The application of the projection method for constructing the shape of a body with minimum drag

The problem is considered of constructing a semi-infinite axisymmetric body with minimum drag in subsonic flow of an ideal gas. This problem is formulated as the problem of finite-dimensional minimization by prescribing the shape of the body in parametric form and applying the projection method for solving a flow problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 108–113, March–April, 1985.     

Three-dimensional shape of a body of minimum drag in a hypersonic gas stream

The three-dimensional aerodynamic shape of a slender body of minimum drag is determined. The solution to the corresponding variational problem is considered in a special class of surfaces, among which there are surfaces of revolution. An approximate analytic investigation is made, and the results are given of a numerical calculation by the method of local variations. It is shown that the profile of the transverse section of the optimal body has a petal shape which becomes a circle in the midsection.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 98–103, October–December, 1981.     

Skip trajectory flight of a ramjet-powered hypersonic vehicle

Possible skip trajectories of a flying vehicle with a periodically actuated ramjet are numerically simulated. An optimal choice of ramjet actuation areas and duration is demonstrated to ensure the maximum flight range with a given amount of the fuel. The main advantage of skip trajectories is found to be a significant (by an order of magnitude) decrease in thermal loads on the flying vehicle.     

Explosion of a body in flight

Little attention has been paid up to now in the theory of explosions to such an important and interesting problem as the explosion of a body in flight. A formulation of the problem presented by such an explosion in connection with the problem of simulating the explosion of a meteorite body flying at cosmic velocity is given in [1]. In this case the kinetic energy of the translational motion may be comparable to or even in excess of the internal energy of the explosive transformation, which will lead to a significant distortion of the flow pattern compared with the usual explosion process. An analysis of the effect of the initial velocity of particles on the course of an explosion in idealized formulations in the framework of one-dimensional flows with plane, cylindrical, and spherical waves was first made in [2–4]. The asymptotic flow properties were found in these papers. It is shown that if the internal energy E_o and the kinetic energy K_o are separated (the specification of the latter for a fixed mass is equivalent to specification of the initial momentum), some intermediate self-similar regimes corresponding to a short pulse [2] or to flows with a sink [3, 4] are observed, these becoming the solution for a strong explosion at long times [1]. The time of transition from one qualitative regime to another depends on the ratio K_o/E_o. In the present paper the next step in the investigation of the question is taken. An axisymmetric, basically realistic flow model is studied.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 126–129, September–October, 1984.     

The complex deformation of metals along a plane curvilinear astroid-type trajectory

The constitutive relations of the complanarity hypothesis are used to construct an image of the process of loading of 9×2 steel for a plane deformation.astroid-type trajectory, which is realized in the plain Э₁-Э₃ of the deviator subspace of Il'yushin's deformation. The laws governing changes in the scalar and vector properties of the material are considered. The computed results are compared with experimental data obtained on a CH-DC computer-aided system. State Technical University, Tver', Russia. Translated from Prikladnaya Mekhanika, Vol. 36, No. 7, pp. 130–136, July,2000.     

Finite element analysis of conductive and radiative heating of a thin skin calorimeter

The main purpose of the present work is to investigate the influence of normal and lateral conduction on the temperature distribution and heat transfer coefficient on the surface of a typical sounding rocket. A two-dimensional heat conduction equation with a time dependent aerodynamic heating condition at one surface and a radiation boundary condition at the other end is solved using finite element method.     

Hamiltonian structure for a neutrally buoyant rigid body interacting with N vortex rings of arbitrary shape: the case of arbitrary smooth body shape

We present a (noncanonical) Hamiltonian model for the interaction of a neutrally buoyant, arbitrarily shaped smooth rigid body with N thin closed vortex filaments of arbitrary shape in an infinite ideal fluid in Euclidean three-space. The rings are modeled without cores and, as geometrical objects, viewed as N smooth closed curves in space. The velocity field associated with each ring in the absence of the body is given by the Biot–Savart law with the infinite self-induced velocity assumed to be regularized in some appropriate way. In the presence of the moving rigid body, the velocity field of each ring is modified by the addition of potential fields associated with the image vorticity and with the irrotational flow induced by the motion of the body. The equations of motion for this dynamically coupled body-rings model are obtained using conservation of linear and angular momenta. These equations are shown to possess a Hamiltonian structure when written on an appropriately defined Poisson product manifold equipped with a Poisson bracket which is the sum of the Lie–Poisson bracket from rigid body mechanics and the canonical bracket on the phase space of the vortex filaments. The Hamiltonian function is the total kinetic energy of the system with the self-induced kinetic energy regularized. The Hamiltonian structure is independent of the shape of the body, (and hence) the explicit form of the image field, and the method of regularization, provided the self-induced velocity and kinetic energy are regularized in way that satisfies certain reasonable consistency conditions.      

Memory of body shape in a far wake

The possibility of memory of the body shape in a far wake is investigated within the framework of the complete Navier-Stokes equations. It is shown that for a far wake there can be no memory of the shape as a result of the laminarization of the flow. On the interval of intermediate asymptotics the presence of memory leads to the problem of nonequivalence of the momentum sources and sinks for a self-similar turbulent wake, since there can be no memory of the shape for a source of momentum. The asymptotics for the average velocity defect in the wake are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 43–46, July–August, 1990.     

Calculation of hypersonic flow over a body with a discontinuity,allowing for two-dimensional radiative transfer

It is shown that the degree of the integrals appearing in the general expressions for radiative flux and its divergence can be reduced to one in the two-dimensional case by analytical integration with respect to one of the angular variables. The resulting formulas contain some special functions whose role is analogous to that of the integral exponents E_n(x) in the one-dimensional case. The authors postulate and numerically solve the problem of flow in a radiative absorbing shock layer near the downstream of a discontinuity of shape. It is shown that at high hypersonic speed the two-dimensional radiation near the discontinuity can appreciably affect the pressure distribution downstream. It is shown that the radiative flux to the lateral surface directly behind the discontinuity is comparable to the flux on the forward surface and can be calculated by using appropriate two-dimensional formulas.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 114–121, March–April, 1976.The author thanks V. V. Lunev for formulating the problem and for technical advice.     

Determination of trajectory parameters for a small satellite using raw satellite measurements

The problem of determining the trajectory parameters of a small satellite using a satellite navigation equipment is studied. A raw data processing algorithm is proposed when the measurements from a global navigation satellite system are not always regular.     

Optimization of the earthreentry trajectory of a blunted body by the integral heat flux

The paper deals with optimization of the Earth reentry trajectory by the magnitude of the total convective heat flux at the stagnation point of a blunted body. The equations of a thin (hypersonic) viscous shock layer taking into account the nonequilibrium nature of chemical reactions and multicomponent diffusion are used as the initial mathematical model for heat flux calculations. The optimal solution is obtained by an effective robust method using the basic ideas of genetic algorithms. Institute of Applied Mathematics and Mechanics, Tomsk State University, Tomsk 634050. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 112–123, July–August, 2000.     

Transient motion of a floating body having a rectangular shape

The twodimensional transient problem of a floating body having a rectangular shape in a fluid layer of finite depth is considered. Vertical displacements of the body are specified. The problem is studied within the framework of the linear theory of potential ideal incompressible flow. The fluid flow equations reduce to an infinite system of Volterra integral equations of the second kind by the method of decomposition of the flow region. The system obtained is studied and solved numerically by the reduction method. A method of solving the problem for the flow velocity potential is proposed. The distribution of the hydrodynamic pressure and force acting on the body is determined.     

Hypersonic flow past a flat body in a regime of intense radiative heat transfer

The paper is devoted to the investigation of hypersonic flow regimes in which radiative transfer plays a significant part. A numerical solution is obtained to the two-dimensional steady problem of hypersonic flow past a flat thermally insulated body of an inviscid radiating gas with allowance for radiative transfer of energy in the approximation of radiative thermal conductivity. It is noted that a heated region is formed around the body, its dimensions exceeding by an order of magnitude those of the body itself; the temperature is effectively equalized, and the gas velocity is close to the velocity of the oncoming flow. Heated gas flows past the body at a moderate Mach number (M ～ 3–6). A thin region of strongly compressed gas is formed directly in front of the body.     

Estimates of nonequilibrium radiative heating of blunt bodies in a hypersonic flow of carbon dioxide gas

The solution to the problem of hypersonic nonequilibrium flow over cones with rounded noses [1, 2] is used to estimate the radiative heating of the surfaces of the bodies.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 158–160, November–December, 1979.     

Convective heating of a blunt-nosed body in a nonuniform hypersonic gas stream

An investigation is made into the convective heating of a blunt-nosed body in an expanding stream of heated gas. The gas parameters at the outer edge of the boundary layer are determined on the basis of a solution obtained earlier by the authors [3]. Expressions are obtained which make it possible to convert the convective heat flux to a body in a uniform gas stream to one in a nonuniform stream. Dimensionless numbers are found and their influence on the convective heat flux to the body is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 127–133, July–August, 1981.     

Three-dimensional turbulent boundary layer on a body of complex shape

Flow and heat transfer problems associated with three-dimensional compressible gas flow past a body of complex shape at a small angle of attack are investigated on the basis of a finite-difference calculation. The results of a numerical solution of the equations of the three-dimensional turbulent boundary layer are presented. The effect of the leading parameters on three-dimensional flow development and heat transfer is analyzed. The characteristic flow regions in the boundary layer are found: lines of divergence and convergence on the surface, separation zones and flow interfaces. The location of the maximum values of the heat flux and friction on the surface is determined, the behavior of the limiting streamlines on the body is described, and the intensity of the secondary flows in the boundary layer is estimated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 25–35, September–October, 1986.