Analysis of the Influence of Aerodynamic Qualities of the Components of Mixtures on Separation in Power-Saving Vortex Vehicles

The object of research is gas-dynamic vortex processes in heterogeneous polydisperse flows. One of the most problematic issues is the determination of the aerodynamic characteristics of the components of a heterogeneous polydisperse medium, which are necessary to create a mathematical model of the separation process. The study used methods of mathematical modeling based on the theory of similarity. A technique has been developed for assessing the aerodynamic parameters of mixture components, on the basis of which a number of aerodynamic similarities have been compiled. The coefficients of lift, aerodynamic drag, lateral force, longitudinal, transverse and rotational moments of the components of the grain mixture are obtained. This is necessary for theoretical studies of gas-dynamic processes in vortex separators in unsteady three-dimensional flow with variable flow density, concentration and flow rate of the separated mixture components and the carried fractions. The Reynolds vibration criterion is obtained, based on which the trajectories and energy of the vortex motion of individual components and the separation degree of heterogeneous mixtures are determined. This allows to improve the mathematical model of the distribution process of heterogeneous polydisperse mixtures in the proposed energy-saving vortex separators. The obtained results provide the basis for improving the general theory of heterogeneous vortex flows by introducing an external disturbance criterion that takes into account the drag of the vortex force field and the amplitude-frequency energy level. Thanks to this, it is possible to evaluate the influence of any argument in the desired function. The research results make it possible to automate the analysis of process characteristics and compare them by parameters with experimental data. And also to evaluate the correspondence of dynamic, kinematic and gas-dynamic functions calculated from the given geometric parameters of the vortex devices with the functions obtained from the averaged values. These data makes it possible to work out a range of variations in the parameters of the geometric design of vortex apparatuses by zones, parameters at the inlet, outlet, and degrees of separation, minimize the number of manufactured laboratory and semi-industrial vortex apparatuses, and unify a number of units. Compared with similar known separators, vortex apparatuses are proposed that reduce the cost of preparing raw materials in the grain mill area by a factor of tens due to the elimination of moving working parts, assemblies and screens.


Introduction
The development of the theory of optimization of heat and mass transfer of heterogeneous vortex flows for sepa ration of the components of the mixture is relevant, as it allows to solve an important economic problem of energy saving and environmental improvement. Let's offer a solu tion to this problem by introducing vortex devices into the technological processes, which by their design can reduce energy consumption and operate in a closed cycle [1,2]. Comprehensive studies of the separation of heteroge neous mixtures show that the main characteristics of vor tex separators, such as efficiency and clarity, do not always meet the requirements of technological processes [3,4]. This is primarily due to the fact that the separated mix tures consist of components that vary widely in particle size distribution, density, aerodynamic parameters, criti cal speeds, concentration, etc. [5,6]. In the literature on a number of experimental studies of the aerodynamics of aggregates or individual elements, the aerodynamic and gasdynamic processes of flow around, stalling, jumping of seals and rarefaction for objects of various shapes and sizes are well and fully developed [7,8]. But the issue of developing a flow around small objects is associated with certain difficulties, in particular, with modeling [9,10]. The transition from an enlarged model to its original size leads to unreasonable increases in errors for two reasons. Firstly, an increase in the model leads to a distortion of the pic ture of flow separation and a change in the direction of an increase in the boundary layer, which may not be possible on a small scale, since in twophase flows the magnitude of the slip coefficient lies within wide limits. And, secondly,

ISSN 2664-9969
there is an error in the measurement of flow parameters. In addition, the movement of particles in a twophase flow is movement in the accompanying flows, and not of the individual components, as is considered in a wind tunnel. Thus, the development of methods for assessing aerody namic parameters is an urgent task. The object of research is gasdynamic vortex processes in heterogeneous polydisperse flows. The aim of research is to improve the general theory of separation of heterogeneous polydisperse flows.

Methods of research
Research on the determination of aerodynamic drag for a twophase medium was carried out on the basis of the theory of vortex gasdynamic separation of a hete rogeneous polydisperse flow. Using the theory of simi larity and mathematical modeling methods, the aerody namic series of bodies was constructed from the obtained data [10] (Table 1). The solution to the above problem was carried out theoretically and experimentally by blowing models of the components of the grain mixture made in scale 43:1. For comparison, let's used a car, plate, etc. in scale 1:43, as standard models for a small wind tunnel with constant pressure and flow air. Based on the results of the experi ments, the criteria of Strouhal, Froude, Euler, Reynolds, Archimedes and Barsukov were determined [10].
The external perturbation on discrete components (deviation of streamlines) was estimated with the derived Barsukov's criterion:

Bs
Eu

Research results and discussion
The accuracy of theoretical studies depended on how close to the actual values the aerodynamic drag coef ficients of the flow components are determined for the models. With the free spatial positions of the component models during blowing, the obtained coefficients of lift, aerodynamic drag, lateral force, longitudinal, transverse and rotational moments. The flow pattern (streamlines) for grain and impurity models was determined using a uniformly distributed smoke comb with an elementary jet diameter of 2 mm, with a constant Reynolds number. Based on the data obtained, the values of the coefficients were determined depending on the characteristic posi tions with respect to flows and grain sizes of wheat and impurities, as for standard automobile models, plates, etc. (Table 1).
The reliability of the selected value of the drag coef ficient in the constructed series of bodies was confirmed on the basis of the midsection intersection f 1 and the ratio of characteristic sizes (l/h or l/d) along the x axis. In addition, the flow velocity, the characteristic profiles of the parts of the bodies, their sizes and the completeness of the shape along the x, y, z axes were additionally taken into account. In this case, it was necessary to evaluate the state of the surface of the bodies and their location relative to the x axis.
Some error can only be from the impact of flows, breaks, and the rotation of bodies relative to the axes, as well as impacts. External disturbances of the incident flow, which changes the trajectories of the individual components of the mixture, were determined by the criterion of drag of the vortex force field and disturbing vibrations from the incident flow by the criterion Bs (Fig. 1). The obtained results are valid for sulfur compounds, dust, coal; mineral impurities, wheat grains, difficult to separate impurities: sown, locust bean, etc.
In Fig. 1: 1, 2, 3 -heterogeneous mixture components with constant parameters; 4 -flour of the first grade; 5calculation according to experimental data for grain entering the elevator (2 % impurity, 12 % moisture); I -pure wheat II -heavy impurities ρ⋅ > ⋅ ( ) )⋅ kg/m 3 is completely explained by the diffe rence in the vibration Reynolds number Re , H L for impurities. This is explained by the fact that impurities differ from pure grain in the shape, size and relative speed of air without taking into account collisions of components (for pure components, curves 1, 2, 3). . kg, the density of one grain (natural) ρ n = ⋅ 0 875 10 3 . kg/m 3 was obtained. For the volume model V m = ⋅ − 0 34 10 2 . m 3 , the mass den sity for the manufacture of a model from polyurethane was ρ m = 818 kg/m 3 . According to the results of blowing models of components in a small wind tunnel equipped with an aerodynamic threecomponent balance, the data obtained to determine the drag, longitudinal moment and lifting force.

Conclusions
The general theory of heterogeneous vortex flows has been improved with the help of the proposed criterion of external disturbance -the Barsukov's criterion, which takes into account the drag of the vortex force field and the amplitudefrequency energy level.
Differential relationships have been developed for chang ing the energy levels of polydisperse heterogeneous flows with a freeflowing onecomponent flow with specified amplitudefrequency parameters to determine the most