Stability of spatially developing boundary layers in pressure gradients

A new formulation of the stability of boundary-layer flows in pressure gradients is presented, taking into account the spatial development of the flow and utilizing a special coordinate transformation. The formulation assumes that disturbance wavelength and eigenfunction vary downstream no more rapidly than the boundary-layer thickness, and includes all terms nominally of order R(-1) in the boundary-layer Reynolds number R. In Blasius flow, the present approach is consistent with that of Bertolotti et al. (1992) to O(R(-1)) but simpler (i.e. has fewer terms), and may best be seen as providing a parametric differential equation which can be solved without having to march in space. The computed neutral boundaries depend strongly on distance from the surface, but the one corresponding to the inner maximum of the streamwise velocity perturbation happens to be close to the parallel flow (Orr-Sommerfeld) boundary. For this quantity, solutions for the Falkner-Skan flows show the effects of spatial growth to be striking only in the presence of strong adverse pressure gradients. As a rational analysis to O(R(-1)) demands inclusion of higher-order corrections on the mean flow, an illustrative calculation of one such correction, due to the displacement effect of the boundary layer, is made, and shown to have a significant destabilizing influence on the stability boundary in strong adverse pressure gradients. The effect of non-parallelism on the growth of relatively high frequencies can be significant at low Reynolds numbers, but is marginal in other cases. As an extension of the present approach, a method of dealing with non-similar flows is also presented and illustrated. However, inherent in the transformation underlying the present approach is a lower-order non-parallel theory, which is obtained by dropping all terms of nominal order R(-1) except those required for obtaining the lowest-order solution in the critical and wall layers. It is shown that a reduced Orr-Sommerfeld equation (in transformed coordinates) already contains the major effects of non-parallelism.

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

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

The stability of Hagen-Poiseuille flow of a Newtonian fluid of viscosity eta in a tube of radius R surrounded by a viscoelastic medium of elasticity G and viscosity eta(s) occupying the annulus R < r < HR is determined using a linear stability analysis. The inertia of the fluid and the medium are neglected, and the mass and momentum conservation equations for the fluid and wall are linear. The only coupling between the mean flow and fluctuations enters via an additional term in the boundary condition for the tangential velocity at the interface, due to the discontinuity in the strain rate in the mean flow at the surface. This additional term is responsible for destabilizing the surface when the mean velocity increases beyond a transition value, and the physical mechanism driving the instability is the transfer of energy from the mean flow to the fluctuations due to the work done by the mean flow at the interface. The transition velocity Gamma(t) for the presence of surface instabilities depends on the wavenumber k and three dimensionless parameters: the ratio of the solid and fluid viscosities eta(r) = (eta(s)/eta), the capillary number Lambda = (T/GR) and the ratio of radii H, where T is the surface tension of the interface. For eta(r) = 0 and Lambda = 0, the transition velocity Gamma(t) diverges in the limits k much less than 1 and k much greater than 1, and has a minimum for finite k. The qualitative behaviour of the transition velocity is the same for Lambda > 0 and eta(r) = 0, though there is an increase in Gamma(t) in the limit k much greater than 1. When the viscosity of the surface is non-zero (eta(r) > 0), however, there is a qualitative change in the Gamma(t) vs. k curves. For eta(r) < 1, the transition velocity Gamma(t) is finite only when k is greater than a minimum value k(min), while perturbations with wavenumber k < k(min) are stable even for Gamma--> infinity. For eta(r) > 1, Gamma(t) is finite only for k(min) < k < k(max), while perturbations with wavenumber k < k(min) or k > k(max) are stable in the limit Gamma--> infinity. As H decreases or eta(r) increases, the difference k(max)- k(min) decreases. At minimum value H = H-min, which is a function of eta(r), the difference k(max)-k(min) = 0, and for H < H-min, perturbations of all wavenumbers are stable even in the limit Gamma--> infinity. The calculations indicate that H-min shows a strong divergence proportional to exp (0.0832 eta(r)(2)) for eta(r) much greater than 1.

Passive pressure coefficients, critical failure surface and its kinematic admissibility

Using a combination of a logarithmic spiral and a straight line as a failure surface, comprehensive charts have been developed to determine the passive earth pressure coefficients and the positions of the critical failure surface for positive as well as negative wall friction angles. Translational movement of the wall has been examined in detail, considering the soil as either an associated flow dilatant material or a non-dilatant material, to determine the kinematic admissibility of the limit equilibrium solutions.

Pressure-induced charge transfer in lanthanum nickel ferrate (LaNi0.5Fe0.5O3) and analogies to composition-driven charge transfer in dilanthanum cuprate (La2CuO4): an infrared study

A reversible pressure-induced phase transition in lanthanum nickel ferrate (LaNi0.5Fe0.5O3) manifests itself in the infrared spectrum of the transition metal-oxygen stretching (nu(TM-O)) modes by the emergence of new peaks at pressures greater than similar to 1.4 x 10(9) Pa. Analogies to this transition are made by considering charge transfer in dilanthanum cuprate (La2CuO4) and its modification by partial substitution of copper ions by chromium ions.

A molecular dynamics study and molecular level explanation of pressure dependence of ionic conductivity of potassium chloride in water

Experimental ionic conductivity of different alkali ions in water shows markedly different dependences on pressure. Existing theories such as that of Hubbard-Onsager are unable to explain these dependences on pressure of the ionic conductivity for all ions. We report molecular dynamics investigation of potassium chloride solution at low dilution in water at several pressures between 1 bar and 2 kbar. Two different potential models have been employed. One of the models successfully reproduces the experimentally observed trend in ionic conductivity of K+ ions in water over the 0.001-2 kbar range. We also propose a theoretical explanation, albeit at a qualitative level, to account for the dependence of ionic conductivity on pressure in terms of the previously studied Levitation Effect. It also provides a microscopic picture in terms of the pore network in liquid water.

Micromechanical modeling of granular materials: effect of confining pressure on mechanical behavior

This paper reports the effect of confining pressure on the mechanical behavior of granular materials from micromechanical considerations starting from the grain scale level, based on the results of numerically simulated tests on disc assemblages using discrete element modeling (DEM). The two macro parameters which are influenced by the increase in confining pressure are stiffness (increases) and volume change (decreases). The lateral strain coefficient (Poisson's ratio) at the beginning of the test is more or less constant. The angle of internal friction slightly decreases with increase in confining pressure. The numerical results of disc assemblages indicate very clearly a non-linear Mohr-Coulomb failure envelope with increase in confining pressure. The increase in average coordination number and accompanying decrease of fabric anisotropy reduce the shear strength at higher confining pressures. Micromechanical explanations of the macroscopic behavior are presented in terms of the force and fabric anisotropy coefficients. (C) 1999 Elsevier Science Ltd. AII rights reserved.

Stability of non-parabolic flow in a flexible tube

Flows with velocity profiles very different from the parabolic velocity profile can occur in the entrance region of a tube as well as in tubes with converging/diverging cross-sections. In this paper, asymptotic and numerical studies are undertaken to analyse the temporal stability of such 'non-parabolic' flows in a flexible tube in the limit of high Reynolds numbers. Two specific cases are considered: (i) developing flow in a flexible tube; (ii) flow in a slightly converging flexible tube. Though the mean velocity profile contains both axial and radial components, the flow is assumed to be locally parallel in the stability analysis. The fluid is Newtonian and incompressible, while the flexible wall is modelled as a viscoelastic solid. A high Reynolds number asymptotic analysis shows that the non-parabolic velocity profiles can become unstable in the inviscid limit. This inviscid instability is qualitatively different from that observed in previous studies on the stability of parabolic flow in a flexible tube, and from the instability of developing flow in a rigid tube. The results of the asymptotic analysis are extended numerically to the moderate Reynolds number regime. The numerical results reveal that the developing flow could be unstable at much lower Reynolds numbers than the parabolic flow, and hence this instability can be important in destabilizing the fluid flow through flexible tubes at moderate and high Reynolds number. For flow in a slightly converging tube, even small deviations from the parabolic profile are found to be sufficient for the present instability mechanism to be operative. The dominant non-parallel effects are incorporated using an asymptotic analysis, and this indicates that non-parallel effects do not significantly affect the neutral stability curves. The viscosity of the wall medium is found to have a stabilizing effect on this instability.

Diaphragmless shock wave generators for industrial applications of shock waves

The prime focus of this study is to design a 50 mm internal diameter diaphragmless shock tube that can be used in an industrial facility for repeated loading of shock waves. The instantaneous rise in pressure and temperature of a medium can be used in a variety of industrial applications. We designed, fabricated and tested three different shock wave generators of which one system employs a highly elastic rubber membrane and the other systems use a fast acting pneumatic valve instead of conventional metal diaphragms. The valve opening speed is obtained with the help of a high speed camera. For shock generation systems with a pneumatic cylinder, it ranges from 0.325 to 1.15 m/s while it is around 8.3 m/s for the rubber membrane. Experiments are conducted using the three diaphragmless systems and the results obtained are analyzed carefully to obtain a relation between the opening speed of the valve and the amount of gas that is actually utilized in the generation of the shock wave for each system. The rubber membrane is not suitable for industrial applications because it needs to be replaced regularly and cannot withstand high driver pressures. The maximum shock Mach number obtained using the new diaphragmless system that uses the pneumatic valve is 2.125 +/- 0.2%. This system shows much promise for automation in an industrial environment.

An interesting feature of the vapour pressure curve

There exists a maximum in the products of the saturation properties such as T(p(c) - p) and p(T-c - T) in the vapour-liquid coexistence region for all liquids. The magnitudes of those maxima on the reduced coordinate system provide an insight to the molecular complexity of the liquid. It is shown that the gradients of the vapour pressure curve at temperatures where those maxima occur are directly given by simple relations involving the reduced pressures and temperatures at that point. A linear relation between the maximum values of those products of the form [p(r)(1 - T-r)](max) = 0.2095 - 0.2415 [T-r(1 - p(r))](max) has been found based on a study of 55 liquids ranging from non-polar monatomic cryogenic liquids to polar high boiling point liquids.

Constant pressure laminar, transitional and turbulent flows - An approximate unified treatment

A nondimensional number that is constant in two-dimensional, incompressible and constant pressure laminar and fully turbulent boundary, layer flows has been proposed. An extension of this to constant pressure transitional flow is discussed.

Converging swirling liquid jets from pressure swirl atomizers: Effect of inner air pressure

Converging swirling liquid jets from pressure swirl atomizers injected into atmospheric air are studied experimentally using still and cine photographic techniques in the context of liquid-liquid coaxial swirl atomizers used in liquid rocket engines. The jet exhibits several interesting flow features in contrast to the nonswirling liquid jets (annular liquid jets) studied in the literature. The swirl motion creates multiple converging sections in the jet, which gradually collapse one after the other due to the liquid sheet breakup with increasing Weber number (We). This is clearly related to the air inside the converging jet which exhibits a peculiar variation of the pressure difference across the liquid sheet, DeltaP, with We. The variation shows a decreasing trend of DeltaP with We in an overall sense, but exhibits local maxima and minima at specific flow conditions. The number of maxima or minima observed in the curve depends on the number of converging sections seen in the jet at the lowest We. An interesting feature of this variation is that it delineates the regions of prominent jet flow features like the oscillating jet region, nonoscillating jet region, number of converging sections, and so on. Numerical predictions of the jet characteristics are obtained by modifying an existing nonswirling liquid jet model by including the swirling motion. The comparison between the experimental and numerical measurements shows that the pressure difference across the liquid sheet is important for the jet behavior and cannot be neglected in any theoretical analysis. (C) 2002 American Institute of Physics.

A method for the calculation of the adsorbed phase volume and pseudo-saturation pressure from adsorption isotherm data on activated carbon

We propose a new method for evaluating the adsorbed phase volume during physisorption of several gases on activated carbon specimens. We treat the adsorbed phase as another equilibrium phase which satisfies the Gibbs equation and hence assume that the law of rectilinear diameters is applicable. Since invariably the bulk gas phase densities are known along measured isotherms, the constants of the adsorbed phase volume can be regressed from the experimental data. We take the Dubinin-Astakhov isotherm as the model for verifying our hypothesis since it is one of the few equations that accounts for adsorbed phase volume changes. In addition, the pseudo-saturation pressure in the supercritical region is calculated by letting the index of the temperature term in Dubinin's equation to be temperature dependent. Based on over 50 combinations of activated carbons and adsorbates (nitrogen, oxygen, argon, carbon dioxide, hydrocarbons and halocarbon refrigerants) it is observed that the proposed changes fit experimental data quite well.