Building a mathematical model for the heat build-up in the oil tank shell under the thermal effect of a combustible liquid pool fire within the tank dike. methodology. A thermal balance equation for an oil tank exposed to heat from the pool fire has been worked out. Both radiant and convective heat transfer processes between the pool fire and the environment have been taken into account. Estimates for the distribution of temperatures and airflow velocities in the plume above the fire have been used to account for the convection component of the heat flux from the pool fire. findings. Dynamics of the tank shell temperature change in time under the thermal effect of the pool fire within the dike has been obtained. The obtained expression is the solution of the differential equation worked out on the basis of the thermal balance analysis for the oil tank shell exposed to heat. originality. The convective component of the heat flux from the pool fire to the oil tank is taken into account and estimates of the distribution of temperatures and velocities in the plume are built. Practical value. The proposed model of the tank shell heat exposure to the pool fire within the dike could provide the basis for building a decision-making system for the fire response manager, outlining safe zones for positioning the equipment and personnel involved in fire-fighting, while developing fire pre-plans at the oil refining facilities and designing security systems for oil tanks.
Purpose. To construct a model of extinguishing a spill fire spreading on a nonsmooth horizontal surface using water mist. Methodology. A force balance equation for the forces influencing the spilled liquid spread has been worked out. The equation takes into account the change in the mass of the spilled liquid due to its burnout and possible inflow in the case of a continuous spill. Filling of the surface irregularities in the spill area has also been taken into account. There has been worked out a thermal balance equation for the fuel surface under sprayed water mist, based on the assumption that the water droplets completely evapo rate before they reach the surface of the burning fuel. Findings. The dynamics has been obtained for the radius change of the fuel spill for the spread and burnout on a nonsmooth horizontal surface under the assumption of a circular shape of the spill. Relation has been determined between the time required to suppress a spill fire with water mist and the intensity of water feed. Originality. The scientific originality consists in taking into account the surface irregularities and fuel burnout during the spill spread, as well as determining the time required to suppress a spill fire with water mist, depending on the intensity of the water feed. Practical value. The proposed model for the fuel spill spread and fire extinguishing can serve as the basis for the design of a fire protection system for the processing equipment and, in particular, of an automatic water mist fire extinguishing system, at oil ex tracting and oil refining facilities.
A method for determining the dynamic parameters of the operator of a mobile fire engine based on a segway, which fully characterize its dynamic properties – delay time and inertia was developed. The development of the method includes four stages. At the first stage, the problem of obtaining analytical relationships for determining the dynamic parameters of the operator is solved. These relationships include the frequency characteristics of the operator at a fixed frequency and its static parameter. At the second stage, the choice of a fixed frequency is substantiated using a criterion that minimizes errors in determining the dynamic parameters. It is shown that the fixed frequency for the characteristic parameters of the operator does not exceed 0.5 Hz. The third stage includes substantiation of the procedure for determining the frequency characteristics of the operator and its static parameter. The frequency characteristics of the operator at a fixed frequency and its static parameter are determined numerically. This procedure is based on using the data obtained by measuring the values of the operator’s transfer function at fixed time intervals. To obtain data, an interactive analog engine is used, which can also perform the functions of a simulator. The time intervals are chosen according to the Kotelnikov-Nyquist-Shannon theorem. At the last stage, the procedure for determining the dynamic parameters of the operator of a segway-based mobile fire engine is described. It is shown that the error in determining the dynamic parameters of the operator of a mobile fire engine does not exceed 9.0 %, if the error in determining its frequency characteristics at a frequency of 2.5 s–1 does not exceed 2.0 %
При формуваннi алгоритму контролю технiчного стану генераторiв водню в якостi вихiдних даних використовуються їх амплiтудно-частотнi та фазово-частотнi характеристики. При використаннi класичного методу визначення таких характеристик мають мiсце декiлька недолiкiв. Одним iз суттєвих недолiкiв є великий час, який необхiдний для формування масиву вихiдних даних. Для скорочення цього часу визначення частотних характеристик генератора водню здiйснюється за результатами вимiрювань його перехiдної функцiї в дискретнi моменти часу. В цi моменти часу перехiдна функцiя апроксимується функцiями Хевiсайда. Такий пiдхiд дозволяє скоротити час визначення частотних характеристик генератора водню на 1-2 порядки. Використання теореми Котельнiкова-Найквиста-Шеннона для визначення цих дискретних моментiв часу пов'язано iз невизначенiстю стосовно максимальної частоти спектру тест-сигналу. Для зняття цiєї невизначеностi вибiр дискретних моментiв часу для вимiру перехiдної функцiї генератора водню здiйснюється за умови допустимої похибки її апроксимацiї. Похибка апроксимацiї визначається за результатом розв'язання тест-задачi, в якiй в якостi еталону частотних характеристик використовуються модельнi характеристики. Показано, що при iнтервалi дискретностi (0,252,5) мс величина такої похибки не перевищує 1,7 %. Враховано iнерцiйнi властивостi пристрою для формування тест-впливу. Показано, що доцiльнiсть використання такої процедури має мiсце, якщо еквiвалентна постiйна часу такого пристрою перевищує величини постiйних часу генератора водню. Iнерцiйнi властивостi врахованi шляхом введення додаткового множника, який мiстить еквiвалентну постiйну часу пристрою, в аналiтичних виразах для частотних характеристик генератора водню Ключевi слова: генератор водню, вихiднi данi, частотнi характеристики, тест-задача, похибка апроксимацiї
One of the tasks to be solved when deploying fire extinguishing systems is to determine the range of the fire extinguishing agent supply to the combustion center. This problem is solved using data on the trajectory of the fire-extinguishing agent in the combustion center. The presence of wind impact on the process of supplying a fire extinguishing agent will lead to a change in its trajectory. To take into account wind impact, it becomes necessary to assess the result of such impact. Using the basic equation of dynamics for specific forces, a system of differential equations is obtained that describes the delivery of a fire extinguishing agent to the combustion center. The system of differential equations takes into account the presence of wind impact on the movement of the extinguishing agent. The presence of wind action is taken into account by the initial conditions. To solve such a system, the integral Laplace transform was used in combination with the method of undefined coefficients. The solution is presented in parametric form, the parameter of which is time. For a particular case, an expression is obtained that describes the trajectory of the supply of the extinguishing agent into the combustion center. Nomograms are constructed, with the help of which the operative determination of the estimate of the maximum range of the fire-extinguishing agent supply is provided. Estimates are obtained for the time of delivery of a fire-extinguishing agent to the combustion center, and it is shown that for the characteristic parameters of its delivery, this value does not exceed 0.5 s. The influence of wind action on the range of supply of a fire extinguishing agent is presented in the form of an additive component, which includes the value of the wind speed and the square of the time of its delivery. To assess the effect of wind impact on the movement of the fire extinguishing agent, an analytical expression for the relative error was obtained and it was shown that the most severe conditions for supplying the fire extinguishing agent to the combustion center, the value of this error does not exceed 5.5%. Taking into account the wind effect when assessing the range of supply of a fire-extinguishing agent makes it possible to increase the efficiency of fire-extinguishing systems due to its more accurate delivery to the combustion center
This paper substantiates the pulse method for determining the time parameter for fire detectors with a thermoresistive sensing element ‒ the time constant. The method is based on using the Joule-Lenz effect, which manifests itself when an electric current pulse passes through the thermoresistive sensing element of fire detectors. Thermal processes in such a sensing element are described by a mathematical model that belongs to the class of equations of mathematical physics. The solution to the differential equation of this class was derived using the Hankel integral transformation and is represented as a series relative to the Bessel functions. The resulting solution is used to construct a mathematical model of a thermoresistive sensing element in the form of a transfer function, which takes the form of the transfer function of the inertial link. To trigger the thermoresistive sensing element of fire detectors, a single pulse of electric current in the shape of a rectangular triangle is used. The integral Laplace transformation was applied to mathematically describe the response of a thermoresistive sensing element to the thermal effect of such a test influence. To obtain information about the time parameter of fire detectors with a thermoresistive sensing element, the ratio of its output signals is used, which are measured in the a priori defined moments. A two-parametric expression was built to determine the time parameter of fire detectors; a verbal interpretation of the pulse method to determine it was provided. The implementation of this method ensures the invariance of the time parameter of fire detectors with a thermoresistive sensing element relative to the amplitude of a single pulse of an electric current, as well as relative to the parameter that is included in its transfer coefficient.
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