Effect of friction on motion of a piston driven by combustion products

In recent years the two-stage light gas ballistic apparatus with deformable plastic pistons has become widely used in experimental aerodynamics. The existing methods of calculating such devices either completely neglect friction of the piston on the channel wall [1–3] or use a schematization of the frictional forces [4–6], which does not have a satisfactory physical basis. In a number of studies [7, 8] the friction force was considered constant, and its value was specified not from physical considerations, but to produce the best agreement between calculated and experimental values of object velocity or driving gas pressure. Since friction is such a significant factor, its proper consideration in calculating piston motion parameters requires special study. In this connection, it is useful to consider the operation of only the first stage of the ballistic apparatus, which sets the piston in motion. Below we will consider the problem of the internal ballistics of a one-stage powder-driven apparatus in the column channel of which a piston made of polymer material moves, experiencing friction. The friction model is constructed on the basis of a series of experiments on the slow forcing of polymer specimens compressed in the longitudinal direction through a steel channel. An experimental study was made of the relationship between the gunpowder gas pressure and time within a constant volume chamber, allowing establishment of the true powder-burning law, and its deviation from the geometric law of [9]. Calculated and experimental values of maximum gas pressure and muzzle velocity of a polyethylene piston are compared.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 73–80, September–October, 1978.The authors express their gratitude to S. S. Grigoryan for his interest in the study and valuable advice, and to G. N. Suntsov for aid in performing the experimental studies.     

Problem of a piston in a plastic medium with cultivation

The article discusses the self-similar problem of the motion of a spherical piston in a medium with dry friction and the differential connection between the first invariant of the stress tensor and the second invariant of the tensor of the deformation rates. For the case of flow with a shock wave, the method of a stationary wave is used to obtain the required relationships at a strong discontinuity. It is disclosed that the velocity of the piston, as well as the relationship between the cultivation coefficients and the dry friction, are determined by the smoothness of the friction.Translated from Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, 86–93, September–October, 1974.     

Motion of a piston in a cylindrical tunnel with allowance for the additional mass of the gas

We propose to derive relations for the motion of a piston, taking into account the variation of its mass due to the additional mass of the gas entrained by the motion of the piston. We show that the gas entrained by the piston has an appreciable effect on the acceleration of the piston and the acceleration length, with the piston attaining a velocity close to the limiting value.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 167–169, September–October, 1971.     

Experimental investigation of the internal ballistics of a pulsed water cannon

Measurements were made of the piston velocity and water pressure in the tube of a pulsed water cannon. The results are compared with calculations, which show that the quasistationary formulation of the problem gives sufficient accuracy.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 150–152, May–June, 1979.     

Problem concerning a spherical piston in a compressible medium with “dry” friction

We study the self-similar problem concerning the motion of a spherical piston in a medium with dry friction. The piston moves with constant velocity in a nonideal medium.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 136–140, January–February, 1973.The authors thanks T. F. Kryukov for performing the major part of the calculations.     

Motion of a piston under the influence of gas pressure in the presence of an initial temperature gradient

A study is made of the motion of a piston without initial velocity under the influence of gas pressure. Under the assumption that the temperature gradient is constant and fairly small, expressions are obtained for the distributions of the gas-dynamic parameters in the disturbed region between the piston and the leading edge of the sound wave propagating through the gas at rest.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 177–180, March–April, 1984.     

Plane nonstationary gas flow with a strong discontinuity

The problem of plane, nonstationary gas motion under the effect of a piston in the shape of a dihedral angle moving at constant velocity in the gas is considered. In contrast to one-dimensional motion under the effect of a flat piston, a curvilinear shockwave originates here, and the flow becomes nonisentropic and vortical. This problem is examined herein in a linear formulation when the angle of the piston breakpoint is assumed small. The linear problem reduces to an inhomogeneous Riemann—Hilbert problem whose solution is found explicitly. The problem under consideration adjoins a circle of problems associated with shockwave diffraction and reflection studied by Lighthill [1], Smyrl [2], Ter-Minassiants [3], etc.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 45–50, May–June, 1971.The author is grateful to L. V. Ovsyannikov for interest in the research and useful comments.     

Investigation of the flow structure in a plane turbulent jet

Results of an experimental investigation of a plane, submerged air jet are elucidated. The distribution of the mean velocity, the longitudinal and transverse velocity component pulsations, the tangential friction stress, and the correlation coefficient in jet cross sections are presented. The results of measurements are compared with the data of other authors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 176–179, July–August, 1970.     

Direct initiation of detonation in a hydrogen-oxygen mixture diluted with nitrogen

The direct initiation of plane and cylindrical detonation waves in a hydrogen-oxygen mixture diluted with nitrogen using an exploding copper wire and a moving piston is investigated.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 151–156, November–December, 1992.The authors are grateful to G. D. Smekhov for calculating the Chapman-Jouguet detonation parameters and to V. V. Mitrofanov, who reviewed the article, for his useful comments.     

Determination of the coefficient of longitudinal mixing in a undeformed porous medium in the presence of sorption

The article gives and analysis of an expression for the overall coefficient of longitudinal mixing in a porous undeformed medium and obtains analytical expressions for the initial and central moments. The distribution of the concentrations along the filtration channel for a fixed value of the time and the distribution of the concentrations at the outlet of a channel of fixed length are obtained in the form of Hermite polynomials (the forward problem). A method is outlined for determining the coefficient of longitudinal mixing from the experimental distributions and analytical expressions for the moments (the reverse problem). The article gives numerical values of the coefficient of longitudinal mixing found using the method under consideration.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 155–161, July–August, 1972.     

Calculation of accelerated motion of fluid in a tube

The results of calculation of accelerated flow of a fluid in a tube are compared with known experiments [1] in the laminar regime. The difference method was used to obtain a solution for unsteady axisymmetric flow that becomes steady over the length of the tube; this case was calculated earlier by Gromeka in the form of a series. An expression is derived for the coefficient of friction as a function of the Reynolds number Re and the acceleration of the fluid. The comparison reveals agreement between the results with an error not worse than 37%. However, the calculation gives a coefficient of friction proportional to Re to the power –1.5, whereas the experiment [1] reveals a weaker dependence proportional to Re to the power –1.15.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 158–160, September–October, 1981.     

Boundary layer in the vicinity of the stagnation point of a body of axial symmetry in a turbulent stream

The flow in the boundary layer in the vicinity of the stagnation point of a flat plate is examined. The outer stream consists of turbulent flow of the jet type, directed normally to the plate. Assumptions concerning the connection between the pulsations in velocity and temperature in the boundary layer and the average parameters chosen on the basis of experimental data made it possible to obtain an isomorphic solution of the boundary layer equations. Equations are obtained for the friction and heat transfer at the wall in the region of gradient flow taking into account the effect of the turbulence of the impinging stream. It is shown that the friction at the wall is insensitive to the turbulence of the impinging stream, while the heat transfer is significantly increased with an increase in the pulsations of the outer flow. These properties are confirmed by the results of experimental studies [1–4].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 83–87, September–October, 1973.     

The motion of snow avalanches in the conditions of limiting friction

We investigate the equations of motion of large snow avalanches, and in contrast with [1–3] we take into account the fact that the dry friction can reach a critical value above which the snow in the avalanche or the underlaying material cannot sustain the friction. We find asymptotic solutions for long times after the beginning of motion. These solutions describe the avalanche motion in which a part of the snow moves in the conditions of limiting friction over a tilted plane with a uniform layer of snow. The equations which are used to find these asymptotic solutions have the property that for certain depths the flow velocity of small perturbations decreases with increasing depth. This is related to a number of unusual features (from the hydraulic point of view) of the solutions. In particular, on relatively gentle slopes two zones are formed in the avalanche: the forward part, with a large velocity and thickness of the moving layer, and the rear part, which is significantly slower and thinner. The two parts are separated by a narrow region characterized by a sharp decline in velocity and thickness of the moving layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 30–37, September–October, 1977.     

Unsteady-state flow of a gas in a channel,resulting from the motion of a piston,with magnetohydrodynamic offtake of energy and luminescence of the gas

The present paper discusses the one-dimensional unsteady-state flow of a gas resulting from the motion of a piston in the presence of weak perturbing factors, with which the investigation of the perturbed (with respect to the usual self-similar conditions) motion reduces to the solution of ordinary differential equations, is indicated. The distributions of the parameters of the gas between the piston and the shock wave are found. The conditions under which there is acceleration or slowing down of the shock front are clarified. As an example, this paper considers the unsteady-state motion of a conducting gas in a channel with solid electrodes under conditions where electrical energy is generated, and the flow of a gas taking radiation into account, under the assumption of optical transparency of the medium. The theory developed is used to solve the problem of the motion of a thin wedge with a high supersonic velocity in an external axial magnetic field, taking account of the luminescence of the layer of heated gas between the wedge and the shock wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 17–25, September–October, 1970.     

Friction and heat transfer with simultaneous convection on a permeable surface

The velocity and heat transfer fields near a vertical permeable surface with simultaneous convection are investigated. A solution is found for the boundary layer equations with known laws of surface temperature and flow velocity change. The transformed boundary layer equations contain the parameter G/R², which determines the effect of free convection on friction and heat transfer for constrained motion. Calculations of friction and heat transfer as functions of draft (suction) with simultaneous convection are presented.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 96–100, March–April, 1973.     

Distribution of the velocity profiles of the liquid phase in a gas-liquid flow with small gas contents

Artilce [1] gives the results of measurement of the friction at the wall of a channel under bubble conditions, in a wide range of Reynolds numbers. It is shown that the concept of laminar flow conditions has no meaning when it is applied to the flow of a two-phase mixture, since, even with very small Reynolds numbers, the level of the pulsations of the friction is high, and the spectrum of the pulsations of the friction is continuous. In this case, the mean friction is much greater than the calculated; here the value of the resistance coefficient is not a single-valued function of the Reynolds number. The present article gives the results of measurement of the velocity profiles of the liquid phase, carried out using an electro diffusion method. It is shown that, with Reynolds numbers corresponding to turbulent flow conditions, the profile of the velocity in a two-phase mixture is close to turbulent and does not depend on the gas content.     

Slow rotation of a sphere in a confined volume of a dilute gas

The axially symmetric motion of a gas in a volume confined between an external immobile surface of rotation and a coaxial surface of a rotating sphere is considered. A solution is obtained by the moment method based on the Boltzmann equation with a collision integral of Maxwellian molecules. The gas-velocity distribution and an expression for the friction torque exerted on the sphere are obtained for arbitrary Knudsen numbers and for an arbitrary shape of the outer surface. The proportionality of the gas slip velocity over the surface of the sphere to the friction strain is shown. The friction torque is investigated for specific shapes of the outer surface. The motion of a gas filling the space between concentric spheres, each of which rotates about an arbitrary axis, is treated. In the limiting case of small Knudsen numbers the expressions obtained are compared with the corresponding results for a continuous medium.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 117–124, July–August, 1978.The authors are grateful to the participants of the seminars guided by G. I. Petrov and A. M. Golovnyi for discussions concerning this work.     

The problem of a dihedral piston

The problem of the plane nonstationary motion of a gas behind a dihedral piston is considered. The problem is linearized on the assumption that the piston angle is small. The mixed problems and the Goursat problem are solved for the linearized double-wave equation in the region of hyperbolicity and then the mixed boundary value problem is solved in the region of ellipticity. The solutions are obtained in elementary functions and quadratures.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 10, No. 3, pp. 74–81, May–June, 1969.The author thanks L. V. Ovsyannikov for his interest and helpful advice.     

Approximate solution to nonself-similar problem of motion of a piston after an impact

An approximate solution is obtained to the problem of the motion of a piston after an impact and under the influence of gas pressure under the assumption that the parameter = u_o/a _o, where u_o is the initial velocity of the piston anda _o is the velocity of sound in the gas at rest, is small. Functions that determine the law of motion of the piston and the shock wave, and also the gas flow in the disturbed region are found explicitly to terms of order ³ Translated from Izvestiya Akadeinii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 167–171, November–December, 1982.     

Unsteady-state periodic jet structure created by the pulsed motion of a piston jet generator

The results of an experimental and theoretical investigation of the process of formation of an unsteady-state water jet by the pulsed motion of the piston of a piston jet generator are given. An approximate mathematical model of the generator dynamics which can explain the mechanism of formation of the experimentally obtained periodic transverse thickening structure is considered.Nikolaev. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 172–178, July–August, 1996.