STUDYING GAS PHASE FLOW BASED ON THE BOUNDARY LAYER THEORY

ABSTRACT

This article presents the equations of the boundary layer of micelles during the process of processing the micelles with sharp water steam in the oil and fat industry. In the production of vegetable oils, it is important that the micelles must be at the required level when bubbling them with sharp water vapor during the processing of the micelles. If the micelle level is higher than necessary, this will negatively affect the release of light volatile components, if the micelle level is lower than necessary, this will negatively affect process efficiency and economic indicators.

АННОТАЦИЯ

В статье представлены уравнения пограничного слоя мицелл в процессе обработки мицелл острым водяным паром в масложировой промышленности. При производстве растительных масел важно, чтобы мицеллы находились на необходимом уровне при барботировании их острым водяным паром в процессе обработки мицелл. Если уровень мицелл образования выше необходимого, это отрицательно скажется на выделении легких летучих компонентов, если уровень мицеллообразования ниже необходимого, это отрицательно скажется на эффективности процесса и экономических показателях.

Keywords: longitudinal speed, longitudinal length, transverse length, border layer.

Ключевые слова: продольная скорость, продольная длина, поперечная длина, пограничный слой.

Introduction: Dispersed flow phenomena are encountered in a wide variety of industrial applications. In two-phase dispersed gas–solid as well as gas–liquid pipe flow a so-called core–annulus behavior can be observed. This means that the high-density component (i.e. the solid particles or the liquid drops) is found preferentially near the wall. This affects the flow pattern: the central lean phase (the core) flowing faster than the annulus dense phase. Under certain conditions downflow near the wall can even occur

We will record the equation of the Nave Steks for a constant () and stable (stationary) condition [1,2]:

                     (1.1)

Here the first two equation in the equation system (1.1) represents the differential equation of the movement, and the third represents the continuity equation.

We are going to assess the members of the system of equations (1.1). For this we will enter value of scale: is for longitudinal speed,  is for longitudinal length and  is transverse length. Now we determine  - the scale unit of transverse velocity. To do this, we find the velocity of the system from the third equation of the system (1.1):

            ,   from this                        (1.2)

From (1.2) it is clear that the transverse velocity is proportional to the thickness of the boundary layer. This is one of the main characteristics of the boundary layer.

Using this, we estimate the members of the second equation (1.1):

                          (1.3)

                          (1.4)

Now let’s substitute (1.2), (1.3) and (1.4) into the second equation of system (1.1) and in the case of         will be remain equal to 0.

It follows that the pressure in the transverse section in the boundary layer does not change. Let's start estimating the terms of the first equation of system (1.1). Based on Bernoulli's equation, that is, will be ; in other cases it is as follows:

                     (1.5)

If we substitute these terms into the equation and make the necessary reductions, then in the case of Re=0 we get the following equation:

So, as a result, it should be said that the boundary layer equations have the following form:

                            (1.6)

or

                                  (1.7)

This system was first demonstrated by L. Prandtl in 1904.

Currently, equations are used in modeling many processes.

Using the previously presented boundary layer equations, the following special differential equations can be used to estimate the boundaries and the length of the flow in our case(1.7):

              (1.8)

                               (1.9)

               (1.10)

    (1.11)

In these equations, u is the longitudinal velocity, v is the transverse velocity, r is the density, T is the temperature, n is the molecular viscosity, n_t is the turbulent viscosity, C is the flow concentration, number, Sc is the Schmidt number.

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

                                            (1.12)

To calculate the coefficient of turbulent viscosity, we use a one-parameter partial differential equation

;  (1.14)

The effective (total) viscosity is equal to the sum of laminar and turbulent viscosities:

When setting boundary conditions for a given system of equations, we are guided by the form given below. In it, the x coordinate is oriented vertically, and the pipe is placed at the beginning of the coordinate. Let's assume that the coordinate head is located in the center of the pipe and the flow is symmetrically directed upwards, that is, it can be affected by a force from the side in the direction of the satellite flow. In this case, it is enough if we 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 form:

                                                                                                  (1.15)

It can be seen from (1.15) that index 1 indicates the values of the components coming out of the pipe, and index 2 indicates the values of the satellite flow.

Conclusion: An important issue is 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 in our example are different liquids, their interaction can be represented as a viscous force at the boundary.

Since motion in turbulent flows is less dependent on molecular viscosity, it follows from the measurement theory that this force is associated with a combination of the main flow and the velocities of the external medium.

Using this balance equation, we can find the width r of the transverse boundary of the flow along the x axis.

References:

1. М.С. Нарзиев, Ф.Ю. Ҳабибов, Д.С. Каримова Разработка системы управления процессом окончательной дистилляции мисцеллы хлопкового масла на основе адекватной математической модели // Международная научно-практическая конференция “Интеграция современных научных исследований в развитие общества” I- том. 28-29 декабр, 2016. Кемерово. - С.41-44.
2. M. S. Narziev, O. R. Abdurakhmanov, F. Y. Khabibov, Karimova, D. sh. Investigation of flow hydrodynamic structures in the final distillation of a cotton miccella. "Problems and prospects of development of innovative cooperation in research and training." Bukhara. 2017.- Pp. 52-53.
3. М.С. Нарзиев, О.Р.Абдурахмонов, Ф.Ю.Хабибов. Системный анализ технологического процесса окончательной дистилляции мисцеллы хлопкового масла // Научно-технический журнал “Равзвитие науки и технологий”. - Бухара. 2017. №3. - С. 5-10.
4. М.С. Нарзиев, Ф.Ю. Хабибов, Б.И. Рустамов. Системный анализ аппаратов окончательной дистилляции растительных масел и разработка новой конструкции распылительной форсунки для массообменных аппаратов // Научно-технический журнал “Равзвитие науки и технологий”.- Бухара. 2018. №1. -122-129 б.
5. M.S. Narziev, R.B. Gʼoyibov, F.Yu. Xabibov, D.Sh. Karimova, S.M. Sattorov. Jondor EVRO SNAR oʼsimlik yogʼi ishlab chiqarish zavodidagi yakuniy distillyatsiya jarayonining avtomatik boshqaruvini takomillashtirish. // Fan va texnologiyalar taraqqiyoti jurnali. - Buxoro. 2018. №2. -126-135 b
6. M.S. Narziеv, F.Y. Habibоv. определение оптималных технологических параметров процесса окончательной дистилляции бинарных смесей  // “Оliy ta’lim innоvatsiоn faоliyati va faоl tadbirkоrlik intеgratsiyasi rivоjlanishining muammоlari” mavzusida prоfеssоr-o`qituvchilar, ilmiy izlanuvchilar, magistrlar va talabalarning ilmiy-amaliy anjumani matеriallari. II-tоm. 17-19 aprеl, 2019. -Buxоrо. -96-98 b.
7. M.S.Narziеv, F.Y.Xabibоv. Использование методологии экспериментального планирования для изучения процесса окончательной дистилляции растительных масел // “Оliy ta’lim innоvatsiоn faоliyati va faоl tadbirkоrlik intеgratsiyasi rivоjlanishining muammоlari” mavzusida prоfеssоr-o`qituvchilar, ilmiy izlanuvchilar, magistrlar va talabalarning ilmiy-amaliy anjumani matеriallari. II-tоm. 17-19 aprеl, 2019. - Buxоrо. -96-98 b.
8. M.S. Narziyev, Sh.B. Raxmonov, S.X. Xalilov, D.M. Astanov. Barbоtajli massa almashinish qurilmalarida gaz fazasi gidrоdinamikasini ekspеrimеntal tadqiq qilish// «Sanoat injiniringida innovatsion yechimlar» mavzusida xalqaro ilmiy-amaliy anjumani. 24-25 noyabr, 2023.–Buxoro. 213-214 b.
9. M.S. Narziyev, Sh.B. Raxmonov, S.X. Xalilov, Sh.K. Madiyev. Systematic analysis hierarchical structure of cotton seed oil micelle final distillation equipment// “Sanoat injiniringida innovatsion yechimlar” mavzusida xalqaro ilmiy-amaliy anjumani. 24-25 noyabr, 2023.–Buxoro. 211-212 b.
10. Sh.B. Raxmonov. Calculation of the smooth distribution of sharp steam supplied in a bubble-type mass exchange apparatus over the sectional surface of the apparatus// Universum: Технические науки, Выпуск: 11(116) Ноябрь 2023, cт. 18-20.
11. Джураев Х.Ф., Рустамов Э.С., Гафуров К.Х. Новый метод подготовки абрикоса к сушке. Международная научно-практическая заочная конференция «Биотехнологические, экологические и экономические аспекты создания безопасных продуктов питания специализированного назначения». Краснодар, 2020. С.438-441.
12. Рустамов Э.С. Зависимость влажности и температуры воздуха в процессе сушки плодов.// “Universum: технические науки” Научный журнал. Москва, 2022 №11(104(4)). С.57-60.