Dynamics of temperature regime of lives young dairy animals with local electricity of mathematical model

Abstract

One of the ways to increase the production of livestock products, which simultaneously provides significant energy savings, is the introduction into the energy system of livestock premises with young local means of local electric heating.

The use of infrared (IR) and conductive (contact) electrical heaters intended for the creation of young animals of farm animals and birds of optimum thermal conditions directly in local zones of accommodation can significantly reduce the thermal background in the premises and provide a significant (up to 50 %) energy savings spent on electric heating The maintenance of the created optimal thermal regimes necessitates the automation of the control of electrotechnical means of local electric heating. For the synthesis of automatic control systems for local electric heating parameters, it is necessary to have mathematical formalization of static and dynamic characteristics as means of local electric heating and premises for keeping young animals in general.

Analysis of recent research and publications. Necessity, expediency and efficiency of using modern means of local electric heating of young animals are sufficiently covered in general works [1-6]. The question of the use of infrared heating of young animals is presented in works [1-4], calculation of parameters and operating modes of infrared emitters in animal housing is given in works [3-4].

The justification of the energy parameters and the calculation of the modes of local electric heaters of the floor parts and special electrically heated rugs (panels) is given in [6-7]. Modeling of the processes of thermal interaction of animals with the environment of the premises is described in detail in [5]. But despite the existence of different methods of calculating equipment and models of thermal processes, the mathematical description of the dynamic modes of operation of electrical local heating equipment in the literature is not sufficiently highlighted.

Creation of an improved mathematical description of non-stationary thermal regimes of premises for keeping young animals in the presence of means of local electric heating.

Specificity of the investigated object, which is characterized in the general case, the presence of two types of electric heating appliances (illuminator, electric heating mat) that can be placed in any way indoors makes the expediency of using the analytical method of research without specifying the design parameters of the object. The basis of theoretical research is the analysis of balance relations in the form of a system of differential equations of structural models and transfer functions.

The mathematical description of the control object serves as the basis for the design of systems for the automatic control of thermal regimes. The accuracy of the approximation of the mathematical model to the real processes determines the quality of the calculations of the SAC, and sometimes the principle of control.

Description of the principle scheme of premises for the maintenance of animals with local electric heating young animals.

The mathematical description of the control object serves as the basis for the design of systems for the automatic control of thermal regimes. The accuracy of the approximation of the mathematical model to the real processes determines the quality of the calculations of the SAC, and sometimes the principle of control.

Description of the principle scheme of premises for the maintenance of animals with local electric heating young animals.

The exterior exhaust air with the temperature t_z is preheated to the temperature t₁ in the calorifier and slowly (at a speed of 0.1…0.15 m/s) circulates in the volume of the room, absorbing excess moisture and heat, and is removed from the room with a fan with temperature t₂. Young animals (piglets), as a rule, lie on the heated part of the floor (electrically heated mat), whose temperature T_k; The heat to the lower part of the body of animals is transmitted conductively through the lower part of their surface of the F_mv. The heat from the part of the surface of the carpet not occupied by animals F_k is transmitted by convection to air and by radiation - to the interior parts of the surface of the building. Local heating of the upper part of the animal surface is carried out from above the infrared emitter, the equivalent (effective) temperature is equal to T_vn (effective temperature is the average weighted temperature of all surface elements of the radiator). The radiator generates an energy irradiation on the animal surface with the E_nm value, which is used useful and loses heat in the environment: convection in the air and radiation to the surface of the enclosure.

The temperature t₁ of the air supplied to the room stabilizes the SAC at a given level t₁, and humidity stabilizes the SAR of relative humidity φ₁; so the magnitudes are constant (t₁, φ₁=const).

In analyzing the dynamics of the temperature regime, the room for keeping animals is not enough to take into account only the heat accumulation of the properties of the internal air. In livestock buildings with a local heating system young animals of heat storage tanks (media) at least four: air, external fence, electric heater mat, emitter. When placing an electric heater outside the space of the room, its thermal inertia is not taken into account.

In connection with the presence in the premises of different capacities that can accumulate thermal energy, when compiling differential equations for each of them a separate thermal balance is formed. The following factors are taken into account:

-       heat supply due to animal heat dissipation;

-       flow of heat from sources of electric heating;

-       heat loss with ventilation air;

-       heat consumption for evaporation from the floor;

-       heat exchange between the internal and external surfaces of the fence and air;

-       heat transfer by local heating devices: convection and radiation;

-       heat transfer with the surface of animals in the environment.

In general, the simulation object can be described by a system of differential equations (ie equations for each of the above-mentioned capacities).

In the analysis of thermal processes in the cattle-breeding room, assumptions are made that greatly simplify the simulation procedure: the room is considered as an object with lumped parameters; air indoors perfectly moves; the heat transfer coefficients in time do not change and are equal to the mean values during the transition process.

After the substitution of certain components and their grouping, the mathematical description of the heat processes in the room for the maintenance of animals with local heating, in non-stationary mode in general, is presented as a system of nonlinear equations.

Applying directly the Laplace transform to the linearized equations of the system, taking into account the assumptions made earlier and the zero initial conditions, we obtain the equation of the "Incoming-Output" type for the main thermal capacities of the object.

On the basis of equations and defined transfer functions, a structural scheme is presented, which represents a linear model of the dynamics of the thermal regime of the system of local heating of young animals and the thermal regime of the premises of the pig-breeder under the influence of control and disturbing factors.

Conclusions

1. On the basis of the theoretical analysis of the thermal processes of the premises for the maintenance of animals as an object of automation, a mathematical model of nonstationary regimes of local heating systems of young animals is formulated that allows optimizing the regime parameters of the equipment operation.
2. For the synthesis of SAC by the temperature regime of local heating means, taking into account internal and external disturbances, a structural mathematical model of thermal processes in the room with local heating systems is constructed.

Keywords: livestock premises, air temperature, electric heater pad, infrared suppressor