Optimal design of a thick-walled pipeline cross-section against creep rupture

Summary Cylinder under combined loadings (pressure, bending, axial force) is subject to non-linear creep described by Norton-Odqvist creep law. In view of bending a circularly-symmetric cross-section is no longer optimal in this case. Hence we optimize the shape of the cross-section; minimal area being the design objective under the constraint of creep rupture. Kachanov-Sdobyrev hypothesis of brittle creep rupture is applied. The solution is based on the perturbation method (expansions into double series of small parameters), adjusted to optimization problems.Notation A cross-sectional area - C, , creep rupture constants - K, n, _C , _C creep constants - F dimensionless creep modulus - M bending moment - N axial force - a(),b() internal and external radii of the cross-section - j creep modulus - p internal pressure - r, ,z cylindrical coordinates - s _r ,s ,s _z ,t _r dimensionless stresses - t _R time to rupture - stress function - , () dimensionless internal and external radii - _e effective strain rate - _kl strain rates - rate of curvature - rate of elongation of the central axis - dimensionless radius - _e effective stress - _I maximal principal stress - _S Sdobyrev's reduced stress - _r , , _z , _r components of the stress tensor - measure of material continuity - measure of deterioration With 7 Figures     

Exotic low-energy separation in 1D quantum liquids

We define the low-energy separation of the Hubbard chain in a magnetic field and chemical potential in terms of two c and s bosonic algebras. This generalizes the usual charge-spin separation, which is recovered in the limit of zero magnetization only. The corresponding pseudoparticle bosonization follows directly from the perturbative character of the pseudoparticle operator basis.     

Formation of Friction Layers and Wear Resistance of Steels under Conditions of Boundary Friction

We studied the influence of the lubricant compositions Grafitol with 10% graphite (1), Aerol containing 17% MoS₂ (2), Limol containing 60% MoS₂ (3), Limol + 10% chlorine-paraffin (4), and Limol + 10% copper powder (5) on the wear rate and formation of the fine structure of surface friction layers of structural steels. We established a correlation between the tribological characteristics of steels and lubricants. The abrasive wear of 40KhFA steel was minimum if it was lubricated with Limol + 10% copper powder. In this case, its wear was smaller by a factor of 10, 2, 1.25, and 7.25 as compared with lubricant compositions 1–4, respectively. In the course of minimum wear of 40KhFA steel, in the surface friction layers, we observed the minimum values of second-kind distortions (a/a) and of the true size of domains of X-ray coherent scattering (D) as well as the minimum difference between the crystal lattice constants (a) of steel before and after friction.     

Die Entwicklung von Längswirbeln in zeitlich anwachsenden Grenzschichten an konkaven Wänden

Zusammenfassung Messungen des Anwachsens von Längswirbeln in zeitlich anwachsenden Grenzschichten an konkav gekrümmten Wänden (Görtler-Taylor-Wirbel) ergaben drei deutlich getrennte Bereiche: Es traten zunächst Wirbel mit der Wellenläge 0,9 auf (=Grenzschichtdicke, =Höhe einer Zelle, die zwei gegensinnig drehende Wirbel enthält). Je nach Größe der mit der Verdrängungsdicke ₁ der Grenzschicht gebildeten Reynolds-Zahl erschienen dann kurze Zeit später Wirbel mit 2,5, wenn war. Im Bereiche dagegen traten stattdessen bei den hier durchgeführten Versuchen immer Wirbel mit der Wellenlänge 6,5 auf. Bei werden die ersten Tollmien-Schlichting-Wellen mit der Wellenlänge _TS 6· angefacht. In ihren wandnahen Bereichen der Wellentäler könnten sich dann die oben genannten Längswirbel der Wellenlänge 6,5· ausbilden, die die zwei-in eine dreidimensionale Störung allseits gleicher Größenordnung verwandeln können.

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The development of longitudinal vortices in boundary layers growing with time along concave walls

Summary Measurements of the growth of longitudinal vortices in boundary layers growing with time along concave walls (Görtler-Taylor vortices) rendered three distinctly separated regions. First, vortices with a wave-length 0.9 appeared (-boundary layer thicness, =height of a cell containing two counterrotating vortices). Then, depending on the Reynolds number R _{a 1}/v ₁=displacement thickness), vortices with 2.5 appeared shortly afterwards, provided . In the region , however, the wave-length was 6.5. For the first Tollmien-Schlichting waves with _TS 6 were excited. In the wave-throughs close to the wall the abovementioned longitudinal vortices with wave length 6.5 may then be formed. This might transform the two-dimensional into a three-dimensional flow of equal order of magnitude in all directions.

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Zeichenerklärungen R _a Innenradius - Re _a Reynolds-Zahl gebildet mit dem InnenradiusR _a - Reynolds-Zahl gebildet mit der Verdrängungsdicke ₁ - kritische Taylor-Zahl - h Standhöhe der Flüssigkeit im Zylinder - t Zeit - z Anzahl - Steigungswinkel der Geraden - Grenzschichtdicke - ₁ Verdrängungsdicke - Wellenlänge (enthält ein gegensinnig rotierendes Längswirbelpaar) - v kinematische Zähigkeit - Winkelgeschwindigkeit Indizes K Knickpunkt der Geradensteigung - L unterhalb des Knickpunktes der Geradensteigung - TS Tollmien-Schlichting - e Einsatz der Wirbelentstehung     

Forced convection over a continuous sheet with suction or injection moving in a flowing fluid

Summary The analysis of forced convection flow and heat transfer about a flat sheet with suction or injection continuously moving in a quiescent or flowing fluid has been carried out. This kind of problem finds applications in a variety of manufacturing processes such as hot rolling, extrusion of plastic sheets, continuous casting, and cooling of a metallic plate in a cooling bath. The governing differential equations are reduced to nonlinear ordinary differential equations by similarity transformations. These equations are solved numerically based on a finite difference algorithm. Representative velocity and temperature profiles within the boundary layer are presented at selected values of free stream velocity and injection parameter. The friction factor and Nusselt number are illustrated for a wide range of governing parameters. For the same injection parameter, Prandtl number, and normalized velocity difference |U _w–U |, higher values of the Nusselt number and friction factor result fromU _w>U than fromU _w<U . Also, an increase in the velocity ratioU /U _w results in an increase in the heat transfer rate, but a decrease in the friction factor. Furthermore, the heat transfer is enhanced due to increasing the values of the free stream velocity, the injection parameter, and Prandtl number; while it is reduced due to increasing the velocity difference.Nomenclature C _f friction factor, _w/(u_r ²/2) - F dimensionless stream function - F _w injection parameter - h local heat transfer coefficient - k thermal conductivity - Nu Nusselt number,hx/k - Pr Prandtl number, / - q _w wall heat flux - Re Reynolds number,u _rx/ - T temperature - T _w temperature at the fluid-sheet interface - T free stream temperature - U _w normalized velocity of the sheet,u _w/u_r - U normalized free stream velocity,u /u _r - u fluid velocity component inx-direction - u _r reference velocity, Eq. (8) - u _w velocity of the continuous sheet - u free stream velocity - v fluid velocity component iny-direction - v _w fluid velocity component iny-direction at the fluid-sheet interface - x streamwise coordinate - y cross-stream coordinate Greek symbols thermal diffusivity - boundary-layer thickness - dimensionless cross-stream coordinate - dimensionless temperature - kinematic viscosity - _w wall shear stress - stream function     

Anisotropic spin diffusion and multiple spin echoes in3He-4He solutions

We propose a ₁-t₁-₂ pulse-NMR experiment to detect the spin-diffusion anisotropy, =D-D, in degenerate spin-polarized³He-⁴He mixtures, where D and dare the transverse and longitudinal spin diffusion coefficients. In such an experiment the nonlinearity of the dynamics produces multiple spin echoes (MSE). At the ³He concentration x₃ 4% the spinrotation parameter vanishes (M 0), so that the nonlinearity of the equations of motion is entirely due to the anisotropy. In this situation, detection of MSE amounts to observation of D. For slight anisotropy, i.e. D/D 0.25, we use a perturbation scheme similiar to that developed by Einzel et al. (in that case, for small M and small demagnetizing field) to calculate the second and third echo heights. For larger anisotropy we numerically calculate the echo heights. We find that for D/D = 0.5 the heights are 2 % of the first echo, and should be detectable. The (₁, ₂) tip-angle dependence of the D echoes is different from that of the M and demagnetization echoes, and furthermore, they occur at right angles to these echoes (in spin space). Thus, even when small spin-rotation and demagnetization effects are present, the ₁-t₁-₂ experiment provides a sensitive means of detecting the anisotropy.     

Localized spin fluctuations

Scaling arguments and renormalization group techniques are used in the Anderson model Hamiltonian for the nonmagnetic limit of a magnetic impurity. The range of validity of the theory is limited toU/ 1, where the electron-electron collisions can already compete strongly with the electron-hole collisions. A parquet approximation is developed; it gives for the static susceptibility in the symmetric case = ()^–1 exp (+U/). There are some hints that the exchange force might play a crucial role in the formation of localized magnetic moment. These considerations are consistent with the electron-hole symmetry in the symmetric Anderson model.     

Heat conduction in a multilayer composite wedge

A new method for analytically solving a problem of steady-state heat conduction for multilayer composite wedge-shaped bodies is suggested based on a generalization of the integral Mellin transform.Notation T temperature - _rr, thermal conductivity coefficients - thickness of composite material layers (1) - N₁(), N ₂ ⁽¹⁾ (), N ₂ ⁽²⁾ () auxiliary local functions from the rapid variable =r/ - m(r, p) auxiliary function entering the core of the generalized integral Mellin transform - ₀ half of the wedge aperture angle Moscow Institute of Chemical Engineering. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 4, pp. 487–491, April, 1993.     

Free convective flow in an enclosure with a cooled inclined upper surface

Natural convective air flow in an enclosure with a horizontal lower wall, vertical side-walls and a straight inclined top wall has been numerically studied. The lower wall is at a uniform high temperature while the top wall is cooled to a uniform lower temperature. The temperature of the side-walls varies in a prescribed way between the temperatures of the bottom and top walls. This flow situation is related to that occurring in a proposed system for use in developing countries for drying crops such as corn and rice. It has been assumed that the flow is steady, laminar, and two-dimensional and that the fluid properties are constant except for the density change with temperature that gives rise to the buoyancy forces. The governing equations have been expressed in terms of stream function and vorticity and written in dimensionless form. The finite element method has been used to obtain the solution to these dimensionless equations. Results have been obtained for enclosures with aspect ratios of between 0.25 and 1 for top surface angles of inclination of between 0 and 45° and for Rayleigh numbers, based on the enclosure width, of between 1000 and 10⁷. The results have been used to study the effect of changes in the governing parameters on the flow pattern in the enclosure and on the mean heat transfer rate to the upper surface.List of symbols A aspect ratio, h/w - h mean height of cavity - k thermal conductivity - Nu local Nusselt number based on w - mean Nusselt number for top surface based on w - n n/w - n coordinate measured normal to boundary surface considered - p pressure - Pr Prandtl number - q local dimensionless heat transfer rate - mean heat transfer rate to top surface - Ra Rayleigh number based on w - T dimensionless temperature - T temperature - T _H temperature of bottom surface - T _C temperature of top surface - u velocity component in x direction - v velocity component in y direction - w width of cavity - x dimensionless x coordinate - x horizontal coordinate position - y dimensionless y coordinate - y vertical coordinate position - thermal diffusivity This work was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada.     

A new parameter for describing the structure bifurcation in two-phase alloys containing coherent particles

The so-called bifurcation diagrams for precipitate particles in nickel-based alloys were obtained by calculating the energy state for a pair of particles on the basis of the bifurcation theory. Based on the bifurcation diagrams, we have proposed a new parameter for describing the two-phase structure containing coherent particles. The parameter is defined as the mean particle radius at the intersection of the energy ridge and the line ofR=–0.5 orR=0.5 in the bifurcation diagram (R(r –r )/(r +r ), wherer andr are the radii of and ), and is symbolized by¯r ^* _±0.5. Because the energy state of the paired and is maximum at¯r ^* _±0.5 whenR=±0.5,¯r ^* _±0.5 is just like the watershed and hence we have termed it structureshed. This parameter successfully describes the effects of elastic energy as well as surface energy on the microstructural changes during coarsening of precipitate particles.     

A texture formation mechanism during electrodeposition

The texture of electrodeposited iron foil has been measured. It was observed that the deposited iron foil had a {110} uvw type texture. If a sufficiently strong magnetic field was applied along the deposited layer during the deposition process, a {110} 001 texture developed from the initial {110} uvw texture, with the 001 axis parallel to the direction of the applied field. An attempt has been made to explain the mechanism of texture development, as well as the effect of the magnetic field during the deposition process.     

The constitution of the Ni-Al-Ru system

The constitution of the Ni-Al-Ru system has been investigated in the range 0 to 50 at% Al. Isothermal sections at 1523 and 1273 K have been determined using microstructural observations, electron probe microanalysis and X-ray diffraction. The phases present were: nickel-based solid solution (); (based on Ni₃Al); solid solutions based on NiAl and RuAl, respectively (designated ₁ and ₂), and ruthenium-based solid solution (Ru). The maximum solubility of Ru in was 5 at%. ₁, and ₂ show extensive range of solubilities, namely up to 20at% Ru in ₁ and up to 25 to 35 at% Ni in ₂. Three-phase equilibrium between , ₂ and (Ru) existed at 1523 and 1273 K. Also at 1523 K, three-phase equilibria existed between , and ₁ and ,₁ and ₂, while at 1273 K, the equilibria were between , ₁,₂ and , , ₂ indicating the occurrence of a reaction +₁, +₂ at a temperature between 1523 and 1273 K. Liquidus features have been deduced from data on as-solidified structures. Lattice parameter data and hardnesses are also reported.     

Motion of a thermal wave front in a nonlinear medium with absorption

We study the evolution of a thermal perturbation in a nonlinear medium whose thermal conductivity depends on the temperature and the temperature gradient according to a power law.Notation u temperature - k coefficient of thermal conductivity - t time - x spatial variable - x₊ a point on the thermal wave front - a ² generalized coefficient of thermal diffusivity - , , , and s parameters of the process - (x^s) Dirac delta-function - B[, ] a beta function - v(, x), (t) auxiliary functions - A, C, T_o, T_m, T*, R, r, p, and _m constants and parameters Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 4, pp. 728–731, October, 1980.     

Vertical motion of a sphere in an electrically conducting,stratified, diffusive medium

Summary The vertical (upwards) flow of an incompressible, Newtonian, viscous, stratified, diffusive, electrically conducting fluid embedded with a uniform magnetic field that is applied in the vertical direction, past a non-conducting sphere is considered. Quasisteady approximation is made allowing for a time dependent buoyancy force. Method of matched asymptotic expansions is employed to obtain the drag exerted on the sphere, for small values of a stratification parameter such that 1,R _e ^1/3, ^–1/3,P _e ^2/3 andR _m =O(^2/3). The drag is computed for certain typical values of the magnetic interaction parameter and diffusivity parameter. The results reveal the fact that while the stratification and magnetic field have the enhancing effect over the drag, the effect of diffusivity is to decrease it.With 3 Figures     

A scaled equation of state for real fluids in the critical region

A scaled equation of state is proposed for real fluids in the critical region which incorporates asymmetry with respect to the critical isochore. In the range of reduced densities 0.65(/ _c)1.4 and for reduced temperatures (T/T _c)1.2, the equation represents P-V-T data for steam within the experimental accuracy.     

Nucleate boiling

The study deals with the effect of the surface conditions on the nucleate boiling curve. A relation is proposed which describes the complete nucleate boiling curve.Notation q thermal flux - q* thermal flux at which the liquid boils after one-phase convection - q_c thermal flux during one-phase convection - q_cr1, q_cr2 first and the second critical thermal flux - T saturation temperature - T superheat of the heating surface relative to the saturation temperature - T* superheat prior to boiling of the liquid after one-phase convection - T_cr1 superheat during the first boiling crisis - T_cr3min minimum superheat at which the third boiling crisis can occur - P pressure - P_cr critical pressure - heat transfer coefficient during nucleate boiling - R_cr radius of a critical vapor forming nucleus - coefficient of surface tension - r latent heat of evaporation - thermal conductivity of the liquid - kinematic viscosity of the liquid - , densities of the liquid and the vapor - g gravitational constant - k Boltzmann constant - N Avogadro number - h Planck's constant Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 394–401, March, 1981.     

Microstructural study of ε-iron-carbonitrides formed by a glow discharge technique

The microstructure and phase transformations occurring in-iron-carbonitrides have been studied by means of X-ray and electron diffraction, electron microscopy and Mössbauer spectrometry. Ordering of the interstitial atoms, N or C, results in a hexagonal unit cell for Fe₃(C, N) with parametersa=a3 andc=c wherea andc are the lattice parameters of the hexagonal close-packed (h c p) iron unit cell. Stacking faults on (0001) planes and partial dislocations with Burgers vector b=1/31 0 ¯1 0 are observed in quenched-Fe₄ (C, N). After quench-aging, the carbonitrides show a structural hardening due to the precipitation of a metastable phase. Slow cooling of-carbonitrides with less than 25 at% interstitials leads to the precipitation of-carbonitride and ferrite in-phase grains which allows the orientation relationships between the-,- and-phases to be defined and a model of the-phase--phase transformation to be proposed.     

Microstructure and mechanical properties of rapidly quenched L20 and L20+L12 alloys in Ni-Al-Fe and Ni-Al-Co systems

Ductile L2₀-type wires and+L1₂-type duplex wires with high strengths and large elongation in the Ni-Al-Fe and Ni-Al-Co ternary systems have been manufactured directly from the liquid state by an in-rotating-water spinning method. The wire diameter was in the range 80 to 180m and the average grain size was 2 to 4m for the wires and 0.2 to 1.0m for the+ wires. _y, _f and _p of the wires were found to be about 360 to 760 MPa, 560 to 960 MPa, and 0.2 to 5.5%, respectively, for the Ni-Al-Fe system, those of the+ wires were about 395 to 660 MPa, 670 to 1285 MPa, and 3.5 to 17%, respectively, for the Ni-Al-Fe system, and about 260 to 365 MPa, 600 to 870 MPa, and 4.0 to 7.0%, respectively, for the Ni-Al-Co system. Cold-drawing caused a significant increase in _y and _f and the values attained were about 1850 and 2500 MPa, respectively, for Ni-20Al-30Fe and Ni-25Al-30Co wires drawn to about 90% reduction in area. The high strengths, large elongation and good cold-workability of the melt-quenched and+ compound wires have been inferred to be due to the structural change into a low-degree ordered state containing a high density of phase boundaries, suppression of grain-boundary segregation and refinement of grain size.     

Transmission electron microscopic observations of a commercial Nb-Ti superconducting alloy

Microstructures in a commercial Nb-Ti alloy heat-treated or repeatedly aged and cold worked have been investigated by transmission electron microscopy. In the aged samples after solution treatment,-phase forms at ageing temperatures below 673 K and-phase precipitates at 773 K. Cold work after solution treatment or heavy cold work without prior solution treatment results in accelerated precipitation of-phase on ageing at 623 K and of-phase on ageing at 773 K, while it gives-precipitation instead of on ageing at 673 K. Repeated ageing and cold work make the microstructures very fine. The refinement is due to formation of dislocation cell structures and subgrains and precipitation of- and-phases.     

Spin hydrodynamic equations with external disturbances and suitable Green's functions for superfluid3He-B. New onsager relations

The spin hydrodynamic equations for superfluid³He-B have been obtained for the case of external, time-dependent fields. On the basis of a microscopic approach, expressions are found for additional terms in equations containing these fields. Considering the linear response of the system to the switching on of external fields, formulas are found for suitable Green's functions (magnetization-magnetization, rotation-rotation, magnetization-rotation, rotation-magnetization). The rotation-rotation Green's function has the 1/q ² singularity characteristic of superfluid systems. Connections between Green's functions lead to relations among kinetic coefficients v, ₁, and ₂. It is also shown that there is a conserved quantityQ ^(B) = div v _s ^(B) that describes sources or magnetic type charges (monopoles) of the superfluid velocity v _s ^(B) . Comparison with the phenomenological approach suggests thatQ ^(B) is proportional to a pseudoscalar giving the projection of the spin density onto the vector describing the axis of rotation.