CALCULATION OF THE SMOOTH DISTRIBUTION OF SHARP STEAM SUPPLIED IN A BUBBLE-TYPE MASS EXCHANGE APPARATUS OVER THE SECTIONAL SURFACE OF THE APPARATUS

ABSTRACT

This article develops a mathematical model for determining the hydrodynamic parameters of the acute vapor phase in the bubbling layer during the final distillation of cottonseed oil mistella in industry using the bubbling method and describes its scientific basis.

АННОТАЦИЯ

В данной статье разработана математическая модель определения гидродинамических параметров острой паровой фазы в барботажном слое в процессе окончательной перегонки мистеллы хлопкового масла в промышленности барботажным методом и описаны ее научные основы.

Keywords: mass transfer apparatus of the bubbling type, cross-sectional surface of the apparatus, steam distribution.

Ключевые слова: массообменный аппарат типа барботаж, поверхность сечения аппарата, распределение пара.

Today, in our country, as in the whole world, it is an urgent issue to satisfy the population's demand for food products and to ensure the stability of the continuous supply of these products to the domestic market. As a result of the implemented measures, oil and fat products in the amount of 4.5 trillion soums were produced in our country in January-September 2023, and in this regard, a growth rate of 119 percent was achieved compared to the same period last year. In particular, 140,000 tons of vegetable oil and 18,000 tons of margarine were produced [1].

Bubble distillation is used for micelles with a high boiling point and a high concentration (80-85%). In this case, the solvent is removed by evaporation. To speed up this process, a vacuum is created in the apparatus, and open steam is supplied to the thick layer of micelles through a barbator.

During distillation in a thick layer, the pressure in the micelle is not the same in the upper and lower layers, so the temperature of the solution is also different depending on the height of the layer. The vapor bubbles in the lower layer of the liquid must overcome its pressure through the layer, therefore, it must have a higher pressure compared to the surface. Because of this, the boiling temperature of the micelles in the lower layer is high.

With the loss of solvent and the increase in micelle concentration, the hydraulic pressure increases because the resulting micelle density increases. The smaller the thickness of the layer, the less the effect of hydraulic pressure.

Different methods can be used to model such processes[2,3].

The following differential equations with specific derivatives can be used to estimate the limits and length of the current [4,5]:

                        (1)

                                        (2)

                         (3)

        (4)

In these equations, u- the longitudinal speed,  - the transverse speed, - density, T – temperature,  – molecular viscosity, turbulent viscosity,  C – flow concentration, Pr – Prandtl number, Sc – Smidt number.

The initial stream concentration is related to the mass of the main stream and satellite stream as follows:

                                  (5)

In the main stream, since =0, C=1, and in the satellite stream, since m_gaz=0, C=0. These values are considered as boundary conditions for concentration.

Using the Mendeleev-Clapeyron equation for an ideal gas, we can write for the flux density:

                       (6)

We express the coefficient of turbulent viscosity by Prandtl's first formula:

                                            (7)

Effective (total) viscosity is equal to the sum of laminar and turbulent viscosities . When setting the boundary conditions for the given system of equations, we refer to the form given below. In it, the x-coordinate is oriented vertically, and the pipe is placed at the beginning of the coordinate. We assume that the coordinate head is located in the center of the pipe, and the flow is symmetrically directed upward, that is, it can be affected by a force from the surrounding flow. In this case, it is enough for us to see one side of the x-axis, because the parameters on the other side will be the same. Given these assumptions, the boundary conditions can be written in general as:

                                      (8)

it can be seen (8) that 1 index indicates the magnitudes of the components coming out of the pipe, and 2 the satellite flow magnitudes.

It is an important issue to determine the limits of the flow of water vapor coming out of the nozzle in the area of the oil-gasoline mixture. Since the turbulent flow and the external field are different fluids in our example, their interaction can be imagined as the viscous force at the boundary. Since the motion in turbulent flows is less dependent on molecular viscosity, it follows from gauge theory that this force is due to some combination of the velocity of the main flow and the external environment, and the mass balance equation for a turbulent fluid along the x-axis is can be written[6]:

Using this balance equation, it is possible to find the width r of the transverse boundary of the flow along the x-axis.

The formed system of equations is brought to a system of algebraic equations through a two-layer, four-point finite difference scheme and solved using the progonka (distillation) method. Iteration was used to ensure the required accuracy.

Figure 1. Changes in the longitudinal speed and limits of the main flow (steam).

Figure 1 shows the limits of the vapor flow in the liquid and the longitudinal speed change. It can be seen in the diagram that the boundary of the flow, which has little effect on the main flow, is not very large, because the density of the surrounding fluid is small compared to the density of the main flow. By the effective expansion range, if we say that the maximum dimensionless speed is equal to 1, then we understand its limit equal to 0.2.

If we put these results into the system of flows, we can get the result of which dimensions to place steam nozzles (Figure 2). When the main flow rate decreases to 0.3-0.4, the effective expansion limit expands to a value equal to the value of the nozzle radius. Using this conclusion, if we increase the distance between the two nozzles by one diameter, we will get the liquid placed in the area under the influence of the main steam flow. In this case, the length of the main stream reaches 0.5 meter. Therefore, it is better to take the height of the liquid in the field to be around 0.5 meter.

Figure 2. Determining the scope of the steam flow coming out of the nozzle

References:

1. Ёғ-мой маҳсулотларига аҳоли талабини қондириш мақсадида жорий йилда 246 минг тонна мойли экинлар етиштирилади - Review.uz
2. Деменков А.Г., Илюшин Б.Б., Черных Г.Г. Численное моделирование осесимметричных турбулентных струй//Прикладная математика и техническая физика. 2008. Т. 49, № 5. С.55-60.
3. Иващенко В.А., Муллажанов Р.И. Численное моделирование затопленной струи переменной плотности//Сибирский физический журнал. 2018, том.13, № 1. С.45-52.
4. Мордасов М.М., Савенков А.П., Чечетов К.Е. Методика исследования взаимодействия струи газа с поверхностью жидкости//Журнал технической физики, 2016, том 86, вып.5. с.20-29.
5. Могаддам В.Г., Казачков И.В. Моделирование проникания струй кориума в подреакторный бассейн с испаряющимся охладителем//Ядерна физика та энергетика. 2010, т.11, № 2, с. 151-158.
6. Westerwell J., Fukushima C., Pedersen J.M. and Hunt J.C.//J. Fluid Mech. 631, 199(2009).