THERMAL STRESSES IN ORTHOTROPIC DISK DUE TO ROTATING HEAT SOURCE

A quasi-state stress-field generated in an orthotropic elastic circular disk by a heat source rotating on a concentric circular path is investigated. An exact solution is developed in terms of doubly infinite series, using a stress-function approach. Numerical results are given for a boron-epoxy fiber-reinforced composite material and the effect of orthotropy on the distribution of thermal stresses is studied by comparing the orthotropic results with those for an isotropic material.     

NOTE ON THE SOLUTION OF THE EQUATIONS CONTROLLING STABILITY OF NONLINEAR THERMOELASTIC WAVES IN A SPINNING DISK

A general solution to the system of coupled differential equations with periodic coefficients, established in [1] and determining the stability of a spinning heated disk, is given.     

Sub-critical stable hydrogen-air premixed laminar flames in micro gaps

Sub-critical burning of lean hydrogen-air mixtures in micro gaps between two quartz disks was investigated both experimentally and numerically. Stationary regimes for different compositions and gap sizes were found when sub-critical flames remained in a stable position relative to the disk surfaces. The burning velocity in the micro gaps was observed to reach values much larger than the laminar burning velocity. A reaction-diffusion numerical model was proposed to corroborate experimental results. Different factors, such as boundary conditions for velocity, irradiation of the disk surfaces contacting the gas, and an increase in the chemical reaction rate near disk surfaces were modeled numerically in order to explain the increase in burning velocities. The best correlation between the numerical results and experimental data was observed in the scenario proposing as increased chemical reaction rate near the disk surfaces. Numerical simulations also showed that for large flame front velocities and wider sub-critical gaps, the flame front becomes unstable. The reason for this instability is the asynchronization of the combustion near the disk surfaces and the subsequent turbulization of the flame.     

New Integral Representations in the Dynamic Uncoupled Thermoelasticity

New integral representations of homogeneous 3D uncoupled dynamic thermoelasticity for semi-infinite cylindrical domains with curvilinear surfaces placed at infinity and subject to mixed boundary conditions on the plane boundaries are obtained. The representations are given in the form of integral convolutions involving a Green's function for the parabolic heat conduction equation, as well as Green's function for the isothermal elastodynamics. A multi-integral representation of solution to a particular initial-boundary value problem for an infinite wedge is included.     

FAILURE-MODE TRANSITION SPEED IN THREE-DIMENSIONAL TRANSIENT DEFORMATIONS OF A MICROPOROUS HEAT-CONDUCTING THERMOELASTOVISCOPLASTIC PRENOTCHED PLATE

ABSTRACT

We analyze three-dimensional finite coupled thermomechanical deformations of a rectangular plate with two parallel notches placed symmetrically about the horizontal centroidal plane of the plate. The edge surface of the plate between the two notches is struck by a cylindrical projectile of diameter equal to the distance between the notches and made of the same material as the plate. The plate material is modeled as heat-conducting, microporous, elastoviscoplastic, and isotropic. Both the brittle and the ductile failures initiate at points adjoining the notch-tip surface that are on the midplane of the plate and propagate toward the outer surfaces. Even for a relatively thin plate, the difference in the times of initiation of failures on the mid and front surfaces is significant. Also the two failure modes on the mid surface initiate much later than that predicted by the plane strain analysis. Thus an experimentalist observing fracture on the front or the back face of the plate will see it initiate much later than the times given by the plane strain analysis of the problem. For a steel plate, it is found that the failure mode transitions from brittle to ductile at an impact speed of about 21.8 m/s.     

Heat transfer in pool fires at a certain small lip height

Under the assumptions of a gray-diffuse and homogeneous disk flame at the top plane of the vessel, a diffuse-gray fuel and vessel wall surfaces, and a transparent medium in the ullage space of the vessel, the longitudinal temperature and heat flux distributions at the vessel wall surface for ethanol and kerosene pool fires were calculated numerically. The calculations were performed using the data of Rasbash et al. The emissive power of the disk flame assumed at the top plane of the vessel, which is determined from the heat balance in the combustion system, is approximately equal to the mean values of the radiative flux measured near the top plane of the vessel in the similar fuel type and pool size at the relatively small lip height. The calculated emissive power of the assumed disk flame decreases with time and approaches the asymptote, depending on the depth of the vapor zone. The heat of evaporation and the rate of increase of the sensible heat of the liquid increases and decreases, respectively, with time and approach asymptotes. The time evolution of the sum of them is similar to that of the emissive power of the disk flame derived from the heat balance in the combustion system. Even in relatively small lip heights and low emissive power flames, as in non-hot-zone-forming pool fires, the rates of heat transfer between the wall and the ambient fluids are large, and cannot be neglected in comparison to the heat input from above to the fuel surface.     

ON AXISYMMETRIC THERMAL STRESSES IM AN ANISOTROPIC HOLLOW CYLINDER

Abstract

This paper deals with the problem of thermal stresses in a hollow anisotropic cylinder of finite extent arising from axisymmetric temperature variations at the plane ends, the inner and outer curved surfaces being in contact with rigid and smooth insulators. An exact solution is developed using potential functions of displacement. Numerical results are given for cylinders made of magnesium (anisotropic) and copper (isotropic).     

THERMAL STRESSES IN A LONG ELASTIC CYLINDER CONTAINING A PENNY-SHAPED CRACK AND EMBEDDED IN A THERMALLY CONDUCTIVE ELASTIC INFINITE MEDIUM

This paper is concerned with- the state of stress in a long circular elastic cylinder with a concentric penny-shaped crack whose surfaces are subjected to a prescribed temperature. The plane of the crack is assumed to be perpendicular to the axis of the cylinder. The cylinder is bonded to a thermally conductive elastic infinite medium. The thermal and elastic constants of the cylinder and infinite medium are assumed to be different. By assuming suitable representations for the temperature function, the heat conduction problem is reduced to the solution of a Fredholm integral equation of the second kind. Similarly, the thermoelastic problem is also reduced to the solution of a Fredholm integral equation of the second kind. A closed-form expression is obtained for the stress-intensity factor. The integral equations are solved numerically, and the results are used to obtain numerical values for the stress intensity factor. These values are presented graphically.     

PROPAGATION OF A PLANE WAVE IN A THERMOELASTIC HALF-SPACE UNDER SMOOTH HEATING OF ITS BOUNDARY

In this paper a closed-form solution to a plane wave propagation problem for a half-space subject to a uniform time-dependent healing of its boundary in the framework of dynamic theory of thermal stresses is presented. The solution is given for two variants of smooth boundary heating. The numerical results are shown in the form of graphs of stress and temperature versus the distance from the loaded boundary.     

CONTROL OF TRANSIENT THERMOELASTIC DISPLACEMENT IN A COMPOSITE DISK

Control of displacement in a composite disk subjected to axisymmetric heating is investigated. The disk consists of a transversely isotropic structural layer to which is bonded a layer of piezoceramic material of crystal class 6mm. First, a solution procedure based on potential functions is used to analyze the elastic and electric fields induced in the disk when a transient ambient temperature acts on the free surface of the structural layer. Then a transient distribution of electric potential across the piezo-electric layer is determined such that the resultant displacement at the surface of the structural layer has a prescribed distribution. Numerical results are obtained for the resulting thermal, elastic, and electric fields.     

Highly accurate error estimate of the momentum theory as applied to wind turbines

The paper provides a verification of the well‐known momentum theories by comparing their results with those of a semi‐analytical method based on the exact solution of the flow through an actuator disk. In fact, many error sources are disseminated in these theories. Specifically, the axial momentum balance is diffusely applied in an approximate differential form, and several linearization are customarily introduced in the equations of the motion. In the present study, an analytical formulation of these two kinds of errors is provided and a set of data generated with controlled accuracy is used to quantify them both in terms of global (power coefficient) and local (axial velocity at the disk plane) quantities. The overall errors increase by increasing the thrust coefficient and decreasing the tip speed ratio. Although the errors can be generally considered small in terms of global performance coefficients, the differences between the two methods are significant when looking at local quantities. In particular, for the cases presented herein, the momentum theory is shown to overestimate the axial velocity at the tip and at the disk centre regions and to underestimate this velocity elsewhere. For low values of the tip speed ratio, an underestimation also occurs in the zone near to the disk centre. Copyright © 2017 John Wiley & Sons, Ltd.     

DISCONTINUITIES IN GENERALIZED THERMO-VISCOELASTICITY UNDER FOUR THEORIES

A model of the equations of generalized thermoviscoelasticity for isotropic media is given. The formulation is applied to the generalized thermoelasticity theories—Lord–Shulman, Green–Lindsay, and Chandrasekharaiah and Tzou—as well as to the dynamic coupled theory. The state-space approach is adopted for the solution of the one-dimensional problem of plane distribution of heat sources. The Laplace transform technique is used. The expansions of the stress component, the temperature increment, and the displacement, in Laplace transform domain, in power series, and the exact inversions for arbitrary time, are given. The jump discontinuities are calculated for the four theories and the kinematic conditions of compatibility are verified. Numerical results are given and illustrated graphically by employing the numerical method for the inversion of the Laplace transforms. Comparisons are made with the results predicted by the four theories.     

同向旋转盘间非稳态传热特性的实验研究

将航空发动机中同向旋转的高低压涡轮盘简化成了几何形状相对简单的同向旋转盘系统.用实验的方法研究了非稳态情况下改变冷气流量和改变两盘转速对两盘温度和盘面平均Nu的影响.结果表明:进气Re是最重要的影响因素, 它对传热的影响是瞬时的,Re升高两个盘面的Nu同时增加;当一个盘的转速增大时,此盘的传热有一定的增强,但对另外一个盘传热影响很小.     

Study of the corrective factor involved when measuring the diffuse solar radiation by use of the ring method

By comparing the diffuse solar radiation on a horizontal plane as continuously measured in Geneva over a full year by using both a fixed ring and a moving disk, we conclude that the ring corrective factor can be evaluated on the basis of simple models, but with a daily uncertainty of the order of 5 per cent. In this study, the isotropy of the diffuse radiation can be used as a reasonable approximation, even if this assumption is not fully verified. More precise measurements would require the use of a disk.     

Steady-state estimation of thermal contact conductance between sliding disk and stationary cylinder with similar/dissimilar materials under the isothermally heated boundary condition

An accurate understanding of the thermal contact conductance (TCC) is imperative for the enhancement of the performance and service life of metallic cylindrical joints. However, the evaluation of the TCC between conforming cylindrical solids is quite intricate, as it depends on the temperature, pressure, roughness, relative sliding speed, and thermophysical properties of solids. Instead of generating contacting surfaces stochastically, in this communication, an experimental setup in the lab-scale consisting of a stationary cylinder and a sliding hot disk has been fabricated in which temporal evolutions of the temperature on both solids are recorded by thermocouples. Effects of the disk temperature and relative sliding speed on the steady-state TCC have been investigated. There is a cylindrical interface between two conforming smooth solids of similar/dissimilar materials. As there is the differential expansion of cylindrical solids due to the temperature gradient, the diameter of sliding disks has been truncated to fix the radial gap (contact pressure). Inverse solution with the conjugate gradient method along with the adjoint problem has been applied to estimate the steady-state TCC. One-dimensional heat transfer analysis shows that frictional heating is negligible. The steady-state TCC is almost constant longitudinally along the axis of the steel cylinder. Under identical initial and isothermally heated boundary conditions, the TCC between the aluminum disk and cylinder is higher than that between steel disk and cylinder. Also, the TCC has been increased with a rising slope when the working temperature is enhanced. However, the augmentation of the relative sliding speed engenders a decreasing slope in the TCC graph.     

Study of the corrective factor involved when measuring the diffuse solar radiation by use of the ring method

By comparing the diffuse solar radiation on a horizontal plane as continuously measured in Geneva over a full year by using both a fixed ring and a moving disk, we conclude that the ring corrective factor can be evaluated on the basis of simple models, but with a daily uncertainty of the order of 5 per cent. In this study, the isotropy of the diffuse radiation can be used as a reasonable approximation, even if this assumption is not fully verified. More precise measurements would require the use of a disk.     

THERMOELASTIC STRESS OF MULTILAYER CYLINDRICAL BODIES

An effective solution of the boundary value and boundary contact problems of thermal stress of elastic one- and multilayer bodies bounded by the coordinate surfaces of generalized cylindrical coordinates 𝜌 , f , z ( 𝜌 , f are orthogonal curvilinear coordinates on the plane and z is a linear coordinate) is given. The body occupies the domain z = { 𝜌 0 < 𝜌 < 𝜌 1 , f 0 < f < f 1 , 0 < z < z 1 } ; and a thermal disturbance is defined on the free of stress planar parts z = 0 and z = z 1 of the boundary surface, while homogeneous conditions of either symmetry or antisymmetry type are given for the remaining part of the boundary. The elastic body is assumed to be nonhomogeneous along z and transversally isotropic with the plane of isotropy z = const . The transversally isotropic layers of the multilayer body make contact along the planes z = const .     

TRANSIENT THERMOELASTIC CONTACT STRESS IN A SHORT-LENGTH CIRCULAR CYLINDER

This paper is a treatment of a transient thermoelastic contact problem in a short-length circular cylinder, to which a heated rigid band is bonded. The problem may be reduced to that of solving dual-series equations. The solution meets the boundary conditions on both the lateral surface and the plane ends of the cylinder. The radial, hoop, and axial stresses have singularities at the end of a rigid band on the cylindrical surface.     

Optimal Heating Control of Thermosensitive Rectangular Domain under Restrictions on Stresses in a Plastic Zone

A numerical algorithm to solve the problem on optimal heating control for a long isotropic homogeneous rectangular parallelepiped under plane strain has been proposed. The control (the surrounding temperature at one of the boundary surfaces of a parallelepiped) which in a minimal time, carries the body from the initial thermal state to the final one characterized by the given mean-integral temperature has been determined. In addition, restrictions both to the control function and to the maximal tangential stress intensity have been considered. The case of elastoplastic deformation of the material has been studied in the framework of the theory of the body element deformation along small curvature paths.