The article deals with the implementation of computer program for calculating the basic characteristics of granule movement in vortex granulator: speed and trajectory. For the calculation software programs Vortex Granulator© and Classification in vortex flow© were applied, as well as software package ANSYS CFX. Software allow to automatize the calculation simultaneously on multiple criteria optimization and visualization of calculation results in the form of plots or three-dimensional images. Calculation results are the base for the optimal choice of dispersant location and optimal sizes of the working chamber of the granulator. Vortex granulator; software; trajectory; classification; calculation.
methodology of vortex granulators engineering calculation.
The main stages of granulating calculation process in vortex machines we need to allocate blocks determining the hydrodynamic characteristics of granule motion (full speed and speed components), calculating the granules trajectories and granules classification process calculating. These characteristics allow to make optimal selection of dispersant location places, as well as to design the optimal granulator workspace configuration (when provided that the classification of granules to desired number of fractions). e Fig. 1. Software Product Vortex Granulator©: a - window of plots creation of constituting granules components speed; b radial component of granules speed movement; c - vertical component of granules speed movement; d - peripheral component of granules speed movement; e - total velocity of granules speed movement
Granulator with constant cross-sectional area do not provide the full process of classification and separation of non-tradables granules fraction in the granulator`s volume. This is because in the workspace vortex granulator consistency remains upward gas flow rate that corresponds to granules speed (or granules factions within a narrow range). To carry out granules classifications processes in device with a constant cross-sectional area if possible with the gas introduction to unit with several streams with different injection site altitude mark. This classification method is quite energy intensive and doesn`t get widespread application.
Much more effective method of classification is the use of solid phase devices with variable
crosssectional workspace area [
Software product Vortex Granulator© (program interface is presented on fig.1, this article presents
the unit for calculating the granule`s hydrodynamic characteristics) is based on Navier-Stokes equations
system and flow continuity equation (single stream) and system of differential equations of granules
movement in cylindrical coordinate system [
In software product Vortex Granulator © Granuly.java class are presented that displays a graph of speed components (vertical, radial and circumferential) of gas flow and granules. Class Traektory.java displays overall speed and trajectory of granules movement. Class Functional.java retains the program input values and includes methods of forming solutions and data to display graphic dependencies.
The main class of program Classification in vortex flow© is Main.java class that is responsible for displaying the main menu and connection other classes to it.
Program has two calculation areas to determine the optimum size of vortex granulator working space: 1. The gas flow speed (fig.2). 2. The workspace geometry: • calculation with variable air expenditure - are displayed depending on the height of working space and the radius of cross section of air flow to dry and wet granules (fig.3);
• calculation at diffuser disclosure opening angle - are displayed depending on the height of working space from the diffuser opening angle for dry and wet granules (fig.4); • calculation of granules distribution on fractions in granulator working space - shows the distribution of granules with different diameters at the height of working space vortex granulator (fig 5.).
In solving the equations of mathematical model [
Investigation of granules effect on change gas flow circumferential speed component
The flow of continuous phase, which flow is modeled with system Navier-Stokes equations and flow continuity equation gives the angular momentum of discrete particles. In the case of liquid phase appearing in the working volume of device it is pulled into rotary motion by gas stream energy. This entry dispersed phase to continuous cause significant change in the value component of gas flow circumferential speedV .
Qg of sustainable granulator work are defined. 4 2 0 0,05 0,1 0,15 0,2
0,25
R, m b Fig. 9. Calculation of granules total speed (a) and direction of granules speed vector (b) at Q = 0,63 m3 / s, φ = 13 °, z = 0,8 m
In mode of advanced weighted vortex layer granules movement trajectory in the working space of vortex granulator has characteristic spiral trajectory, formed progressively as granulator start function in working mode.
Dispersed phase moves along similar trajectory with gas flow, but at a slower rate: for the same period of time it cross the way smaller than the dispersion due to the fact that the height granulator in each section varies its value forces, acting on granule. As granules movements up by drying it loses part of its mass (thus decreasing the force of gravity acting on granule), cross section granulator increases, which tends to reduce aerodynamic drag force, gas flow twist is also reduced, which reduces the centrifugal force. Given the very complex hydrodynamic situation, calculation of granules trajectory is based on solving differential equations of movement in each direction.
Granules movement trajectory causes time its stay in vortex granulator workspace. This time should be
sufficient to make the process of crystallization in all granule`s layers and no more to avoid the granules core
destruction [
The calculation is carried out for cylindrical sections and the calculation results at one section is the original data to calculate the next section in the direction of granules movement.
The flow of granules in vortex granulator workspace is complex spatial structure, the configuration of which is affected by device constructive system design and granules properties. The solution of differential equations of movement allows to predict the granule`s location at a given time.
Determination of granules speed movement components, granules full speed movement, its direction vector and overall movement trajectory.
The results of calculation of granules total speed and determination of direction of speed vector and its change in height of device are shown in figs 9-11. The analysis shows that in height of device granules movement total speed is decreasing by reducing of expenditure and radial component.
The degree of granules spin is almost equal to degree of gas flow spin that suggests the angular gas flow speed component as determining to directed and uniform granules vortex movement. Concerning the regard preferred direction of granules speed vector, analysis results based on above mentioned figures allow to say that the zone of granules pronounced vortex movement, combined vortex and ascending movement and granules upward movement can expand or contract depending on initial spin of gas flow. b Fig. 10. Calculation of granules total speed (a) and direction of granules speed vector (b) at Q = 0,63 m3 / s, φ = 13 °, z = 1 m b Fig. 11. Calculation of granules total speed (a) and direction of granules speed vector (b) at Q = 0,63 m3 / s, φ = 13 °, z = 1,2 m
Using of granules movement differential equations in cylindrical coordinates and numerical solution method of Runge-Kutt using copyright software Vortex Granulator© trajectory depending on the design of the vortex granulator, granules properties and the cost of gas flow were obtained. All trajectories have spiral form with different geometrical characteristics.
Analysis of results calculation showed that with the granules movement from the center to wall full speed vector changes in direction depending on the preferences of particular component. At the initial time granule moves from the axis of device perpendicular to it due to the predominance of speed radial component. As we approach the half radius of vortex granulator granule begins to be drawn into the vortex motion due to the predominance of speed angular component. Near the wall of granulator granule moves along a spiral path of gradually moving vertically by increasing expenditure component impact its speed; does not change the trajectory to reach the upper section of vortex granulator.
Analysis of trajectories showed that: - Increasing the gas flow consumption and cone angle of opening vortex granulator workspace leads to reduction of spiral turns, increasing their step and reducing the time of granules spent in vortex granulator workspace;
- Increasing the value of initial gas flow spin (defined angle blades eddy and their number) and the diameter of granules change the trajectory of its movement by increasing the number of spiral turns, reducing their step, increasing the diameter of spiral upper section and increasing the granules time spent in vortex granulator workspace.
Granules are moving along the vortex granulator walls and actually do not stay in its central zone. This is the direction vector of action full speed of their movement from the center to the periphery due to the predominance of radial component of granules movement to two thirds of device radius. Closer to the walls of the granulator performance radial component decreases and the granules begin to get involved in rotary motion with vertical movement.
By rational selection of cone opening angle, angle of inclination of blades eddy and their number, gas flow consumption we can control granules movement to delay at certain section of vortex granulator.
Figs 12, 13 present the calculated granules trajectory at different components of its speed components. Trajectories were built using the author's mathematical model of granules movement with software system ANSYS CFX.
b Fig. 12. Granules movement trajectories: а – Wz=1 m/s; Wr=1 m/s; Wφ=1 m/s; b – Wz=1 m/s; Wr=1 m/s; Wφ=15 m/s c Fig. 13. Granules movement trajectories: a – Wz = 8 m / s; Wr = 1 m / s; Wφ = 15 m / s; b – Wz = 15 m / s; Wr = 1 m / s; Wφ = 1 m / s; c – Wz = 15 m / s; Wr = 1 m / s; Wφ = 15 m / s Calculation of granules classification process Calculation results in Classification in vortex flow© are shown in figs 14-16.
Directed drainage of small granules in space with internal seeding agent circulation is provided by abrupt change in cross-sectional area after the gas output from the inner cone. By reducing the aerodynamic resistance force small granules begin to fall down through the cross-section between annular space, passing all of its height and in the inferior cross section are taken up by ejected gas flow.
6 5,5
5 ,m4,5 Z
4 3,5
U=3%
U=6%
U=9% 2mm 2,5mm 3 0,00E+00 5,00E-06 1,00E-05 1,50E-05 2,00E-05 2,50E-05
m, kg Fig. 15. Classification of granules by weight depending on moisture content and angle of opening vortex granulator cone at Q = 1 m3/s
Fig. 16. Classification of granules by weight depending on moisture content and heat transfer agent consumption at
angle of opening vortex granulator cone φ=12.
Separation of small grains is important to ensure their integrity. With intensive gas flow swirling fine granules after output from the inner cone are discarded to outer housing wall, bump against him and destroyed. Given that small fraction is heated in suspended layer in its core additional stresses, that reduce strength, are appeared.
At small angles of opening cone polydispersed system consists of separate layers: - one above the other from large (heavy) fraction in lower section to small (light) in upper section without crossing each other layers. This option is possible with wide cut polydispersed system; - one above the other from large (heavy) fraction in lower section to small (light) in upper section of the section layers separate factions together This variant is observed in narrow fractional composition of polydispersed system.
The calculation results to estimate the size of the granules that are outside the workspace granulator (above section, in which granules commodity faction minimum size are moving). These granules are separated in the top of space, and then go from the granulation area with gases.
The results of experimental studies [
Given algorithm for calculation of hydrodynamic characteristics of vortex granulating equipment allows to predict the behavior of a drop (pellets) from its departure from the dispersion device (nozzle, melt granulator) until the end of crystallization.
The results of analytical solution of mathematical model equations using software products Vortex Granulator© and Classification in vortex flow© allow to design granulator which along with granulation will make possible implementation classification and internal seeding agent circulation process.
This work was carried out under the project «Improving the efficiency of granulators and dryers with active hydrodynamic regimes for obtaining, modification and encapsulation of fertilizers», state registration No. 0116U006812. While preparing the article it was used information about the original designs of vortex granulators (patents Nos 99023 Ukraine IPC (2012.01) B01J2/16, Ukraine IPC 110992 В01J 2/00, В01J 2/16, 111406 Ukraine IPC В01J 2/04, В01J 2/16 etc.) and author`s software products (certificates of authorship No 65140, 67472). The authors thank researchers of department "Processes and equipment of chemical and refining industries", Sumy State University for their valuable comments during the article preparation.