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The use of modern computer systems for calculating the aerophysical characteristics of supersonic bodies of revolution together with the calculation of the flight trajectory under conditions of continuously changing Mach and Reynolds numbers of the oncoming flow, the presence of transient regimes and non-isothermality in near-wall flows is often not possible due to the complexity of the organisation of the computational process. By using a number of integral methods for calculating inviscid flows and viscous compressible near-wall flows, talcing into account the non isothermality and intermittency of the boundary layer, a method has been developed for calculating the friction and heating of supersonic bodies of revolution on the flight trajectory. On the basis of well-known flight experiments, the correlation dependences of the Reynolds numbers of the beginning of the transition on sharp cones were obtained and the method of corrections for spherical blunting of the head part was implemented. By calculating the intermittency function, the changeability of flow regimes in the boundary layer is established for a number of trajectories of the supersonic uncontrolled rocket projectile. Calculated dependences for aerodynamic friction, heat fluxes and projectile wall temperature on the flight time are obtained. The concept of combined calculation of aerophysical characteristics on the flight trajectory using numerical and integral methods is proposed. [ABSTRACT FROM AUTHOR]

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 of Emmons of the 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. [ABSTRACT FROM AUTHOR]

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 of Emmons of the 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. [ABSTRACT FROM AUTHOR]

The paper presents computational and mathematical model of the spatial motion of a rocket with centering bulges and a pin on the body in a thinwalled tubular guide mounted on two fixed supports and equipped with a screw groove. The models take into account the interaction of the projectile with the inner surface of the guide tube at the locations of the drive pin and the centering bulge. The strength of the normal reaction of the inner surface of the guide is found as a reaction to the elastic deformation of the pipe caused by normal to its inner surface displacements of the centering thickening at the point of contact with the guide. In this case, the tubular guide is considered as an elastic thinwalled shell. To calculate the values of the shell stiffness coefficient along its length, the finite element method implemented in the ANSYS Mechanical software package is used. The translational component of the projectile motion is investigated on the basis of the theorem on the motion of the center of mass. The rotational component is investigated on the basis of the Lagrange equations of the second kind. The generalized parameters of the rotational motion are the yaw Ψ and pitch θ angles, the angle of attack α, the angle of slip β, and the angle of rotation of the projectile around the longitudinal axis φ. The aerodynamic angle of heel γа is found from the transition formulas for the adopted coordinate systems.The yaw velocity angle Ψ, the pitch velocity angle θ, and the aerodynamic roll angle γа as well as the first time derivatives of these angles are converted into the yaw angles ψ and pitch υ of the projectile axis and their derivatives in the starting coordinate system. [ABSTRACT FROM AUTHOR]