EMERGENCY BURNING OF SOLID ROCKET PROPELLANT: DAMAGE RISK ASSESSMENT TO PEOPLE IN THE WORKPLACE

Dep. «Hydraulics and Water Supply», Dnipro National University of Railway Transport named after Academician V. Lazaryan, Lazaryana St., 2, Dnipro, Ukraine, 49010, tel. +38 (056) 273 15 09, e-mail water.supply.treatment@gmail.com, ORCID 0000-0002-1531-7882 Dep. «Life Safety», Prydniprovska State Academy of Civil Engineering and Architecture, Chernyshevskoho St., 24а, Dnipro, Ukraine, 49600, tel. +38 (056) 756-34-57, e-mail berlov@pgasa.dp.ua, ORCID 0000-0002-7442-0548 Dep. «Fluid Dynamics, Energy and Mass Transfer», Oles Honchar Dnipro National University, Haharina Av., 72, Dnipro, Ukraine, 49000, tel. +38 (056) 374 98 22, e-mail water.supply.treatment@gmail.com, ORCID 0000-0003-2399-3124 Dep. «Hydraulics and Water Supply», Dnipro National University of Railway Transport named after Academician V. Lazaryan, Lazaryana St., 2, Dnipro, Ukraine, 49010, tel. +38 (056) 273 15 09, e-mail v.kozachyna@gmail.com, ORCID 0000-0002-6894-5532 Kharkiv Branch Office «Design and Research Institute of Railway Transport» of the Ukrainian Railway PJSC, Kotliara St., 7, Kharkiv, 61052, tel. +38 (057) 724 41 25, e-mail uzp38@ukr.net, ORCID 0000-0002-2814-380


Introduction
Particularly dangerous are industrial sites, where emergencies are possible with the sudden formation of intense, diverse impact factors (shock wave, heat wave, emission of toxic substances). In this case, it is extremely important to predict the risk of damage to personnel in the workplace during emergencies.
Analytical and numerical forecasting methods are used to determine the risk of personnel damage in case of emergencies [3,[6][7][8][9][10][11][12][13][14][15]. These methods are focused on assessing the risk of toxic damage to humans during accidental releases of toxic substances. At the same time, the task of predicting the risk of thermal damage to people during emergencies is also relevant. This is especially important in cases where there is a fire inside industrial shops with a significant number of workers. The risk of thermal damage may occur, for example, in the event of emergency ignition of solid rocket propellant in the shops. The temperature of the combustion products of solid rocket propellants is very high. Due to the high emission of heated propellant combustion products, the area of thermal contamination spreads across the shop and there is a risk of thermal damage to personnel in the work areas. To assess the risk of thermal damage to personnel, it is necessary to have mathematical models. The paper envisages the development of a numerical model for assessing the risk of thermal damage to people in the workplace in the event of emergency burning of solid rocket propellant (SRP) for Thunder-2 rocket (Fig. 1).

Methodology
To assess the risk of thermal damage to people in the workplace in the event of emergency burning of solid rocket propellant, we will use the equation of convective heat transfer (two-dimensional, planned model, Boussinesq approximation) [4,7]: where TT  , where 0 T is the known air temperature in the calculation area, for example 0 in TT  . The temperature of burning products is set at the place of solid propellant combustion [7]. By solving equation (1) we can determine the temperature distribution in the working areas in the shop. The important thing is that one can obtain a non-steady solution to the problemthe data of changes in the temperature distribution in the shop over time. The risk of thermal damage [7] is determined from the following condition: if the air temperature in the working area is more than 100 ºC, at which there is a complete protein denaturation, then at this point in the working area it is assumed that the risk of damage is 100 %. To numerically solve equation (1), we split the energy equation at the differential level into a sequence of such equations [5,7]: (3) Next, we use a non-explicit difference scheme to numerically integrate one-dimensional energy equations [5,7]. Let us perform the following transformations: The splitting scheme for equation (2) is written as follows [5,7]: in the first step, the difference equation has the form: ,, in the second step, the difference equation takes the form: 1 ,, 11 .
The splitting scheme for numerical integration of equation (3) will be as follows: in the first step we obtain the difference equation: in the second step of splitting, the difference equation will have the form:

M T M T t
The unknown value of temperature T at each splitting step (4) - (7) is calculated by the formula of the point-to-point computation.
The air velocity field u, v, in the presence of obstacles at the industrial site, is determined based on the model of the movement potential [2,3,7]: The boundary conditions for equation (8) are as follows [2,3,7] 3) P = constat the boundary of the outflow of the calculation area.
To numerically solve this equation, we will use the scheme of conditional approximation [5]. The difference splitting equations in this case are as follows [5]: in the first step of splitting: ; (9) in the second step of splitting: Unknown values of the velocity potential To start the calculation it is necessary to set the «initial» value of the velocity potential in the calculation area, during the calculation we take the value 0 , 0 ij P  . The components of the air velocity vector are calculated on the sides of the computational cell as follows [3,7]: After calculating the velocity component, we perform the solution of the energy equation where this field is used.
Let us consider the algorithm for solving the problem of determining the potential risk of thermal damage to personnel in the shop [1,2,7]. First, based on numerical integration of fundamental equations (energy equations and equations for velocity potential) we perform the calculation of the temperature distribution in the shop for different emergencies. When assessing the risk, we assume that the probability of each emergency is known. After calculating the temperature field for different accident scenarios in the shop, the computer program determines the areas where the value of air temperature is greater than the temperature of the damage.
Then we print the forecast results of the thermal damage risk for a certain time point. In this article the various probability of fire point of rocket propellant in shop is considered.
The numerical solution of all difference equations has been programmed. FORTRAN was used to create computer code to simulate the process of thermal air pollution.

Findings
The constructed numerical model was used to assess the potential risk of thermal damage to people in the shop where the solid rocket propellant of Thunder-2 rocket is located. In the event of emergency that leads to the burning of solid rocket propellant inside the shop, there may be a «domino» effectthe ignition of the propellant of a neighboring rocket engine.
The scheme of the calculation area is shown in Fig. 2. The arrow in the Figure shows the direction of air movement in the shop. During the calculations, the task was set to determine the level of temperature pollution in the shop over time and in the working area (position no. 2 in Fig. 2). The air exchange rate in the shop is equal to кр = 15. The initial air temperature in the shop is 20 ºС. We assumed that the temperature of combustion products at the accident site is equal to 1 000 ºC [7]. For the calculations, the influence of the engine housings in the shop on the formation of temperature fields was taken into account. Below Fig. 3 and 4 show the changes dynamics in air temperature in the shop for different time periods after the emergency. The analysis of the given Figures shows that the thermal pollution zone is formed very quickly in the shop. A zone with a high temperature gradient is formed near the emission source. Fig. 5 shows the temperature change over time in the working area. As we can see from the Figure, the air temperature rises very quickly in the working area. In 7 seconds it almost reaches the value of 270 ºC, i.e. there is a risk not only of thermal damage to personnel, but also of a «domino» effectignition of a neighboring rocket engine, which is located at a distance of 5 m from the engine where the fire started. Fig. 7, 8 show the results of solving another problem to assess the risk of thermal damage to personnel in the shop. The situation when several solid propellant engines are located in the shop is considered (Fig. 6), and the further probability of emergencythe probability of engine ignition in zone no. 1 is 25 %, and in zone no. 2 -75 %.  It should be noted that it took about 5 seconds computer time to solve the problem.

Originality and practical value
A computer model has been built to quickly assess the potential risk of thermal damage to people in the shop in the event of emergency ignition of solid rocket propellant. A code has been developed that allows to quickly model the formation of temperature fields in the shop in case of emergency ignition of solid rocket propellant and to determine the areas of potential thermal damage to workers based on this information.
The developed computer program can be used to assess the risk of thermal damage in the chemical industry in the event of emergency.

1.
A computer model has been proposed to predict the risk of thermal damage to shop workers in the event of emergency that results in the ignition of solid rocket propellant.
2. Based on computer simulation data, it can be concluded that in the event of emergency in the shop, there will be lethal thermal damage to workers.