Mathematical modeling of factory ventilation. Mathematical model of the process of ventilation of industrial premises, selection and description of automation equipment and controls Supply and exhaust centrifugal fans

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

Antyushin S. S., post-graduate student (Moscow State Institute of Electronics and Mathematics (Technical University)

PRACTICAL ASPECTS OF MATHEMATICAL MODEL IDENTIFICATION

VENTILATION UNIT

Due to the emergence of new requirements for ventilation systems, experimental tuning methods closed loops management cannot fully solve the tasks of automation technological process. Experimental tuning methods have embedded optimization criteria (control quality criteria), which limits their scope. Parametric synthesis of a control system that takes into account all the requirements of the technical specifications requires a mathematical model of the object. The article provides an analysis of the structures of mathematical models ventilation unit, a method for identifying a ventilation unit is considered, and the possibility of using the obtained models for practical application is assessed.

Key words: identification, mathematical model, ventilation unit, experimental study of the mathematical model, quality criteria of the mathematical model.

PRACTICAL ASPECTS OF IDENTIFICATION OF MATHEMATICAL MODEL

OF VENTILATING INSTALLATION

In connection with the occurrence of new requirements to ventilation systems, 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 their application. Parametrical synthesis of the control system, the technical project considering all requirement, demands mathematical model of object. of ventilating installation is considered, the possibility of application of the received models for application in practice is estimated.

Key words: identification, mathematical model, ventilating installation, experimental research of mathematical model, criteria of quality of mathematical model.

Introduction

Control of ventilation systems is one of the main tasks of automation engineering systems building. Requirements for control systems of ventilation units are formulated as quality criteria in the time domain.

Main quality criteria:

1. Transition process time (tnn) - the time the ventilation unit enters the operating mode.

2. Steady error (eust) - maximum tolerance supply air temperature from the set one.

Indirect quality criteria:

3. Overshoot (Ah) - excessive power consumption when controlling the ventilation unit.

4. The degree of fluctuation (y) - excessive wear of ventilation equipment.

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

The main task of automating the ventilation system is the parametric synthesis of the controller. Parametric synthesis consists in determining the coefficients of the controller to ensure the quality criteria for the ventilation system.

For the synthesis of a ventilation unit controller, engineering methods are chosen that are convenient for application in practice and do not require the study of a mathematical model of the object: the Nabo18-21Seg1er(G) method, the CHen-NgoneS-KeS, schk(SNK) method. To modern systems ventilation automation are presented high requirements quality indicators, admissible boundary conditions of indicators are narrowed, there are multicriteria problems of management. Engineering methods for adjusting regulators do not allow changing the control quality criteria embedded in them. For example, when using the N2 method to tune the controller, the quality criterion is a damping factor of four, and when using the SHA method, the quality criterion is the maximum slew rate in the absence of overshoot. The use of these methods in solving multicriteria control problems requires additional manual adjustment of the coefficients. Time and quality of control loop tuning, in this case depends on the experience of the field engineer.

Application modern means mathematical modeling for the synthesis of the ventilation unit control system significantly improves the quality of control processes, reduces the system setup time, and also allows the synthesis of algorithmic means for detecting and preventing accidents. To simulate the control system, it is necessary to create an adequate mathematical model of the ventilation unit (control object).

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

1. The controller settings obtained by mathematical modeling do not guarantee the compliance of quality indicators in practice.

2. The use in practice of controllers with a built-in mathematical model (forcing control, Smith's extrapolator, etc.) can cause a deterioration in quality indicators. If the time constant does not match or the gain is underestimated, the time for the ventilation unit to reach the operating mode increases; if the gain is too high, excessive wear occurs ventilation equipment, etc.

3. The practical application of adaptive controllers with an estimate according to the reference model also causes a deterioration in quality indicators similar to the above example.

4. Controller settings obtained by optimal control methods do not guarantee compliance with 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 loop temperature regime) and assessment of its adequacy to real physical processes of air heating in ventilation systems.

The experience of designing control systems shows that it is impossible to obtain a mathematical model adequate to a real system only on the basis of theoretical studies of the physical processes of the system. Therefore, in the process of synthesizing the ventilation unit model, simultaneously with theoretical research experiments were carried out to determine and refine the mathematical model of the system - its identification.

Technological process of the ventilation system, 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 processed and supplied to the ventilated premises. The task of the local ventilation control system is to automatically maintain the temperature of the supply air in the duct. The current value of the air temperature is estimated by a sensor installed in the supply duct or in the serviced room. The supply air temperature is controlled by an electric or water heater. When using a water heater, the executive body is three-way valve, when using an electric heater - pulse-width or thyristor regulator power.

The standard supply air temperature control algorithm is a closed-loop control system (CAP), with a PID controller as a control device. Structure automated system supply air temperature control ventilation is shown (Fig. 1).

Rice. one. Structural scheme automated control system of the ventilation unit (supply air temperature control channel). Wreg - PF of the regulator, Lio - PF executive body, Wcal - PF of the air heater, Wvv - transfer function of the air duct. u1 - temperature setpoint, XI - temperature in the duct, XI - sensor readings, E1 - control error, U1 - control action of the controller, U2 - working out executive device controller signal, U3 - heat transferred by the heater to the channel.

The synthesis of a mathematical model of a ventilation system assumes that the structure of each transfer function that is part of it is known. The application of a mathematical model containing the transfer functions of individual elements of the system is challenging task and does not guarantee in practice the superposition of individual elements with the original system. To identify the mathematical model, it is convenient to divide the structure of the ventilation control system into two parts: a priori known (controller) and unknown (object). The transfer function of the object ^ob) includes: the transfer function of the executive body ^o), the transfer function of the air heater ^cal), the transfer function of the air duct ^vv), the transfer function of the sensor ^dat). The task of identifying the ventilation unit when controlling the temperature of the air flow is reduced to determining the functional relationship between the control signal to the actuating element of the air heater U1 and the temperature of the air flow XI.

To determine the structure of the mathematical model of the ventilation unit, it is necessary to conduct an identification experiment. Obtaining the desired characteristics is possible by passive and active experiment. The passive experiment method is based on the registration of controlled process parameters in the mode of normal operation of the object without introducing any deliberate perturbations into it. 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 introduced into the object according to a pre-planned program.

There are three principal methods of active object identification: the method transient response(reaction of an object to a “step”), a method of perturbing an object with signals of a periodic form (reaction of an object to harmonic disturbances with different frequencies) and a method of an object’s response to a delta pulse. Due to the large inertia of ventilation systems (TOB ranges from tens of seconds to several minutes), identification by signals of peri

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Supply and exhaust centrifugal fans

A conventional centrifugal fan is a wheel with working blades located in a spiral casing, during the rotation of which the air entering through the inlet enters the channels between the blades and moves through these channels under the action of centrifugal force, is collected by the spiral casing and directed to its outlet. The casing also serves to convert dynamic head to static head. To increase the pressure, a diffuser is placed behind the casing. On fig. 4.1 presented general form centrifugal fan.

A conventional centrifugal wheel consists of blades, a rear disc, a hub, and a front disc. A cast or turned hub, designed to fit the wheel on the shaft, is riveted, screwed or welded to the rear disc. The blades are riveted to the disk. The leading edges of the blades are usually attached to the front ring.

Spiral casings are made of sheet steel and are installed on independent supports, near fans low power they are attached to the beds.

When the wheel rotates, part of the energy supplied to the engine is transferred to the air. The pressure developed by the wheel depends on the density of the air, geometric shape blades and circumferential speed at the ends of the blades.

The exit edges of the blades of centrifugal fans can be bent forward, radial and bent back. Until recently, the edges of the blades were mainly bent forward, as this made it possible to reduce dimensions fans. Nowadays, impellers with backward curved blades are often found, because this allows to increase the efficiency. fan.

Rice. 4.1

When inspecting fans, it should be borne in mind that the outlet (along the air) edges of the blades should always be bent in the direction to ensure a shock-free entry. reverse direction wheel rotation.

The same fans, when changing the rotational speed, can have a different supply and develop different pressures, depending not only on the properties of the fan and the rotational speed, but also on the air ducts connected to them.

Fan characteristics express the relationship between the main parameters of its operation. The complete characteristic of the fan at a constant shaft speed (n = const) is expressed by the dependencies between supply Q and pressure P, power N and efficiency. Dependencies P (Q), N (Q) and T (Q) are usually built on one chart. They select a fan. The characteristic is built on the basis of tests. On fig. 4.2 shows the aerodynamic characteristics of the centrifugal fan VTS-4-76-16, which is used as a supply fan at the implementation site

Rice. 4.2

The fan capacity is 70,000 m3/h or 19.4 m3/s. Fan shaft speed - 720 rpm. or 75.36 rad/s, drive power induction motor fan is 35 kW.

Fan blows outdoor atmospheric air into the heater. As a result of heat exchange of air with hot water passed through the tubes of the heat exchanger, the passing air is heated.

Consider the scheme for regulating the operation mode of the fan VTS-4-76 No. 16. On fig. 4.3 is given functional diagram fan unit when speed control.

Rice. 4.3

The transfer function of the fan can be represented as a gain, which is determined based on aerodynamic characteristics fan (Fig. 4.2). The fan amplification factor at the operating point is 1.819 m3/s (minimum possible, experimentally established).

Rice. 4.4

experimental it was found that in order to implement the required operating modes of the fan, it is necessary to supply the control frequency converter following values voltage (Table 4.1):

Table 4.1 Operating modes supply ventilation

At the same time, in order to increase the reliability of the electric motor of the fans of both the supply and exhaust sections, there is no need to set their operating modes with maximum performance. The task of the experimental study was to find such control voltages at which the norms of the air exchange rate calculated below would be observed.

Exhaust ventilation is represented by three centrifugal fans VC-4-76-12 (capacity 28,000 m3/h at n=350 rpm, asynchronous drive power N=19.5 kW) and VC-4-76-10 (capacity 20,000 m3 /h at n=270 rpm, asynchronous drive power N=12.5 kW). Similarly to the supply for the exhaust branch of ventilation, the values of the control voltages were experimentally obtained (Table 4.2).

To prevent the state of "oxygen starvation" in the working shops, we calculate the air exchange rates for the selected fan operation modes. It must satisfy the condition:

Table 4.2 Operating modes of exhaust ventilation

In the calculation, we neglect the supply air coming from outside, as well as the architecture of the building (walls, ceilings).

The dimensions of the rooms for ventilation: 150x40x10 m, the total volume of the room is Vroom? 60,000 m3. The required volume of supply air is 66,000 m3 / h (for a coefficient of 1.1, it was chosen as the minimum, since the air inflow from the outside is not taken into account). It is obvious that the selected operating modes of the supply fan satisfy the set condition.

The total volume of exhaust air is calculated using the following formula

To calculate the exhaust branch, the modes of "emergency extraction" are selected. Taking into account the correction factor of 1.1 (since the emergency operation mode is taken as the least possible), the volume of exhaust air will be equal to 67.76 m3 / h. This value satisfies condition (4.2) within the limits of permissible errors and previously accepted reservations, which means that the selected fan operation modes will cope with the task of ensuring the air exchange rate.

Also in the electric motors of the fans there is a built-in protection against overheating (thermostat). When the motor temperature rises, the thermostat relay contact will stop the motor. The differential pressure sensor will record the stop of the electric motor and give a signal to the control panel. It is necessary to provide for the response of the ACS of the PVV to an emergency stop of the fan motors.

Forecasting the thermal regime in serviced areas is a multifactorial task. It is known that the thermal regime is created with the help of heating, ventilation and air conditioning systems. However, when designing heating systems, the impact of air flows created by other systems is not taken into account. This is partly justified by the fact that the effect of air flows on the thermal regime can be insignificant with the normative air mobility in the serviced areas.

Application systems radiant heating requires new approaches. This includes the need to comply with human exposure standards at workplaces and taking into account the distribution of radiant heat over the internal surfaces of building envelopes. Indeed, with radiant heating, these surfaces are mainly heated, which, in turn, give off heat to the room by convection and radiation. It is due to this that the required temperature of the internal air is maintained.

As a rule, for most types of premises, along with heating systems, ventilation systems are 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 vapors is stipulated by SP 60.13330.12. Heating ventilation and air conditioning and is at least once, and at a height of more than 6 m - at least 6 m 3 per 1 m 2 of floor area. In addition, the performance of ventilation systems is also determined by the purpose of the premises and is calculated from the conditions of assimilation of heat or gas emissions or compensation for local suction. Naturally, the amount of air exchange must also be checked for the condition of assimilation of combustion products. Compensation of volumes of the removed air is carried out by supply ventilation systems. At the same time, a significant role in the formation of the thermal regime in the serviced areas belongs to the supply jets and the heat introduced by them.

Research method and results

Thus, there is a need to develop an approximate mathematical model of complex processes of heat and mass transfer occurring in a room with radiant heating and ventilation. Mathematical model is a system of equations of air-heat balances for the characteristic volumes and surfaces of the room.

The solution of the system allows you to determine the parameters of the air in the serviced areas when various options placement of radiant heating devices, taking into account the influence of ventilation systems.

We will consider the construction of a mathematical model using the example of a production facility equipped with a radiant heating system and not having other sources of heat generation. Heat fluxes from radiators are distributed as follows. Convective flows rise to the upper zone under the ceiling and give off heat to the inner surface. The radiant component of the heat flux of the radiator is perceived by the inner surfaces of the outer enclosing structures of the room. In turn, these surfaces give off heat by convection to the internal air and by radiation to other internal surfaces. Part of the heat is transferred through the external enclosing structures to the outside air. The calculation scheme of heat transfer is shown in fig. 1a.

We will consider the construction of a mathematical model using the example of a production facility equipped with a radiant heating system and not having other sources of heat release. Convective flows rise to the upper zone under the ceiling and give off heat to the inner surface. The radiant component of the heat flux of the radiator is perceived by the inner surfaces of the outer enclosing structures of the room

Next, consider the construction of the air flow circulation scheme (Fig. 1b). Let's accept the scheme of the organization of air exchange "top-up". Air is supplied in quantity M pr in the direction of the serviced area and is removed from the upper zone with a flow rate M in = M etc. At the level of the top of the serviced area, the air flow in the jet is M page The increase in air flow in the supply jet occurs due to the circulating air, which is detached from the jet.

Let us introduce the conditional boundaries of flows - surfaces on which the velocities have only components normal to them. On fig. 1b, the flow boundaries are shown by a dashed line. Then we select the estimated volumes: serviced area (a space with a permanent stay of people); volumes of the supply jet and near-wall convective flows. The direction of near-wall convective flows depends on the ratio of the temperatures of the inner surface of the outer enclosing structures and the ambient air. On fig. 1b shows a diagram with a falling near-wall convective flow.

So, the air temperature in the serviced area t wz is formed as a result of mixing air from supply jets, near-wall convective flows, and convective heat from the internal surfaces of the floor and walls.

Taking into account the developed schemes of heat transfer and circulation of air flows (Fig. 1), we will compose the equations of heat-air balances for the allocated volumes:

Here With— heat capacity of air, J/(kg °C); Q from is the power of the gas radiant heating system, W; Q with and Q* c - convective heat transfer from the inner surfaces of the wall within the serviced area and the wall above the serviced area, W; t page, t c and t wz are the air temperatures in the supply jet at the entrance to the working area, in the near-wall convective flow and in working area, °C; Q tp - heat loss of the room, W, equal to the sum heat loss through external enclosing structures:

The air flow in the supply jet at the entrance to the serviced area is calculated using the dependencies obtained by M. I. Grimitlin.

For example, for air diffusers that create compact jets, the flow rate in the jet is:

where m is the velocity damping factor; F 0 - cross-sectional area of the inlet pipe of the air distributor, m 2; x- distance from the air distributor to the place of entry into the serviced area, m; To n is the coefficient of non-isothermality.

The air flow in the near-wall convective flow is determined by:

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

Equations heat balance for boundary surfaces have the form:

Here Q c , Q* c , Q pl and Q pt - convective heat transfer from the inner surfaces of the wall within the serviced area - walls above the serviced area, floor and coating, respectively; Q tp.s, Q* tp.s, Q m.p., Q tp.pt - heat losses through the corresponding structures; W With, W* c , W pl, W fri - radiant heat flows from the emitter arriving at these surfaces. Convective heat transfer is determined by the known dependence:

where m J is a coefficient determined taking into account the position of the surface and the direction of the heat flow; F J is the surface area, m 2 ; Δ t J is the temperature difference between the surface and the ambient air, °C; J— surface type index.

Heat loss Q tJ can be expressed as

where t n is the outside air temperature, °C; t J is the temperature of the internal surfaces of the external enclosing structures, °C; R and R n - thermal and heat transfer resistance of the outer fence, m 2 ° С / W.

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

Radiant heat fluxes from emitters of radiant heating systems wj are calculated in terms of mutual radiation areas according to the method for arbitrary orientation of emitters and surrounding surfaces:

where With 0 is the emissivity of an absolutely black body, W / (m 2 K 4); ε IJ is the reduced degree of emissivity of the surfaces involved in heat exchange I and J; H IJ is the mutual radiation area of the surfaces I and J, m 2 ; T I is the average temperature of the radiating surface, determined from the heat balance of the radiator, K; T J is the temperature of the heat-receiving surface, K.

By substituting the expressions for heat flows and air flow rates in jets, we obtain a system of equations that is an approximate mathematical model of heat and mass transfer processes in radiant heating. Standard computer programs can be used to solve the system.

Daria Denisikhina, Maria Lukanina, Mikhail Samoletov

AT modern world it is no longer possible to do without mathematical modeling of air flow in the design 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 to typical rooms and standard solutions for air distribution. When a designer encounters non-standard objects, mathematical modeling methods should come to his aid. The article is devoted to the study of air distribution during the cold period of the year in a pipe production workshop. This workshop is part of the factory complex, located in a sharply continental climate.

Back in the 19th century, differential equations were obtained to describe the flow of liquids and gases. They were formulated by French physicist Louis Navier and British mathematician George Stokes. The Navier-Stokes equations are among the most important in hydrodynamics and are used in the mathematical modeling of many natural phenomena and technical challenges.

Per last years a wide variety of geometrically and thermodynamically complex objects in construction has accumulated. The use of computational fluid dynamics methods significantly increases the possibilities of designing ventilation systems, making it possible to predict with a high degree of accuracy the distributions of velocity, pressure, temperature, and concentration of components at any point in a building or any of its premises.

Intensive use of computational fluid dynamics methods began in 2000, when universal software shells (CFD-packages) appeared, making it possible to find numerical solutions to the system of Navier-Stokes equations in relation to the object of interest. From about that time, BUREAU TEHNIKI has been engaged in mathematical modeling in relation to the problems of ventilation and air conditioning.

Task description

In this study, numerical simulations were performed using STAR-CCM+, a CFD package developed by CD-Adapco. The performance of this package in solving ventilation problems was
repeatedly tested on objects of varying complexity, from office space to theater halls and stadiums.

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

Outside temperature -31 °C. Objects with significant heat inputs are located in the room: hardening furnace, tempering furnace, etc. Thus, there are large temperature differences between the external enclosing structures and internal heat-generating objects. Therefore, the contribution of radiative heat transfer cannot be neglected in the simulation. An additional difficulty in the mathematical formulation of the problem lies in the fact that a heavy train with a temperature of -31 °C is brought into the room several times per shift. It gradually heats up, cooling the air around it.

To maintain the required 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 supply air necessary to maintain the required parameters were calculated. The question remained - how to supply air to the volume of the workshop in order to ensure the most uniform temperature distribution throughout the volume. Simulation made it possible to see the air flow pattern for several air supply options in a relatively short time (two to three weeks), and then compare them.

STAGES OF MATHEMATICAL MODELING

Construction of solid geometry.
Partitioning the workspace into cells of the computational grid. It is necessary to foresee areas in which additional cell refinement is required. When building a grid, it is very important to find that golden mean, in which the cell size is small enough to obtain the correct results, while the total number of cells is not so large as to drag out the calculation time to unacceptable times. Therefore, building a grid is a whole art that comes with experience.
Setting the boundary and initial conditions in accordance with the problem statement. An understanding of the specifics of ventilation tasks is required. plays an important role in the calculation right choice turbulence models.
Selection of suitable physical and turbulence models.

Simulation results

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

To compare the ventilation efficiency, three options for air supply were chosen: at angles to the vertical of 45°, 60° and 90°. Air was supplied from standard air distribution grilles.

The temperature and velocity fields obtained as a result of the calculation at various angles of supply of supply air are shown in Fig. . one.

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

Final decision

The fields of temperature and velocity in three cross sections passing through the supply gratings are shown in Figs. 2 and 3. The temperature distribution throughout the room is uniform. Only in the area where the furnaces are concentrated are higher temperatures under the ceiling observed. There is a colder area in the far right corner of the room far from the stoves. This is the place where cold wagons from the street enter.

From fig. 3 clearly shows how horizontal jets of supplied air propagate. With this method of supply, the supply jet has a sufficiently large range. So, at a distance of 30 m from the grid, the flow velocity is 0.5 m/s (at the exit from the grid, the speed is 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 supply air jet upwards (Fig. 4 and 5). The stove heats up the air around it very strongly. The temperature near the floor is higher here than in the middle part of the room.

The temperature field and streamlines in two sections of the hot shop are shown in fig. 6.

conclusions

The performed calculations made it possible to analyze the efficiency various ways air supply in the pipe production shop. It was found that when a horizontal jet is supplied, the supply air further spreads into the room, contributing to its more uniform heating. This does not create areas with too much air mobility in the working area, as happens when the supply air is supplied at an angle downwards.

The use of mathematical modeling methods in ventilation and air conditioning problems is very promising direction, allowing at the project stage to correct the solution, to prevent the need to correct unsuccessful design solutions after commissioning. ●

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

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Supply and exhaust centrifugal fans

Task description

Simulation results

Final decision

conclusions