Application of Artificial Viscosity in Establishing Supercritical Solutions to the Transonic Integra

The nonlinear singular integral equation of transonic flow is examined in the free-stream Mach number range where only solutions with shocks are known to exist. It is shown that, by the addition of an artificial viscosity term to the integral equation, even the direct iterative scheme, with the linear solution as the initial iterate, leads to convergence. Detailed tables indicating how the solution varies with changes in the parameters of the artificial viscosity term are also given. In the best cases (when the artificial viscosity is smallest), the solutions compare well with known results, their characteristic feature being the representation of the shock by steep gradients rather than by abrupt discontinuities. However, 'sharp-shock solutions' have also been obtained by the implementation of a quadratic iterative scheme with the 'artificial viscosity solution' as the initial iterate; the converged solution with a sharp shock is obtained with only a few more iterates. Finally, a review is given of various shock-capturing and shock-fitting schemes for the transonic flow equations in general, and for the transonic integral equation in particular, frequent comparisons being made with the approach of this paper.

Separation β-apocarotenals and related compounds by reversed-phase paper and thin-layer chromatography

Abstract is not available.

Propagation characteristics in distensible tubes containing a visco-elastic fluid

The propagation characteristics of a visco-elastic fluid in a distensible tube tube are studied. The linear visco-elastic nature of the fluid is described by a complex coefficient of viscosity η*. The equation of motion of the vessel wall takes into account the pulsatile nature of the wall. Results are presented for wave propagation velocity, the resistance and the reactance of the fluid and the wall impedance. It is seen that the visco-elastic influence is significant for high values of the frequency of oscillation in various arterial vessels.

Effect of ionic temperature on propagation of ion-acoustic solitary waves in a collisionless plasma of warm-ion fluid and non-isothermal electrons

Using a perturbation technique, we derive Modified Korteweg—de Vries (MKdV) equations for a mixture of warm-ion fluid (γ i = 3) and hot and non-isothermal electrons (γ e> 1), (i) when deviations from isothermality are finite, and (ii) when deviations from isothermality are small. We obtain stationary solutions for these equations, and compare them with the corresponding solutions for a mixture of warm-ion fluid (γ i = 3) and hot, isothermal electrons (γ i = 1).

Intrinsic equations of steady rotating, incompressible viscous fluid flow

The equations governing the flow of a steady rotating incompressible viscous fluid are expressed in intrinsic form along the vortex lines and their normals. Using these equations the effects of rotation on the geometric properties of viscous fluid flows are studied. A particular flow in which the vortex lines are right circular helices is discussed.

Peristaltic motion of a micropolar fluid

Peristaltic motion of a micropolar fluid is studied for small amplitudes of peristalic waves under low Reynolds number analysis. The effect of pressure gradient on the secondary motion reveals many interesting and useful results. The critical value of the pressure gradient ensuing the reversal effect in both velocity field and microrotation is evaluated and discussed.

Steady motion of a rotating stratified fluid bounded by porous disks

Abstract is not available.

Unsteady Natural Convection Flow over a Heated Cylinder Buried in a Fluid Saturated Porous Medium

Transient natural convection flow on a heated cylinder buried in a semi-infinite liquid-saturated porous medium has been studied. The unsteadiness in the problem arises due to the cylinder which is heated (cooled) suddenly and then maintained at that temperature. The coupled partial differential equations governing the flow and heat transfer are cast into stream function-temperature formulation, and the solutions are obtained from the initial time to the time when steady state is reached. The heat transfer is found to change significantly with increasing time in a small time interval immediately after the start of the impulsive change, and steady state is reached after some time. The average Nusselt number is found to increase with Rayleigh number When the surface of the cylinder is suddenly cooled, there is a change in the direction of the heat transfer in a small time interval immediately after the start of the impulsive change in the surface temperature;however when the surface temperature is suddenly increased, no such phenomenon is observed.

Solubilities of palmitic and stearic fatty acids in supercritical carbon dioxide

The solubilities of two fatty acids, namely hexadecanoic acid (palmitic acid) and octadecanoic acid (stearic acid) in supercritical carbon dioxide (SCCO2), were determined at T = (328 and 338) K from 12.8 MPa to 22.6 MPa. Three models, namely a thermodynamic model based on the Peng-Robinson equation of state with Kwak and Mansoori mixing rules, a model based on dilute solution theory proposed by Mendez-Santiago and Teja and a new reformulated Chrastil equation model, were used to correlate the solubilities. In all the models, the correlation constants are temperature independent. All the models successfully correlated the experimental results for the solubilities of hexadecanoic acid within 3%.

Solubilities of Some Chlorophenols in Supercritical CO2 in the Presence and Absence of Cosolvents

The solubilities of three chlorophenols, namely, 4-chlorophenol, 2,4-dichlorophenol, and 2,4,6-trichlorophenol, in supercritical carbon dioxide were determined at temperatures from (308 to 3 18) K in the pressure range of (8.8 to 15.6) MPa. The Solubilities were determined both in the absence of cosolvents and in the presence of two cosolvents, methanol and acetone. The solubilities (in the absence of cosolvents) in mole fraction of 4-chlorophenol, 2,4-dichlorophenol, and 2,4,6-trichlorophenol at 308 K were in the range of (0.0113 to 0.0215), (0.0312 to 0.0645), and (0.008 to 0.0173), respectively. The Solubilities of the chlorophenols followed the order 2,4-dichlorophenol & 4-chlorophenol & phenol & 2,4,6-trichlorophenol & pentachlorophenol. The solubility data were correlated with the Charstil model and with the Mendez-Santiago and Teja model. The overall deviation between the experimental data and the correlated results Was less than 6 % in averaged absolute relative deviation (AARD) for both of the models.

Asymptotic analysis for the coupled wavenumbers in an infinite fluid-filled flexible cylindrical shell: The beam mode

Using asymptotics, the coupled wavenumbers in an infinite fluid-filled flexible cylindrical shell vibrating in the beam mode (viz. circumferential wave order n = 1) are studied. Initially, the uncoupled wavenumbers of the acoustic fluid and the cylindrical shell structure are discussed. Simple closed form expressions for the structural wavenumbers (longitudinal, torsional and bending) are derived using asymptotic methods for low- and high-frequencies. It is found that at low frequencies the cylinder in the beam mode behaves like a Timoshenko beam. Next, the coupled dispersion equation of the system is rewritten in the form of the uncoupled dispersion equation of the structure and the acoustic fluid, with an added fluid-loading term involving a parameter mu due to the coupling. An asymptotic expansion involving mu is substituted in this equation. Analytical expressions are derived for the coupled wavenumbers (as modifications to the uncoupled wavenumbers) separately for low- and high-frequency ranges and further, within each frequency range, for large and small values of mu. Only the flexural wavenumber, the first rigid duct acoustic cut-on wavenumber and the first pressure-release acoustic cut-on wavenumber are considered. The general trend found is that for small mu, the coupled wavenumbers are close to the in vacuo structural wavenumber and the wavenumbers of the rigid-acoustic duct. With increasing mu, the perturbations increase, until the coupled wavenumbers are better identified as perturbations to the pressure-release wavenumbers. The systematic derivation for the separate cases of small and large mu gives more insight into the physics and helps to continuously track the wavenumber solutions as the fluid-loading parameter is varied from small to large values. Also, it is found that at any frequency where two wavenumbers intersect in the uncoupled analysis, there is no more an intersection in the coupled case, but a gap is created at that frequency. This method of asymptotics is simple to implement using a symbolic computation package (like Maple). (C) 2008 Elsevier Ltd. All rights reserved.

Asymptotic analysis for the coupled wavenumbers in an infinite fluid-filled flexible cylindrical shell: The axisymmetric mode

The coupled wavenumbers of a fluid-filled flexible cylindrical shell vibrating in the axisymmetric mode are studied. The coupled dispersion equation of the system is rewritten in the form of the uncoupled dispersion equation of the structure and the acoustic fluid, with an added fluid-loading term involving a parameter e due to the coupling. Using the smallness of Poisson's ratio (v), a double-asymptotic expansion involving e and v 2 is substituted in this equation. Analytical expressions are derived for the coupled wavenumbers (for large and small values of E). Different asymptotic expansions are used for different frequency ranges with continuous transitions occurring between them. The wavenumber solutions are continuously tracked as e varies from small to large values. A general trend observed is that a given wavenumber branch transits from a rigidwalled solution to a pressure-release solution with increasing E. Also, it is found that at any frequency where two wavenumbers intersect in the uncoupled analysis, there is no more an intersection in the coupled case, but a gap is created at that frequency. Only the axisymmetric mode is considered. However, the method can be extended to the higher order modes.

Turbulence-induced melting of a nonequilibrium vortex crystal in a forced thin fluid film

To gain a better understanding of recent experiments on the turbulence-induced melting of a periodic array of vortices in a thin fluid film, we perform a direct numerical simulation of the two-dimensional Navier-Stokes equations forced such that, at low Reynolds numbers, the steady state of the film is a square lattice of vortices. We find that as we increase the Reynolds number, this lattice undergoes a series of nonequilibrium phase transitions, first to a crystal with a different reciprocal lattice and then to a sequence of crystals that oscillate in time. Initially, the temporal oscillations are periodic; this periodic behaviour becoming more and more complicated with increasing Reynolds number until the film enters a spatially disordered nonequilibrium statistical steady state that is turbulent. We study this sequence of transitions using fluid-dynamics measures, such as the Okubo-Weiss parameter that distinguishes between vortical and extensional regions in the flow, ideas from nonlinear dynamics, e.g. Poincare maps, and theoretical methods that have been developed to study the melting of an equilibrium crystal or the freezing of a liquid and that lead to a natural set of order parameters for the crystalline phases and spatial autocorrelation functions that characterize short- and long-range order in the turbulent and crystalline phases, respectively.

Solubility of n-(4-Ethoxyphenyl)ethanamide in Supercritical Carbon Dioxide

The solubility of a drug, n-(4-ethoxyphenyl)ethanamide (phenacetin), in supercritical carbon dioxide was determined by a Saturation method at (308, 318, and 328) K from (9 to 19) MPa. The Solubilities in mole fraction of n-(4-ethoxyphenyl)ethanamide in supercritical carbon dioxide were in the range of 1.29.10(-5) to 2.88.10(-5), 1.13.10(-5) to 3.65.10(-5), and 0.91.10(-5) to 4.28.10(-5) at (308, 3 18, and 328) K, respectively. The solubility data were correlated with the Peng-Robinson equation of state models and the Mendez-Santiago and Teja model.