Numerical simulation of slurry basin impeller operation for mixing slurry mixtures in the production of cement compositions

. The issues of numerical modeling of hydrodynamic resistance of the impeller for mixing slurry mixtures in the production of cement compositions are considered. Mathematical models based on the finite element method to analyze the hydrodynamic processes occurring in the mixing of cement-containing mixtures are developed. The influence of rotor design on the value of torque power on the impeller shaft has been investigated. It is established that the most acceptable option is a vane design that creates a good turbulence of the fluid medium in almost the entire volume of the process equipment, contributing to high-quality hydration of cement composites. Optimized power of the drive by the criterion of hydraulic resistance and the number of revolutions of the impeller


Introduction
In today's construction industry, the main emphasis is placed on economically viable and environmentally friendly production. The choice is made in favor of simple and accessible technologies capable of implementing a waste-free, closed cycle of production, the products of which will meet the consumer demands of users, including the criterion of affordability.
Cement composition of the product material includes additives of sludge waste from a number of chemical, energy, mining and other industries, which significantly increases the consumer properties of products for strength, sound and thermal insulation, their use simplifies the technology of production products, solves the problem of sludge waste disposal.
Mineral slurries are heterogeneous colloidal highly dispersed systems (fine gypsum, calcium hydroxide (or carbonate), soluble and insoluble calcium, sodium, potassium salts, metal hydroxides), which are used as hardening activators and fillers of cement compositions. Inorganic salts contained in slurries have a significant impact on the formation of active crystallization centers is one of the reasons for activation of cement hydration processes.

Subject of research
Uniform mixing of raw material components is carried out with the help of a mixing device, which is a container for mixed components, and an impeller with a mechanical drive (Fig. 1).
In the considered standard design, the electric motor 1 and the reducer are rigidly fixed in the design position with a frame structure (gantry). Transmission of torque to the impeller shaft 7 is carried out by means of a chain compensating clutch. Impeller shaft has three supports 4 -directly under the portal, 5 -in the intermediate section of the shaft, with support on the tank wall 6, 8 -hub, installed on the tank bottom.
The mixing process is initiated by the mixing device (impeller) the mutual movement of the mixture components along complex concentric trajectories within the volume of the device container, until a fairly uniform distribution of the concentration of substances.
High-quality mixing of the mixture occurs when creating a sufficiently high value of turbulence, which causes a corresponding increase in the power of the drive. Finding the optimal combination of these parameters of the equipment will allow obtaining costeffective and reliable technological equipment.
In the investigated design of the slurry pool the standard design of the impeller in the form of a shaft with a two-level arrangement of the blades, set radially on the rods within the volume of the mixing tank is used. The drive of the equipment rotates at a frequency of 25 rpm.
Practical experience in operating this equipment showed the presence of design imperfection, expressed as intensive wear (more than 70% of the cross-section) of the contact surface of the worm wheel teeth (Fig. 2). The cause of intensive wear was incorrect selection of drive elements parameters, in particular -power. The gearbox size depends on the torque on its output shaft, which is determined by hydrodynamic resistance forces to the rotation of the impeller in the volume of the stirred substance, determined by the dynamic pressure of the stirred liquid multiplied by the area of the impeller blade.  Due to the misalignment of supporting devices, the impeller shaft is in a stressdeformed state and has a certain deflection. As a consequence, when rotating, the shaft performs a complex circular spatial movement, periodically exerting force on support units, displacing them in the radial direction.
The resulting radial movement is compensated to some extent by the chain coupling, but part of it is transmitted to the gearbox, creating conditions of abnormal loading and additional resistance to rotation of the impeller. The fact of additional resistance to the impeller rotation is confirmed by typical radial movements of the gearbox during operation with loosened bolt connections to the gantry.
Operation of equipment with such defects after a certain period of time leads to fatigue failure of the main load-bearing elements of the machine.

Calculation of torque and power required to ensure the preparation of concrete mixture
In view of the fact that the energy required to perform circulation is communicated to the mixing volume by means of the impeller, the power N expended on mixing can be written as: on the other hand: = where M is the torque on the impeller shaft, Н·м; ωangular speed of the impeller, rad/s; Vfluid flow through the device (pumping effect of the impeller), m 3 /s; router radius of the impeller, m; wcircumferential component of fluid velocity at the impeller outlet, m/s; ρfluid density, Н/m 3 .
Solving together equations (1) and (2), and knowing that the speed of the impeller ω = 2πn, can be expressed through the physically understandable torque on the impeller shaft. The torque on the impeller shaft must be calculated as the product of the hydrodynamic resistance force to rotation Fг on the shoulder of this force, which can be expressed as: is dynamic pressure of the stirred liquid on the impeller blade (Pa). Expression (4) can also be written as:

= ·
The main problem is the determination of the coefficient of cx The solution to this problem can be the application of computational fluid dynamics (CFD). The solution can be the application of computational fluid dynamics (CFD). A detailed representation of the geometrical features of the structure by means of finite element technology makes it possible to avoid forced simplifications of the device, and thus significantly increase the accuracy of the calculations.

Problem statement
The Comsol Multiphysics program [10] was used to solve the hydrodynamic calculation problem. The calculation task in this case is divided into two stages: at the first stage, the hydrodynamic calculation is performed for a given geometry of the computational domain, and at the second stage, the values of momentum and power are calculated based on the results obtained.
The following assumptions and simplifications are made when performing the calculation: 1. The fluid is considered homogeneous and isotropic. The influence of suspended particles is negligible.
2. temperature of liquid and tank does not change during the mixing process. The density of the liquid is taken equal to 1600 kg/m3. Due to the fact that the kinematic viscosity of cement-sand mortars significantly depends on the ratio of cement to water and sand, as well as brand and concentration of plasticizer [11], in the calculation used the average value of kinematic viscosity equal to 1 Pa˖c. The diameter of the tank for all variants of the design is 3800 m, and the height is 2800 mm. The diameter of the shaft is 89 mm. The impeller is raised above the surface of the tank by 20 mm.
Rotation of the rotor is taken into account by defining a rotating mesh region with special periodic boundary conditions using the built-in Rotating Mesh tool [10]. The shape of the computational domain is cylindrical. The rotational axis of the shaft and the computational domain coincide with the z. The calculation reveals that the distribution of velocities over the volume of the tank is uneven. The maximum values of velocities are obtained in the lower zone of the tank. There are also significant pressure drops in the volume of liquid.

Hydrodynamic calculation of the mixing process
The results of calculation of velocity and pressure fields in the anchor and frame impellers are shown in Fig. 6-9. Compared with the previous version, only rotor design has been changed. All other parameters and assumptions remained unchanged. To simplify the calculation, the computational domain is divided along the ZX plane and the symmetry boundary condition is introduced.
Maximum values of velocities as a result of calculation were obtained in the lower zone of the tank (at rotor speed of 12 rpm). It was revealed that there are significant pressure drops along the volume of liquid.

Calculation of torque
To calculate the moment acting on the impeller shaft, we will use the method presented in [12]. The moment is calculated as the surface integral by the formula: where rradius-vector determining the minimum distance from the axis of rotation to the point under study, m; Тforce acting on the surface from the flow side, at the specified point, Н; zblade number; Asurface area, m 2 .
The power is calculated as follows: where Ωangular speed of rotation, rad/s.
To calculate the total power and torque, integration was performed over the surface presented in Table 1 using the built-in Global Evaluation utility [12].  Under the conditions discussed above, performed a series of hydrodynamic calculations in order to build the static characteristics of the impeller. Considered values of speed 12, 14, 17 and 23 r/min. The results of calculations of torque and power are shown in Table 2.