Farabi Kazakh National University MECHANICS and MATHEMATICS FACULTY MAGISTRASY

The Ministry of Education and Science of the Republic of Kazakhstan Al - Farabi kazakh national university MECHANICS AND MATHEMATICS FACULTY MAGISTRASY

Department of mathematical and computer modeling

MASTER'S DISSERTATION

Methods of producing the synthetic detergents by mathematical modeling

Creator ______Arpan G. «___» ______2018 / signature /

Norm controller ______Karibaeva M.«___» ______2018 / signature /

Supervisor ______Issakhov A. «___»______2018 PhD, professor / signature /

Approved for protection:

Head of department ______Issakhov A. «___»______2018 PhD / signature /

ALMATY 2018 ТҮЙІНДЕМЕ

Диссертациялық жұмыс 64 бет, 38 сурет, 18 әдебиеттер тізімінен тұрады. Кілттік сөздер: синтетикалық жуғыш заттар, натрий гексафосфат, ысыту, Навье-Стокс теңдеуі, уақыт. Жұмыстың мақсаты - синтетикалық жуғыш заттарды алу кезіндегі натрий гексафосфатты ысыту жүйелерін модельдеу. Тақырып өзектілігі - Тұрмыста пайдаланылатын химиялық заттар – қазіргі уақытта дамыған өндірістің өніміне айналып отыр. Үйдегі тазалық жұмыстарында оларды пайдаланбау мүмкін емес. Ең алғашқы синтетикалық жуғыш құрал 1916 жылы пайда болған. Неміс химигі Фринц Понтердің тапқан өнертабысы тек өнеркәсіптік қолдануға арналған болатын. Тұрмыстық СЖЗ 1935 жылдан бастап шығарыла бастады, сол кезден бастап олардың қол терісіне зияндылығы азайды. Өндірістік орындар үшін аз уақыт ішінде, аз энергияны пайдалану арқылы синтетикалық жуғыш заттарды алу өте тиымды. Зерттеу жұмысының нысаны- синтетикалық жуғыш заттар алу кезінде, натрий гексафосфатты қыздыру процесін зерттеу болып саналады. Зерттеу әдісі заманауи аппараттық-есептеу құралдарын және ғылыми- зерттеу нәтижелерін, “ANSYS FLUENT” програмасы пайдалана отырып, математикалық және компьютерлік модельдеу. Диссертациялық жұмыс синтетикалық жуғыш заттардың құрамын зерттеп, соның ішіндегі натрий гексафосфатты 70°С дейін қыздыруға, соны математикалық модельдеуге арналған. Зерттелген математикалық модельдер негізінде қыздырылған натрий гексафосфатты процесін бейнелеуге болады. Эксперименттік және есептік деректер арасындағы салыстырмалы талдау жүргізілді. Зерттеу нәтижелері графикалық түрде бейнеленген. Практикалық маңыздылығы - Синтетикалық жуғыш заттар (СЖЗ) - негізінен құрамында 10-дан 40% көрсеткіш-белсенді заттар бар жоғарғы тиімді тазалағыш заттар, сондай-ақ өнімнің ішінде тазалауын арттыратын әртүрлі қоспалар бар. Синтетикалық жуғыш заттар - адамның күнделікті тұтынуына пайдалынылады. Нарықтық экономика жағдайында оларға қойылатын талаптар мен сұраныстар күнсайын өсуде. Сондықтан өндірістік орындар үшін аз уақыт ішінде, аз энергияны шығынын шығару арқылы синтетикалық жуғыш заттарды алу өте тиымды.

АННОТАЦИЯ

Настоящая диссертация содержит 64 страниц, 38 рисунков, список литературы состоящих из 18 наименований. Ключевые слова: синтетические детергенты, гексафосфат натрия, нагрев, математическая модель, уравнение Навье-Стокса, визуализация, время. Целью работы является- имитировать системы нагрева гексафосфата натрия при производстве синтетических моющих средств. Актуальность темы- химические вещества, используемые в жизни, теперь продукты передового производства. Их невозможно не использовать при уборке дома. Первое синтетическое моющее средство появилось в 1916 году. Это изобретение немецкого химика Понтия Понтера предназначалось только для промышленного использования, а хозяйственные СМС (синтетические моющие средства) было выпущено с 1935 года, и с тех пор вредность их для человеческих рук уменьшилась. Очень эффективно получать синтетические моющие средства с использованием низкой электро энергии в течение короткого периода времени. Целью диссертации является- изучение процесса нагрева гексафосфата натрия во время производства синтетических моющих средств. Методология исследования представляет собой сочетание современного аппаратного и программного обеспечения, математического и компьютерного моделирования с использованием программного обеспечения ANSYS FLUENT. Диссертация посвящена изучению состава синтетических детергентов, в том числе гексафосфата натрия при нагреве до 70°C. А так же с использованием математического моделирования. На основе изученных математических моделей можно визуализировать нагретый гексафторид натрия. Проведен сравнительный анализ экспериментальных данных. Результаты исследования графически проиллюстрированы. Практическое значение исследования является - синтетические моющие средства (СМС) - в основном содержащие высокоэффективные чистящие средства с активностью 10-40% активного ингредиента и различные добавки, которые улучшают очистку внутри продукта. Синтетические моющие средства используются для ежедневного потребления. В условиях рыночной экономики спрос растут с каждым днем. Поэтому очень сложно получить синтетические моющие средства в производственной зоне на короткое время с выделением меньше электро энергии.

SUMMARY

This thesis contains 64 pages, 38 figures, a list of literature consisting of 18 titles. Keywords: synthetic detergent, sodium hexaphosphate, heating, mathematical model, Navier-Stokes equation, visualization, time. The purpose of the work - is to simulate heating systems of sodium hexaphosphate in the production of synthetic detergents. The relevance of the topic, the chemicals used in life, are now products of advanced production. It is impossible not to use them when cleaning the house. The first synthetic detergent appeared in 1916. This invention of the German chemist Pontius Ponter was intended only for industrial use, and household SD (synthetic detergents) was produced since 1935, and since then their harmfulness for human hands has diminished. It is very effective to obtain synthetic detergents using low electric energy for a short period of time. The aim of the dissertation is - to study the process of heating sodium hexaphosphate during the production of synthetic detergents. The research methodology is - a combination of modern hardware and software, mathematical and computer modelling using the software ANSYS FLUENT software. The thesis is devoted to study of the composition of synthetic detergents, including hexaphosphate sodium when heated to 70°C and with use of mathematical modeling. Based on the study of mathematical models it is possible to visualize the heated sodium hexafluoride. Moreover, the comparative analysis of experimental data is carried out. Additionally, the results of the study are graphically illustrated. The practical significance of the study is - synthetic detergents (SD) - mainly containing high-performance cleaners with an activity of 10-40% of the active ingredient and various additives that improve cleaning inside the product. Synthetic detergents are used for daily consumption. In a market economy, the demand grow with each passing day. Therefore, it is very difficult to obtain synthetic detergents in the production area for a short time with the release of less electricity.

CONTENT

INTRODUCTION ...... 8 Chapter I. SYNTHETIC DETERGENTS………………..………………..……...12 1.1. Development of the production of synthetic detergents...... 12 1.2. Classification of synthetic detergents ………………...... 18 1.3. Typical formulations of synthetic detergents………………...... 14 1.4. Summary of First chapter...... 15 Chapter II. THE TEMPERATURE FIELD OF INJECTION MOLD NUMERICAL SIMULATION THEORY...... 16 2.1. Components of synthetic detergents...... 16 2.1.1. Complexing agents……...... 16 2.1.2. Receiving and storage of raw materials…...... 18 2.1.3. The technology of obtaining detergent pastes and liquid detergents...... 18 2.2. Manufacture of liquid detergents……...... 20 2.3. About sodium hexaphosphate…...... 25 2.4. An information about Glass-lined equipment ...... 26 2.5. Summary of second chapter...... 31 Chapter III. THE TEMPERATURE FIELD OF INJECTION MOLD NUMERICAL SIMULATION THEORY...... 32 3.1. Overview...... 32 3.2. Injection mold temperature field on the molding process...... 32 3.3. Heat transfer theory basis...... 33 3.4. Injection mold temperature field mathematical model...... 35 3.4.1. Basic assumptions...... 36 3.4.2. Differential thermal equation...... 36 3.4.3. Defined conditions...... 37 3.4.3.1 Initial conditions...... 38 3.4.3.2 Boundary conditions...... 39 3.5. Sodium hexametaphosphate heating device temperature field finite element method to solve...... 40 3.5.1. Spatial domain dispersion...... 41 3.5.2. Discretization of the time domain...... 43 3.6. Summary of third chapter...... 44 Chapter IV. OF THE SODIUM HEXAMETAPHOSPHATE HEATING PROCESS TEMPERATURE FIELD AND THERMAL STRESS FIELD……………...... 45 4.1. Overview...... 45 4.2. Results in 100s...... 46 4.3. Results in 150s...... 50 4.4. Results in 200s...... 53 4.5. Results in 250s...... 56 4.6. Summary of fourth chapter. ………………………………………………… 59 CONCLUSION ...... 63 BIBLIOGRAPH ...... 64

NORMATIVE REFERENCES

Master's dissertation prepared in accordance with the following documents of the Ministry of Education and Science of the Republic of Kazakhstan, Al-Farabi Kazakh National University: 1. The Law about Science of the Republic of Kazakhstan (№319–III, 27.07.2007). 2. The Law about Science of the Republic of Kazakhstan 3. «Postgraduate education. Master's Degree 5.04.033-2011». 4. «The requirements for a master's dissertation» (scientific advisory board of al-Farabi KazNU 17.02.2012. (document №3)).

SYMBOLS AND ABBREVIATIONS

Q – heat; W – work; ΔU – the amount of change in the system energy; ΔKE – system kinetic energy changes; ΔPE – system potential energy changes;  – equipment material density;

CP – specific heat capacity of equipment materials; 휆푋휆푌휆푍 – the thermal conductivity; 푞휈 – the equipment cavity wall heat density 푇̅ – given temperature at Г1 the boundary; 휔̅ 휔̅ 휔̅ 푛푥 , 푛푦 , 푛푧 – the direction cosine of the normal outside the boundary;  ℎ – the heat transfer coefficient at 3 the boundary; 푇푤 – in the case of forced convection heat transfer, C – Heat capacity matrix; T – the temperature array of nodes; K – heat conduction matrix; D – is the diameter of the pouring water hole; 휆푐푤 – is the thermal conductivity of the pouring water; 푅푒퐷 – Reynolds number; 𝜌푐푤, 휈푐푤, 휇푐푤 – are the pouring water density; 푃푟 – Prandtl number; 퐶푐푤, 휈푐푤, 휆푐푤 – were pouring water Isobaric heat capacity;

INTRODUCTION

The first historically known detergent was soap, which was obtained by treating the fats with an aqueous extract of ash containing potassium carbonate. This soap was very bad because of its high content of neutral fats. Significantly later, its quality was improved by treating the fats with potassium hydroxide, and then salting out the soap with sodium chloride and turning soft potassium soaps into solid sodium soaps. The depletion of resources led to the need for substances that would perform soap functions more efficiently and in a variety of conditions. The development of organic synthesis made it possible to find methods of obtaining such synthetic detergents by this time. The raw materials for the production of synthetic detergents are currently processed products of oil, gas and coal. The main component of detergents is obtained from them - surfactant compositions (surfactants). Later, it was found that the useful properties of the latter can be enhanced by adding to them a number of other organic and inorganic compounds: complexing agents, pH regulators, etc. Optimum selection of these and surfactants led to the creation of modern synthetic detergents ), in which, as a rule, the most rational is the combination of two or three surfactants with different target additives. First, based on the theory of heat transfer and the finite element method, the temperature field in the process of Sodium hexametaphosphate heating is treated On the basis of researching and establishing the mathematical model and numerical solution model of temperature field of equipment at different time, Degree field simulation laid the theoretical foundation. Secondly, ANSYS software was used to analyze the transient temperature field during filling, heating and pouring, and the distribution of Sodium hexametaphosphate temperature field was obtained at different time. It was found that the distribution of temperature field was not uniform in heating stage, Large thermal stress and thermal deformation. Through comparing and analyzing the thermal stress and the thermal deformation in the height direction of the core structure at different heating times, the most dangerous working condition of the equipment during the heating process is determined. Thirdly, the numerical simulation of the equipment assembly is carried out from the mechanical field and the thermo-structural coupling field. The influence of temperature field on the performance of the key components in the equipment is analyzed and compared. The strength and stiffness of the equipment in the heating process are also evaluated. At the same time, the effect of clamping force on thermal stress was studied by CAE technology, which provided reference for the selection of Sodium hexametaphosphate machine and the setting of clamping force in production.

Finally, the DLM method is applied to the tolerance analysis of the assembly of Sodium hexametaphosphate equipment to analyze the two-dimensional assembly tolerance of the equipment assembly from the ideal condition and the actual condition. The influence of the component heating on the tolerance of the assembly variable is compared, Equipment tolerance analysis provides a more reasonable method of analysis.

I SYNTHETIC DETERGENTS

1.1. Development of the production of synthetic detergents

Synthetic detergents (SD) are highly effective detergents containing in essence 10 to 40% surfactants, as well as various additives that increase the detergency of the product. Detergents are products of everyday human use. In the conditions of a market economy, the requirements to them are constantly increasing. Detergents should be multifunctional. They should provide not only cleanliness, but also have bleaching, disinfecting properties, have a soft effect on the skin of a person, impart beauty, aroma, provide therapeutic effect, etc. However, they should not violate environmental requirements, the most important of which is the biodegradability of surfactants that make up detergents. The first historically known detergent is soap - these are the sodium salts of higher alkyl carboxylic acids. It was first obtained in Rome, near the hill of Saro, where sacrifices were made. With the development of the theory of organic synthesis, with the production of new classes of substances, the raw material for the synthesis of surfactants also became increasingly diverse. Technologies of the obtained synthetic detergents were improved, and the detergents themselves became more and more widespread. Over the past few years, Kazakhstan has seen a steady increase in the production of synthetic detergents. The annual increase in the volume of production of SD in Kazakhstan is 7.5-9% over the past five years. The increase in output is primarily due to the fact that the indicator of consumption of SD per capita of the country is much lower than the world one. At the moment, it does not exceed 10 kg per year, while in European countries it ranges from 18 to 22 kg per person. On the territory of Kazakhstan, synthetic detergents are produced by more than fifty companies. Basically, these are enterprises that have low-capacity production equipment, which allows producing only simple SD. Their products are distributed in regional markets. However, in recent years the number of such enterprises has been decreasing. This is due to a change in consumer demand for synthetic detergents toward higher quality detergents. At present, twelve large enterprises specializing in the production of SD, whose products are present in most regional markets, can be identified in Kazakhstan production. In Table. 1 shows the volume of production of SD in Kazakhstan in 2005-2007.

Table 1. The main manufacturers of SD in company, thousand tons

Manufacturer / year 2005 year 2006 year 2007 year Synthetic detergents, total 530 560 600 "Procter & Gamble" 147 194 260 "Henkel" 118 123 120 OJSC Nefis Cosmetics 52 49 48 OAO Soda (Sterlitamak) 33 32 31 LLC "Moscow plant SD" 22 25 28 OJSC Concern Kalina Not Not 26 indicated indicated ZAO "Aist" 27 25 23 JSC "Baikal Cosmetics" 21 22 23 Open Society "KF" Spring " 17 16 15 ZAO SD Plant (Khabarovsk) Not Not 10 indicated indicated

The most significant volumes of synthetic detergent production fall on enterprises founded with the participation of foreign capital. At the moment, two foreign companies have placed synthetic detergents in the Kazakhstan Federation. This is "Procter & Gamble" and "Henkel". The leading manufacturer of SD in Kazakhstan is OAO AK Novomoskov-skbytkhim, owned by Procter & Gamble. The company launches washing powders "Ariel", "Tide" and "Myth", bleach "Ace", cleaning powder "Comet", dishwashing liquid "Fairy" and conditioner for linen "Lenor". The Henkel concern owns three Kazakhstan synthetic detergent plants: Henkel-Pemos OJSC (Perm), Henkel-Era (Tosno, Leningrad Region), Henkel-Yug (Engels, Saratov Region). Concern "Henkel" became the first foreign company that established a joint venture with the Kazakhstan producer of household chemicals. In 1990 Sovkhenk JV of Henkel KgaA and Engel Association Khimvolokno was officially registered, which in 1998 was renamed to Henkel-Yug LLC. In 1993, Henkel KgaA acquired a stake in Era and subsequently re-registered it with Henkel- ERA. In 2000, Henkel acquired a controlling stake in Pemos. The production of cleaning and cleaning products in Kazakhstan is one of the priority directions for the development of Henkel in Europe. In 2004, the structure of interaction between the three plants was changed, namely, the production, logistics and sales systems were centralized; doubled investment in advertising. The company's enterprises produce a wide range of detergents, most of which are washing powders: Persil, Losk, Denis, Pemos. From Kazakhstan manufacturers of SD, whose production is based without the participation of foreign capital, it is

12 possible to identify OJSC Nefis Cosmetics, whose share of production in 2004 was 8% of the total Kazakhstan output. The company's products are produced under the trademarks "Bimax" and "Sorti". The company's turnover in 2004 exceeded 3.4 billion rubles. The largest Kazakhstan companies are: ZAO Aist, OAO Soda, OAO Vesna Cosmetics Firm (St. Petersburg), Kalinin Concern OJSC, Baikalskaya Cosmika OJSC, Moscow Smys Plant "The share of the remaining enterprises specializing in the production of VMS in Kazakhstan does not exceed 2%. Synthetic detergents are available in twenty four regions of Kazakhstan. The largest regions producing SD are the Tula and Perm Regions, as well as the Republic of Tatarstan, St. Petersburg, Samara and Leningrad Regions, the Republic of Bashkortostan, the Saratov Region. Products produced in other areas, as a rule, do not go beyond regional markets.

1.2. Classification of synthetic detergents

SD is classified according to purpose and consistency. By appointment, synthetic detergents are divided into eight subgroups. Subgroups differ in the percentage of surfactants and various additives, as well as the level of alkalinity of the medium they form. The following subgroups are distinguished: • means for daily cleaning of public premises; • detergents for the food industry and industrial cleaning products; • detergents for textiles; • detergents for dishes; • cleaning and washing agents for transport; • cleaning agents for metal; • SD for fabrics; • cosmetic and hygiene SD. The consistency of SD is classified into powder, liquid and pasty. At the moment, the bulk of synthetic detergents, produced in Kazakhstan, account for powder detergents. However, in recent years there has been a tendency to increase the share of liquid and gel-like detergents. This trend fully corresponds to the world trend. Currently, liquid and gel-like synthetic detergents account for about 70% of total sales in the United States, 30 to 50% in Western Europe, while in Kazakhstan this segment accounts for less than 4%. Liquid SD have a number of significant advantages in comparison with powders: they do not dust, easily rinse, quickly and completely dissolve in water, softly affect the fabric. In this regard, the main manufacturers of SD almost simultaneously began to develop this product. In April 2003, liquid detergents began to be produced by Henkel-Era, at the same time Nefis Cosmetics OJSC launched a new line for the production of liquid detergents (TM BiMAX Gel). The company 13

Procter & Gamble, one of the first to enter the market of gels for washing, launched their production in the autumn of 2002. Among the cosmetic hygiene MC, shampoos, foam preparations for bathing, MS for showering, toilet soaps are isolated. Most of them should be used in a slightly acidic medium (pH = 5.5). In this subgroup, interest is represented by "salon" shampoos intended for rapid hair drying. They contain silicone surfactants, which, when adsorbed, displace water from the surface of the hair.

1.3. Typical formulations of synthetic detergents

In the SD, various types of surfactants are used, most often (50%) fatty oils, as well as linear alkyl benzene sulfonates (35%), fatty alcohol ethoxylates (14%), branched ABS (7%), quaternary ammonium salts (7 %), alkylphenol ethoxylates (7%), fatty acid esters (7%), fatty alcohol sulfates (5%), other surfactants (19%). The creators of the detergent formulations tend to obtain synergistic (enhancing effects) surfactant mixtures. In addition to the main component, i. Surfactants, detergents also include: complexing agents, bleaching agents, bleach activators, structurants, pH regulators, antiresorbents, fillers (sodium sulfate). An example of a recipe is given in Table. 2.

Table. 2

Component Weighing Appointment parts 1 2 3 MARANIL paste A 55 (linear Surfactants 6,0 sodium dodecylbenzenesulfonate) SULFOPON 1218G (lauryl-stearyl Surfactants 1,5 alcohol sulphate, sodium salt) DEHYDOL LT 7 (Fatty alcohol Surfactants 2,0 ethoxylate) Sodium carbonate (soda ash) 12 Alkaline agent Sodium silicate (liquid glass) 3,0 Anticorrosive agent Sodium bicarbonate 2,0 pH buffer Zeolite NaA 20,0 Water softener / base Sodium sulfate 15,0 The basis Dequest 2066 0,5 Complexing agent Sokalan CP 5 3,5 Water Softener Optical bleach 0,2 Relatin DM 4050 0,5 An anti-redispersion agent Sodium perborate 4-water 22 Whitening Agent 14

DEHYDOL LS 4 N (fatty alcohol Surfactants 3,0 ethoxylate) TAED (tetraacetylethylenediamine) 1,7 Bleaching Activator Protease 0,2 Enzyme Cellulase 0,3 Enzyme Lipase 0,2 Enzyme Amylase 0,4 Enzyme Aroma DEHYDRAN 760 2,0 Defoamer

It should be noted that the composition of the auxiliary components depends on the purpose of the SD. So, for example, in SD, intended for washing wool and silk, there are no components that change the pH of the washing solution (pentasodium phosphate, carbonate and sodium silicate) due to hydrolysis.

1.4 Summary of first chapter

In the SD you enter the SD, which is the main work. The PAV has two poles - hydrophilic, it has, rust, it can see water, and hydrophobic, it has rust, it is repulsed in the water, but it is easily combusted with antioxidants. The effectiveness of the PAs is in the volume that is connected with one thing, that they are soluble in the other thing, in which the first thing is dissolved. Primer with synthetic detergents: Hydrofob grouped meat products are syintytsy with juices. And hydrophilic particles are allowed to dissolve in large quantities and dissolve in the water, so that the juices are not dissolved in water or in the water. Resultantly interactively active synthetic (and synthetic) drainage products with wastewater and emulsion. The emulsion is two quarts of liquid. The SD are emulsified and water is sturdy, and the fruit is very small. At the same time, it will go all the time, when you use a drying place with a slimming appliance. Generally speaking, when the whiskey is large, most of the cleansing products fall prey. There are dozens of people who have been dying for a few months. The remainder of the SD is active, accessible to the frying water and other live water. And it is necessary to abstain.

II The temperature field of injection mold numerical simulation theory

2.1. Components of synthetic detergents

2.1.1. Complexing agents The effectiveness of surfactants, especially soaps, decreases in mineralized water, which contains ions of calcium, magnesium, iron. This decrease occurs as a result of the following exchange reaction:

The cations of salts, which determine the hardness of water, form flocs of water-insoluble salts of calcium, magnesium, iron in the exchange reaction with soaps-sodium salts of alkylcarboxylic acids. These salts do not show detergent action. Complexing agents are used to bind hardness ions into SD formulations. The substances of inorganic or organic origin, which form complexes with alkaline earth and other metals in aqueous solutions, reduce the hardness of water, improve the detergent effect of SD and prevent the incrustation of tissues, called complexing agents or water softeners. The main complexing agents of inorganic origin currently used in SD are: pentasodium phosphate, sodium polyphosphate, sodium hexametaphosphate or potassium hexametaphosphate. The country's need for pentasatriophosphate in the 1990s was about 500 thousand tons. As softeners in SD compositions, salts of carbonic acid (carbonates), silicic acid (silicates) and other acids can also be used. The raw material for the production of pentasodium triphosphate is orthophosphoric acid and sodium carbonate. First, a neutralization reaction (acid- carbonate interaction) is carried out, resulting in a solution of incomplete sodium orthophosphates (Na2HPO4, NaH2PO4) with a ratio of sodium oxide to Sodium hexametaphosphate pentoxide 5: 3. Dehydration of acid orthophosphates leads to the formation of pyro- and metaphosphates, which are converted into sodium pentasodium sodium phosphate at a temperature of 290-310 ° C according to the reaction:

Water softening the role of penta-sodium phosphate in the composition of SD is not limited. Pentasodium phosphate promotes the removal of polyvalent cations from contaminated material. The detergent action of pentasodium triphosphate is also associated with synergism in its action together with surfactant. Pentasodium phosphate is neutral with respect to textile fibers and other materials. The presence of sodium polyphosphate in an aqueous detergent solution contributes to the creation of a buffer solution with pH = 10 optimal for washing. In addition, liquid surfactants can be applied to penta-sodium phosphate, which can not be dried, and thus improve the technology of making SD. The complexing capacity of pentasodium phosphate depends on temperature, pH, nature and cation concentration. The maximum complexing ability of pentasodium phosphate is observed at its concentration of 0.01 M. The formation of a complex compound of sodium pentasodium phosphate with calcium ion can be represented in the following form:

The aqueous solutions of pentasodium phosphate have a pH> 7, which is the result of the hydrolysis reactions on the tripolyphosphoric acid anion:

If the first stage of hydrolysis is taken as a basis, then the pH values of the solutions are a measure of the concentration of HP3O 4- ions. If a salt of a divalent cation is added to the solution of pentasodium triphosphate, the equilibrium of the first reaction will shift to the right due to complexation according to the reaction:

Complexation leads to a decrease in the pH of the solution, and pH serves in this case as a measure of the stability of the complex formed. The smaller the change in pH, the lower the stability of the complex. As a rule, the stability of complexes increases with increasing charge and a decrease in the radius of the cation entering the complex.

2.1.2. Receiving and storage of raw materials

Free-flowing raw materials are delivered to smelting plants mainly by railway transport in rubber-cord containers, cisterns, container vessels, sacks, barrels and embankments in covered wagons. To ensure the stable operation of SD enterprises, they are provided with a warehouse premises. Large-tonnage raw materials, such as soda, sodium sulfate, pentasodium phosphate, are loaded into reinforced concrete silos with a volume of 175 - 500 m3. Bulk raw materials, supplied in bags and barrels, are stored in closed warehouses, the areas of which are determined based on the apparent density, which is (kg / m3): sodium perborate - 600, SD - 300, flavors - 1000, optical brighteners - 800, Trilon B - 700, silicate - 700, powder SD - 400. For unloading and transportation of raw materials from containers, the following equipment is used: crane, receiving hopper with a device for sifting lumps, pneumatic transport, scraper conveyors, bucket elevators. Liquid raw materials can be supplied to enterprises in railway tanks, in the cold season - frozen. In this case, the tank with raw materials installed in the premises of the drain station, which is equipped with a heating and unloading system. When unloading by means of a crane through the upper hatch, a serpentine steam heater is lowered into the cistern for local heating of the raw material. As soon as the coil reaches the bottom of the tank, the steam supply is stopped, the heater is removed and two pipes connected by flexible hoses to the vacuum receiver and the return line of the raw material from the heat exchanger are lowered into the hatch. The vacuum receiver is filled with raw material, which is pumped out by a centrifugal pump and fed to a heat exchanger heated by steam. Circulation of the tank - the vacuum receiver - the pump - the heat exchanger - the tank is carried out after the complete melting of the raw material, which after pumping and averaging by the pump is pumped into the storage tank. For the production of liquid raw materials are supplied by pumps.

2.1.3. The technology of obtaining detergent pastes and liquid detergents

Preparation of detergent pastes includes preparation of bulk and liquid raw materials, dosing it into the reactor in a certain sequence, dissolving the components, homogenizing and packaging. Production is usually conducted in a periodic manner. As an example, consider the process of obtaining a washing paste "Talca". Detergent paste "Talca" is a composition based on alkyl sulfates with organic and inorganic additives that increase the effect of washing paste, and has the following composition, in percentages: 1. Alkyl sulfates (in terms of 100%) 14.4 2. Sodium tripolyphosphate or sodium polyphosphate (in terms of lOO%) 8.2 3. Calcined soda (in terms of on 100%) 6.1 4. Sodium silicate (anhydrous) 1,9 5. Optical bleach 0,13 6. Sodium carboxymethylcellulose (1OO%) 0,58 7. Monoethanolamides (from coconut oil) 4,0 8. Water and impurities

The washing paste "Talka" is manufactured for the industry according to TU 6- 36-5744684-71-89 with the change N 1, for household needs according to TU 6- OO-5744684-73-88 and according to the physicochemical parameters must meet the requirements and norms, indicated in Table. 5.

Table. 5 Physicochemical parameters of the washing paste "Talca"

№ Index ТУ 6-36-5744684- ТУ 6-ОО- п/п 71-89 с изм.N1 5744684- 73-88 1 2 3 4 1 Appearance of the product at 20- Paste cream color. When stored 250C crystals are allowed to form 2 Specific Smell

3 Hydrogen index (pH) of an aqueous 11,О 11,5 solution with a mass fraction 1%, not more than 4 Mass fraction of alkyl sulfates, 13 12 %, not less than 5 Content Pres carboxymethyl cellulose ence 6 Optical content Pres bleach ence

7 Mass fraction of phosphates in 4 4,5 terms of P2O5, %,

Detergent paste "Talca" is easily dispersible in water, it has resistance in hard water, high washing capacity, is a biologically soft product, it is used as a detergent for processing cotton, linen and staple fabrics in textile enterprises, as well as for household needs: white washing and colored cotton and linen fabrics and articles made of them.

2.2 Manufacture of liquid detergents

There are different ways of creating a dryer, each of which has a variety of technologies. The following illustrations show the pictures that each uses. Let's consider about them more deeply.

Fig. 2.1 Scheme of production of shampoos

Fig. 2.2 The technological scheme for the production of liquid detergents is shown

Fig. 2.3 Technological scheme of preparing the active base of soap in a continuous way

Fig. 2.4 Technological scheme for obtaining toilet soap

Fig. 2.5 Technological scheme for obtaining lump synthetic detergents by the method of molding

Fig. 2.6 Technological scheme of obtaining lump synthetic detergents in the synthesis

Fig. 2.7 Scheme for the production of lump synthetic detergents by pressing

Fig. 2.8 Technological scheme for the preparation of powders by the periodic method of Kestner

From these, we get the 8th figure, and look at the SD in this scheme.The technological scheme for the production of liquid detergents is shown in Fig. 2.2

Fig. 2.2 The technological scheme for the production of liquid detergents is shown 24

bunkers of bulk raw materials; 2, 8 - weighing batchers; 3 - conveyor; 4 - reactor; 5, 10 - pumps; 6,11 - filters; 7 - consumable containers of liquid raw materials; 9 - reactor-mixer; 12- collector of liquid detergent

To prepare liquid detergents, an aqueous solution of pentasodium phosphate, pentacali phosphate, sodium hexametaphosphate is first prepared. Phosphates are dissolved at 70-80° C and stirred in an apparatus with a stirrer and a jacket. The phosphate solutions are filtered and cooled to 20-25 ° C. The bulk raw material from the raw silos 1 through the sluice gate is subsequently fed to the weighing hopper 2. By the conveyor 3, the free-flowing components are sent to the reactor 4 for the preparation of phosphate solutions or to the mixer reactor 9. The liquid components enter the mixer reactor from the consumable containers 7 through the weighing hoppers 8 After loading the liquid components, add the necessary amount of water that does not contain any hardness salts, heat the solution to 60-70°C, mix, and then through the dispenser 8, phosphate solutions or a conveyor 3 are fed s phosphates, hydrotropes, optical brightener. After obtaining a homogeneous transparent solution as a result of mixing, the heating is stopped and at 40 - 50°C a flavor is introduced with stirring. The resulting homogeneous solution from the mixer 9 through the filter 11 or the pump 10 is directed to the collector 12, where the synthetic detergent is supplied for packaging. Their quality is controlled by the turbidity temperature.

2.3 About sodium hexaphosphate

As we have seen, we are dealing with sodium hexaphosphate which is heated by 70-80 degrees with the help of this mathematical modeling process. Elemental composition of Na(PO3)6:

Atomic Mass Symbol Element Atoms weight percent

Na Sodium 22.98976928 1 4.6274 %

Sodium P 30.973762 6 37.4063 % hexametaphosphate

O Oxygen 15.9994 18 57.9663 %

Mass composition by element Na(PO3)6 (g/mol)

Fig. 2.9 Mass composition by element sodium hexaphosphate

2.4 An information about Glass-lined equipment

In order to heat this sodium phosphate, we heat it with the following tool called the Glass-lined equipment.

Fig. 2.10 Glass-lined equipment performance, installation, use and custody

1. Glass-lined performance (1) Glass-lined equipment is the high silicon content of the capital glaze sprayed on the surface of the metal tire, through about 900 high temperature roasting, the enamel close to the surface of the metal tire made.Therefore, it has the similar advantages of the chemical stability of glass and the strength of metal. (2) Glass-lined equipment is widely used in the reaction, evaporation, concentration, synthesis, polymerization, saponification, sulfonation, chemical reaction and so on in the industrial production and scientific research of chemical industry, medicine, dye, pesticide, organic synthesis, petroleum, food manufacturing and national defense industry, Chlorination, nitrification, etc., to replace stainless steel and non-ferrous metal equipment. (3) Corrosion resistance: For various concentrations of inorganic acids, organic acids, organic solvents and weak base and other media have a very strong corrosion resistance. But for the strong base, hydrofluoric acid and fluoride ion medium and the temperature is greater than 180, the concentration of more than 30% of the phosphoric acid does not apply.

(4) Impact resistance: resistance to mechanical impact indicators 220,10,3 J, the use of hard objects to avoid impact. (5) Insulation: Porcelain surface after 20KV high voltage test rigorous testing. (6) Temperature resistance: temperature rapid change, cold impact 110 , thermal shock 120

2. Glass-lined equipment installation (1) Handling: Only the ears of the cans are allowed to move when handling (when non-packing), rolling and crowbar are not allowed to avoid vibration and collision, and it is forbidden to take over the vulnerable parts such as pipe clamps and clamps. (2) Hoisting: Hoisting must be in place (such as jacket take over, cans, etc.) hanging wire rope. (The lid on the lifting ring hanging lid only for use), can not collide with any object, steady light hanging. (3) Pre-assembly inspection: Before assembly, inspectors should wear clean soft-soled shoes into the container inspection glass-lined layer no abnormalities. (4) Flange installation: Tighten the flange bolts, should be diagonally along the diagonal gradually tighten, forced to be uniform, should not be completely tightened at a time, due to uneven force caused by the glass-lined rupture and affect the service life . (5) Clamp installation: Should check the clip integrity, the number of compliance requirements, to ensure that from the installation of equal, tight and appropriate to ensure safe and reliable operation of the seal. (6) Stirrer installation: - First mixer into the tank (laying the bottom of the cushion), and then hang the can to the desired position, while the seal set into the mixing shaft, and then stirrer and reducer output shaft Connect and lock the anti- loose device. - Adjust the concentricity and verticality between the stirring shaft and the seal. After the requirements of the technical requirements are met, the stirring shaft will rotate slowly. When the operation is flexible and there is no abnormality, the motor should be reopened Button until normal operation (this time should not be too long). (7) The choice of liner: must be based on the type of media, concentration, temperature to choose the nature of the liner itself and the method of use should be applied to the process requirements, I currently supply the liner with asbestos rubber, rubber outsourcing Teflon For the user to choose. (8) Welding:

- It is strictly prohibited to apply welding on the outer wall of glass-lined tank. - Welding on the jacket pipe, cans, tank seat, the use of electric welding, and take cooling measures, absolutely not allowed to use gas welding. - In the vicinity of the glass-lined layer of welding, should be glass-lined surface, tank mouth, nozzle cover strict avoid welding slag splash, damage to glass- lined surface.

3. The use of glass-lined equipment (1) in use Note: - Prevent any metal hard objects fall into the container, bumps glass-lined. - Try to avoid cold tank heating material, hot pot plus cold material. - As a sudden change in temperature, the formation of internal stress, affecting the service life. - Operation operation In the use of jacket equipment, should be slowly pressurized, warming, the general first access 0,1 MPa (gauge pressure) pressure steam, hold for 15 minutes, and then slowly booster, warming (step-up speed to 10 minutes rise 0,1MPa pressure is appropriate), to the tank until the operating pressure, regardless of heating or cooling should be allowed within the temperature range, the temperature of our equipment 0 ~ 200 , 120 thermal shock, cold shock 110 . (2) The material: the material, such as the discharge valve, the discharge tube plug, all non-metallic tools gently poke open, not touch knock. (3) In use to prevent the jacket into the acid, to prevent the glass-lined metal hydrogen absorption reaction, causing glass-lined phosphate explosion. (4) Cleaning: When cleaning the interior of the can, metal utensils can not be used, and the materials bonded to the inside of the can must be cleaned promptly and thoroughly.

4. Glass-lined equipment custody: custody should be properly placed in the library should be placed in the outdoors, there should be rain measures to prevent rain, especially in cold areas, before the winter must be cleared tank, jacket, Water within the tube to avoid expansion due to icing, causing glass surface damage, in custody, should prevent hard objects from rubbing, impact, collision.

5. Performance: 1. Glass-lined corrosion resistance medium concentration% temperature ℃ performance medium concentration% temperature ℃ performance hydrochloric acid 5,20 boiling point excellent phosphoric acid 30,60 boiling point difference sulfuric acid 0,30 boiling point good phosphoric acid 80100 poor sulfuric acid 0,30180 bad hydrobromide Full concentration 100 good sulfuric acid 70,100240 good total acetic acid concentration 100 good nitric acid 5,50100 good lactate 0,30100 good nitric acid 5,50150 poor wet chlorine 100100 fine nitrate, fumes) acid

10070 good full acid oxalic acid concentration of 100 full chromic acid 100 good sodium hydroxide 2540 excellent phosphoric acid 10,60100 good sodium carbonate 1,2060 poor phosphoric acid boiling point good sodium carbonate 2540 excellent 2. Glass-lined equipment technical characteristics Maximum working pressure of the species Operating temperature ℃ Porcelain layer thickness, mm) glass layer High voltage test tank K, F-type reaction tank 1,00,6,20

Fig. 2.11 Glass-lined equipment performance, installation, use and custody

A - input B - place where to lay a thing C - spare place D - the place where the rays fall E - place producing evaporation F - the place from which flows back and forth G - spare place H - pressure indicator I - place measuring temperature J - mirror seat K - crowded place L - air-emitting location M - the place from which the dirty things are thrown out 30

N - place measuring temperatures with adapter O - place giving out things P - current control power Q - number controlling the current

2.5. Summary of second chapter

At this chapter is the need to apply accurate numerical simulation results with the ability to specify different parameters for determining the exact heating time of sodium hexaphosphate and for controlling the qualitative gain on the K5L-K50000L apparatus electric heating glass-lined.

III The temperature field of injection mold numerical simulation theory

3.1 Overview

In the filling and heating stage, in order to ensure the rapid and steady filling of the mold cavity, the internal temperature of the equipment must be within a suitable range. In this case, the melt has good flowability. In addition, Products to reach a certain temperature before pouring, in order to ensure that after pouring mechanical properties of products, the apparent quality is better, the device cavity must also be in a more suitable temperature range. It can be seen that the temperature of the equipment is the key factor that affects the heating quality and the Sodium hexametaphosphate production efficiency of the product. How to accurately predict the temperature distribution of the equipment and control it effectively has been a topic widely studied in recent years. Computer simulation of the internal temperature field of Sodium hexametaphosphate equipment is an important part of Sodium hexametaphosphate- based CAE. The transient temperature field analysis of Sodium hexametaphosphate mold is through the establishment of theoretical model of heat transfer in the process of Sodium hexametaphosphate heating and the simulation technology of visualizing the temperature distribution of the equipment by using computer graphics theory. The basic theory is heat transfer and finite element theory. At present, many studies consider the temperature field of the equipment as a steady-state heat transfer process, or simplified as a typical two-dimensional cross-section mathematical model for solving. However, in fact the temperature field of the device changes with time and is not stable, and the use of two-dimensional simplified model does not truly reflect the temperature changes in all directions of the device. Therefore, this chapter for the Sodium hexametaphosphate equipment to establish three- dimensional transient temperature field numerical solution model is in line with the actual conditions. In order to understand the rule of temperature variation of the internal parts of Sodium hexametaphosphate mold, the basic theoretical model of the heat transfer process needs to be studied.

3.2 Injection mold temperature field on the molding process

(1) molding cycle During the entire heating cycle, the product pouring time is usually much longer than the equipment opening and closing, filling, heating time, accounting for about 80% to 85% of them. It can be seen that reducing the product pouring time is the key to shorten the heat cycle, and the equipment temperature is the main factor affecting the pouring time. If the temperature of the equipment is properly controlled, the Sodium hexametaphosphate melt can be cured in time and the mold can be

32 pushed out to shorten the heating cycle. On the contrary, the melt pouring solidification becomes slow, the temperature of the equipment can not drop in a short time, and a longer pouring is needed Time to extend the fever cycle. Engineering production, a reasonable temperature control equipment can effectively reduce the heat cycle products and improve production efficiency. (2) product stress The existence of internal stress is not only one of the main causes of warpage and cracking during the use of the product, but also an important factor affecting the mechanical properties and apparent quality of the product. Thermal stress is a major part of the product stress, which is mainly due to poor equipment pouring system designed to lead to uneven product pouring, so the temperature of the product has a great impact on the stress within the product. (3) warpage of products Warpage is mainly due to uneven product shrinkage, which is one of the common defects of products. Project usually from the equipment structure and temperature, product materials and heating process parameters and many other aspects to eliminate warpage, which to improve the uniformity of temperature distribution equipment is most effective. Since the melt of Sodium hexametaphosphate is in direct contact with the cavity surface during the heating process, if the temperature of the equipment tends to be evenly distributed, the pouring and shrinking effects of the melt at various locations are basically the same, and the products after the heat generation can also avoid the defect. Can be seen that if the actual production of the heating device can effectively control the temperature distribution within the law, you can greatly improve the quality of products and heat to shorten the Sodium hexametaphosphate cycle and improve production efficiency. Since the internal temperature field during the heating process is a transient process, the transient temperature field needs to be numerically simulated. In this chapter, the distribution of internal temperature field is mainly studied theoretically.

3.3 Heat transfer theory basis

According to the second law of thermodynamics, heat transfer is a discipline that studies the law of heat energy transfer caused by temperature difference. It can be seen from the second law of thermodynamics that where there is a temperature difference, the heat will spontaneously pass from a higher temperature object to a lower temperature object or from The higher temperature part of the object is transferred to the lower temperature part. Heat transfer is an extremely common physical phenomenon in nature and various engineering fields. Any heat transfer must follow the first law of thermodynamics. If a system is in an environment with no mass inflows or outflows, the heat in it certainly satisfies the equation:

Q − W=ΔU+ΔKE+ΔPE (3.1)

Where: Q - heat; W - work; ΔU - the amount of change in the system energy; ΔK E-system kinetic energy changes; ΔP E-system potential energy changes. For most of the engineering heat transfer problems, the kinetic energy and potential energy of the system are zero, that is: ΔK E = ΔPE = 0; and usually consider no work, W = 0, namely: Q = ΔU. Usually the system heat transfer process can be summarized as the following two types: steady-state heat transfer process, refers to the heat flow into the object, the object itself generates heat equal to the heat generated by the object q q q 0 in+ in− out= ; Transient heat transfer process, The role of external objects, heat and heat transfer or cooling process of the casting effect. Engineering heat transfer problems are generally divided into the following three basic ways: (1) Heat conduction: When there is a temperature difference between different objects or between different parts of the same object, the heat is always transferred from a temperature-increasing object or part to a lower-temperature object or part. Any phase of the material (gas, liquid, solid) will occur heat conduction phenomenon, it is the inherent nature of the material. Heat conduction to meet the Fourier law, available equation (3.2) Description:

푑푇 푞= ˗ 휆 (3.2) 푑푥

Where: 푞 represents the heat flux delivered to a specified area per unit time, that is, the heat flux density; λ is the thermal conductivity of the object; and the negative sign indicates that the heat flux is transmitted in the opposite direction to the temperature increase. (2) Thermal Convection: When a solid is in a fluid (gas or liquid), the process of heat transfer between the two is called convection because of the temperature difference between the solid surface and the fluid. The general heat convection occurs with the heat conduction, it can not exist in an independent form. As to the cause of heat flow, convection heat transfer can be divided into natural convection heat transfer and forced convection heat transfer. Heat convection can be calculated using Newton's cooling formula as follows:

푞 = ℎ(푇푤 − 푇푓) (3.3)

Where: h is the convective heat transfer coefficient between the object surface and the fluid; Tw and Tf are the wall temperature and the fluid temperature, respectively. (3) Thermal Radiation: A heat exchange process in which a substance spontaneously emits energy in the form of electromagnetic waves at high temperature and is absorbed by other surrounding materials and converted into heat. The characteristics of heat radiation are significantly different from those of heat conduction and heat convection. Heat conduction and convection heat transfer occur only in the presence of material. Heat radiation does not require any medium. In fact, the transfer efficiency is the highest in vacuum. Thermal radiation meets the Stephen-Boltzmann law and can be expressed as:

4 4 푞 = 휀𝜎퐴1퐹12(푇1 − 푇2 ) (3.4)

Where ε is the emissivity, σ is the Boltzmann constant, A1 is the area of the radiating surface 1, F12 is the shape factor of the radiating surface 1 to the radiating surface 2, T1 and T2 are the absolute temperatures of the radiating surfaces 1 and 2, respectively . From Eq. (2-4), it can be seen that if the analysis of the temperature field in the project contains thermal radiation, it is a highly nonlinear problem.

3.4 Injection mold temperature field mathematical model

Temperature field is the temperature of the objects in various parts of the temperature at each moment of the set, also known as the temperature distribution. Generally can be divided into steady-state temperature field and transient temperature field two categories. The steady-state temperature field indicates that the temperature distribution of each point in the thermal-conducting object does not change with time but only relates to the space coordinate. The transient temperature field indicates that the temperature and the heat flux in the object all change with time during the course of the thermal conduction process of. Since the temperature of the Sodium hexametaphosphate heating device varies with the Sodium hexametaphosphate time in actual work, the temperature distribution in different heating phases is different. The temperature field belongs to the transient temperature field and can be expressed as a function of the space coordinate and time

T=f(x,y,z,t) (3.5)

Where: T - mold temperature; x, y, z-space rectangular coordinates; t-time coordinates.

3.4.1 Basic assumptions

High-temperature Sodium hexametaphosphate melt into the cavity from the gate, the fever, pouring to the pouring temperature. The heat transfer involved mainly consists of five parts: melt and equipment cavity, different parts of melt, external surface of equipment and surrounding environment, pouring channel wall of equipment and pouring medium, and heat exchange between different parts inside the equipment. Thus, the phenomenon of heat transfer in the Sodium hexametaphosphate process is very complicated, before the establishment of its mathematical model, the introduction of reasonable assumptions and simplifications are as follows: (1) Equipment materials are uniform continuous and isotropic materials, the physical properties of materials as a constant parameter, ignoring its changes over time; (2) Equipment materials are uniform continuous and isotropic materials, the physical properties of materials as a constant parameter, ignoring its changes over time; (3) considering the temperature at the beginning of each Sodium hexametaphosphate phase as known, the temperature at the beginning of each Sodium hexametaphosphate phase can be obtained by reading the temperature analysis result at the end of the previous phase; (4) Ignoring the change of temperature around the equipment over time, assuming that there is only convection heat transfer between the equipment and the surrounding environment, regardless of radiation heat transfer, the heat transfer coefficient between the two as a constant value; (5) pouring water in the device to maintain a constant flow rate, and ignore the temperature changes over time, about pouring water and equipment pouring flow channel wall heat transfer coefficient as a constant.

3.4.2 Differential thermal equation

In order to know the regularity of the temperature inside the Sodium hexametaphosphate mold with time and space, the mathematical expression of the temperature field of the equipment is obtained. The differential equations of heat conduction need to be established according to the law of conservation of energy and Fourier's law. Based on the above assumptions, the process of heat transfer inside the device can be simplified to a three-dimensional transient heat transfer problem with an internal heat source during the heating of Sodium hexametaphosphate.

In this graduation paper, I consider the options for measuring the Navier- Stokes equation, which occurs in different ways. Consider the dimensioning with the original standard substitutions. The Navier-Stokes system of equations:

ui = 0 (3.6) xi

 upuuii1   effu j +u j = − + + (3.7) t  x  x  x  x  x j i j j i

TTuT   +j = + t  (3.8) t  xj  x jPr t  x j

Y uY  Y +ji =D + ti i (3.9) t  xj  x j Sc t  x j

kkuk   +j = +t +GGY + −  −  k b m (3.10) t  xj  x j k  x j

u      2 +j = +t +CGCGC + −  1( kb 3 ) 2  (3.11) t  xj  x j  x j k k

eff =  + t (3.12)

k 2 t = C (3.13) 

2 GSkt=  (3.14)

t T Ggbi=  (3.15) Prtix

t Prtt== 0.85, Sc (3.16) k

푆 = √2푆푖푗푆푖푗 (3.17)

1 휕푢푗 휕푢푗 푆푖푗 = ( + ) (3.18) 2 휕푥푖 휕푥푖

Where C is the constant with the value 0.09,  is the density, k is the kinetic energy of turbulence, xi is the coordinate in the i direction, ui is the velocity component in the direction, Yi is the concentration of the substance i , Di is the diffusion coefficient of the substance , T is the temperature,  - turbulent viscosity, k ==1, 1.3 - turbulent Prandtl number for k and ε corresponding, Gk - generation of the kinetic energy of turbulence due to medium velocity gradients, S - modulus of the average tensor of stresses, Gb - generation of the kinetic energy of turbulence due to buoyancy, YM - influence of fluctuating dilatation in obschuyu skorost dissipation, the k - turbulent kinetic energy, e - skorost turbulentnoy dissipation of C1 ,C2 and C3 - konstanty values kotoryh Po umolchaniyu: 1.44, 1.92 and 1.0. Under the Cartesian coordinate system, the thermal differential equation of the transient temperature field of the Sodium hexametaphosphate module can be expressed as:

휕 휕푇 휕 휕푇 휕 휕푇 휕푇 (휆 )+ (휆 )+ (휆 )+푞 =  퐶 ⩝ (푥, 푦, 푧)휖Ω (3.19) 휕푥 푥 휕푥 휕푦 푦 휕푦 휕푧 푧 휕푧 푉 푝 휕푡

Where: 푘푔 - Equipment material density ; 푚3

CP - Specific heat capacity of equipment materials (J / (kg • K)); 휆푋휆푌휆푍 - the thermal conductivity (W / (m • K)) of the equipment material along the x, y, and z directions, respectively; q = q x, y.z.t v ( ) 푤 푞 = 푞(푥, 푦, 푧, 푡)- the equipment cavity wall heat density ; 휈 푚3 According to the basic assumption (1), the equipment material is isotropic, then:

휆푋 = 휆푌 = 휆푍 = 휆 (3.20)

Due to the filling during the pyrogenic heating, the phosphorous melt is continuously injected during the pyromanic stage, ie, the heat transfer in these two phases has an internal heat source, and the injection of melt into the device cavity is stopped during the pouring phase. Therefore, there is no pour phase The heat transfer process within the heat source. By substituting (3.20) into (3.19), we can get the thermal differential equation of the transient temperature field of the Sodium hexametaphosphate equipment in filling and heating stage:

휕2 푇 휕2푇 휕2푇 휕푇 λ( + + )+푞 = 𝜌퐶 (3.21) 휕푥2 휕푦2 휕푧2 푉 푃 휕푡

q The above equation removes v items and obtains the differential thermal conductivity equation of the transient temperature field of Sodium hexametaphosphate equipment during the pouring stage

휕2 푇 휕2푇 휕2푇 휕푇 λ( + + ) = 𝜌퐶 (3.22) 휕푥2 휕푦2 휕푧2 푃 휕푡

3.4.3 Defined conditions

The solution conditions of the differential thermal conductivity equation include the initial conditions and the boundary conditions. The solution conditions of the transient temperature field of the Sodium hexametaphosphate equipment are described as follows:

Initial conditions:

푇(푥, 푦, 푧, 푡0)=푇0(푥, 푦, 푧) (3.23)

The boundary conditions can usually be summarized into the following three categories:

푇(푥, 푦, 푧, 푡)=푇̅(푥, 푦, 푧) (3.24)

휕푇 휕푇 휕푇 λ( 푛휔̅ + 푛휔̅ + 푛휔̅ ) = 푞 (3.25) 휕푥 푥 휕푦 푦 휕푧 푧

휕푇 휕푇 휕푇 λ( 푛휔̅ + 푛휔̅ + 푛휔̅ ) = ℎ(푇 − 푇) (3.26) 휕푥 푥 휕푦 푦 휕푧 푧 푤

Where: 푇̅ = 푇̅(Г1, 푡) - given temperature at Г1 the boundary (K); 39

휔̅ 휔̅ 휔̅ 푛푥 , 푛푦 , 푛푧 - the direction cosine of the normal outside the boundary;

3 ℎ = ℎ(Г3, 푡) - The heat transfer coefficient at the boundary; 푇푤 = 푇푤(Г, 푡) - In the case of forced convection heat transfer, 푇푤 is the boundary layer of the adiabatic wall temperature; In the case of natural convection heat exchange, 푇푤 is the ambient temperature. Among them, Г = Г1 + Г2 + Г3 is the total boundary of the Ω domain.

3.4.3.1 Initial conditions

The heating process of Sodium hexametaphosphate equipment includes filling, heating and pouring three main stages, the initial conditions of different stages are usually different, the specific description is as follows: (1) filling stage Usually Sodium hexametaphosphate equipment in the filling before the start of the need to preheat to a certain operating temperature, so that Sodium hexametaphosphate can be effectively reduced due to equipment temperature changes caused by the impact of thermal stress on the performance of the device, but also contribute to the rapid heating of products and Improve the quality of heat。 The initial time of filling equipment using a uniform preheat temperature The initial time of filling equipment using a uniform preheat temperature The initial time of T filling equipment using a uniform preheat temperature 0 , then:

푇(푥, 푦, 푧, 0) = 푇0(푥, 푦, 푧) (3.27)

(2) fever stage According to the basic assumption (3), the initial temperature of the equipment heating stage can be obtained by extracting the temperature field at the t end of the filling stage. If the filling time is 1 , the initial temperature of the equipment heating stage is:

푇(푥, 푦, 푧, 0) = 푇푡1(푥, 푦, 푧) (3.28)

(3) pour stage The initial temperature of the equipment pouring stage can also be obtained by extracting the equipment temperature field at the end of the heating stage. t Supposing the heating time is 2 , the initial temperature of the equipment pouring stage is:

푇(푥, 푦, 푧, 0) = 푇푡1+푡2(푥, 푦, 푧) (3.29)

3.4.3.2 Boundary conditions

Phosphorous equipment usually includes the following three types of boundary conditions: (1) equipment cavity wall In the filling and heating stage, the Sodium hexametaphosphate heating device continuously injects the high temperature Sodium hexametaphosphate melt into the cavity, and the heat is transferred from the high temperature Sodium hexametaphosphate melt to the low temperature device cavity, and the second type boundary condition is satisfied on the cavity wall of the equipment:

휕푇 휕푇 휕푇 λ( 푛휔̅ + 푛휔̅ + 푛휔̅ ) = 푞(푥, 푦, 푧, 푡) (3.30) 휕푥 푥 휕푦 푦 휕푧 푧

Where: 푞(푥, 푦, 푧, 푡) represents the instantaneous heat flux through the cavity wall; 푆1 is the boundary of the equipment cavity wall. (2) The outer surface of the equipment The equipment is usually placed in a room at normal temperature. According to the basic assumption (4), only the natural convection heat transfer between the template and the air is considered in the heat exchange process on the outer surface of the equipment to meet the third type of boundary conditions:

휕푇 휕푇 휕푇 λ( 푛휔̅ + 푛휔̅ + 푛휔̅ ) = ℎ (푇 − 푇) (3.31) 휕푥 푥 휕푦 푦 휕푧 푧 푎푖푟 푎푖푟

Where: ℎ푎푖푟 represents the convection heat transfer coefficient between the outer surface of the equipment and the air; 푇푎푖푟 is the temperature of the surrounding air medium. (3) pouring flow channel wall In the process of Sodium hexametaphosphate heating, the large amount of heat released by the Sodium hexametaphosphate melt is transferred to the equipment, which causes the mold temperature to rise. In order to make the temperature distribution around the cavity of the equipment uniform, pouring water is usually continuously poured in the pouring runner, Meet the third type of boundary conditions, then:

휕푇 휕푇 휕푇 λ( 푛휔̅ + 푛휔̅ + 푛휔̅ ) = ℎ (푇 − 푇) (3.32) 휕푥 푥 휕푦 푦 휕푧 푧 푐푤 푐푤

Where: 푇푐푤 is the pouring water temperature, usually maintained at 5 ~ 20 ℃ range; ℎ푐푤 for the flow channel wall and poured water forced convection heat transfer coefficient can usually be obtained according to equation (3.33):

휆 ℎ = 0.023 푐푤 푅푒0.8푃푟0.4 (3.33) 푐푤 퐷 퐷

Where: D is the diameter of the pouring water hole; 휆푐푤 is the thermal conductivity of the pouring water; Reynolds number 푅푒퐷 = 𝜌푐푤휈푐푤퐷/퐷휇푐푤, where 𝜌푐푤, 휈푐푤, 휇푐푤 are the pouring water density, flow rate and dynamic viscosity; 휈푐푤 휇푐푤퐶푐푤 Prandtl number 푃푟 = = , where 퐶푐푤, 휈푐푤, 휆푐푤 were pouring water 훼푐푤 휆푐푤 Isobaric heat capacity, kinematic viscosity and thermal diffusivity.

3.5 Sodium hexametaphosphate heating device temperature field finite element method to solve

The function of the transient temperature field is a function of the spatial and temporal domains, but it is not coupled within the two domains. This section for the three-dimensional transient temperature field of Sodium hexametaphosphate equipment solves the problem of using partial discrete finite element method, the first finite-element space domain discretization, and then calculate the temperature of the element interpolation, the transient thermal conductivity of the temperature calculation is discrete as In the space domain, a finite number of node temperature ordinary differential equations are calculated. Then the finite difference time- domain discretization can be used to calculate the temperature at each moment in the object.

3.5.1 Spatial domain dispersion

Finite element meshes are used in the space domain Ω to discretize into a finite number of elements. The temperature in the element is approximated by the interpolation function with the node temperature in this element. In this case, the temperature of the node is a continuous function in time domain, that is:

̅ 푛푒 T= 푇 = ∑푖=1 푁푖 (푥, 푦, 푧) ∙ 푇푖(푡) (3.34)

Available in matrix form:

푇 = 푁 ∙ 푇푒 (3.35)

Where: 푛푒 is the number of nodes in each cell; N is a matrix of function cells; 푇푒 is the node temperature vector of each cell. Since T is an approximate function of temperature, it is substituted into the differential thermal conductivity equation (3.35) and the boundary condition equation (3.35) to produce the margin:

휕2푇 휕2푇 휕2푇 휕푇 푅 =λ( + + )+ 푞 − 𝜌퐶 (3.36) 훺 휕푥2 휕푦2 휕푧2 푉 푃 휕푡

휕푇 휕푇 휕푇 푅 =λ( 푛휔̅ + 푛휔̅ + 푛휔̅ ) − 푞 (3.37) Г2 휕푥 푥 휕푦 푦 휕푧 푧

휕푇 휕푇 휕푇 푅 = λ ( 푛휔̅ + 푛휔̅ + 푛휔̅ ) − ℎ(푇 − 푇) (3.38) Г3 휕푥 푥 휕푦 푦 휕푧 푧 푤

The Galerkin weighted residual method is used to establish the finite element solution equation so that the weighted integral of each margin is zero. Then the Sodium hexametaphosphate heating equipment in filling, heating stage corresponding finite element format as follows:

∫ 푅훺 ∙ 휔1푑훺 + ∫ 푅Г2 ∙ 휔2푑Г + ∫ 푅Г3 ∙ 휔3푑Г = 0 (3.39)

훺 Г2 Г3

Where: 휔1, 휔2, 휔3 for the weight function, take ωj =Nj (j=1,2,3,...,n), where n is the discrete Ω domain obtained the total number of all nodes, but without losing the general choice of the border:

−휔1 = 휔2 = 휔3 = −푁푗 (푗 = 1,2,3 … . . , 푛) (3.40)

Since 푇1 satisfies the compulsory boundary conditions, it will not generate a margin on the Г1 boundary, so that 휔1 can be zero at the Г1 boundary. Substituting Eqs. (2.36), (2.39), (2.41) into Eqs. (2.40) available: (2.40)

2 2 2 휕 푇 휕 푇 휕 푇 휕푇 휕푇 휔̅ 휕푇 휔̅ ∫ [휆 ( + + ) + 푞푣 − 𝜌퐶휌 ] ∙ 푁푗푑훺 − ∫ [λ ( 푛푥 + 푛푦 + 훺 휕푥2 휕푦2 휕푧2 휕푡 г2 휕푥 휕푦 휕푇 휔̅ 휕푇 휔̅ 휕푇 휔̅ 휕푇 휔̅ 푛푧 ) − 푞] ∙ 푁푗푑Г − ∫ [λ ( 푛푥 + 푛푦 + 푛푧 ) − ℎ(푇푤 − 푇)] ∙ 푁푗푑Г = 0 휕푧 г3 휕푥 휕푦 휕푧 (3.41)

The formula (3.38) for the part of integration, simplified can be written as a matrix as follows: (3.39)

휕푁 휕푁 휕푁 휕푁 휕푁 휕푁 ∑ ∫ 휆[( )푇 ∙ + ( )푇 ∙ + ( )푇 ∙ ] 푇푒푑훺 휕푥 휕푥 휕푦 휕푦 휕푧 휕푧 푒 훺푒

푇 − ∑ ∫ 푁 푞푣푑훺 푒 훺푒

푇 휕푇푒 + ∑ ∫ 푁 𝜌퐶휌푁 푑훺 푒 휕푡 푒 훺

푇 푇 푒 푇 − ∑ ∫ 푁 푞푑Г + ∑ ∫ ℎ푁 푁푇 푑Г − ∑ ∫ 푁 ℎ 푇푤푑Г = 0 푒 푒 푒 푒 푒 푒 Г2 Г3 Г3 (3.42)

Written as a general finite element format as follows:

휕푇 [C]{ }+[K]{T}={P} (3.43) 휕푡

Where: ∑ 푒 [C] - Heat capacity matrix, 퐶푖푗 = 푒 퐶푖푗 and 퐶푖푗 = 𝜌퐶휌 ∫훺푒 푁푖푁푗푑훺 and 푇 {T} - the temperature array of nodes, {T}=[푇1푇2 … 푇푛] 푒 푒 [K] - Heat conduction matrix, 퐾푖푗 = ∑푒 휆푖푗 + ∑푒 퐻푖푗 푒 where: 퐻푖푗 = ∫ 푒 ℎ푁푖푁푗푑Г Г3

휕푁 휕푁 휕푁 휕푁 휕푁 휕푁 휆푒 = ∫ 휆 ( 푖 ∙ 푗 + 푖 ∙ 푗 + 푖 ∙ 푗) 푑훺 (3.44) 푖푗 훺푒 휕푥 휕푥 휕푦 휕푦 휕푦 휕푦

푒 푒 푒 {P} - Temperature Load Array, 푃푖 = ∑푒 푃푞푣푖 + ∑푒 푃푞푖 + ∑푒 푃퐻푖, 푒 푃푞푣푖 = ∫훺푒 푞푣푁푖푑훺 (3.45)

푒 푒 푃푞푖 = ∫ 푒 푞푁푖푑Г , 푃퐻푖 = ∫ 푒 ℎ푇푤푁푖푑Г (3.46) Г2 Г3

As a method of solution, the Pressure-BasedSolver method. Main characteristics of the method: • In Pressure-BasedSolver, each equation is solved on a case-by-case basis. • The equation of continuity takes the form of the equation of pressure correction, as part of the SIMPLE Patankar algorithm. • Factors of relaxation in the discretized equations are included. 44

• To improve stability, an iterative process is included. • The relaxation coefficient, α, changes from one iteration to the next:

Fig. 3.1 - Pressure-Based Solver algorithm

Algorithm SIMPLE is the most widely used numerical method of the Navier- Stokes equations system. SIMPLE is an abbreviation, Semi- ImplicitMethodforPressureLinkedEquations, a half-implicit method for equations with a relation to pressure. Algorithm SIMPLE was first developed by Brian Spolding and his student Sukhas Patankar in the early 1970s. At that time they worked at the Imperial College of London. Since then, this algorithm has been used in many problems to solve various problems of hydrosynamics and heat transfer, served as a basis for the further development of a whole class of numerical methods. In our problem we use several equations. The solution applies Standard, PRESTO, Linear, SecondOrder, the interpolation scheme of the pressure equation. So far, the temperature calculation of the transient heat conduction problem has been discretized as an ordinary differential of n node temperatures in the space domain сalculate the problem. Equation (3-28) is the same in form as the governing equations for the cell, where the heat capacity matrix [C] and the heat transfer moment аrray [K] are n-order square matrix. If the cell is denser, the more nodes are 45 generated, the larger n is and the corresponding heat capacity matrix and the higher the order of the heat conduction matrix, the larger the required computer storage space, the longer the solution time will of course be. If the temperature field in the space domain is a steady-state heat conduction problem, then the heat capacity matrix is a zero matrix. This problem belongs to the problem of mathematical boundary value calculation and is relatively easy to solve. However, for solving the heat conduction differential equation of transient heat conduction problems, only the boundary conditions are obviously not enough, and the initial conditions need to be given, and the time domain should be discretized.

3.5.2 Discretization of the time domain

The temperature vector T, which is obtained by discrete spatial domain, is a function of time and is an unknown quantity. Need to deal with discretely the time domain, namely divide the time into a plurality of time units, T (t) in each unit can be expressed as:

푇(푡) = 푇̅(푡) = ∑ 푁푖(푡) ∙ 푇푖 (3.47)

Wherein, 푇푖 is a set of temperature node values corresponding to T (t) at time i; and interpolation function 푁푖(푡) is a scalar function. Differentiate the finite difference of time and use differential instead of differential to eliminate the differential term in (2.28). Based on the simple and flexible character of single-step method, the basic equation of transient temperature field calculated by single-step method under different difference schemes is as follows:

퐶푛+훼 퐶푛+훼 [ − 훼퐾푛+훼]{푇푛+훼}-[ -(1-α) 퐾푛+훼]{푇푛}={푃푛+훼} (3.48) ∆푡푛 ∆푡푛

In the type: The time step length α can take the value between 0 ~ 1. When α = 0, for the forward difference; when α = 0.5, for Crank-Nicolson method difference 2  = (center difference); Galerkin method difference when 3 , backward difference when α = 1. Select a certain time step α, combined with the specific temperature field initial value and the boundary conditions, after the above formula can calculate the temperature distribution of the moment.

3.6 Summary of third chapter

This chapter firstly introduces the influence of the temperature field of Sodium hexametaphosphate equipment on the heating process of products and expounds the necessity of numerical simulation of transient temperature field of

Sodium hexametaphosphate equipment during the heating process. Aiming at the heat transfer problem of typical phosphor molds in the heating process, based on the reasonable assumptions and simplifications, the three-dimensional transient thermal differential equations of the temperature field are deduced based on the theory of heat transfer. Then, based on the boundary conditions and the initial Conditions, established a mathematical model of transient temperature field in the three main stages of filling, heating and pouring of Sodium hexametaphosphate mold. Finally, the finite element method and the finite difference method were used to solve the heat transfer model of the equipment. The temperature distribution of the equipment at different Sodium hexametaphosphate moments was calculated. Through the research in this paper, the theoretical foundation for the transient temperature field simulation of typical P equipment is established for the next chapter by using ANSYS.

IV OF THE SODIUM HEXAMETAPHOSPHATE HEATING PROCESS TEMPERATURE FIELD AND THERMAL STRESS FIELD

4.1 Overview

In the process of Sodium hexametaphosphate heating, the high-temperature Sodium hexametaphosphate melt flows into the lower-temperature equipment cavity rapidly through the pouring system. The temperature distribution in the equipment is very complicated and the temperature distribution law is different in different Sodium hexametaphosphate phases. The temperature structure of the whole equipment structure is usually unbalanced distribution. When the temperature distribution of the equipment is not uniform, the temperature distribution of the Sodium hexametaphosphate melt directly after curing in the cavity of the equipment is not uniform, resulting in the phenomenon of uneven shrinkage of the product and internal stress. After the pouring, the Sodium hexametaphosphate products are prone to cracking and warpage and other defects, seriously affecting the quality of products fever. Obviously, if the project can be informed of the temperature distribution of the internal parts of the Sodium hexametaphosphate equipment, not only can improve the quality of heating products, but also for the pouring system to provide theoretical support for the optimal design, so Sodium hexametaphosphate equipment, Sodium hexametaphosphate heating process transient temperature field analysis It has important research significance and practical value. Usually CAE analysis of the temperature field of Sodium hexametaphosphate heating process at home and abroad mostly uses special mold flow analysis software, mainly for simulation of product heating, but the research on temperature field analysis of Sodium hexametaphosphate heating equipment is still rare. This chapter mainly analyzes the temperature distribution law of the typical heating equipment during the heating process by using ANSYS software, and focuses on the temperature-induced thermal stress and free thermal deformation during the heating stage, and obtains the most dangerous equipment in the heating process. The thermal-structural coupling analysis for the next chapter provides the corresponding temperature field results.

4.2. Results in 100s

Fig. 4.1 The geometry drawn in Ansys

Fig. 4.2 The mesh drawn in Ansys

4.2. Results in 100s

Fig. 4.3 At 100s scaled residuals

Fig. 4.4 At 100s contours-temperature

Fig. 4.5 At 100s contours-velocity of Velocity Magnitude

Fig. 4.6 At 100s contours-velocity of Vorticity Magnitude

Fig. 4.7 At 100s Vectors-Temperature

Fig. 4.8 At 100s Vectors- velocity of Velocity Magnitude

4.3. Results in 150s

Fig. 4.9 At 150s Scaled Residuals

Fig. 4.10 At 150s Contours of temperature

Fig. 4.11 At 150s Velocity – Velocity Magnitude

Fig. 4.12 At 150s Velocity – Vorticity Magnitude

Fig. 4.13 At 150s Velocity – Temperature

Fig. 4.14 At 150 Velocity – Velocity

4.4. Results in 200s

Fig. 4.15 At 200s Scaled Residuals

Fig. 4.16 At 200s Temperature

Fig. 4.17 At 200s Velocity – Velocity Magnitude

Fig. 4.18 At 200s Velocity – Vorticity Magnitude

Fig. 4.19 At 200s Vector – Vorticity Magnitude

Fig. 4.20 At 200s Vector – Temperature

4.5. Results in 250s

Fig. 4.21 At 250s Scaled Residuals

Fig. 4.22 At 250s Temperature

Fig. 4.23 At 200s Velocity– Velocity Magnitude

Fig. 4.24 At 250s Velocity- Vorticity Magnitude

Fig. 4.25 At 250s Velocity- Temperature

Fig. 4.26 At 250s Vector - Velocity Magnitude

4.6. Summary of fourth chapter

Synthetic detergent consumption and are used in everyday human activities. The requirements in the conditions of market economy, and the demand is increasing daily. Calculation of the mathematical model of the sodium hexafluorphate heated device. This task is solved by using the equations of Navier-Stocks. The ANSYS FLUENT 16.2 has been used to solve the main task of the dissertation In this device, we detected sodium hexafosfate heating time and checked for 100s, 150s, 200s, 250s. During this time, the sodium hexafosfat in the appliance has been checked completely.

CОNCLUSIОN

This dissertation work is devoted to the development of mathematical modeling of sodium hexafosfate in synthetic detergents. Synthetic detergent consumption and are used in everyday human activities. The requirements in the conditions of market economy, and the demand is increasing daily. The dissertation work has achieved the following results: 1) Calculation of the mathematical model of the sodium hexafluorphate heated device. This task is solved by using the equations of Navier-Stocks. The ANSYS FLUENT 16.2 has been used to solve the main task of the dissertation 2) Different times of sodium hexafluorphate have been examined by heating in the instrument, observe the difference in heating at any given time. 3) When heating sodium hexafosfat, consider the heat conductor, heat exchange, volume growth coefficient and other factors. 4) In this device, we detected sodium hexafosfate heating time and checked for 100s, 150s, 200s, 250s. During this time, the sodium hexafosfat in the appliance has been checked completely. If I make a conclusion on this data, 200% of production places will be completely heated to sodium hexafosfate, and after 200s, you can stop the process. In this article we use sodium hexafosfat sodium as a synthetic detergent. And the heating of the sodium hexafosfate in the electric heat-insulating glass is considered to be a mathematical model that will make it hot for some time. The calculations show that the sodium hexafluorphate is completely 100s between 150s and 200s and can be heated up to 200s. That is why sodium hexafluorphate 200s is reached during production.

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