Calculating friction force and thermal action of a jet engine jet on the inner surface of a tubular guide Текст научной статьи по специальности «Физика»

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CALCULATING FRICTION FORCE AND THERMAL ACTION OF A JET ENGINE JET ON THE INNER SURFACE OF A TUBULAR GUIDE

Oleksandr M. Shyikoa, Anatoly M. Pavlyuchenkob, Olexii A. Obukhovc

a National Agricultural University, Sumy, Ukraine, e-mail: shyikoa@ukr.net, corresponding author, ORCID iD: http://orcid.org/0000-0002-4297-911X b National Agricultural University, Sumy, Ukraine, e-mail: apavlucenko22@gmail.com, ORCID iD: https://orcid.org/0000-0003-0827-2847 c Research Center of Rocket Forces and Artillery, Sumy, Ukraine, e-mail: obukhov.olexii@gmail.com, ORCID iD: https://orcid.org/0000-0003-0846-2288

DOI: 10.5937/vojtehg68-24619; https://doi.org/10.5937/vojtehg68-24619

FIELD: Mechanics, Artillery and Rocket Weapons ARTICLE TYPE: Original scientific paper ARTICLE LANGUAGE: English

Summary:

Introduction/purpose: To study the dynamics of launchers with sources of high-energy gas jets, it is relevant to calculate shear forces from the action of a high-temperature supersonic jet on the inner surface of a cylindrical channel and the temperature of the channel walls. The aim of this work is to develop a comprehensive method for calculating aerodynamic friction and heating on the inner surface of a tubular guide of a rocket. Methods/results: The research method is based on the theory of supersonic gas flows in cylindrical channels and the theory of the boundary layer. The gas jet is considered continuous, stationary and axisymmetric. The system of differential equations of motion of the projectile in the guide integrates numerically over time. The flow parameters in the pipe sections are found according to the dependences of the theory of supersonic gas flows, taking into account friction losses. To calculate shear stress on the guide wall, we use the relations of the asymptotic theory of the turbulent boundary layer, the theory of turbulent spots ofEmmons ofthe transition boundary layer, and data on the Reynolds numbers of the beginning of the laminar-turbulent transition in wind tunnels. At the same time, the differential equation for heating the thin wall of the guide in the range of contact between the surface of the guide and the jet is numerically integrated. The calculations of the distribution of flow parameters, friction force and the temperature of the

wall of the tubular guide during the movement of the projectile inside the jet from the moment the engine is started to the moment the shell exits completely from the guide are performed and graphically presented. Conclusions: This method of calculating aerodynamic friction and heating on the inner surface of a tubular guide of a rocket due to a high temperature supersonic gas jet - taking into account the effects of nonisothermality, compressibility and laminar-turbulent transition in the boundary layer - can be used to study the dynamics of the launch of rockets from launchers equipped with tubular guides.

Keywords: launcher, tubular guide, rocket, engine jet, boundary layer, friction force of the jet, heating the tubular guide.

Introduction

The movement of certain mechanical objects in cylindrical channels, for example, rockets in tubular guides of launchers (Fig. 1), occurs under the influence of a high-temperature supersonic gas jet. To ensure strength from power and thermal load of the jet, to create physical and mathematical models of the dynamics of propulsion systems with sources of high-energy gas jets, it is relevant to calculate the normal and tangential forces from the action of a high-temperature supersonic jet on the inner surface of the cylindrical channel and the temperature of the channel walls.

Many publications devoted to the oscillations of launchers at the launch of rockets from tubular guides do not take into account the action of gas-dynamic friction forces on the inner surface of the tubular guide from the side of the high-energy high-temperature jet of gases from the rocket engine during its movement inside the tubular guide (Svetlickij, 1986), (Somoiag et al, 2007, pp.95-97), (Dziopa et al, 2015, pp.72-73). Some of these publications (Antunevich et al, 2017, pp.209-210), (Svetlickij, 1986) contain an indication of the need to use the pressure of the gas jet in the calculations of launcher oscillations. At the same time, the content embedded in this concept is not disclosed and the method for calculating the force is not described.

In his work, Bogomolov (2003, pp.89-97) describes in detail a method for calculating the friction force of a gas jet of a jet engine on the inner surface of a tubular guide. The disadvantage of the described method is that the calculation of the friction force is based on the equations of an incompressible fluid, without taking into account the compressibility of the jet and heating of the guide wall.

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Figure 1 - Mobile launcher with a tubular guide Рис. 1 - Мобильная пусковая установка с трубчатой направляющей Слика 1 - Самоходни вишецевни ракетни лансер

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Purpose of the research

This work aims at developing a comprehensive method for calculating aerodynamic friction and heating on the inner surface of a rocket tubular guide from the action of a high-temperature supersonic gas jet. The calculation method should take into account the effects of non-isothermality, compressibility and laminar-turbulent transition in the boundary layer on the streamlined inner surface of the tubular guide. The aim is also to perform and graphically present the calculations of the distribution of flow parameters, friction force, and the temperature of the wall of the tubular guide when the projectile moves inside the tubular guide from the moment the engine starts and until the projectile completely leaves the guide.

Presentation of the main material

In this paper, we consider the methodology and the results of calculating the time-variable total friction force on the inner surface of a cylindrical channel and heating a thin channel wall from the passage of a source of a high-temperature supersonic gas jet. The calculation is performed under the following assumptions: the gas jet is continuous, stationary, one-dimensional and axisymmetric; the parameters at the beginning of the jet are determined by the parameters in the outlet

section of the nozzle of the jet source and are constant over the pipe section. Constant along the pipe cross section, the average flow parameters in the channel are found according to the dependences of the theory of adiabatic supersonic gas flows in cylindrical channels of a constant cross section, taking into account friction losses.The calculation of the friction force and heating of the wall of the tubular guide is carried out using the calculation model of the translational motion of the projectile in the guide (Fig. 2).

The system of differential equations for the accelerated motion of the center of mass of the projectile takes into account the action of the engine's traction force P, the force of gravity Mg, the friction force FT, the support reaction R, and the components of the helical groove reaction Nx and Ny. The system of equations is solved numerically by

the Runge-Kutta method. At each next step of numerical integration, there is an elementary movement of the projectile inside the tubular guide and the flow parameters are calculated in the interval between the engine nozzle cross section and the cross section of the tubular guide exit. At the same time, the numerical integration of the differential equation for heating the wall of the tubular guide in this interval occurs. The calculations occur in the following sequence.

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Figure 2 - Calculation model of the movement of the projectile in the tubular guide Рис. 2 - Расчетная модель движения снаряда в трубчатой направляющей Слика 2 - Модел прорачуна креташа проjектила у лансирноj цеви

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The gas flow velocity at the nozzle exit of the jet engine will be found by the dependence (Abramovich, 1991)

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Va = Aa •aKp \l~k^j 'Tk (1)

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g constant. The pressure, density and temperature of the gas at the nozzle

° exit of the jet engine will be found from the corresponding known

< dependencies for the adiabatic flow:

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In this case, the reduced mass flux density at the nozzle exit q(Aa) is equal to the ratio of the mass flux density (pa • Va) at the nozzle exit to the mass flux density in the critical nozzle section. For the known areas of the critical SKp and output Sa sections of the nozzle, we perform a

calculation from the dependence q(Aa) = SKp/ Sa (pK ,VK - the density and

velocity of the gas flow in the critical section of the nozzle, respectively).

The relative velocity in the section is related to the relative velocity in the previous section A;-i by the specific work of the friction forces with the following dependence (Abramovich, 1991):

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The friction drag coefficient of the elementary region ^ is determined by the Nikuradze formula for the turbulent adiabatic flow of an incompressible fluid in a technically smooth cylindrical channel

t = 0.0032 + 0.2211Rei0237 , (5)

V = v-1 ; Pi =Pi-i -A (6)

p = ^-|i-I+fA2)/(i-I+Hi>V (7)

where p; is the static pressure p according to (7) in kgf/m2.

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where the local Reynolds number Re; = V; -D/; Y,^ - average velocity and kinematic viscosity of the flow in the elementary region. In the future, when calculating all other parameters of the gas jet, we will consider them as the average cross section. Due to the constant braking temperature, the critical velocity along the pipe also does not change. In connection with this, the ratio of the relative velocities in the pipe sections § is equal to the ratio of velocities and, based on the continuity equation, the inverse ratio of densities. The velocity and density in an arbitrary section is related to the velocity and density in the previous section of the pipe by the given velocities as follows:

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In this case, the static pressure in an arbitrary section of the tubular guide p; is expressed through the pressure pi-1 in the previous section, the relative velocity in this and the previous section of the pipe in this way (Abramovich, 1991) o

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where - the relative velocity in the tubular guide section, and A;-1 - 3

the relative velocity in the previous tubular guide section. o

The dependence of the kinematic viscosity coefficient (m2/s) on 0 pressure is taken into account using the dependence (Bogomolov, 2003)

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The elementary friction force is determined using the theory of the boundary layer. Depending on the values of the Reynolds number calculated from the average values of the flow parameters in the channel, <3 the flow in each elementary section of the pipe is considered laminar, ° transitional or developed turbulent. The calculated value of the Reynolds number of the beginning of the laminar-turbulent transition is taken from the given experiments on the transition in supersonic wind tunnels. The R, average values of the flow parameters in the guide tube calculated from dependences (6)^(7) are taken as the values of the flow parameters at the outer boundary of the boundary layer (velocity ue = Vi, static pressure

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Cfl = Cfo y y (9)

where y,y* are the parameters that take into account the non-Q isothermal flow around the flat plate with the laminar boundary layer; d y = Tw/Tre - the temperature factor, y* = Tre/Te - the kinetic temperature factor; Tw - the temperature of the surface of the channel J wall; Te - the temperature at the outer boundary of the boundary layer; o Tre - the temperature recovery boundary layer; cf0- the local coefficient o of friction for the laminar boundary layer of an incompressible fluid on a flat longitudinally streamlined plate with the same Reynolds number on the outer boundary of the boundary layer, which can be calculated, for example, according to the Blasius formula (Kutateladze, 1979)

Cfo = ; Re,e (10)

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where X is the distance from the nozzle exit of the gas stream source to the place of determination of the Reynolds number of the elementary section of the channel and is the dynamic coefficient of viscosity of fuel combustion products at the outer boundary of the boundary layer.

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Pe,ue, cp,e - the density, speed and heat capacity, respectively, of the

fuel combustion products in the solid propellant rocket engine at the outer boundary of the boundary layer in the guide tube at constant pressure.

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The recovery temperature Tr,e calculated from the parameters Te and Me at the outer boundary of the laminar boundary layer g-(Kutateladze, 1979) is

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The non-isothermal flow of a high-temperature supersonic gas stream around the inner surface of the tubular guide is taken into account using the temperature of the guide wall, which is included in the expressions for the temperature factor r- Tw /Tre, using the differential o

heat balance equation for a thin wall (Leontiev & Pavlyuchenko, 2008):

dT

Pw • cw -Sw-—¡f-a'(Tr: - Tw ) (13)

where Tw - the wall temperature; f - the time; pw,cw,8w - the wall density, heat capacity and thickness; a - the heat transfer coefficient for external laminar or turbulent flow.

In the case of a laminar flow regime, the heat transfer coefficient al

according to the formula containing the Stanton number St (Kutateladze, 1979) reads:

al - Stl - P:-u:-cp,, , (14)

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To calculate the local coefficient of friction and the heat transfer coefficient in the boundary layer on the inner surface in the guide tube in the case of a turbulent boundary layer, we use the results of the asymptotic theory of the turbulent boundary layer by academicians S.S. Kutateladze and A.I. Leontiev. The theory is valid both for Reynolds numbers Re and for their arbitrarily large finite values. Based on this theory, the method of calculating heat transfer and friction has demonstrated its effectiveness in solving complex problems of heat transfer and turbulent friction both in internal flow conditions (nozzles, heat exchangers, etc.) and in solving aerodynamic problems in external flow. An important advantage of the method is its efficiency and, to a certain extent, universality, which is determined by the possibility of separately accounting for the influence on heat transfer and friction of compressibility, non-isothermal and longitudinal pressure gradient by the corresponding relative laws of friction when calculating heat transfer and surface friction resistance in a boundary turbulent layer.

In accordance with (Kutateladze et al, 1985), the local coefficient of friction for a non-isothermal compressible turbulent boundary layer can be calculated from the dependence:

Cf0 - the local coefficient of friction for a turbulent boundary layer of an incompressible fluid on a flat plate is the same Rexe; , - the value

of the dynamic viscosity coefficient of the liquid at the wall temperature Tw and the flow temperature at the outer boundary of the boundary layer Te, respectively; Rex,e - the Reynolds number at the outer boundary of

the boundary layer, which is determined taking into account the dependence of the velocity ue on the longitudinal pressure gradient gradPx; ¥M and ¥t - relative laws of friction resistance, taking into account compressibility and non-isothermality in the boundary layer, respectively

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aT = StT • Pe ' ue ' cp ,e (18)

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Tr,e - the recovery temperature calculated by the parameters Te and Me

at the outer boundary of the turbulent boundary layer; = ^Pr -the coefficient of temperature recovery for a turbulent boundary layer; Pr -the Prandtl number; k = 1.25 (Bogomolov, 2003) is the adiabatic index of ^ the propellant products of solid propellant combustion. The Stanton r number, which determines the heat transfer in a non-isothermal compressible turbulent boundary layer to the surface of the streamlined body, in accordance with (Kutateladze et al, 1985), can be calculated from the following relationships:

StT = St0 -(YM -YJ0'8.^wj''2 ; Sto = 0, 0288-Ree%2 - Pr~23 , (17)

In this case, the heat transfer coefficient for a non-isothermal ° compressible turbulent boundary layer has the expression: ^

The calculation of the local values of the coefficient of friction and the heat transfer coefficient on the inner surface of the tubular guide under conditions of laminar-turbulent transition is carried out using the theory of turbulent spots of Emmons (Emmons, 1951, p.490). According to Emmons, the transition region is characterized by the alternating appearance of turbulent spots which do not interact with each other and which, expanding along the flow, merge to form a turbulent boundary layer. The intermittency of turbulent spots relative to a streamlined surface is characterized by the alternation of laminar and turbulent flows in the transition zone. This process is quantified using the intermittency g coefficient y. The expressions for y, which varies from 0 to 1, are used in calculating the coefficients of friction and heat transfer resistance in the region of the laminar-turbulent transition using the values of the friction and heat transfer coefficients for the laminar and turbulent flow regimes ^ under given conditions at the outer boundary of the boundary layer. o

In (Chen & Thyson, 1971, p.821), on the basis of the theory of o Emmons's turbulent spots and the established relationship between the spot formation rate and the Reynolds number at the beginning of the transition zone, an expression was obtained for the intermittency coefficient which is valid for a laminar-turbulent flow around a thermally insulated surface:

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^ turbulent transition in the boundary layer; Retr - the Reynolds number at q the beginning of the transition zone. ^ In the case of the laminar-turbulent transition in the supersonic

< boundary layer, the heat balance equation for a thin wall under the Biot criterion Bi □ 1.0 has the form (Leontiev & Pavlyuchenko, 2008)

dTw

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where aj and aT are the heat transfer coefficients for laminar and

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turbulent flows in the boundary layer, respectively, according to w dependences (14) and (18).

If the Reynolds numbers at the points of the streamlined surface 2 reach the beginning of the laminar-turbulent transition Retr, the calculation of the local friction coefficient in the transition zone should be

w carried out according to

i— o

Cf = Cfl-(1 -r) + Cjr-r, (21)

where Cjj and cfT are the local friction coefficients for the laminar and turbulent boundary layer and y is the intermittency coefficient according to dependence (19). The elementary friction force of a gas jet in a section of a rocket tube guide with a diameter D is determined by the local coefficient of friction, the velocity-head of the stream, calculated from the parameters at the outer boundary of the boundary layer, and the area of the elementary section of the inner surface of the tubular guide:

F. = cf. = 0-5 ' n-Di-a f ■pi-yi2-dxi (22)

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Using the above dependencies, the distribution of the average parameters of the gas flow from the jet engine inside the tubular guide, the friction force on the inner surface of the tubular guide, and the temperature of the wall of the tubular guide from the action of a high-temperature gas jet were calculated for the following parameters: the ^ inner diameter of the guide D = 0.122 m, the length of the guide L = 3.0 m, the estimated time of the projectile in the guide x = 0.131 s., the critical

sectional area of the nozzle of the solid propellant motor Skrr = 19.6-10 4

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m2, and the cut-off area of the nozzle of the solid propellant motor Sa = 75.2-104 m2. The pressure in the chamber of the rocket engine pc = 13 mPa, the temperature in the chamber of the rocket engine TK = 2200 K, the density of the products of combustion of rocket powder in the combustion chamber of the engine pc = 17.06 kg/m3, the specific gas constant for the products of combustion of rocket powder RM = 346.42 J/(kgK), the adiabatic index for the products of combustion

of rocket powder k=1,25, the Prandtl number Pr = 0.75 , and the Reynolds number at the beginning of the transition zone Retr = 5 -106. ^

The relative velocity at the nozzle exit of the engine is found from equation (3) by the method of successive approximations. The average flow parameters over the pipe cross section are found according to the theory of supersonic one-dimensional adiabatic gas flows in cylindrical | channels of constant cross section, taking into account viscous friction losses in accordance with the Darcy-Weisbach formula and the friction coefficient calculated by the Nikuradze formula (5). The relative velocity at each elementary section of the tubular guide is found from equation (4) by the method of successive approximations. The friction force is calculated on the basis of the theory of a compressible boundary layer £ taking into account the non-isothermal flow around the inner surface of the tubular guide, the use of relations for friction and heat transfer of the laminar boundary layer, the asymptotic theory for the turbulent boundary layer S. S. Kutateladze and A. I. Leontyev, the theory of turbulent spots $ of Emmons of the transition boundary layer, and the data on the Q-Reynolds numbers of the beginning of the laminar-turbulent transition obtained in wind tunnels. hy

Fig. 3 shows the results of the calculations of the friction force of a gas jet on the inner surface of a tubular guide.

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Figure 3 - Calculated dependences of the friction force F of the gas jet on the inner surface of the tubular guide on the displacement X of the nozzle of the projectile's engine inside the guide (the projectile moves from left to right) Рис. - 3 Расчетная зависимость силы трения F газовой струи на внутренней

поверхности трубчатой направляющей от перемещения X среза сопла двигателя снаряда внутри направляющей (снаряд движется слева направо) Слика - 3 Израчуната зависност силе треша F млаза гаса на унутрашшоj површини лансирне цеви од креташа X пресека млазнице мотора проjектила унутар водилице (проjектил се помера са леве на десну страну)

In Fig. 4, the calculated dependence of the Mach number and the relative flow velocity Л along the length of the tubular guide at the moment the projectile leaves the guide is shown. The dependences for the velocity and density of the gas flow along the length of the pipe are shown in Fig. 5. Fig. 6 shows the calculated distribution of the dependence of the intermittency coefficient y along the tubular guide length. Fig. 7 presents the calculated dependence of the tubular guide length on its wall temperature calculated using the differential equation for a thin wall, taking into account fluid compressibility and non-isothermality in the boundary layer. The temperature distribution corresponds to the moment the projectile leaves the guide.

Figure 4 - Calculated dependence of the Mach number M (1) and the relative velocity of the gas stream A (2) along the length of the tubular guide at the moment the projectile

leaves the guide (the flow moves from right to left) Рис. 4 - Расчетная зависимость числа Маха М (1) и относительной скорости газового потока A (2) по длине трубчатой направляющей в момент выхода

снаряда из направляющей (поток движется справа налево) Слика 4 - Израчуната зависност маховог броjа М (1) и релативне брзине протока гаса A (2) дуж лансирне цеви у тренутку избациваша проjектила из цеви (проток се креПе са десне на леву страну)

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Figure 5 - Calculated dependence of the velocity V (1) and density p (2) along the length of the tubular guide at the moment the projectile leaves the guide (the flow moves from

left to right)

Рис. 5 - Расчетная зависимость скорости V (1) и плотности p (2) по длине трубчатой направляющей в момент выхода снаряда из направляющей (поток

движется слева направо) Слика 5 - Процежена зависност брзине V (1) и густине p (2) дуж лансирне цеви у тренутку избациваша проjектила из цеви (проток се помера са леве на десну

страну)

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Figure 6 - Calculated dependence of the intermittency coefficient y along the length of the tubular guide at the moment the projectile leaves the guide (the flow moves from left

to right)

Рис. 6 - Расчетная зависимость коэффициента перемежаемости y по длине трубчатой направляющей в момент выхода снаряда из направляющей (поток

движется слева направо) Слика 6 - Процежена зависност коефици'ента испрекиданости дуж лансирне цеви у тренутку избациваша проjектила из цеви (проток се помера са леве на

десну страну )

Figure 7 - Calculated dependence for the temperature of the wall Tw of the tubular guide along its length at the moment the projectile leaves the guide (the flow moves from right

to left)

Рис. 7 - Расчетные значения температуры стенки трубчатой направляющей Tw по ее длине в момент выхода снаряда из направляющей (поток движется справа

налево)

Слика 7 - Прорачунате вредности температуре зида лансирне цеви Tw дуж цеви у тренутку избациваша проjектила из цеви (проток се креПе са десне на леву

страну)

Conclusions

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1. A complex method has been developed for calculating aerodynamic friction and heating on the inner surface of a rocket-guiding tube due to the action of a high temperature supersonic gas jet, taking into account the effects of non-isothermality, compressibility and laminarturbulent transition in the boundary layer on the streamlined inner surface of the tubular guide.

2. The developed method is based on the use of relations for the laminar boundary layer, the asymptotic theory for the turbulent boundary S layer of S.S. Kutateladze and A.I. Leontyev, the theory of turbulent spots of Emmons of the transition boundary layer and the data from the Reynolds numbers of the beginning of the laminar-turbulent transition obtained in wind tunnels.

3. The obtained numerical results show calculating the friction force of a high-temperature gas jet on the inner surface of the tubular guide and the temperature of the thin-walled tubular guide when moving inside the guide of a missile with a working engine in real time. 'j?

4. The results of the calculations of the gas jet friction force, obtained on the basis of the developed method, can be used to study the dynamics of the launch of rockets from launchers equipped with tubular o guides.

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References I

Abramovich, G.N. 1991. Prikladnaja gazovaja dinamika. Moscow: Nauka, Glavnaja redakcija fiziko-matematicheskoj literatury (in Russian). (In the original: Абрамович, Г.Н. 1991. Прикладная газовая динамика. Москва: Наука, | Главная редакция физико-математической литературы).

Antunevich, A.L., Il'jov, I.G., Goncharenko, V.P.& Mironov, D.N. 2017. J Application of mathematical models for the analysis of complex mechanical system undergoing heterogeneous variable actions. Repository of Belarusian National Technical University, pp.207-213 (in Russian). (In the original: Антуневич, А.Л., Ильёв, И.Г., Гончаренко, В.П., Миронов, Д.Н. 2017. Применение математической модели для анализа сложной механической ^ системы, подверженной неоднородным переменным воздействиям. Q-Репозиторий БНТУ, с.207-213). [online]. Available at: http://rep.bntu.by/handle/data/28261. [Accessed: 21 December 2019].

Bogomolov, A. I. 2003. Osnovanija ustrojstva i raschet reaktivnyh system. £ Penza: Penza Artillery Engineering Institute (in Russian). (In the original: Богомолов, А.И. 2003. Основания устройства и расчет реактивных систем. Пенза: Пензенский артиллерийский инженерный институт).

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о

о

Chen, K.K., & Thyson, N.A. 1971. Extension of Emmons' spot theory to flows on blunt bodies. AIAA Journal, 9(5), pp.821-825. Available at: https://doi.org/10.2514/3.6281. jg Dziopa, Z., Buda, P., Nyckowski, M., & Pawlikowski, R. 2015. Dynamics of

-5 an unguided missiles launcher. Journal of theoretical and applied mechanics, > 53(1), pp.69-80. Available at: https://doi.org/10.15632/jtam-pl.53.1.69. eg Emmons, H.W. 1951. The Laminar-Turbulent Transition in a Boundary

° Layer. Part I. Journal of the Aeronautical Sciences, 18(6), p.490. Available at: oc https://doi.org/10.2514/8.2010.

¡2 Kutateladze, S.S. 1979. Osnovy teorii teploobmena. Moscow: Atomizdat (in

g Russian). (In the original: Кутателадзе, С.С. 1979. Основы теории

0 теплообмена. Москва: Атомиздат).

< Kutateladze, S.S. et al. 1985. Teplomassoobmen i trenie v turbulentnom

^ pogranichnom sloe. Moscow: Jenergija (in Russian). (In the original:

1 Кутателадзе, С.С. и др. 1985. Тепломассообмен и трение в турбулентном ш пограничном слое. Москва: Энергия).

Leontiev, A.I., & Pavlyuchenko, A.M. 2008. Investigation of laminaron turbulent transition in supersonic boundary layers in an axisymmetric ^ aerophysical flight complex and in a model in a wind tunnel in the presence of heat transfer and suction of air. High Temperature, 46(4), pp.542-565. Available at: https://doi.org/10.1134/s0018151x08040159.

Somoiag, P., Moraru, F., Safta, D., & Moldoveanu, C. 2007. A S Mathematical Model for the Motion of a Rocket-Launching Device System on a Heavy Vehicle. WSEAS transactions on applied and theoretical mechanics, 4(2), _ pp.95-101 [online]. Available at: https://www.researchgate.net/publication/261708644. о [Accessed: 21 December 2019].

Svetlickij, V.A. 1986. Dinamika starta letatelnyh apparatov. Moscow: Nauka ш (in Russian). (In the original: Светлицкий, В.А. 1986. Динамика старта о летательных аппаратов. Москва: Наука).

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РАСЧЕТ СИЛОВОГО И ТЕРМИЧЕСКОГО ВОЗДЕЙСТВИЯ СТРУИ ДВИГАТЕЛЯ РЕАКТИВНОГО СНАРЯДА НА ВНУТРЕННЮЮ ПОВЕРХНОСТЬ ТРУБЧАТОЙ НАПРАВЛЯЮЩЕЙ

Александр Н. Шийко, корреспондент3, Анатолий М. Павлюченко®, Алексей А. Обухов6

' Национальный аграрный университет, Сумы, Украина Научно-исследо Сумы, Украина

б Научно-исследовательский центр ракетных войск и артиллерии,

РУБРИКА ГРНТИ: 78.25.16 Вооружение и техника ракетных войск;

78.25.17 Вооружение и техника войск ПВО ВИД СТАТЬИ: оригинальная научная статья ЯЗЫК СТАТЬИ: английский

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Резюме:

Введение/цель: Для исследования динамики пусковых установок с источниками высокоэнергетических газовых струй актуальным является расчет касательных усилий от действия высокотемпературной сверхзвуковой струи на внутреннюю ^ поверхность цилиндрического канала и температуры стенок ^ канала. Целью данной работы является разработака комплексного метода расчета аэродинамического трения и нагрева на внутренней поверхности трубчатой направляющей реактивного снаряда.

Методы/результаты: Метод исследования основывается на теории сверхзвуковых газовых течений в цилиндрических каналах и теории пограничного слоя. Газовая струя считается непрерывной, стационарной и осесимметричной. Система дифференциальных уравнений движения снаряда в направляющей интегрируется численно по времени. Параметры потока в сечениях трубы расположены по зависимостям теории сверхзвуковых газовых течений с учетом потерь на трение. Для расчета касательного напряжения на стенке направляющей ^ используются соотношения асимптотической теории турбулентного пограничного слоя, теория турбулентных пятен Эммонса переходного пограничного слоя и данные о числах Рейнольдса начала ламинарно-турбулентного перехода в аэродинамических трубах. В то же время численно интегрируется дифференциальное уравнение нагрева тонкой стенки направляющей в интервале контакта поверхности направляющей со струей. Выполнены и графически представлены расчеты распределения параметров потока, силы трения и температуры стенки трубчатой направляющей при движении снаряда внутри напавляющей с момента запуска двигателя и до момента полного выхода снаряда из направляющей.

Выводы: Данный метод расчета аэродинамического трения и нагрева на внутренней поверхности трубчатой направляющей реактивного снаряда от высокотемпературной сверхзвуковой газовой струи с учетом эффектов неизотермичности, сжимаемости, ламинарно-турбулентного перехода в пограничном слое, может быть использован при исследовании динамики старта реактивних снарядов из пусковых установок, оборудованных трубчатыми направляющими.

Ключевые слова: пусковая установка, трубчатая ^ направляющая, ракета, реактивный двигатель, пограничный слой, сила трения струи, нагрев трубчатой направляющей.

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ПРОРАЧУН СИЛЕ ТРЕ^А И ТОПЛОТНОГ УТИЦАJА МЛАЗА МЛАЗНОГ МОТОРА НА УНУТРАШ^У ПОВРШИНУ ЛАНСИРНЕ ЦЕВИ

ю Александар Н. ШИко, аутор за преписку , Анатоли М. Пав^ученко

о Алексе] А. Обухов

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а Национални по^опривредни универзитет, Суми, Украина

Научно-истраживачки центар арти^ери]ско-ракетних ]единица, Суми, Украина

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о^ ОБЛАСТ: механика, арти^ери]ско-ракетно наоружа^е

^ ВРСТА ЧЛАНКА: оригинални научни рад

с; иЕЗИК ЧЛАНКА: енглески

< Сажетак:

Увод/цил>: За проучаваъе динамике лансера са изворима млазева о гаса велике енерги]е важно }е израчунати силе смицаъа услед

де}ства суперсоничног млаза високе температуре на £ унутрашъу површину цилиндричног канала и температуру

¡5 зидова канала. Цил> овог рада }есте развц'ак>е свеобухватне

методе израчунаваъа аеродинамичког треъа и загреваъа на унутрашъо] површини вишецевног ракетног лансера. Методе/резултати: Метода истраживаъа заснована ¡е на ^ теори]и стру]ак>а гаса при суперсоничним брзинама у

^ цилиндричним каналима и на теори]и граничног сло}а. Полази се

^ од претпоставке да }е млаз гаса непрекидан, стационаран и

осносиметричан. Систем диференцц'алних ]едначина кретаъа про]ектила у лансеру нумерички се интегрише с временом. ш Параметри стру]ак>а у деловима цеви утвр^у]у се у зависности

о од теорбе стру]ак>а гаса при суперсоничним брзинама,

узима}уЬи у обзир губитке због треъа. Да би се израчунао напон о смицаъа на зиду лансера, користили су се: однос асимптотске

теорбе турбулентног граничног сло}а, Емонсова теори]а турбулентних тачака прелазног граничног сло}а, као и подаци о Ре}нолдсовим бро}евима почетка ламинарно-турбулентне транзици}е у аеро-тунелима. Истовремено се интегрише диференци]ална ]едначина загреваъа танког зида лансирне цеви у распону контаката измену површине лансера и млаза. Израчуната }е расподела параметара стру]ак>а, сила треъа и температура зида лансирне цеви током кретаъа про]ектила од тренутка покретаъа мотора до тренутка када про]ектил потпуно излази из лансера, што }е и графички представлено. Закъучци: Узима}уЬи у обзир ефекте неизотермичности и стишъивости при прелазу из ламинарног у турбулентни гранични сло], ова метода прорачуна аеродинамичког треъа и загреваъа на унутрашъоу површини ракетног лансера, услед

де}ства суперсоничног млаза гаса велике енерги]е, може да се ¡^ користи за проучаваъе динамике лансираъа ракета из ракетних лансера ко\и су опремъени лансирним цевима. S

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Къучне речи: лансер, лансирна цев, ракета, млазни мотор, гранични сло], сила треъа млаза, загреваъе лансирне цеви.

Дата получения статьи / Paper received on / Датум приема чланка: 30.12.2019. Дата получения откорректированной версии статьи / Manuscript corrections submitted on / Датум достав^а^а исправки рукописа: 14.01.2020.

Дата окончательного согласования статьи / Paper accepted for publishing on / Датум коначног прихвата^а чланка за об]ав^ива^е: 16.01.2020.

© 2020 Авторы. Опубликовано в журнале "Военно-технический вестник / Vojnotehnicki glasnik / Military Technical Courier" (www.vtg.mod.gov.rs, втг.мо.упр.срб). Данная статья в открытом доступе и распространяется в соответствии с лицензией "Creative Commons" (http://creativecommons.org/licenses/by/3.0/rs/).

© 2020 The Authors. Published by Vojnotehnicki glasnik / Military Technical Courier (www.vtg.mod.gov.rs, втг.мо.упр.срб). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/rs/).

© 2020 Аутори. Обjавио Воjнотехнички гласник / Vojnotehnicki glasnik / Military Technical Courier (www.vtg.mod.gov.rs, втг.мо.упр.срб). Ово jе чланак отвореног приступа и дистрибуира се у складу са Creative Commons лиценцом (http://creativecommons.org/licenses/by/3.0/rs/).

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