Stability of the viscous flow of a fluid through a flexible tube

The stability of the Hagen-Poiseuille flow of a Newtonian fluid in a tube of radius R surrounded by an incompressible viscoelastic medium of radius R < r < HR is analysed in the high Reynolds number regime. The dimensionless numbers that affect the fluid flow are the Reynolds number Re = (rho VR/eta), the ratio of the viscosities of the wall and fluid eta(r) = (eta(s)/eta), the ratio of radii H and the dimensionless velocity Gamma = (rho V-2/G)(1/2). Here rho is the density of the fluid, G is the coefficient of elasticity of the wall and V is the maximum fluid velocity at the centre of the tube. In the high Reynolds number regime, an asymptotic expansion in the small parameter epsilon = (1/Re) is employed. In the leading approximation, the viscous effects are neglected and there is a balance between the inertial stresses in the fluid and the elastic stresses in the medium. There are multiple solutions for the leading-order growth rate s((0)), all of which are imaginary, indicating that the fluctuations are neutrally stable, since there is no viscous dissipation of energy or transfer of energy from the mean flow to the fluctuations due to the Reynolds stress. There is an O(epsilon(1/2)) correction to the growth rate, s((1)), due to the presence of a wall layer of thickness epsilon(1/2)R where the viscous stresses are O(epsilon(1/2)) smaller than the inertial stresses. An energy balance analysis indicates that the transfer of energy from the mean flow to the fluctuations due to the Reynolds stress in the wall layer is exactly cancelled by an opposite transfer of equal magnitude due to the deformation work done at the interface, and there is no net transfer from the mean flow to the fluctuations. Consequently, the fluctuations are stabilized by the viscous dissipation in the wall layer, and the real part of s(1) is negative. However, there are certain values of Gamma and wavenumber k where s((1)) = 0. At these points, the wall layer amplitude becomes zero because the tangential velocity boundary condition is identically satisfied by the inviscid flow solution. The real part of the O(epsilon) correction to the growth rate s((2)) turns out to be negative at these points, indicating a small stabilizing effect due to the dissipation in the bulk of the fluid and the wall material. It is found that the minimum value of s((2)) increases proportional to (H-1)(-2) for (H-1) much less than 1 (thickness of wall much less than the tube radius), and decreases proportional to H-4 for H much greater than 1. The damping rate for the inviscid modes is smaller than that for the viscous wall and centre modes in a rigid tube, which have been determined previously using a singular perturbation analysis. Therefore, these are the most unstable modes in the flow through a flexible tube

Thermal expansion studies of substituted CTP derivatives

Several new Na, Y and Zr substituted derivatives of Ca-0.5 Ti-2(PO4)(3) (CTP) have been synthesized. These derivatives retain the hexagonal structure of the parent (CTP) compound with minor changes in lattice parameters. Linear thermal expansion coefficients (alpha) have been obtained using a high sensitivity dilatometer.

Variability of sif and cod of stochastic structural systems

Stochastic structural systems having a stochastic distribution of material properties and stochastic external loadings in space are analysed when a crack of deterministic size is present. The material properties and external loadings are considered to constitute independent, two-dimensional, univariate, real, homogeneous stochastic fields. The stochastic fields are characterized by their means, variances, autocorrelation functions or the equivalent power spectral density functions, and scale fluctuations. The Young's modulus and Poisson's ratio are treated to be stochastic quantities. The external loading is treated to be a stochastic field in space. The energy release rate is derived using the method of virtual crack extension. The deterministic relationship is derived to represent the sensitivities of energy release rate with respect to both virtual crack extension and real system parameter fluctuations. Taylor series expansion is used and truncation is made to the first order. This leads to the determination of second-order properties of the output quantities to the first order. Using the linear perturbations about the mean values of the output quantities, the statistical information about the energy release rates, SIF and crack opening displacements are obtained. Both plane stress and plane strain cases are considered. The general expressions for the SIF in all the three fracture modes are derived and a more detailed analysis is conducted for a mode I situation. A numerical example is given.

Thermal expansion of LaBa2Cu2CoO7+delta

In this paper, we report high-temperature X-ray diffraction (HTXRD) and dilatometric studies on LaBa2Cu2CoO7+delta. Bulk and volume thermal expansion studies, along with a study of its phase transition, were carried out. The linear and volume thermal expansion coefficients were found to be 11.7 X 10(-6) K-1 and 42.3 X 10(-6) K-1, respectively. (C) 2000 Elsevier Science Ltd.

Wavelet based compression and denoising of optical tomography data

Two methods based on wavelet/wavelet packet expansion to denoise and compress optical tomography data containing scattered noise are presented, In the first, the wavelet expansion coefficients of noisy data are shrunk using a soft threshold. In the second, the data are expanded into a wavelet packet tree upon which a best basis search is done. The resulting coefficients are truncated on the basis of energy content. It can be seen that the first method results in efficient denoising of experimental data when scattering particle density in the medium surrounding the object was up to 12.0 x 10(6) per cm(3). This method achieves a compression ratio of approximate to 8:1. The wavelet packet based method resulted in a compression of up to 11:1 and also exhibited reasonable noise reduction capability. Tomographic reconstructions obtained from denoised data are presented. (C) 1999 Published by Elsevier Science B.V. All rights reserved,

California bearing ratio behavior of cement-stabilized fly ash-soil mixes

Thermal power stations using pulverized coal as fuel generate large quantities of fly ash as a byproduct, which has created environmental and disposal problems. Using fly ash for gainful applications will solve these problems. Among the various possible uses for fly ash, the most massive and effective utilization is in geotechnical engineering applications like backfill material, construction of embankments, as a subbase material, etc. A proper understanding of fly ash-soil mixes is likely to provide viable solutions for its large-scale utilization. Earlier studies initiated in the laboratory have resulted in a good understanding of the California Bearing Ratio (CBR) behavior of fly ash-soil mixes. Subsequently, in order to increase the CBR value, cement has been tried as an additive to fly ash-soil mixes. This paper reports the results.

Crystal structure, thermal expansion and electrical conductivity of Nd0.7Sr0.3Fe1-xCoxO3 (0 <= x <= 0.8)

The crystal structure, thermal expansion and electrical conductivity of the solid solution Nd0.7Sr0.3Fe1-xCoxO3 for 0 less than or equal to x less than or equal to 0.8 were investigated. All compositions had the GdFeO3-type orthorhombic perovskite structure. The lattice parameters were determined at room temperature by X-ray powder diffraction (XRPD). The pseudo-cubic lattice constant decreased continuously with x. The average linear thermal expansion coefficient (TEC) in the temperature range from 573 to 973 K was found to increase with x. The thermal expansion curves for all values of x displayed rapid increase in slope at high temperatures. The electrical conductivity increased with x for the entire temperature range of measurement. The calculated activation energy values indicate that electrical conduction takes place primarily by the small polaron hopping mechanism. The charge compensation for the divalent ion on the A-site is provided by the formation of Fe4+ ions on the B-site (in preference to Co4+ ions) and vacancies on the oxygen sublattice for low values of x. The large increase in the conductivity with x in the range from 0.6 to 0.8 is attributed to the substitution of Fe4+ ions by Co4+ ions. The Fe site has a lower small polaron site energy than Co and hence behaves like a carrier trap, thereby drastically reducing the conductivity. The non-linear behaviour in the dependence of log sigmaT with reciprocal temperature can be attributed to the generation of additional charge carriers with increasing temperature by the charge disproportionation of Co3+ ions. (C) 2002 Elsevier Science B.V. All rights reserved.

Swelling pressure of sodium montmorillonites

Determination of the swelling pressure of montmorillonitic clays is required in many situations concerned with stability problems of foundations, retaining walls, slope stability of embankments and excavations in expansive soils. Recently expansive soils such as bentonite have been used as a mixture backfill material, for example as backfill material for nuclear waste disposal systems, for which a knowledge of the swelling pressure is desirable. This is the pressure required to keep the clay-water system at the required void ratio when it is allowed to absorb water or electrolyte. If the pressure is less than the swelling pressure, volume expansion occurs; if the pressure is more than the swelling pressure, volume compression occurs. Because of isomorphous substitutions in the crystal lattice, in general the clay particles carry negative charges at the surfaces of the platelets. Exchangeable cations in the clay media are attracted to these negative charges, but this attraction is opposed by the tendency of ions to be distributed. As a result, an electric diffuse double layer is formed (Gouy, 1910).

Synthesis and thermal expansion hysteresis of Ca1-xSrxZr4P6O24

The low thermal expansion ceramic system, Ca1-xSrxZr4P6O24, for the compositions with x = 0, 0.25, 0.50, 0.75 and 1 was synthesized by solid-state reaction. The sintering characteristics were ascertained by bulk density measurements. The fracture surface microstructure examined by scanning electron microscopy showed the average grain size of 2.47 mum for all the compositions. The thermal expansion data for these ceramic systems over the temperature range 25-800degreesC is reported. The sinterability of various solid solutions and the hysteresis in dilatometric behaviour are shown to be related to the crystallographic thermal expansion anisotropy. A steady increase in the amount of porosity and critical grain size with increase in x is suggested to explain the observed decrease in the hysteresis.

Water content - void ratio swell-shrink paths of compacted expansive soils

This paper addresses the behaviour of compacted expansive soils under swell-shrink cycles. Laboratory cyclic swell-shrink tests were conducted on compacted specimens of two expansive soils at surcharge pressures of 6.25, 50.00, and 100.00 kPa. The void ratio and water content of the specimens at several intermediate stages during swelling until the end of swelling and during shrinkage until the end of shrinkage were determined to trace the water content versus void ratio paths with an increasing number of swell-shrink cycles. The test results showed that the swell-shrink path was reversible once the soil reached an equilibrium stage where the vertical deformations during swelling and shrinkage were the same. This usually occurred after about four swell-shrink cycles. The swelling and shrinkage path of each specimen subjected to full swelling - full shrinkage cycles showed an S-shaped curve (two curvilinear portions and a linear portion). However, the swelling and shrinkage path occurred as a part of the S-shaped curve, when the specimen was subjected to full swelling - partial shrinkage cycles. More than 80% of the total volumetric change and more than 50% of the total vertical deformation occurred in the central linear portion of the S-shaped curve. The volumetric change was essentially parallel to the saturation line within a degree of saturation range of 50-80% for the equilibrium cycle. The primary value of the swell-shrink path is to provide information regarding the void ratio change that would occur for a given change in water content for any possible swell-shrink pattern. It is suggested that these swell-shrink paths can be established with a limited number of tests in the laboratory.

Stability of the flow of a fluid through a flexible tube at high Reynolds number

The stability of the Hagen-Poiseuille flow of a Newtonian fluid in a tube of radius R surrounded by an incompressible viscoelastic medium of radius R < r < HR is analysed in the high Reynolds number regime. The dimensionless numbers that affect the fluid flow are the Reynolds number Re = (ρVR / η), the ratio of the viscosities of the wall and fluid ηr = (ηs/η), the ratio of radii H and the dimensionless velocity Γ = (ρV2/G)1/2. Here ρ is the density of the fluid, G is the coefficient of elasticity of the wall and Vis the maximum fluid velocity at the centre of the tube. In the high Reynolds number regime, an asymptotic expansion in the small parameter ε = (1/Re) is employed. In the leading approximation, the viscous effects are neglected and there is a balance between the inertial stresses in the fluid and the elastic stresses in the medium. There are multiple solutions for the leading-order growth rate do), all of which are imaginary, indicating that the fluctuations are neutrally stable, since there is no viscous dissipation of energy or transfer of energy from the mean flow to the fluctruations due to the Reynolds strees. There is an O(ε1/2) correction to the growth rate, s(1), due to the presence of a wall layer of thickness ε1/2R where the viscous stresses are O(ε1/2) smaller than the inertial stresses. An energy balance analysis indicates that the transfer of energy from the mean flow to the fluctuations due to the Reynolds stress in the wall layer is exactly cancelled by an opposite transfer of equal magnitude due to the deformation work done at the interface, and there is no net transfer from the mean flow to the fluctuations. Consequently, the fluctuations are stabilized by the viscous dissipation in the wall layer, and the real part of s(1) is negative. However, there are certain values of Γ and wavenumber k where s(l) = 0. At these points, the wail layer amplitude becomes zero because the tangential velocity boundary condition is identically satisfied by the inviscid flow solution. The real part of the O(ε) correction to the growth rate s(2) turns out to be negative at these points, indicating a small stabilizing effect due to the dissipation in the bulk of the fluid and the wall material. It is found that the minimum value of s(2) increases [is proportional to] (H − 1)−2 for (H − 1) [double less-than sign] 1 (thickness of wall much less than the tube radius), and decreases [is proportional to] (H−4 for H [dbl greater-than sign] 1. The damping rate for the inviscid modes is smaller than that for the viscous wall and centre modes in a rigid tube, which have been determined previously using a singular perturbation analysis. Therefore, these are the most unstable modes in the flow through a flexible tube.

Uncertainty analysis of vibrational frequencies of an incompressible liquid in a rectangular tank with and without a baffle using polynomial chaos expansion

Polynomial chaos expansion (PCE) with Latin hypercube sampling (LHS) is employed for calculating the vibrational frequencies of an inviscid incompressible fluid partially filled in a rectangular tank with and without a baffle. Vibration frequencies of the coupled system are described through their projections on the PCE which uses orthogonal basis functions. PCE coefficients are evaluated using LHS. Convergence on the coefficient of variation is used to find the orthogonal polynomial basis function order which is employed in PCE. It is observed that the dispersion in the eigenvalues is more in the case of a rectangular tank with a baffle. The accuracy of the PCE method is verified with standard MCS results and is found to be more efficient.