The fitting curve of production capacity based on simulating and actual result.
The research is aimed at working principle of new backpressure filling system and acquired the range of backpressure of filling system by theoretical analysis. The physical models of multiphase flow based on CFD simulation for filling system are developed. The relationship between backpressure and exit velocity of the material is found, and finally production capacity of equipment to backpressure curve is achieved. Thus, the backpressure filling system can be manufactured and tested. It has been verified by practical production, and the relationship curve matched the operation of equipment well. The production capacity of packaging equipment could achieve 90~100 t/h, when the backpressure is controlled at 8 kPa~11 kPa.
The new filling system can be applied not only to dry mortar powder, but also to cement, flour, and other pure powders. The CFD models could be applied on the computer simulation for filling system. When the backpressure is beyond the maximum backpressure, the CFD model is no longer applicable. In the future work, according to the material properties, new suggestions on backpressure control could be given, and, based on this, the optimization of filling bin could be achieved.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research was supported in part by a Grant-in-Aid for 44th Scientific returned people start funding from the Education Ministry of China and Six Talent Peaks Funding Program of Jiangsu Province.