The calculation basis for a four-component jet mixer for fertilizer and water

. This article covers calculation basis for a four-component jet mixer for fertilizer and water. The calculation for a four-component jet mixer for fertilizer consists in determining the basic geometric and hydraulic parameters of a four-component jet mixer for fertilizer and water and supplying the mixture to irrigated areas, with fertilizing irrigation, which will allow supplying all types of fertilizers and changing the concentration of mixture in the required proportions. All geometric relative parameters are calculated on the basis of the need to scale the mixer dimensions and are taken as the ratio of the diameters of the mixer elements to the cylindrical part of the mixing chamber. The above calculation bases determine the main parameter of the mixer necessary for determining all the elements – the cross-sectional area of the annular nozzle. It was founded that when calculating the geometric characteristic, you should be guided by the desire to accept the value of the geometric characteristic m= 2.5 ÷ 8.0, corresponding to the maximum value of the efficiency up to 40% and higher.


Introduction
The most common methods of mixing fertilizers and water, during fertilizing irrigation, are mixing tanks, injectors for applying fertilizers, devices mounted on a hydrant of an irrigated area, tanks for preparing mother solution, trailed spreaders, etc.
The analysis of devices in mixing systems shows that the above devices are complicated in design and inconvenient in operation. This publication covers calculation basis for a four-component jet mixer for fertilizer and water (figure 1, 2) [1].
Calculation of a four-component jet mixer for fertilizer consists of determining the optimal relative geometric and hydraulic parameters of the mixer for the possibility of designing and manufacturing its elements when applying fertilizers to a given area in case of fertirrigation. Were: 1 -mineral fertilizers supply pipeline; 2 -working water supply pipeline; 3 -outside case of the mixer; 4 -inner adapter of the annular nozzle; 5 -diffuser; 6 -pipeline for discharging a mixture of fertilizers and water; 7 -mixing chamber; 8 -outer adapter of the annular nozzle; 9 -microelements supply pipeline; 10 -pipeline for supplying livestock waste. − diameters of supplying water pipelines Dw, mineral fertilizers Dm, livestock sewage Dl, a mixture of fertilizers and water Dfw; − m is the geometric characteristic of the mixer (the ratio of the cross-sectional area of the mixing chamber to the cross-sectional area of the annular nozzle end).
All geometric relative parameters are calculated on the basis of the need to scale the mixer dimensions and are taken as the ratio of the diameters of the calculated mixer elements to the cylindrical part of the mixing chamber.
Hydraulic parameters include:

Results and Discussion
The main parameter affecting the mixer operation is the cross-sectional area of the annular , which has the main effect on the outgoing flow rate of the working jet (water) (Figure 3).  in. in. ntr.
Were: a -external annular nozzle; b -internal annular nozzle − the width of the slot h, if possible, is taken as the maximum and is determined by hydraulic calculations; − the end length of the cylindrical sharpening is taken in the amount of 0.1-0.15 diameter and plays a passive role in the mixer operation; − the length lint is determined taking into account the possibility of inserting the fertilizer supply pipelines into the mixer case; it is taken as short as possible to reduce the pressure loss at the inlet ςin of livestock sewage and mineral fertilizers; − The inlet diameter din to the inner surface of the adapter is taken as the maximum possible based on the diameter of the external case of the mixer.
The relative distance from the edge of the annular nozzle to the beginning of the cylindrical part of the mixing chamber Z ( Figure 5) is taken from the literature data as 0.1 ÷ 0.2dts [3]. Were: 1 -case; 2 -outer adapter of the annular nozzle; 3 -mixing chamber; 4 -distance from the nozzle edge to the beginning of the cylindrical part of the mixing chamber; 5 -inner adapter of the annular nozzle In fact, the diameter of the mixing chamber dts also depends on many factors, and basically all other diameters of the mixing chamber in their final form are bound to it. The flows are mixed in the mixing chamber, the velocity diagram of the working and suction jet is leveled, according to the energy losses in the mixing chamber, the efficiency of the entire mixer is determined and the amount of vacuum required for fertilizers suction is determined. The calculation of the mixing chamber diameter is mainly based on the condition of the presence of such a value of kinetic energy in it, which is capable of creating the maximum value of negative pressure. The length of the mixing chamber determines the main energy losses in the mixer due to the presence of the maximum speed of the two flows. The design of the proposed annular two-surface four-component mixer [4] offers the shortest possible length of the mixing chamber due to the presence of a concave velocity curve diagram [5] (Figure 6). − reducing the coefficient of hydraulic resistance, reducing losses and, accordingly, increasing the efficiency of the mixer.
The above mentioned two conditions depend on one factor -the expansion angle, which, based on the literature data [6], corresponds to 6-10 о for the smallest pressure losses.
When determining the diameters of pipelines, you should be guided by the known value of the relative flow rate in pressure pipelines, corresponding to 2-2.5 m/s [6].
When calculating the geometric characteristics 0   ц m = (the ratio of the crosssectional area of the mixing chamber to the cross-sectional area of the annular nozzle), you should be guided by the desire to accept such a value that contributes to an increase in the efficiency of the mixer. Optimal values of the geometric characteristic m for jet mixers are taken in the range of 2.5 ÷ 8 and depends on the jet unit pattern of use. For fertilizer mixers, the optimal value "m" corresponds to values of 4.0-5.0 [7].
The above mentioned hydraulic parameters of the mixer are directly related to its geometric parameters. The main defining condition for the mixer operation is the value of the created reduced header pressure Нg.pr, the maximum value of which for jet mixers was determined earlier and corresponds to the value of 20-25 m. (This header pressure is created by the device of this type and was previously determined with all optimal geometric and hydraulic parameters).
When calculating the mixer header pressure, it is necessary to keep in mind the fact that the header pressure of the mixer shall exceed the header pressure in the network by at least 3-5 m. Before the theoretical calculation of the required header pressure in the mixer, it is necessary to calculate the required header pressure of the network Нg.pr, determined by the dependence where Нg is the geometric height of the mixture supply by the mixer;  wc h -pressure losses in the system. It is required to have in mind that the value of Нg.pr depends on the technology used for irrigation.
The above-described dependence is suitable for use in case of using drip irrigation under the condition that the value of the header pressure loss Σhw, the required pressure for the operation of drip lines is 20-25 m.
When using other types of irrigation equipment, it is necessary to increase the design header pressure by the amount of free header pressure, providing for the operation of the machine used. For all hydraulic parameters of the mixer, an important role is played by the working flow rate in the nozzle V0, which depends on the pressure of the working water flow generated by different types of sources (centrifugal nozzles). The header pressure flow rate in the nozzle is determined by the known dependence [8]   sharply increases, but its total value will remain the same, equal , the potential energy 0 0  g p will obviously become negative, the maximum value of which reaches 9.5 m.
The value of such a vacuum is considered deep, which differs from the value of the vacuum in the suction pipelines of centrifugal pumps by almost 2-2.5 times. This calculation proves the superiority of the jet mixer suction capacity in comparison with the suction capacity of all types of pumping equipment.
When the flow enters the mixing chamber, the rate and kinetic energy decrease due to a change in the header pressure rate in the mixed flow. But it is required to have in mind that complete mixing of the working and suction flows occurs not at the beginning, but at the end of the mixing chamber. In jet mixers with a central supply, the velocity curve is elongated ( Figure 8) and for complete mixing of flows, in such mixers the length of the mixing chamber, in contrast to the length of the mixing chamber of annular mixers (1.5-2 chamber diameters), is assumed to be 6-7 diameters, which when increased velocities play a significant role in both the total header pressure loss and the efficiency of the mixer. Were: 1 -nozzle; 2 -mixing chamber; 3 -velocity curve in the mixing chamber.
The mixing chamber in the existing designs of mixers begins at the nozzle end, in the cross-section 0-0, in which two flows are actually transported: calculated and sucked in, with different values of kinetic and potential energy. The kinetic energy of the working flow, as mentioned above, has a value that exceeds the kinetic energy of the sucked flow by many times due to the high difference in velocities and to determine the boundary of the transition of high vacuum to medium (vacuum in a mixed flow) in the mixing chamber, it is necessary to carry out special investigations, not carried out so far. According to the literature data, experiments [10,11] show that the kinetic energy from the zero cross-section to the average length of the mixing chamber remains high, and its value differs from the energy in the 0-0 cross-section by 1-1.5%, which indicates a high suction capacity mixer and high vacuum in the suction lines. The rate Vm.с and the rate header pressure in the mixing  When calculating the vacuum values in the suction pipelines, it is required to have in mind that if it is necessary to have a high suction header pressure in the mixer (suction vacuum), the mixer header pressure Нg.pr should be calculated in such a way that the value of α0 does not decrease below 1.0.