Supersonic flow over a cone with heat release in the neighborhood of the apex

Supersonic flow over a cone mounted in the wake of a spherical source of heat release is investigated. The free-stream nonuniformity generated by the source leads to effective drag reduction.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 110–114, March–April, 1993.     

Influence of blowing into the boundary layer on supersonic flow past an oscillating cone

The influence of blowing on the unsteady characteristics of a boundary layer is studied for the example of supersonic flow past a sharp cone oscillating about zero angle of attack. The problem of the interaction of the inviscid exterior flow with the laminar boundary layer is solved. It is shown that blowing proportional to the heat flux improves the damping of the oscillations of the cone. If the blowing anticipates the heat flux in phase this effect is strengthened.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 43–46, July–August, 1983.     

Cauchy problem for the equation of evolution of small perturbations of the surface of ablating wedge (cone) shapes

The Cauchy problem for small perturbations of the surface of steady-state ablating shapes was formulated and studied in [1]. The conclusion of that study concerning the fundamental difference between the properties of the problem in the plane (=0) and axisymmetric (v=1) cases is shown to remain valid for wedge and cone shapes — for a cone the solution is unique, but for a wedge the choice of solution requires the introduction of an additional condition.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 179–182, January–February, 1988.     

Heat transfer on the surface of a body near a cylindrical obstacle and a transverse jet

A detailed investigation of the heat transfer is made for the case of a turbulent boundary layer on a cone in front of a cylindrical obstacle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 41–48, May–June, 1982.     

Non-linear finite element analysis of cone penetration in layered sandy loam soil – Considering precompression stress state

Axisymmetric finite element (FE) method was developed to simulate cone penetration process in layered granular soil. The FE was modeled using ABAQUS/Explicit, a commercially available package. Soil was considered as a non-linear elastic plastic material which was modeled using variable elastic parameters of Young’s Modulus and Poisson’s ratio and Drucker–Prager criterion with yield stress dependent material hardening property. The material hardening parameters of the model were estimated from the USDA-ARS National Soil Dynamics Laboratory – Auburn University (NSDL-AU) soil compaction model. The stress–strain relationship in the NSDLAU compaction model was modified to account for the different soil moisture conditions and the influence of precompression stress states of the soil layers. A surface contact pair (‘slave-master’) algorithm in ABAQUS/Explicit was used to simulate the insertion of a rigid cone (RAX2 ABAQUS element) into deformable and layered soil medium (CAX4R ABAQUS element). The FE formulation was verified using cone penetration data collected on a soil chamber of Norfolk sandy loam soil which was prepared in two compaction treatments that varied in bulk density in the hardpan layer of (1) 1.64 Mg m⁻³ and (2) 1.71 Mg m⁻³. The FE model successfully simulated the trend of cone penetration in layered soils indicating the location of the sub-soil compacted (hardpan) layer and peak cone penetration resistance. Modification of the NSDL-AU model to account for the actual soil moisture content and inclusion of the influence of precompression stress into the strain behavior of the NSDL-AU model improved the performance of FE in predicting the peak cone penetration resistance. Modification of the NSDL-AU model resulted in an improvement of about 42% in the finite element-predicted soil cone penetration forces compared with the FE results that used the NSDL-AU ‘virgin’ model.     

Characteristics of laminar-turbulent boundary layer transition on a cone

The effect of the unit Reynolds number and the Mach number on the transition on a slender circular cone is experimentally investigated. The perturbation spectra in the boundary layer on the cone are measured. It is shown that the location of the transition is determined by the perturbation level at the frequencies causing transition.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 23–27, November–December, 1985.     

Gas compression in the interaction of a steady axisymmetric convergent shock wave with the point of a quasi-cone

Two-dimensional axisymmetric steady gas flow with a convergent wave that interacts with the point of a cone shape is considered. Realizing such a flow would make it possible to create a region of dense gas accessible for experimental investigation over an extended period of time.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 162–167, September–October, 1992.     

Asymptotic nonlinear solution of the problem of the penetration of a compressible fluid by a slender body

A combined solution of the problem of the penetration of a compressible fluid by a slender wedge and a cone is found by the method of matched asymptotic expansions. The new solution is based on taking into account the nonlinear terms in the Cauchy-Lagrange integral and is uniformly applicable in the neighborhood of the nose.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 49–57, May–June, 1993.     

Development of two-dimensional perturbations on the surface of a tangential discontinuity

A study is made of the asymptotic behavior at long times of initially localized small two-dimensional perturbations of the interface of two fluids in the presence of a tangential discontinuity of the velocity; surface tension is taken into account. The development of one-dimensional perturbations was considered earlier in [1]. The asymptotic behavior of the perturbed region is found, i.e., in the xyt space there is found a cone with apex at the origin such that perturbations tend to infinity with increasing t along rays within the cone, while perturbations tend to zero along the remaining rays. Conditions are found under which the instability of the tangential discontinuity is not absolute, i.e., when these conditions are satisfied, flows with tangential discontinuity of the velocity can take place. These conditions, like the shape of the cone, do not depend on the magnitude of the surface tension.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 12–16, May–June, 1979.     

Influence of the angle of attack on the transition from a laminar to a turbulent boundary layer in the case of supersonic flow past sharp circular cones

Some results are given of an experimental investigation into the influence of the angle of attack on the transition in the symmetry plane of a sharp cone at Mach number M = 6.1. These results and available experimental data are used to establish the dependence of the transition Reynolds number on the angle of attack on the flow division line of sharp circular cones.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 160–163, July–August, 1982.     

Diffraction of a spherical acoustic wave on a cone

An exact analytic solution of the problem of diffraction of a plane acoustic wave on a cone of arbitrary aperture angle was obtained and studied in [1]. For the case of spherical wave diffraction on a cone a formula is known [2] which relates the solutions of the spherical and plane wave diffraction problems. This study will employ the results of [1, 2] to derive and investigate an exact analytical solution of the problem of diffraction of a spherical acoustic wave on a cone of arbitrary aperture angle. Results of numerical calculations will be presented and compared with analogous results for a plane wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 200–204, March–April, 1976.The author is indebted to S. V. Kochura for her valuable advice.     

Investigation into the interaction of a shock wave with an acute cone

A numerical investigation has been made into the nonstationary axisymmetric flow which arises from the interaction of a shock wave with a fixed acute cone. A solution has been obtained in self-similar coordinates for regimes in which a shock wave attached to the point of the cone is formed in the gas flow. The region of existence of these regimes has been established and the method of stabilization used to calculate the gas-dynamic functions in the disturbed region. The main attention is devoted to studying the transition from regular reflection to Mach reflection, a study of the features of double Mach reflection, and comparison of the results for the axisynuaetric and two-dimensional cases. The pressure distributions along the surface of the cone are given in a form which makes it possible to obtain dependences valid in a wide range of variation of the intensities of the incident shock wave and for different values of the adiabatlc exponent of the gas.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 98–104, May–June, 1980.     

Problem of Increasing the Survivability of Two–Stage Ballistic Guns

The paper proposes methods for increasing the survivability of light–gas guns, including new designs and nonconventional modes of shot. It is established theoretically and experimentally that a decrease in the cone angle of the conical adapter to 2.5 — 3° leads to a severalfold increase in the survivability of the high–pressure chamber. A compound piston with a liquid or gel–like filler is designed. The mode of shot from a light–gas gun with superlight pistons and without a diaphragm is justified and tested experimentally. Conical and measuring adapters with liners made of thermally– and wear–resistant alloys are designed to prevent ablation of the light–gas gun barrel.     

Determination of the parameters of the boundary layer on rotating axisymmetric cones

A method is proposed for solving the three-dimensional equations of laminar and turbulent boundary layers on a pointed rotating axisym-metric cone flying at an angle of attack . New properties of the obtained solutions are found, and a comparison is made with the results of other authors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 34–39, May–June, 1984.     

Dependence of the drag of a conical axisymmetric cavitation body on the cone angle and the cavitation number

Numerical investigations of flow past axisymmetric conical captation bodies have shown that the drag coefficient of the cavitation body, calculated from the maximum cross-sectional area of the cavity (midsection), depends on the cavitation number and the cone angle.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 170–173, May–June, 1995.In conclusion, the author is grateful to G. Yu. Stepanov whose critical remarks were helpful in making this paper more conclusive and more illustrative.     

A study of the dimensions of the wake behind a cone travelling at hypersonic speed

In a series of papers (see, for example, [1–5]) numerous results have appeared detailing experimentally determined dimensions of wakes behind spheres or spherically blunted cylinders travelling with hypersonic speed in air. During this same period substantially less attention has been paid to the study of the parameters of the wake behind a cone, in particular, a cone at an angle of attack. In the present paper we present the results of measuring the mean width of the wake, and the mean-square deviation of the wake boundary, for a spherically blunted cone of 10 half-angle with nose radius 6% of the base diameter, travelling in air at Mach number M=12 and Reynolds number Re=0.3·10⁶, and with an angle of attack varying from 12 to 24.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 161–163, November–December, 1976.The author expresses his thanks to N. N. Baulin for his help In the experimental work.     

Modification of critical state models by Mohr–Coulomb criterion

In order to combine the Mohr–Coulomb criterion and the critical state models for soils, a transformed stress tensor based on the Mohr–Coulomb criterion is proposed. The new stress tensor is determined by a transformation that makes the Mohr–Coulomb criterion become a cone having an axis as the space diagonal in transformed principal stress space, and is applied to the Cam-clay and Sekiguchi–Ohta models, which are two typical isotropic and anisotropic hardening critical state models for soils, for improving modelling capability of describing soil behaviour in general stresses. The revised models give more accurately predicted results than the original ones.     

Features of the Motion of a Gas-Liquid Medium in a Compound Shell (Sphere and Truncated Cone) Subject to Vibration

The results from an experimental study into the dynamic behavior of a gas-liquid medium and solid particles in a compound shell (sphere-truncated cone) are reported on. The following processes are studied: formation of gas bubbles and their clusters, strong macroflows, and intensive chaotic motion of the medium in the truncated cone as a nonlinear vibrating liquid-gas system__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 112–118, January 2005.     

Measuring soil properties to predict tractive performance of an agricultural drive tire

The coefficient of traction for a 9.5–16 R-1 bias ply tire was measured and compared with predictions using equations developed by Janosi and Hanamoto [Proc. 1st Int. Conf. on Mechanics, p. 707–736 (1961)]; Wismer and Luth [J. Terramechanics10, 49–61 (1973)] Gee-Clough et al. [J. Terramechanics15, 81–84 (1978)] and Brixius [ASAE Paper No. 87–1622 (1987)]. For the soft soil condition, with a cone index of 120 kPa, Gee-Clough's equation predicted the coefficient of traction better, but predictions using the Brixius equation were better for soil with a cone index of 225 kPa. An experimental device was developed to simultaneously measure the horizontal and vertical stress-strain relationships of soil. The use of resultant stress from the experimental device data failed to show any improvement in coefficient of traction prediction over using the cone index. The resultant of the normal and shear stress from the experimental device data did not adequately represent the soil properties involved in terrain-vehicle mechanics.     

Influence of viscosity on the flow over the sharp edge of bodies consisting of a spherical segment joined to an inverted cone

The results are given of an experimental investigation of the supersonic axisymmetric flow over a body consisting of a spherical segment joined to an inverted cone in the neighborhood of the point of inflection of the profile (Fig. 1a). For the limiting case of a cylinder with a flat end and M = 3, a study was made of the influence of the Reynolds number and the state of the boundary layer on the parameters of the local separation region formed near the inflection (Fig. 1b). It was found that there is an appreciable decrease in the length of the separation region and the pressure in it when the Reynolds number increases in the range Re = 10⁵– 10⁷ in the case of a laminar boundary layer on the flat end near the inflection point. A low level of the pressure on the surface of the body was achieved — of the order of thousandths of the pressure behind a normal shock. There was found to be a sharp increase in the pressure in the separation region when the boundary layer on the end becomes turbulent with transition to a flow regime that is self-similar with respect to the Reynolds number. Under conditions of a turbulent boundary layer, systematic experimental data on the pressure on the inverted cone near the point of inflection of such bodies were obtained and generalized.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 154–157, January–February, 1981.