Transient thermal stresses in anisotropic bodies with spherical symmetry

Summary The quasi-static thermo-elastic equations are solved for material which is transversely isotropic about the radius vector. The Laplace transform is used to obtain a general solution of the equations in which all quantities are assumed to depend on the radial co-ordinate and the time only. The particular problems of constant temperature suddenly applied to the surfaces of a solid sphere and a spherical cavity in an infinite solid are considered. Numerical results are presented for the second of these problems.     

Transient thermal stresses in an orthotropic hollow cylinder for axisymmetric problems

For the thermoelastic dynamic axisymmetric problem of a finite orthotropic hollow cylinder, one comes closer to reality to involve the effect of axial strain than to consider the plane strain case only. However, additional mathematical difficulties should be encountered and a different solution procedure should be developed. By the separation of variables, the thermoelastic axisymmetric dynamic problem of an orthotropic hollow cylinder taking account of the axial strain is transformed to a Volterra integral equation of the second kind for a function of time, which can be solved efficiently and quickly by the interpolation method. The solutions of displacements and stresses are obtained. It is noted that the present method is suitable for an orthotropic hollow cylinder with an arbitrary thickness subjected to arbitrary axisymmetric thermal loads. Numerical comparison is made to show the effect of the axial strain on the displacements and stresses. The project supported by the National Natural Science Foundation of China (10172075) and China Postdoctoral Science Foundation (20040350712)     

Rotation of axisymmetric bodies in hydromagnetics

Summary This paper deals with the distrubance due to steady rotation of axisymmetric bodies in a viscous incompressible fluid of infinite conductivity in which the uniform ambient flow field is collinear with the uniform magnetic field. The known results of Sowerby¹) for the problem Couple on a rotating spheroid in a slow stream in an incompressible viscous fluid are generalized to apply to all ellipsoids of revolution and a special case of the circular disc has also been investigated in detail. The conditions of flow are assumed to be such as to permit the use of Oseen's approximation in the equations of motion. The coefficient of couple has been found to the first order approximation in terms ofR(1–S) orR(S–1) whereR is the Reynolds number andS=H ₀ ² /4W ² the pressure number which plays an important part. The couple exerted on the body is computed for various values ofS andR.     

Transient development of axisymmetric surface waves

The initial value problem of axisymmetric wave motion generated by a cylindrical wave-maker immersed in an incompressible homogeneous fluid of constant finite depth is solved using the Laplace and Weber transforms. An asymptotic treatment of the problem for sufficiently long time and then for large distances is also carried out in detail to obtain a deeper understanding of the steady and transient motions.

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Sommario Viene risolto con l'uso della trasformata di Laplace e Weber il problema a valori iniziali di onde assialsimmetriche, generate da una sorgente d'onda cilindrica imnersa in un fluido incomprimibile, omogeneo, di profondità finita e costante. È, inoltre, sviluppata in dettaglio una trattazione asintotica del problema per tempi sufficientemente lunghi e grandi distanze, al fine di ottenere una migliore conoscenza sia del moto transitorio che di quello a regime.

     

Transient behavior of an axisymmetric turbulent jet

The prediction of the response of unsteady flows submitted to external excitation is a real challenge for the optimization of industrial processes. As the jet flow is a very basic turbulent flow related to mixing and entrainment phenomena via turbulent structure dynamic, we investigate the transient behavior of an axisymmetric jet submitted to a large and sudden decrease of its ejection velocity. The non stationary flow evolution is studied experimentally. Measurements along the jet axis based on pure ensemble averaging show clearly the convective motion of the perturbation and the adaptation of the local interaction to the local jet time scale. A transverse investigation in the non stationary region show that the mean flow and its turbulence is deeply affected during the local velocity decrease.     

Observations of large-scale structures in wakes behind axisymmetric bodies

Wakes behind disk-shaped axisymmetric bodies of varying solidity are studied using flow visualization and two-dimensional Fourier decomposition of velocity measurements. Evidence of a reverse flow region behind some of the bodies is observed to coincide with the presence of large-scale structures in the near and far wake. Fourier analysis shows that these large-scale structures are predominately helical (m= ±1) and occur at a characteristic frequency which corresponds to their wavelength as observed from flow visualization. Our measured value for this characteristic frequency agrees with vortex shedding frequencies observed for these types of wakes.     

Elastic waves in bodies with initial stresses

Conclusions An analysis of research available on the problem under consideration shows that at this time: a) Wave propagation in unbounded, bounded, and composite laminar bodies with homogeneous initial states has been studied sufficiently extensively; b) methods to determine the third-order elastic constants have been developed on the basis of existing theories; c) an ultrasonic nondestructive method to determine the stress in solids has been developed, where the stresses averaged over the bulk of the body are determined.In light of the above, in the authors' opinion, the following should be considered the most urgent questions for further investigations on the problem: a) the investigation of wave propagation regularities in bodies with inhomogeneous initial states (it is hence important to execute quantitative and qualitative analyses of the phenomenon); b) development of an ultrasonic nondestructive method of determining the stress in the near surface layers of a solid, which will afford a possibility of determining not only the membrane stresses but also the bending stresses; c) an investigation of the wave propagation regularities in fibrous composites with initial stresses.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 15, No. 4, pp. 3–23, April, 1979.     

Optimal shapes of axisymmetric bodies penetrating into soil

This paper presents the results of a study of the shapes of axisymmetric bodies with minimum drag and maximum depth of penetration into the plastic soils. Optimal shapes of bodies of revolution of given length and cross-sectional radius with generatrices represented by line segments are obtained by a modified method of local variations. The problem is solved using a binomial quadratic model of local interaction, including inertial and strength terms containing constant and Coulomb frictions. The drag forces and the penetration depth of cones and the obtained bodies of optimal shape are determined at different penetration velocities.     

Study of residual stresses in linearly varying biaxial-stress fields

A theory has been developed for the calculation of relaxation strains effected by drilling a hole in a plate with a linearly varying stress field. With this theory, a technique was developed for the measurement of residual stress at the toe of tee-fillet welds. The above technique was employed for the measurement of residual stresses at the toe of tee-fillet welds in 11/2-in. HY-80 steel with the fillet in the as-welded, ground, shot peened, ground and shot peened, and mechanically peened condition. It was found that experimental data conform to the assumed theory, and that residual stresses in aswelded tee-fillet welds in both the transverse and longitudinal directions approach the yield strength of the steel. It was also found that residual stresses are reduced approximately 25 percent by grinding, 50 percent by shot peening and 50 percent by grinding and shot peening. Mechanical peening drastically affected residual stresses by converting high tension at the toe of the fillet weld to high compression of approximately the same magnitude.     

Rotation of axisymmetric bodies in hydromagnetics (finite conductivity)

Summary This paper deals with the disturbance due to the steady rotation of some axisymmetric bodies in a viscous incompressible fluid of finite conductivity in which the uniform ambient flow field is collinear with the uniform magnetic field. The known results of Sowerby [1] for the couple on a rotating spheroid in a slow stream in an incompressible viscous fluid are generalized. The special case of a disk is investigated in detail. The assumed conditions of flow permit the use of Oseen's approximation. The couple is found to first order approximation in terms of R and M, where R is the Reynolds number and M the Hartmann number.On leave from Meerut College, Meerut, INDIA.     

Aerodynamics of axisymmetric bodies in supersonic flow with local blowing

Journal of Applied Mechanics and Technical Physics -     

Unsteady mixed convection over two-dimensional and axisymmetric bodies

The unsteady laminar incompressible mixed convection flow over a two-dimensional body (cylinder) and an axisymmetric body (sphere) has been studied when the buboyancy forces arise from both thermal and mass diffusion and the unsteadiness in the flow field is introduced by the time dependent free stream velocity. The nonlinear partial differential equations with three independent variables governing the flow have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. The results indicate that for the thermally assisting flow the local skin friction, heat transfer and mass diffusion are enhanced when the buoyancy force from mass diffusion assists the thermal buoyancy force. But this trend is opposite for the thermally opposing flow. The point of zero skin friction moves upstream due to unsteadiness. No singularity is observed at the point of zero skin friction for unsteady flow unlike steady flow. The flow reversal is observed after a certain instant of time. The velocity overshoot occurs for assisting flows.     

Wake transition of two-dimensional cylinders and axisymmetric bluff bodies

This article presents a short review of the three-dimensional transition of wakes from two-dimensional bodies, such as cylinders of various cross-sectional shape, and axisymmetric tori or rings. The nature and sequence of instabilities are compared and contrasted, especially with reference to the base case of the circular cylinder wake. The latter has been the subject of intense interest and scrutiny for well over a century, and has implicitly assumed the role of providing the generic transition scenario for turbulent wake flow. For elongated cylinders with streamlined leading edges, the analogues of the instability modes for a circular cylinder become unstable in the reverse order, which may have implications for the route to wake turbulence for such bodies. As well, the analogue of mode B has a significantly increased relative spanwise wavelength and appears to have a different near-wake structure. At the other extreme, for a normal flat plate, the wake first becomes unstable to a nonperiodic mode that appears distinct from either of the dominant circular cylinder wake modes. For tori, which have a local geometry approaching a two-dimensional circular cylinder for high aspect ratios (ARs), the sequence of transitions with increasing Reynolds number is a strong function of AR. For intermediate ARs, the first occurring wake instability mode is a subharmonic mode. Possible underlying physical mechanisms leading to some of these instabilities are also examined. In particular, support is provided for the role of idealized physical instability mechanisms in controlling wavelength selection and amplification for the dominant wake instability modes. The results presented in this article focus on relevant research undertaken by the Monash group but draws in results from many other international groups.     

Investigation of supersonic three-dimensional flow past pointed axisymmetric bodies

The flow pattern near bodies of revolution with very long cylindrical and pointed nose sections is studied in the framework of an ideal gas model by means of a numerical method based on MacCormack's difference scheme. The existence of internal shock waves, oriented in both the longitudinal and the transverse directions, in the shock layer is established. The variation of the aerodynamic coefficients of the configuration with its length, angle of attack, and free stream Mach number is investigated. The calculated and experimental data are compared, and the connection between the flow parameters on the body surface and the position of the separation line of the boundary layer on its lateral face is established. A method of calculating the influence of the boundary layer on the values of the aerodynamic coefficients of bodies of revolution of large aspect ratio at small angles of attack is proposed. Axisymmetric flow near blunt bodies has been studied in detail in [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 127–133, September–October, 1986.The author expresses his gratitude to A. N. Pokrovskii for his help in calculating the boundary layer parameters on the surfaces of the considered configurations.