Mathematical modeling of plant ventilation. Modern problems of science and education Mathematical model of subtle ventilation

1

The paper discusses the processes of ventilation modeling and dispersion of its emissions in the atmosphere. Modeling is based on solving the Navier-Stokes system, the laws of preserving mass, pulse, heat. Various aspects of the numerical solution of these equations are considered. A system of equations is proposed that allows you to calculate the value of the background coefficient of turbulence. For the hypocoo approximation, a solution was proposed in conjunction with the equations of the standing of perfect real gas and steam given in the article by the equations of hydrogazodynamics. This equation is a modification of the Van der Waals equation and more accurately takes into account the size of the gas or steam molecules and their interaction. Based on the conditions of thermodynamic stability, a relation was obtained, which makes it possible to exclude physically impossible roots in solving the equation relative to the volume. Analysis of well-known calculated models and computing hydrogazodynamics packages are performed.

modeling

ventilation

turbulence

the Equations of Teplomassoperenos

status equation

real Gas.

dissipation

1. Berlind M. E. Modern problems Atmospheric diffusion and contamination of the atmosphere. - L.: Hydrometeoisdat, 1975. - 448 p.

2. Belyaev N. N. Modeling the process of dispersion of toxic gas under construction conditions // Bulletin diet. - 2009. - № 26 - p. 83-85.

3. Byzov N. L. Experimental studies of atmospheric diffusion and calculations of the scattering of impurities / N. L. Byzov, E. K. Garger, V. N. Ivanov. - L.: Hydrometeoizdat, 1985. - 351 p.

4. Datsyuk T. A. Modeling the dispersion of ventilation emissions. - St. Petersburg: SPbgas, 2000. - 210 s.

5. Sapet A. V. Application of algorithms for cognitive graphics and methods of mathematical analysis to study the thermodynamic properties of isobutane R660A on the saturation line: Grant No. 2C / 10: Report on NIR (conclude.) / GOVPO SPbgas; Hands. Gorokhov V.L., Iz.: Sauts A.V.- SPB, 2011.- 30 C.: Il.- Bibliogr.: With. 30.- NU GR 01201067977.-Inv. №02201158567.

Introduction

When designing production complexes and unique objects, issues related to ensuring the quality of the air and the normalized parameters of the microclimate should be comprehensively substantiated. Given the high price of manufacturing, installation and operation of ventilation and air conditioning systems, increased requirements for engineering calculations. For the choice of rational design solutions In the field of ventilation, it is necessary to be able to analyze the situation as a whole, i.e. Review the spatial relationship of dynamic processes occurring indoors and atmosphere. Evaluate the effectiveness of ventilation, which depends not only on the amount of air supplied to the room, but also from the adopted air distribution and concentration scheme harmful substances In the outside air in the location of the air intakes.

The purpose of the article - The use of analytical dependencies by which the calculations of the number of harmful discharge are performed, determine the size of the channels, air ducts, mines and the choice of air treatment method, etc. In this case, it is advisable to use the "Stream" software product with the "VSV" module. To prepare the source data, it is necessary for the presence of schemes of projected ventilation systems, indicating the lengths of the plots and air costs at the end areas. Input data for calculation is a description of ventilation systems and requirements for it. Using mathematical modeling, the following questions are solved:

  • the choice of optimal options for feeding and removing air;
  • distribution of microclimate parameters in terms of rooms;
  • evaluation of the aerodynamic development mode;
  • selection of places for air intake and air removal.

The field of speed, pressure, temperature, concentrations in the room and the atmosphere are formed under the action of a plurality of factors, the combination of which is rather difficult to consider in engineering methods, without applying computers.

The use of mathematical modeling in ventilation tasks and aerodynamics is based on solving the Navier - Stokes equation system.

To simulate turbulent flows, it is necessary to solve a system of mass conservation equations and Reynolds (Impulse Saving):

(2)

where t. - time, X.= X I. , J. , K. - spatial coordinates, u.=u I. , J. , K. - velocity vector components r - piezometric pressure, ρ - density, τ IJ. - components of stress tensor, s M. - Source of mass, s I. - Pulse source components.

The stress tensor is expressed in the form:

(3)

where s ij. - strain rate tensor; Δ. IJ. - Tensor of additional stresses arising due to the presence of turbulence.

For information about temperature fields T.and concentration from Harmful substances are complemented by the following equations:

the equation of maintaining the amount of heat

passive impurity equation from

(5)

where C. R - coefficient of heat capacity, λ is the coefficient of thermal conductivity, k.= k I. , J. , K. - Turbulence coefficient.

Basic coefficient of turbulence k. The bases are determined using the equation system:

(6)

where k. F. - the background coefficient of turbulence, k. F \u003d 1-15 m 2 / s; ε \u003d 0.1-04;

Turbulence coefficients are determined using equations:

(7)

In an open area at low dissipation, the value k. Z is determined by equation:

k K. = k. 0 z. /z. 0 ; (8)

where k. 0 - Value k K. on high z. 0 (k. 0 \u003d 0.1 m 2 / s z. 0 \u003d 2 m).

In the open area, the wind speed profile is not deformed, i.e.

With unknown stratification of atmospheric in the open area, the wind speed profile can be determined:

; (9)

where Z 0 is the set height (height of the weather); u. 0 - wind speed at height z. 0 ; B. = 0,15.

Subject to condition (10) the local Richardson criterion RI. Determined as:

(11)

Differentiate equation (9), equalize equations (7) and (8), express from there k. Baz

(12)

We equate equation (12) with system equations (6). In the resulting equality, we substitute (11) and (9), in the final form we obtain the system of equations:

(13)

The pulsation member, following the ideas of Boussinesca, appears in the form:

(14)

where μ. T. - Turbulent viscosity, and additional members in the energy transfer equations and the components of impurities are simulated as follows:

(15)

(16)

The closure of the system of equations occurs with one of the turbulence models described below.

For turbulent flows studied in ventilation practice, it is advisable to use Boussinesque hypothesis about the smallness of the density changes, or the so-called "hypocoo" approximation. Reynolds voltages are considered proportional to the rates of deformations. A turbulent viscosity coefficient is introduced, this concept is expressed as:

. (17)

The effective viscosity coefficient is calculated as the sum of molecular and turbulent coefficients:

(18)

The "hypocoo" approximation implies a solution in conjunction with the above equation equations of the standing of the ideal gas above:

ρ = p./(RT) (19)

where p. - Pressure B. environment; R. - Gas constant.

For more accurate calculations, the impurity density can be determined using a modified Van der Waals equation for real gases and vapors

(20)

where constants N. and M. - take into account the association / dissociation of gas or steam molecules; but - takes into account other interaction; b." - taking into account the size of gas molecules; υ \u003d 1 / ρ.

Highlighting pressure from equation (12) r And differentiating it in volume (accounting of thermodynamic stability) will be the following ratio:

. (21)

This approach can significantly reduce the time of calculations compared with the case of using complete equations for compressible gas without reducing the accuracy of the results obtained. Analytical solution of the above equations does not exist. In this regard, numerical methods are used.

To solve ventilation problems associated with the transfer of turbulent flow of scalar substances, in solving differential equations, the splitting circuit on physical processes is used. According to the principles of splitting, of course, the difference integration of the equations of hydrodynamics and convective-diffuse transmission of the scalar substance at each time of time Δ t. carried out in two stages. At the first stage, hydrodynamic parameters are calculated. At the second stage, diffusion equations are solved on the basis of the calculated hydrodynamic fields.

The effect of heat transfer on the formation of the air velocity field is taken into account by the help of the boussinesca approximation: an additional term is introduced to the vertical component of the speed, which takes into account the buoyancy forces.

To solve problems of turbulent movement of fluid, four approaches are known:

  • direct modeling "DNS" (solution of nonstationary Navier - Stokes equations);
  • the solution of the averaged Rans Reynolds equations, the system of which, however, is unlocked and needs additional short-circuit ratios;
  • method of large vortices "LES » which is based on the solution of non-stationary Navier - Stokes equations with parametrization of the vortex of the subsidence;
  • dES method , which is a combination of two methods: in the zone of tear-off flows - "Les", and in the area of \u200b\u200bthe "smooth" flow - "Rans".

The most attractive in terms of the accuracy of the results obtained is undoubtedly the method of direct numerical modeling. However, currently the possibilities of computing technology do not yet allow solving problems with real geometry and numbers Re., and with the resolution of the vortices of all sizes. Therefore, when solving a wide range of engineering problems, the numerical solutions of the Reynolds equations are used.

Currently used to simulate ventilation tasks Certified packages, such as Star-CD, "FLUENT" or "ANSYS / FLOTRAN". With a correctly formulated problem and the rational solution algorithm, the obtained volume of information allows you to choose at the design stage optimal optionBut the execution of calculations using program data requires appropriate training, and their incorrect use may result in erroneous results.

As a "basic version", we can consider the results of generally accepted balanced methods of calculation, which allow you to compare integral values \u200b\u200bcharacteristic of the problem under consideration.

One of important moments When using universal software packages to solve ventilation tasks, the selection of the turbulence model is. To date, it is known a large number of Different turbulence models that are used to close the Reynolds equations. The turbulence models are classified according to the number of parameters for the characteristics of turbulence, respectively, single-parameter, two- and three-parameter.

Most of the semi-empirical turbulence models, one way or another, use the "hypothesis of the locality of the turbulent transfer mechanism", according to which the mechanism of turbulent pulse transfer is fully determined by the task of local derivatives from the averaged velocities and physical properties liquids. The influence of the processes occurring away from the point under consideration, this hypothesis does not take into account.

The most simple are one-parameter models that use the concept of turbulent viscosity "N T.", And turbulence is assumed to be isotropic. Modified version of the model "N T.-92 "is recommended when modeling inkjet and tear-off flows. A good coincidence with the results of the experiment also provides a single-parameter model "S-A" (spoolder - almaras), which contains the transfer equation for magnitude.

The lack of models with one transfer equation is associated with the fact that they do not have information about the distribution of turbulence L.. By magnitude L. The processes of transfer, methods of forming turbulence, the dissipation of turbulent energy are influenced. Versatile addiction to determine L. does not exist. Turbulence equation L. It often turns exactly to the equation that determines the accuracy of the model and, accordingly, its applicability. Basically, the scope of application of these models is limited to relatively simple shift flows.

In two-parameter models, except for the scale of turbulence L.used as the second parameter the speed of dissipation of turbulent energy . Such models are most commonly used in modern computing practice and contain the energy transfer equations of turbulence and energy dissipation.

Well known model, including turbulence energy equations k. and the speed of dissipation of turbulent energy ε. Models like " k.- e » it can be used both for intensive currents and for more complex tear-off flows.

Two-parameter models are used in the low and high-axis version. In the first, the mechanism of interaction of molecular and turbulent transfer near the solid surface is taken into account directly. In a high-aldold version, the turbulent transfer mechanism near the solid boundary is described by special entry functions that bind the flow parameters with the distance to the wall.

Currently, the most promising include the SSG and Gibson-Launder models, which uses a nonlinear tensor tensor of Reynolds turbulent stresses and a tensor of the averaged deformation rates. They were developed to improve the prediction of tear-off flows. Since they calculate all the components of the tensors, they require large computer resources compared to two-parameter models.

For complex disruptive flows, some advantages revealed the use of single-parameter models "N T.-92 "," S-A "with the accuracy of the prediction of the flow parameters and at the rate of the account compared to two-parameter models.

For example, in the Star-CD program, the use of models of type " k-e ", Spookerta - Almaras," SSG "," Gibson-Launder ", as well as the method of large vortices" LES ", and the DES method. The last two methods are better suitable for calculating air movement in a complex geometry, where numerous tear-off vortex areas will arise, but they require large computing resources.

The results of the calculations are significantly dependent on the selection of the computational grid. Currently, special programs for building grids are used. Mesh cells can have a different form and dimensions that are best suited to solve a specific task. The simplest surface of the grid, when cells are the same and have a cubic or rectangular shape. Universal computing programs used now in engineering practice allow you to work on arbitrary unstructured grids.

To perform the calculations of numerical modeling of ventilation tasks, it is necessary to task the boundary and initial conditions, i.e. values \u200b\u200bof dependent variables or their normal gradients at the boundaries of the settlement area.

Task with a sufficient degree of accuracy of the geometric features of the object under study. For these purposes, it can be recommended to build three-dimensional models such packages such as "SolidWorks", "Pro / Engeneer", "NX NASTRAN". When constructing a calculated grid, the number of cells is selected so as to obtain a reliable solution at a minimum calculation time. Select one of the semi-empirical turbulence models, which is most effective for the flow under consideration.

IN conclusion We add that a good understanding of the qualitative side of the processes occurring is necessary to correctly formulate the boundary conditions of the task and evaluate the accuracy of the results. Modeling ventilation emissions at the design stage of objects can be considered as one aspects of information modeling aimed at ensuring the environmental safety of the object.

Reviewers:

  • Volikov Anatoly Nikolaevich, Doctor of Technical Sciences, Professor of the Department of Heat-Goes and Air Basin Protection, FGBOU VPOU "SPBGASU", St. Petersburg.
  • Polushkin Vitaly Ivanovich, Doctor of Technical Sciences, Professor, Professor of the Department of Heating, Ventilation and Air Conditioning, FGBOU VPO SPBGAS, St. Petersburg.

Bibliographic reference

Datsyuk T.A., Sautz A.V., Yurmanov B.N., Taurit V.R. Modeling ventilation processes // Modern problems of science and education. - 2012. - № 5;
URL: http://science-education.ru/ru/Article/View?id\u003d6744 (date of handling: 10/17/2019). We bring to your attention the magazines publishing in the publishing house "Academy of Natural Science"

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Forecasting thermal regime In the served zones is a multifactoric task. It is known that the thermal mode is created using heating, ventilation and air conditioning systems. However, when designing heating systems, the impact of air flows created by the rest of the systems is not taken into account. Partly, this is justified by the fact that the effect of air flows on thermal regime can be insignificant at regulatory air mobility in the served zones.

Application Systems radiant heating Requires new approaches. This includes the need to fulfill the norms of human irradiation at workplaces and accounting for the distribution of radiant heat in the inner surfaces of the enclosing structures. After all, with radiant heating, these surfaces are preferably heated, which, in turn, give heat into the room with convection and radiation. It is at the expense of this that the necessary temperature of the internal air is supported.

As a rule, for most types of rooms, along with heating systems, a device for ventilation systems is required. So, when using gas radiant heating systems, the room must be equipped with ventilation systems. The minimum air exchange of premises with the release of harmful gases and vapor stipulated SP 60.13330.12. Heating Ventilation and air conditioning and is no less single, and at a height of more than 6 m - at least 6 m 3 per 1 m 2 floor area. In addition, the performance of ventilation systems is also determined by the purpose of the premises and is calculated from the conditions for the assimilation of heat or gas divisions or compensation of local suns. Naturally, the magnitude of the air exchange must be checked and on the assimilation condition of combustion products. Compensation of the volume of removed air is carried out by systems supply ventilation. At the same time, a significant role in the formation of the thermal regime in the serviced zones belongs to the supply jet and the warmth introduced by them.

Research method and results

Thus, it is necessary to develop an approximate mathematical model of complex heat and mass transfer processes occurring in a room with radiating heating and ventilation. The mathematical model is a system of equations of air-thermal balances for characteristic volumes and surfaces of the room.

The system solution allows you to determine the parameters of the air in the served zones when different options Placement of radiant heating devices taking into account the influence of ventilation systems.

Building a mathematical model Consider on an example of a production room equipped with a system of radiant heating and having other heat generation sources. The heat fluxes from emitters are distributed as follows. Convective flows rise to the upper area under the overlap and give the heat of the inner surface. The radiant component of the thermal flow of the emitter is perceived by the internal surfaces of the exterior enclosing room designs. In turn, these surfaces give heat convection inner air and radiation - other internal surfaces. Part of the heat is transmitted through the external fencing designs of the outer air. The calculated heat exchange circuit is shown in Fig. 1a.

Building Matmodel Consider on the example of a production room equipped with a system of radiant heating and having other heat generation sources. Convective flows rise to the upper area under the overlap and give the heat of the inner surface. The radiant component of the thermal flux of the emitter is perceived by the internal surfaces of the external enclosing room structures

Next, we consider the construction of the circulation of air flows (Fig. 1b). We will take a scheme of the organization of the air exchange "from above-up". Air is served in an amount M. PR in the direction of the serviced zone and is removed from the upper zone with consumption M. in \u003d. M. Ave. At the top level of the served zone, the air flow in the jet is M. Page The growth of air flow in the supply jet is due to the circulation air disconnected from the jet.

We introduce the conditional boundaries of streams - surfaces on which only normal components have velocities. In fig. 1b the boundaries of the streams are shown by the dash line. Then we highlight the calculated volumes: the served zone (space with a constant stay of people); Complete streams and seated convective flows. The direction of seated convective streams depends on the ratio of the temperature of the inner surface of the external enhancement structures and the surrounding air. In fig. 1B shows a scheme with a drop-down-free convective stream.

So, the air temperature in the serviced zone t. Wz is formed as a result of mixing air of supply jets, used convective streams and conversion of convective heat from internal surfaces Paul and walls.

Taking into account the developed heat exchange and circulation schemes (Fig. 1), the equations of heat-air balances for the selected volumes:

Here from - air heat capacity, J / (kg · ° C); Q. from - power of the gas radiant heating system, W; Q. with I. Q.* C - convective heat transfer in the inner surfaces of the wall within the served zone and the wall above the serviced zone, W; t. page t. C I. t. Wz - air temperature in the supply jet at the entrance to the working area, in a used convective stream and in the working area, ° C; Q. TP - heat loss, WT, equal to the sum of heat loss through external enclosing structures:

Air flow in the supply jet at the inlet to the serviced zone is calculated using the dependences obtained by M. I. Grimitlin.

For example, for air distributors creating compact jets, the flow rate in the jet is:

where m. - speed attenuation coefficient; F. 0 is the cross-sectional area of \u200b\u200bthe inlet pipe of the air distributor, M 2; x. - distance from the air distributor to the place of entry into the serviced zone, m; TO H is the coefficient of non-erosity.

Air flow in a used convective stream is determined by:

where t. C is the temperature of the inner surface of the outer walls, ° C.

Equations thermal Balance For boundary surfaces, look:

Here Q. c, Q.* C, Q. PL I. Q. PT - convective heat transfer in the inner surfaces of the wall within the served zone - the walls above the serviced zone, gender and coating, respectively; Q. TP.S. Q.* TP.S. Q. TP.PL, Q. TP PT - heat loss through the corresponding structures; W. from, W.* C, W. pl W. PT - radiant thermal flows from the emitter entering these surfaces. Convective heat transfer is determined by a certain dependence:

where m. J - coefficient determined taking into account the position of the surface and direction of heat flux; F. J - surface area, m 2; Δ. t. J is the difference in surface temperature and ambient air, ° C; J. - Index of surface type.

Teplopotieri Q. TJ can be expressed as

where t. H is the outdoor temperature, ° C; t. J - the temperature of the internal surfaces of the exterior enclosing structures, ° C; R. and R. H - resistance thermal and heat transfer of external fence, m 2 · ° C / W.

Matmeodel processes of heat and mass transfer during the joint action of radiant heating and ventilation are obtained. The results of the solution allow to obtain the main characteristics of the thermal regime when designing systems of radiant heating of buildings of various purposes equipped with ventilation systems

Radiant thermal flows from radiators of radiant heating systems WJ.calculated through the mutual area of \u200b\u200bradiation according to the procedure for arbitrary orientation of emitters and surrounding surfaces:

where from 0 - the radiation coefficient of absolutely black body, W / (m 2 · K 4); ε ij - the reduced degree of blacks participating in the heat exchange of surfaces I. and J.; H. IJ - Mutual area of \u200b\u200bradiation surfaces I. and J., m 2; T. I - average temperature radiating surface, determined from the thermal balance of the emitter, K; T. J - temperature heat-visible surface, K.

When substituting expressions for heat fluxes and air expenditures in jets, we obtain a system of equations that are an approximate mathematical model of the processes of heat and mass transfer during radiating heating. To solve the system, standard computer programs can be used.

A mathematical model of heat and mass transfer processes in the joint action of radiant heating and ventilation is obtained. The results of the solution make it possible to obtain the main characteristics of the thermal regime when designing systems of radiant heating of buildings of various purposes equipped with ventilation systems.

Daria Denisikhina, Maria Lukanina, Mikhail Airplanes

IN modern world It is no longer possible to do without mathematical modeling of air flow when designing ventilation systems.

In the modern world, it is no longer possible to do without mathematical modeling of air flow when designing ventilation systems. Conventional engineering techniques are well suited for typical rooms and standard solutions on air distribution. When the designer faces non-standard objects, methods of mathematical modeling should come to the rescue. The article is devoted to the study of air distribution during the cold year of the year in the workshop for the production of pipes. This workshop is part of the factory complex located under a sharply continental climate.

Back in the XIX century were obtained differential equations To describe the flow of liquids and gases. They were formulated by the French physicist Louis Navier and British mathematician George Stokes. The Navier - Stokes equations are one of the most important in hydrodynamics and are used in mathematical modeling Many natural phenomena and technical tasks.

Per last years A wide variety of geometrically and thermodynamically complex objects in construction has accumulated. The use of methods of computing hydrodynamics significantly improves the possibilities of designing ventilation systems, allowing with a high degree of accuracy to predict the distribution of speed, pressure, temperature, component concentration at any point of the building or its place.

Intensive use of methods of computational hydrodynamics began in 2000, when universal software shells appeared (CFD packets), which give the possibility of finding numerical solutions of the Navier - Stokes equation system in relation to the object of interest. From this time since this time, the Bureau of Technology is engaged in mathematical modeling in relation to the tasks of ventilation and air conditioning.

Task description

In this study, numerical simulation was carried out using STAR-CCM + - CFD package developed by CD-Adapco. The performance of this package when solving the tasks of ventilation was
It is repeatedly tested on the objects of various complexity, from office space to the halls of theaters and stadiums.

The task is of great interest from the point of view of both design and mathematical modeling.

Outdoor air temperature -31 ° C. In the room there are objects with essential heat gains: an ordinous furnace, a vacation furnace, etc. Thus, there are large temperature differences between the exterior enclosing structures and internal fuel objects. Consequently, the contribution of radiation heat exchange during modeling cannot be neglected. Additional complexity in mathematical formulation of the problem is that a severe railway composition is supplied to the room several times, having a temperature of -31 ° C. It gradually heats up, cooling the air around him.

To maintain the desired air temperature in the volume of the workshop (in the cold season, not lower than 15 ° C) the project provides for ventilation and air conditioning systems. At the design stage, the flow rate and temperature of the supplied air required to maintain the required parameters were calculated. The question remained - how to submit air to the volume of the workshop to ensure the most uniform temperature distribution throughout the volume. Modeling allowed for a relatively small time limit (two or three weeks) to see the air flow pattern for several air supply options, and then compare them.

Stages of mathematical modeling

  • Construction of solid geometry.
  • Fractionment of the working space on the cells of the compaction grid. It should be provided in advance areas in which additional grinding of cells will be required. When building a grid, it is very important to find that golden middle, in which the cell size is quite small to obtain the right results, while the total number of cells will not be so large to tighten the calculation time to unacceptable time. Therefore, the construction of the grid is a whole art that comes with experience.
  • The task of the boundary and initial conditions in accordance with the formulation of the problem. Requires an understanding of the specifics of ventilation tasks. Large role in preparing the calculation plays right choice Turbulence models.
  • Choosing a suitable physical model and turbulence model.

Modeling results

To solve the problem under consideration in this article, all stages of mathematical modeling were passed.

For comparison of the ventilation efficiency, three options for air supply were chosen: at an angles to vertical 45 °, 60 ° and 90 °. Air supply was carried out from standard air distribution lattices.

Temperature and speed fields obtained as a result of calculation at different angles of feed inlet air, presented in Fig. one.

After analyzing the results, the angle of supply air equal to 90 ° was selected as the most successful options for the ventilation of the workshop. With this method of supply, no higher speeds are created in the working area and it is possible to achieve a sufficiently uniform pattern of temperature and speed throughout the volume of the workshop.

Final decision

Temperature and velocity fields in three cross sections passing through the intake grids are shown in Fig. 2 and 3. Distribution of temperature on the room is uniform. Only in the area of \u200b\u200bconcentration of furnaces there are higher temperatures under the ceiling. In the right area of \u200b\u200bthe corner of the room there is a colder area. This is the place where cold cars are entering from the street.

From fig. 3 It is clearly visible how horizontal jets of the supplied air are distributed. With this method of supply, the supply jet has a sufficiently large range. So, at a distance of 30 m from the lattice, the flow rate is 0.5 m / s (at the output of the lattice speed - 5.5 m / s). In the rest of the room, the air mobility is low, at the level of 0.3 m / s.

The heated air from the hardening furnace deflects the jet of the supply air upwards (Fig. 4 and 5). The furnace very much warms the air around him. The temperature of the floor here is higher than in the middle of the room.

The temperature field and current line in two sections of the hot workshop are shown in Fig. 6.

conclusions

Calculations made allowed to analyze the effectiveness different ways Air supply to the pipe manufacturing workshop. It was obtained that when the horizontal jet was submitted, the trimming air further applies to the room, contributing to its more uniform heated. At the same time, there are no areas with too much air mobility in the working area, as it happens when the supply air is applied at an angle down.

The use of mathematical modeling methods in ventilation and air conditioning tasks is a very promising direction that allows you to correct the decision at the project stage, prevent the need to correct unsuccessful design solutions after commissioning objects. ●

Daria Denisikhina - Head of the Department "Mathematical Modeling";
Maria Lukanina - Leading Engineer "Mathematical Modeling";
Mikhail aircraft - Executive Director of MM-Technologies




Glebov R. S., Aspirant Tumanov M.P., Candidate of Technical Sciences, Associate Professor

Antyushin S. S., graduate student (Moscow state Institute Electronics and Mathematics (Technical University)

Practical aspects of identification of the mathematical model

Ventilation unit

Due to the emergence of new requirements for ventilation systems, experimental methods for setting closed control circuits cannot fully solve the task of automation of the process. Experimental settings have laid optimization criteria (management quality criteria), which limits their scope. Parametric synthesis of the management system that takes into account all requirements technical taskrequires a mathematical model of the object. The article analyzes the structures of mathematical models ventilation unitThe method of identifying the ventilation plant is considered, the possibility of applying the obtained models for use in practice is estimated.

Keywords: identification, mathematical model, ventilating installation, experimental study Mathematical model, criteria for the quality of the mathematical model.

PRACTICAL ASPECTS OF IDENTIFICATION OF MATHEMATICAL MODEL

Of Ventilating Installation

In connection with occurrence of new requirements to systems ventilation, experimental methods of adjustment of the closed contours of management can "t solve a problem of automation of technological process to the full. Experimental methods of adjustment have the put criteria of optimization (criterion of quality of management) that limits area of \u200b\u200btheir application. Parametrical synthesis of the control system, the technical project considering all requirement, demands mathematical model of object. In article to be resulted the analysis of structures of mathematical models of ventilating installation, the method of identification Of Ventilating Installation IS Considered, Possibility of Application of The Received Models for Application In Practice Is Estimated.

Key Words: Identification, Mathematic Model, Ventilating Installation, Experimental Research Of Mathematical Model, Criteria of Quality of Mathematical Model.

Introduction

Ventilation system management is one of the main automation tasks. engineering systems building. Requirements for ventilation installation systems are formulated as quality criteria in the time domain.

Main quality criteria:

1. Transition time (TNN) - the output time of the ventilation mode to the operating mode.

2. The established error (EUST) is the maximum allowable deviation of the temperature of the supplied air from the specified one.

Indirect quality criteria:

3. Overbill (AH) - Power Perpection when controlling the ventilation unit.

4. The degree of oscillativity (y) is excessive wear of the ventilation equipment.

5. The degree of attenuation (y) - characterizes the quality and speed of establishing the desired temperature mode.

The main task of automation of the ventilation system is the parametric synthesis of the regulator. Parametric synthesis is to determine the regulator coefficients to provide the quality criteria of the ventilation system.

For the synthesis of the ventilation unit, engineering methods are selected, convenient for use in practice, which do not require research of the mathematical model of the object: Method No. Subso18-21§1Eg (g), method of SYEP-NGOPE8-KE8, SCS (SNK). TO modern systems Ventilation automation The high demands of quality indicators are imposed, the permissible boundary conditions of indicators are narrowed, multicriterial management tasks appear. Engineering methods for setting up regulators do not allow changing the quality criteria laid in them. For example, when using the N2 method for adjusting the regulator, the quality criterion is the attenuation decrement is equal to four, and when using the method of reference, the quality criterion is the maximum increase rate in the absence of overall. Using these methods in solving multi-criteria management tasks requires additional manual correction of coefficients. The time and quality of configuration of control circuits, in this case, depends on the experience of an engineer of the adjuster.

Application modern means Mathematical modeling for the synthesis of the ventilation system control system significantly improves the quality of the control processes, reduces the timeing time of the system, and also allows you to synthesize algorithmic means of detection and prevent accidents. To simulate the control system, you must create an adequate mathematical model of the ventilation unit (control object).

The practical use of mathematical models without evaluating adequacy causes a number of problems:

1. The settings of the regulator obtained during mathematical modeling do not guarantee compliance with quality indicators in practice.

2. Application in the practice of regulators with a mortgaged mathematical model (forced management, smith extrapolator, etc.) may cause deterioration in quality indicators. If the constant time constant or an understated gain increases the exit time of the ventilation unit onto working mode, with an overwhelmed gain coefficient, excessive wear of ventilation equipment occurs, and so on.

3. Application in practice adaptive regulators with an assessment on the reference model also cause deterioration of quality indicators to the same example.

4. The adjustment settings obtained by optimal control methods do not guarantee the compliance of quality indicators in practice.

The purpose of this study is to determine the structure of the mathematical model of the ventilation unit (according to the control circuit temperature regime) and evaluating its adequacy to real physical heating processes in ventilation systems.

Experience in designing management systems shows that it is impossible to obtain a mathematical model, an adequate real system, only on the basis of theoretical studies of the physical processes of the system. Therefore, during the synthesis of the model of the ventilation plant, experiments were carried out at the same time as theoretical studies were carried out to determine and clarify the mathematical model of the system - its identification.

Technological process of the ventilation system, the organization of the experiment

and structural identification

The control object of the ventilation system is the central air conditioner, in which the air flow is accessed and its feeding to ventilated rooms. The task of the local ventilation control system is automatically maintaining the temperature of the supply air in the channel. The current value of the air temperature is estimated by the sensor installed in the supply channel or in the maintenance room. The adjustment of the temperature of the supply air is carried out by electrical or water calorifer. When using a water carrier, the actuator is a three-way valve, when using an electric carrier - a pulse and thyristor power regulator.

The standard air temperature control algorithm is a closed automatic control system (SAR), with a PID controller as a control device. The structure of the automated control system for controlling the air temperature of the air ventilation is given (Fig. 1).

Fig. 1. Structural diagram of an automated ventilation control system (supply air control channel). WTP - PF Regulator, Life - PF of the Executive Organ, WCAl - Calrifer PF, WW - Air Duct Transmission Function. and1 is the temperature setpoint, Xi - the temperature in the channel, Xi - the sensor readings, E1 is the control error, U1-control effect of the regulator, U2 - testing the actuator of the regulator signal, U3 - heat transmitted by the calorior in the channel.

The synthesis of the mathematical model of the ventilation system assumes that the structure of each transfer function is known, which is included in its composition. The use of a mathematical model containing the transfer functions of individual elements of the system is a challenging task and does not guarantee in practice the superposition of individual elements with the source system. To identify a mathematical model, the structure of the ventilation control system is conveniently divided into two parts: a priori known (regulator) and an unknown (object). The gear ratio of the object ^ O) includes: the transfer function of the actuator ^ Io), the transfer function of the Calrifer ^ channel), the transfer function of the duct ^ BB), the gear ratio of the sensor ^ dates). The task of identifying the ventilation unit when controlling the temperature of the air flow is reduced to the definition of the functional dependence between the control signal to the actuator of the Calrifer U1 and the temperature of the XI air flow.

To determine the structure of the mathematical model of the ventilation unit, it is necessary to conduct an experiment on identification. Obtaining the desired characteristics is possible by passive and active experiment. The passive experiment method is based on the registration of the controlled process parameters in the normal operation of the object without making any intentional perturbations. At the setup stage, the ventilation system is not in normal operation, so the passive experiment method is not suitable for our purposes. The active experiment method is based on the use of certain artificial perturbations entered into an object on a predetermined program.

There are three principled methods for active identification of the object: the transient characteristic method (object reaction to the "step"), the method of perturbation of the object by signals of the periodic shape (the reaction of the object for harmonic perturbations with different frequencies) and the method of reaction of the object on the delta-impulse. Due to the large inertia of the ventilation systems (the TOB is from tens of seconds to a few minutes) identification by race signals

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