1.Basic equations of dynamics

The following approaches to the development of mathematical models of technological objects can be distinguished: theoretical (analytical), experimental-statistical, methods for constructing fuzzy models and combined methods. Let's explain these methods.

Analytical methods the methods of deriving the equations of statics and dynamics on the basis of a theoretical analysis of the physical and chemical processes occurring in the object under study, as well as on the basis of the specified design parameters of the equipment and the characteristics of the processed substances, are usually called methods of deriving the equations of statics and dynamics. When deriving these equations, the fundamental laws of conservation of matter and energy, as well as the kinetic laws of the processes of mass and heat transfer, chemical transformations are used.

To compile mathematical models based on theoretical approach no experiments are required on the object; therefore, such methods are suitable for finding the static and dynamic characteristics of newly designed objects, the processes of which are well studied. The disadvantages of such methods for compiling models include the difficulty of obtaining and solving a system of equations for sufficiently full description object.

Deterministic models of oil refining processes are developed on the basis of theoretical ideas about the structure of the described system and the laws of functioning of its individual subsystems, i.e. based theoretical methods. Having even the most extensive experimental data on the system, it is impossible to describe its operation by means of a deterministic model, if this information is not generalized and their formalization is not given, i.e. are presented in the form of a closed system of mathematical dependencies that reflect the mechanism of the processes under study with varying degrees of certainty. In this case, the available experimental data should be used to build a statistical model of the system.

The stages of development of a deterministic model are shown in Fig. four.

Formulation of the problem

Formulation of the mathematical model

Selected analytical method?

Choice of calculation parameters

body process

Experimental

Solution of control problems definition

model constants

Not

Control experiments Adequacy check Correction

rimenty on nature model model

Nom object Yes

Optimization Process optimization with target definition

model using the function model and constraint

Process control with Management model

model

Fig.4. Stages of development of a deterministic model

Despite significant differences in the content of specific tasks of modeling various oil refining processes, building a model includes a certain sequence of interrelated stages, the implementation of which allows you to successfully overcome the difficulties that arise.

The first stage of the work is the task statement (block 1), including the formulation of the task based on the analysis of the initial data on the system and its knowledge, assessment of the resources allocated for building the model (personnel, finance, technical means, time, etc.) in comparison with the expected scientific, technical and socio-economic effect.

The statement of the problem ends with the establishment of the class of the developed model and the corresponding requirements for its accuracy and sensitivity, speed, operating conditions, subsequent adjustment, etc.

The next stage of work (block 2) is the formulation of the model based on understanding the essence of the described process, divided in the interests of its formalization into elementary components of the phenomenon (heat transfer, hydrodynamics, chemical reactions, phase transformations, etc.) and, according to the accepted degree of detail, into aggregates (macro level), zones, blocks (micro level), cells. At the same time, it becomes clear what phenomena it is necessary or inappropriate to neglect, to what extent it is necessary to take into account the interconnection of the phenomena under consideration. Each of the selected phenomena is associated with a certain physical law (balance equation) and the initial and boundary conditions for its occurrence are established. Writing these relationships with mathematical symbols- the next stage (block 3), which consists in the mathematical description of the process under study, which forms its initial mathematical model.

Depending on the physical nature of the processes in the system and the nature of the problem being solved, the mathematical model may include mass and energy balance equations for all selected subsystems (blocks) of the model, kinetic equations chemical reactions and phase transitions and transfer of matter, momentum, energy, etc., as well as theoretical and (or) empirical relationships between various parameters of the model and restrictions on the conditions of the process. Due to the implicit nature of the dependence of the output parameters Y from input variables X in the resulting model, it is necessary to choose a convenient method and develop an algorithm for solving the problem (block 4) formulated in block 3. To implement the adopted algorithm, analytical and numerical tools are used. In the latter case, it is necessary to compose and debug a computer program (block 5), select the parameters of the computing process (block 6) and implement a control account (block 8). An analytical expression (formula) or a program entered into a computer represents a new form of the model that can be used to study or describe the process if the adequacy of the model to the natural object is established (block 11).

To test the adequacy, it is necessary to collect experimental data (block 10) on the values ​​of those factors and parameters that are part of the model. However, it is possible to check the adequacy of the model only if some constants contained in the mathematical model of the process are known (from tabular data and reference books) or additionally experimentally determined (block 9).

A negative result of checking the adequacy of the model indicates its insufficient accuracy and may be the result of a whole set of different reasons. In particular, it may be necessary to remake the program in order to implement a new algorithm that does not give such a large error, as well as adjust the mathematical model or make changes to the physical model, if it becomes clear that neglecting any factors is the cause of failure. Any correction of the model (block 12) will, of course, require the re-execution of all operations contained in the underlying blocks.

A positive result of checking the adequacy of the model opens up the possibility of studying the process by conducting a series of calculations on the model (block 13), i.e. exploitation of the obtained information model. Consistent adjustment of the information model in order to improve its accuracy by taking into account mutual influence factors and parameters, the introduction of additional factors into the model and the refinement of various "tuning" coefficients allows us to obtain a model with increased accuracy, which can be a tool for a deeper study of the object. Finally, the establishment of the objective function (block 15) using theoretical analysis or experiments and the inclusion of an optimizing mathematical apparatus in the model (block 14) to ensure the targeted evolution of the system to the optimum region makes it possible to build an optimization model of the process. Adaptation of the obtained model for solving the problem of real-time production process control (block 16) when automatic control means are included in the system completes the work on creating a mathematical control model.

The analytical method consists in compiling a mathematical description of the object, in which the equations of statics and dynamics are found on the basis of fundamental laws that describe the physical and chemical processes occurring in the object under study, taking into account the design of the equipment and the characteristics of the processed substances. For example: the laws of conservation of matter and energy, as well as the kinetic laws of the processes of chemical transformations, the transfer of heat and mass. The analytical method is used in the design of new technological objects, the physicochemical processes of which are well studied.

Advantages:

Does not require experiments on a real object;

Allows you to determine the mathematical description at the design stage of the control system;

Allows you to take into account all the main features of the dynamics of the control object - non-linearity, non-stationarity, distributed parameters, etc.;

Provides a universal mathematical description suitable for a wide class of similar control objects.

Flaws:

Difficulty in obtaining a sufficiently accurate mathematical model that takes into account all the features of a real object;

Checking the adequacy of the model and the real process requires field experiments;

Many mathematical models have a number of parameters that are difficult to evaluate numerically.

The experimental method consists in determining the characteristics of a real object by setting up a special experiment on it. The method is simple, has low labor intensity and allows one to accurately determine the properties of a particular object.

Experimental methods for determining dynamic characteristics are divided into:

 methods for determining the temporal characteristics of the control object;

 methods for determining the frequency characteristics of the control object.

Time methods for determining dynamic characteristics are divided, in turn, into active and passive. Active methods involve applying test testing signals to the input of the object (stepped or rectangular pulses, periodic binary signal).

Advantages:

 Sufficiently high accuracy of obtaining a mathematical description;

 relatively short duration of the experiment.

In passive methods, no test signals are applied to the input of the object, but only the natural movement of the object is recorded in the process of its normal functioning. The received arrays of data on input and output signals are processed by statistical methods.

Flaws:

 low accuracy of the obtained mathematical description (because the deviations from the normal mode of operation are small);

 the need to accumulate large data arrays in order to improve accuracy (thousands of points);

 if the experiment is carried out on an object covered by the control system, then there is a correlation (interrelation) effect between the input and output signals of the object through the regulator. This relationship reduces the accuracy of the mathematical description.

With the experimental method, it is impossible to identify functional relationships between the properties of processed and obtained substances, regime indicators of the technological process and the design characteristics of the object. This shortcoming does not allow one to extend the results obtained by the experimental method to other objects of the same type.

The most effective is the experimental-analytical method, when, using the analytically obtained structure of the object, its parameters are determined in the course of full-scale experiments. Being a combination of analytical and experimental methods, this method takes into account their advantages and disadvantages.

Smoothing of experimental data, methods

When processing experimental data, approximation and interpolation are used. If the data are recorded with an error, then it is necessary to use an approximation - smoothing the curve data, which generally does not pass through the experimental points, but traces the dependence, eliminating possible errors caused by the measurement error.

If the data error is small, then interpolation is used, i.e. calculate the smoothing curve passing through each experimental point.

One of the best methods of approximation is the way (method) least squares, which was developed by the efforts of Legendre and Gauss over 150 years ago.

The least squares method allows you to get the best functional dependence on the set of available points (the best means that the sum of the squared deviations is minimal).

If we connect the points y1, y2, ... in series with a broken line, it is not a graphic representation of the function y \u003d f (x), since when repeating this series of experiments, we will get a broken line that is different from the first. This means that the measured values ​​of y will deviate from the true curve y = f(x) due to statistical spread. The problem is to approximate the experimental data with a smooth (not broken) curve, which would pass as close as possible to the true dependence y = f(x).

Regression analysis are used to obtain dependencies in processes in which the parameters depend on many factors. Often there is a relationship between the variables x and y, but not a well-defined one. In the simplest case, one value of x corresponds to several values ​​(set) of y. In such cases, the relationship is called regression.

Statistical dependencies are described mathematical models process. The model should be as simple and adequate as possible.

The task of regression analysis is to establish the regression equation, i.e. kind of curve between random variables, and an assessment of the closeness of the relationship between them, the reliability and adequacy of the measurement results.

To preliminarily determine the presence of such a relationship between x and y, points are plotted on the graphs and a so-called correlation field is built. The correlation field characterizes the type of relationship between x and y. By the shape of the field, one can tentatively judge the shape of the graph that characterizes the rectilinear or curvilinear dependences.

If points are averaged on the correlation field, then a broken line can be obtained, called the experimental regression dependence. The presence of a broken line is explained by measurement errors, an insufficient number of measurements, the physical nature of the phenomenon under study, etc.

Phenomenological method

The complexity of food production processes and the variety of acting factors are the objective basis wide application so-called phenomenological dependencies. Historically, a large number of energy and matter transfer phenomena are approximated by dependences of the form

I = aX , (1)

where I the speed of the process; a constant; X driving force of the process.

The class of such phenomena includes: deformation solid body(Hooke's law); the movement of electric current through a conductor (Ohm's law); molecular heat transfer (Fourier's law); molecular mass transfer (Fick's law); generalized (not only molecular) patterns of heat and mass transfer; energy losses during the movement of liquid through the pipeline (Darcy and Weisbach laws); the motion of a body in a continuous medium (Newton's law of friction), etc. In the laws describing these phenomena, the constants have physical meaning and are named respectively: modulus of elasticity, electrical resistance, molecular thermal conductivity, molecular diffusion coefficient, convective thermal conductivity or turbulent diffusion coefficient, Darcy friction coefficient, viscosity, etc.

Drawing attention to this, the Belgian physicist of Russian origin I. Prigogine, the Dutch physicists L. Onsager, S. de Groot, and others generalized these phenomena in the form of relation (1), which was called the phenomenological, or the relation of the logic of phenomena. It formed the basis of the phenomenological research method, the essence of which is briefly formulated as follows: for small deviations from the equilibrium state, the flow rate I of any complex process is proportional to the driving force of this process x.

The main complexity of research using this method is to identify the factors or parameters that are the stimulus of this process, and the factors that characterize its result. Having identified them, the relationship between them is presented in the form of dependence (1), and the numerical value of the coefficient connecting them a determined experimentally. For example, if the driving force of the extraction process is the difference in concentrations ΔС of the extractable substance in the raw material and in the extractant, and the process speed is characterized by the derivative of the concentration of this substance C in the raw material with respect to time, then we can write:

BΔC,

where B extraction rate coefficient.

You can always name a number of parameters that characterize both the driving force and the effectiveness of the process. As a rule, they are clearly related to each other. Therefore, the phenomenological equation can be written in many versions, i.e., for any combination of parameters that characterize the driving force and effectiveness of the process.

The phenomenological method, being formal, does not reveal the physical essence of the ongoing processes. However, it is widely used due to the simplicity of the description of phenomena and the ease of use of experimental data.

experimental method

Based on a preliminary analysis of the problem under study, factors are selected that have a decisive or significant impact on the desired result. Factors that have little influence on the result are discarded. The rejection of factors is associated with the search for compromises between the simplicity of analysis and the accuracy of describing the phenomenon under study.

Experimental studies are carried out, as a rule, on a model, but an industrial installation can also be used for this. As a result of experimental studies carried out according to a specific plan and with the required repetition, dependencies between factors are revealed in graphical form or in the form of calculation equations.

The experimental method has the following advantages:

• the possibility of achieving high accuracy of the derived dependencies
• high probability of getting addictions or physical characteristics object of study that cannot be found by any other method (for example, the thermophysical characteristics of products, the degree of emissivity of materials, etc.).

However, the experimental method of research has two significant drawbacks:

• high labor intensity, due, as a rule, to a significant number of factors affecting the phenomenon under study
• the dependencies found are particular, relating only to the phenomenon under study, which means that they cannot be extended to conditions other than those for which they were obtained.

Analytical method

This method consists in the fact that on the basis of the general laws of physics, chemistry and other sciences, differential equations are compiled that describe a whole class of similar phenomena.

For example, the Fourier differential equation determines the temperature distribution at any point of the body through which heat is transferred by thermal conduction:

A 2 t , (2)

where a coefficient of thermal diffusivity, m 2 /s; t Laplace operator;

2 t = + + .

Equation (2) is valid for any stationary medium.

The advantage of the analytical method is that the resulting differential equations are valid for the entire class of phenomena (thermal conduction, heat transfer, mass transfer, etc.).

However, this method has significant disadvantages:

• the complexity of the analytical description of most technological processes, especially processes accompanied by heat and mass transfer; this explains the fact that few such calculation formulas are known today
• impossibility in many cases to obtain a solution differential equations analytically with the help of well-known formulas in mathematics.

9. Cutting.

Cutting one ofmain technological processes Food Industry.

The most various materials such as: candy mass in the confectionery industry, dough mass in the baking industry, vegetables and fruits in the canning industry, sugar cake in the beet sugar industry, meat in the meat industry.

These materials have a variety of physical and mechanical properties, which is determined by a variety of cutting methods, types of cutting tools, cutting speed, cutting devices.

An increase in the capacity of food industry enterprises requires an increase in the productivity of cutting machines, their efficiency, and the development of rational cutting conditions.

General requirements requirements for cutting machines can be formulated as follows: they must provide high productivity, high product quality, high wear resistance, ease of operation, minimal energy costs, good sanitary condition, small dimensions.

Classification of cutting devices

Food cutting devices can be divided intogroups according to the following criteria:

by appointment: for cutting brittle, hard-like, elastic-viscous-plastic and inhomogeneous materials;

according to the principle of action: periodic, continuous and combined;

by type of cutting tool: lamellar, disk, string, guillotine, rotary, string (liquid and pneumatic), ultrasonic, laser;

Rice. 1. Types of cutting tools:
arotor; b— guillotine knife; c circular knife; gstring

by the nature of the movement of the cutting tool: with rotational, reciprocating, plane-parallel, rotary, vibration;

by the nature of the movement of the material during cutting and by the type of its fastening.

On fig. 1 presents some types of cutting tools: rotary, guillotine, disk, jet.

cutting theory

Cutting has the task of processing the material by separating it in order to give it a given shape, size and surface quality.

On fig. 2 shows a diagram of material cutting.

Fig2. Cxe m a pe material knowledge:
1- pa cut material; 2 - cutting tool, 3 - plastic deformation zone, 4 - elastic deformation zone, 5 - boundary zone, 6 - fracture line

For pe for a In this case, the materials are separated into parts as a result of the destruction of the boundary layer. Fracture is preceded by elastic and plastic deformation, as shown in the figure. These types of deformations are created by applying force to the cutting tool. The destruction of the material occurs when the stress becomes equal to the tensile strength of the material.

The work of cutting is spent on creating elastic and plastic deformation, as well as on overcoming the friction of the tool on the material being cut.

The work of cutting can be theoretically defined as follows.

Let us denote the force that must be applied to the edge of a knife 1 m long to destroy the material through R (vN/m). Work A (in J) is spent on cutting the material with an area l - l (in m 2 ) we will

А (Pl) l - Pl 2

Attributing work to 1 m 2 , we get the specific cutting work (in J/m 2 ).

Some types of cuts

Beet cutters and vegetable cutters. At sugar factories, sugar beet shavings of a grooved or lamellar farm are obtained by cutting. In the canning industry, carrots, beets, potatoes, etc., are cut.

The action of the cutters is based on the relative movement of the cutters knives and material. it relative motion can be done in various ways.

The main types of cutters are disc and centrifugal. Disc cutting for beets is shown in fig. 3. It consists of a horizontal rotating slotted disc and a fixed drum located above it. Frames with knives are installed in the slots of the disk (Fig. 4). The disc rotates on a vertical shaft at a speed of 70 rpm. The average linear speed of the knives is about 8 m/s.

The drum is filled with beets, which are to be cut. As the disk rotates, the beets, pressed under the action of gravity against the knives, are cut into chips, the shape of which depends on the shape of the knives.

In addition to disk, centrifugal cutting is also used. In these x cutting blades are fixed in the slots in the walls of a fixed vertical cylinder. The cut material is set in motion by the blades of the volute rotating inside the cylinder. Centrifugal force presses the product against the knives, which cut it.

P is. 5. Scheme of the rotary cutting device

On fig. 5 shows rotary cutting for confectionery products. Candy mass, decorated in bundles 3from matrix 1 of the forming machine enters the receiving tray 2 and fed through it to the cutting device. cutting e the device consists of a set of freely rotating rotors on the axis 4 with knives attached to them. Each harness has its own rotor. It is driven by a moving harness into rotation. Sliced ​​candy 5 fall on the conveyor belt 6.

On fig. 6 shows two types of machines for cutting frozen and non-frozen meat, bread, potatoes, beets, etc., called tops.

The design of tops used inindustry, copied from meat grinders, xopo sho known and common in everyday life. Three types of cutting tools are used in tops: fixed cutting knives, knife grids and movable flat knives.

Cutting is carried out by a pair of cutting tools flat m rotating knife and knife grid. The material is fed by the screw, pressed against the knife screen, the material particles are pressed into the holes of the screen, and the continuously rotating flat kniveswith blades pressed against the gratings, cut off material particles.

Rice. 6. Two types of tops:
a without forced supply of material; b — with forced material feed

The rotational speed of the auger for low-speed tops is 100-200, for high-speed ones over 300 rpm.

29. Homogenization.

The essence of homogenization. Homogenization (from Greek homogenes homogeneous) the creation of a homogeneous homogeneous structure that does not contain parts that differ in composition and properties and are separated from each other by interfaces. Homogenization is widely used in the canning industry, when the product is brought to a finely dispersed mass with particles 20...30 µm in diameter at a pressure of 10...15 MPa. In the confectionery industry, thanks to homogenization, which consists in the processing of chocolate mass in conch machines, emulsifiers or melangeurs, a uniform distribution of solid particles in cocoa butter is ensured and the viscosity of the mass is reduced.

Particles of emulsions, suspensions, suspensions are significantly smaller in size than the working bodies of any mechanical mixing devices. Particle sizes smaller sizes vortices formed by mixing devices, and smaller than other inhomogeneities in the flow of a continuous medium. Due to the movement of the medium initiated by mechanical mixers, the associations of particles move in it as a single whole without a relative displacement of the components of the dispersed phase and the dispersion medium. Such movement cannot ensure mixing of the medium components on the required scale.

The extent to which it is advisable to mix food particles is determined by the conditions of food assimilation. At present, the boundaries of the scales to which it is advisable to homogenize food mixtures have not been identified. There are, however, a number of studies that demonstrate the feasibility of homogenizing foodstuffs down to the molecular level.

The following physical phenomena are used to homogenize products: crushing of liquid particles in a colloid mill; throttling of the liquid medium in valve clearances; cavitation phenomena in liquid; motion of ultrasonic waves in a liquid medium.

Crushing of liquid particles in a colloid mill.Between the carefully machined hard conical surfaces of the rotor and stator of a colloidal mill (Fig. 7), emulsion particles can be crushed to a size of 2–5 µm, which is often sufficient for homogenization.

Rice. 7. Scheme of the colloid mill:
1- rotor; 2stator; h gap

Throttling of the liquid medium invalve clearances.If a liquid medium compressed to 10...15 MPa is throttled, passing through a small-diameter nozzle or through a throttle (throttle washer), then the spherical formations in it, when accelerated in the nozzle, are drawn into long threads. These threads are torn apart, which is the reason for their fragmentation (Fig. 8).

The elongation of spherical formations into filamentous ones is determined by the fact that the flow acceleration is distributed along the direction of motion. The frontal elements of the formations are accelerated before their rear parts and are under the influence of increased speeds for a longer time. As a result, spherical liquid particles are elongated.

Cavitation phenomena in liquids.They are realized by passing the flow of a continuous medium through a smoothly narrowing channel (nozzle) Figure 8. In it, it accelerates, and the pressure decreases in accordance with the Bernoulli equation

where p pressure, Pa; ρ liquid density, kg/m 3; v her speed, m/s; g- acceleration free fall, m/s 2; H liquid level, m

When the pressure drops below the saturation vapor pressure, the liquid boils. With a subsequent increase in pressure, the vapor bubbles "collapse". High-intensity, but small-scale pulsations of pressure and velocity of the medium generated in this case homogenize it.

Similar phenomena arise when bluff bodies move (rotate) in a fluid. In the aerodynamic shadow behind bluff bodies, the pressure decreases and cavitation caverns appear, moving along with the bodies. They are called attached caverns.

Movement of ultrasonic waves in a liquid medium. AT In ultrasonic homogenizers, the product flows through a special chamber, in which it is irradiated with an ultrasonic wave emitter (Fig. 10).

When traveling waves propagate in a medium, relative displacements of the components occur, repeating with the frequency of the generated oscillations (above 16 thousand times per second). As a result, the boundaries of the components of the medium are blurred, the particles of the dispersed phase are crushed, and the medium is homogenized.

Rice. 8. The scheme of crushing the fat particle when passing through the valve clearance

Rice. 9. Scheme of valve homogenizer operation:
1 working chamber; 2 seal; 3 valve; 4 body

When milk is homogenized by ultrasonic waves and other perturbations, the limiting sizes of milk particles are established, below which homogenization is impossible.

Milk fat particles are rounded, almost spherical particles 1...3 μm in size (primary globules or cores), united by 2...50 pieces or more into conglomerates (aggregates, clusters). In the composition of conglomerates, individual particles retain their individuality, i.e., remain clearly distinguishable. Conglomerates are in the form of chains of individual particles. The integrity of the conglomerate is determined by the forces of adhesive adhesion of rounded particles.

Rice. 10. Scheme of an ultrasonic homogenizer with generation of pulsations directly in its volume:
1homogenization cavity, 2 vibrating plastic; 3 jet nozzle

All homogenization methods implemented in practice ensure crushing of conglomerates, at best, to the size of primary spherules. In this case, the adhesive adhesion surfaces of the primary drops break under the action of the difference in the dynamic heads of the dispersion medium acting on the individual parts of the conglomerate. The crushing of primary drops by ultrasonic waves can take place only by the mechanism of the formation of surface waves on them and the separation of their crests by the flow of the dispersion medium. Fragmentation occurs at the moment when the forces that cause it exceed the forces that hold the original shape of the particles. At this point, the ratio of these forces will exceed the critical value.

The forces leading to the crushing of both primary particles and their conglomerates are the forces (H) created by the dynamic pressure of the dispersion medium:

where Δр d dynamic head of the dispersion medium, Pa; ρ medium density, kg/m 3; u, v velocities of the medium and particle, respectively, m/s; F \u003d π r 2 - midsection area, m 2; r radius of the primary particle, m

Particle speed v(t ) is calculated by the formula reflecting Newton's second law (the equality of the product of the mass of a particle and the acceleration to the drag force of the medium flowing around it):

where C x coefficient of drag against droplet motion; t its mass, kg;

where ρ to particle density, kg/m 3 .

Now the speed of the particle v(t ) is found by integrating the equation

With sinusoidal oscillations with a frequency f (Hz) and amplitude r a (Pa) at the speed of sound in a dispersion medium c (m/s) medium speed u(t) (m/s) is given by

The initial shape of the particles is kept by the forces:

for a spherical particle is the force surface tension

where σ surface tension coefficient, N/m;

for a conglomerate of particles, is the adhesive cohesion force of primary particles

where a specific force, N/m 3; r e equivalent conglomerate radius, m.

Ratio of forces R and R p , called the splitting criterion, or the Weber criterion ( We ), is written as:

for a spherical particle

for particle conglomerate

If the current (time-dependent) value of the Weber criterion exceeds the critical value, i.e., when We (t) > We (t) cr , the radius of the primary particle r(t) and the equivalent conglomerate radius r e (t ) are reduced to a value at which We (t ) = We (t ) Kp . As a result, a mass of matter corresponding to a decrease in the radius within the indicated limits is detached from the primary particle or from their conglomerate. In this case, the relations

In the presented calculation expressions for fragmentation of particles, the only factor that causes fragmentation is the difference in particle velocities and environment [ u (t ) v (t )]. This difference increases with decreasing density ratio ρ/ρ to . When fat particles in milk are crushed, this ratio is greatest and their crushing is the most difficult. The situation is aggravated by the fact that milk fat particles are covered with a more viscous shell of swollen proteins, lipids and other substances. For each cycle of ultrasonic vibrations, a small amount of small droplets breaks off from crushing droplets, and for crushing to proceed as a whole, multiple application of external loads is necessary. Therefore, the duration of crushing is many hundreds and even thousands of oscillation cycles. This is observed in practice during high-speed video filming of oil droplets crushed by ultrasonic vibrations.

Interaction of particles with shock waves.Under the action of ultrasonic vibrations of normal intensity, only droplet conglomerates can be crushed. To grind primary droplets, pressure perturbations with an intensity of about 2 MPa are required. Using modern technology it's unattainable. Therefore, it can be argued that milk homogenization to a particle size of less than 1 ... 1.5 microns is not implemented on any existing equipment.

Further crushing of drops is possible under the influence of a series of shock pulses created in a homogenized medium by a special stimulator, for example, a piston connected to a hydraulic or pneumatic drive of the pulse type. High-speed filming of droplets affected by such pulses shows that in this case, fragmentation occurs according to the mechanism of "blowing off the smallest droplets from their surface." In this case, the perturbation of the speed of the environment leads to the formation of waves on the surface of the drops and the breakdown of their crests. Repeated repetition of this phenomenon leads to a significant grinding of droplets or particles of fat.

73. Requirements for the grain drying process.

Thermal drying of grain and seeds in grain dryers is the main and most highly productive method. Tens of millions of tons of grain and seeds are subjected to such drying every year on farms and at state grain-receiving enterprises. Enormous funds are spent on the creation of grain drying equipment and its operation. Therefore, drying must be properly organized and carried out with the greatest technological effect.

Practice shows that the drying of grain and seeds on many farms is often much more expensive than in the state system of grain products. This happens not only because less productive dryers are used there, but also due to insufficiently clear organization of grain drying, improper operation of grain dryers, non-compliance with the recommended drying modes, and lack of production lines. The current recommendations for drying seeds of agricultural crops provide for the responsibility for the preparation of grain dryers and their operation in collective farms of chairmen and chief engineers, and in state farms - directors and chief engineers. Responsibility for the technological process of drying rests with agronomists and grain dryers. State seed inspections control the sowing qualities of seeds.

In order to organize the drying of grain and seeds in the most rational way, it is necessary to know and take into account the following basic provisions.

1. The maximum allowable heating temperature, i.e., to what temperature a given batch of grain or seeds should be heated. Overheating always leads to a deterioration or even a complete loss of technological and sowing qualities. Insufficient heating reduces the effect of drying and increases its cost, since at a lower heating temperature less moisture will be removed.
2. The optimal temperature of the drying agent (heat carrier) introduced into the grain dryer chamber. When the coolant temperature is lower than the recommended temperature, the grain is not heated to the required temperature, or to achieve this, it will be necessary to increase the time the grain stays in the drying chamber, which reduces the performance of grain dryers. The temperature of the drying agent above the recommended one is unacceptable, as it will cause overheating of the grain.
3. Features of drying grain and seeds in grain dryers of various designs, since these features often entail a change in other parameters and, above all, the temperature of the drying agent.

The maximum permissible temperature for heating grain and seeds depends on:
1) culture; 2) the nature of the use of grain and seeds in the future (i.e., intended purpose); 3) the initial moisture content of grain and seeds, i.e., their moisture content before drying.

Grains and seeds of different plants have different thermal stability. Some of them, other things being equal, can withstand higher heating temperatures and even for a longer time. Others change their physical state, technological and physiological properties even at lower temperatures. For example, seeds of fodder beans and beans at a higher heating temperature lose their shell elasticity, crack, and their field germination decreases. Wheat grain, intended for the production of baking flour, can only be heated up to 4850°С, and rye grain - up to 60°С. When wheat is heated above the specified limits, the amount of gluten sharply decreases and its quality deteriorates. Very fast heating (at a higher coolant temperature) also has a negative effect on rice, corn and many legumes: (seeds crack, which makes it difficult to further process them, for example, into cereals.

When drying, the intended purpose of the parties must be taken into account. So, the limiting temperature of heating seed grain of wheat is 45 ° C, and food 50 ° C . More more difference in the heating temperature of rye: 45 ° C for seed and 60 ° for food (for flour). (In general, all batches of grain and seeds that need to be kept viable are heated to a lower temperature. Therefore, barley for brewing, rye for malting, etc. are dried using the seed setting.

The maximum permissible temperature for heating grain and seeds depends on their initial moisture content. It is known that the more free water in these objects, the less thermally stable they are. Therefore, when the moisture content in them is more than 20% and especially 25%, the temperature of the coolant and heating of the seeds should be reduced. So, with an initial moisture content of peas and rice of 18% (Table 36), the permissible heating temperature is 45 ° C, and the temperature of the coolant is 60 about C. If the initial moisture content of these seeds is 25%, then the allowable temperature will be 40 and 50°C, respectively. At the same time, a decrease in temperature also leads to a decrease in evaporation (or, as they say, removal) of moisture.

It is even more difficult to dry large-seeded legumes and soybeans when, at high humidity (30% and higher), drying in grain dryers has to be carried out at a low heat carrier temperature (30°C) and seed heating (2830°C) with a slight removal of moisture for the first and second pass.

Design features of grain dryers of different types and brands determine the possibility of their use for drying seeds of various crops. So, beans, corn and rice are not dried in drum dryers. The movement of grain in them and the temperature of the drying agent (110130°C) are such that the grains and seeds of these crops crack and are severely injured.

Considering the issues of thermal drying in grain dryers, one must remember the unequal moisture-giving ability of grain and seeds of various crops. If the moisture yield of grain of wheat, oats, barley and sunflower seeds is taken as a unit, then, taking into account the applied temperature of the coolant and the removal of moisture per pass through the grain dryer, the coefficient (K)will be equal to: for rye 1.1; buckwheat 1.25; millet 0.8; corn 0.6; peas, vetch, lentils and rice 0.30.4; broad beans, beans and lupine 0.1-0.2.

Table 1. Temperature conditions(in °С) drying seeds of various crops on grain dryers

It should also be borne in mind that due to a certain moisture-giving capacity of grain and seeds, almost all dryers used in agriculture, provide moisture removal for one pass of the grain mass only up to 6% under modes for food grain and up to 45% for seed. Therefore, grain masses with high humidity have to be passed through dryers 23 or even 4 times (see Table 1).

Task number 1.

Determine the suitability of a drum sieve with the given parameters for sifting 3.0 t/h of flour. Initial data:

Solution

Given:

ρ Bulk weight of the material, 800 kg/m 3 ;

α the angle of the drum to the horizon, 6;

μ material loosening coefficient, 0.7;

n number of revolutions of the drum, 11 rpm;

R drum radius, 0.3 m;

h height of the material layer on the sieve, 0.05 m.

Rice. 11. Diagram of a drum sieve:
1 drive shaft; 2 drum-box; 3 sieve

where μ material loosening coefficient μ = (0.6-0.8); ρ Bulk weight of the material, kg/m 3 ; α drum tilt angle to the horizon, deg; R drum radius, m; h height of the material layer on the sieve, m; n number of revolutions of the drum, rpm.

Q = 0.72 0.7 800 11 tg (2 6) =
= 4435.2 0.2126= 942.92352 0.002 = 1.88 t/h

Let's compare the obtained value of the productivity of the drum sieve with 3.0 t/h given in the condition: 1.88< 3,0 т/ч, значит барабанное сито с заданными параметрами непригодно для просеивания 3,0 т/ч муки.

Answer: unsuitable.

Task number 2.

Determine the dimensions (length) of a flat gyratory screen for sorting 8000 kg/h of material. Initial data:

Solution

r eccentricity, 12 mm = 0.012 m;

α angle of inclination of the spring screen to the vertical, 18º;

f coefficient of friction of the material on the sieve, 0.4;

ρ Bulk weight of the material, 1.3 t/m 3 \u003d 1300 kg / m 3;

h height of the material layer on the sieve, 30 mm = 0.03 m;

φ filling factor, taking into account the incomplete loading of the carrier surface with material, 0.5.

Rice. 12. Scheme of the gyratory screen:
1 spring; 2 sieve; 3 vibrator shaft; 4 eccentricity

The frequency of rotation of the shaft of the gyratory screen:

rpm

The speed of moving the material through the sieve:

m/s,

where n frequency of rotation of the screen shaft, rpm; r eccentricity, m; α angle of inclination of the spring screen to the vertical, degrees; f coefficient of friction of the material on the sieve.

m/s.

Cross-sectional area of ​​the material on the screen S :

kg/h,

where S cross-sectional area of ​​the material on the screen, m 2; v material advancement speed along the screen, m/s; ρ Bulk weight of the material, kg/m 3 ; φ filling factor, which takes into account the incomplete loading of the bearing surface with material.

M 2 .

Screen length b :

h the height of the material layer on the sieve.

Answer: bar length b = 0.66 m.

Task number 3.

Determine the power on the shaft of a suspended vertical centrifuge for separating sugar massecuite if the inner diameter of the drum D = 1200 mm, drum height H = 500 mm, outer drum radius r2 = 600 mm. Other initial data:

D internal diameter of the drum, 1200 mm = 1.2 m;

H drum height, 500 mm = 0.5 m;

r n \u003d r 2 outer drum radius, 600 mm = 0.6 m

n drum rotation frequency, 980 rpm;

m b drum weight, 260 kg;

d shaft journal diameter, 120 mm = 0.12 m;

τ p drum acceleration time, 30 s;

ρ massecuite density, 1460 kg/m 3 ;

m s suspension weight, 550 kg.

Rice. 13. Scheme for determining the amount of pressure on the walls of the drum

Translation of the drum rotation frequency into angular velocity:

rad/s.

Powers N 1, N 2, N 3 and N 4:

kW

where m b mass of the centrifuge drum, kg; r n drum outer radius, m;τ p drum acceleration time, s.

Thickness of the annular layer of massecuite:

where m c mass of the suspension loaded into the drum, kg; H height of the inner part of the drum, m.

The inner radius of the massecuite ring (according to Figure 13):

r n \u003d r 2 outer radius of the drum.

Power to communicate kinetic energy to massecuite:

kW

where η coefficient useful action(for calculations takeη = 0.8).

Separation factor in the centrifuge bowl:

where m mass of drum with suspension ( m = m b + m c), kg; F separation factor:

Power to overcome friction in bearings:

kW

where p ω angular speed of rotation of the drum, rad/s; d shaft neck diameter, m; f coefficient of friction in bearings (take 0.01 for calculations).

kW.

Power to overcome the friction of the drum on the air:

kW

where D and H drum diameter and height, m; n drum rotation frequency, rpm.

Substitute the obtained power values ​​into the formula:

kW.

Answer: centrifuge shaft power N = 36.438 kW.

Task number 4.

R total air pressure, 1 bar = 1 10 5 Pa;

t air temperature, 32.55 ºС;

φ relative air humidity, 75% = 0.75.

According to Appendix B, we determine the pressure saturated steam ( p us ) for a given air temperature and convert to the SI system:

for t \u003d 32.55 ºС p us \u003d 0.05 at 9.81 10 4 \u003d 4905 Pa.

Air moisture content:

where p total air pressure, Pa.

Enthalpy of humid air:

where 1.01 is the heat capacity of air at ρ = const kJ/(kg K); 1.97 heat capacity of water vapor, kJ/(kg K); 2493 specific heat of vaporization at 0 С, kJ/kg; t dry bulb temperature, C.

Moist air volume:

Humid air volume (in m 3 per 1 kg of dry air):

where is the gas constant for air, equal to 288 J/(kg K); T absolute air temperature ( T \u003d 273 + t), K.

M 3 /kg.

Answer: moisture content χ = ​​0.024 kg/kg, enthalpy I = 94.25 kJ/kg and the volume of moist air v \u003d 0.91 m 3 /kg of dry air.

Bibliography

1. Plaksin Yu. M., Malakhov N. N., Larin V. A. Processes and apparatuses of food production. M.: KolosS, 2007. 760 p.

2. Stabnikov V.N., Lysyansky V.M., Popov V.D. Processes and devices of food production. M.: Agropromizdat, 1985. 503 p.

3. Trisvyatsky L.A. Storage and technology of agricultural products. M.: Kolos, 1975. 448 p.