A sufficient criterion for Rayleigh-Taylor instability of incompressible viscous three-layer flow

Using normal mode analysis Rayleigh-Taylor instability is investigated for three-layer viscous stratified incompressible steady flow, when the top 3rd and bottom 1st layers extend up to infinity, the middle layer has a small thickness δ. The wave Reynolds number in the middle layer is assumed to be sufficiently small. A dispersion relation (a seventh degree polynomial in wave frequency ω) valid up to the order of the maximal value of all possible Kj (j less-than-or-equals, slant 0, K is the wave number) in each coefficient of the polynomial is obtained. A sufficient condition for instability is found out for the first time, pursuing a medium wavelength analysis. It depends on ratios (α and β) of the coefficients of viscosity, the thickness of the middle layer δ, surface tension ratio T and wave number K. This is a new analytical criterion for Rayleigh-Taylor instability of three-layer fluids. It recovers the results of the corresponding problem for two-layer fluids. Among the results obtained, it is observed that taking the coefficients of viscosity of 2nd and 3rd layers same can inhibit the effect of surface tension completely. For large wave number K, the thickness of the middle layer should be correspondingly small to keep the domain of dependence of the threshold wave number Kc constant for fixed α, β and T.

Cooling of a composite slab in a two-fluid medium

A mixed boundary value problem associated with the diffusion equation that involves the physical problem of cooling of an infinite parallel-sided composite slab in a two-fluid medium, is solved completely by using the Wiener-Hopf technique. An analytical solution is derived for the temperature distribution at the quench fronts being created by two different layers of cold fluids having different cooling abilities moving on the upper surface of the slab at constant speedv. Simple expressions are derived for the values of the sputtering temperatures of the slab at the points of contact with the respective layers, assuming the front layer of the fluid to be of finite width and the back layer of infinite extent. The main problem is solved through a three-part Wiener-Hopf problem of a special type and the numerical results under certain special circumstances are obtained and presented in the form of a table.

Radiative interactions in boundary layers

A detailed description of radiative interactions in laminar compressible boundary layers for moderate Mach numbers is presented by way of asymptotic analysis and supporting solutions. The radiation field is described by the differential approximation. While the asymptotic analysis is valid for large N (the ratio of photon mean free path to molecular mean free path) and arbitrary Boltzmann number, Bo (the ratio of convective heat flux to radiation heat flux), the solutions are obtained for Bo [double less-than sign] 1, the case of strong radiative interactions. The asymptotic analysis shows the existence of an optically thin boundary layer for large N and all Bo. For Bo [double less-than sign] 1, two outer regions are observed — one optically thin (at short distances from the leading edge) and the other optically thick (at large distances from the leading edge). An interesting feature not pointed out in the previous literature is the existence of a wall layer at large distances from the leading edge where convective heat flux can be ignored to the leading order of approximation. The radiation field in all cases can be very well approximated by a one-dimensional description. The solutions have been constructed using the ideas of matched asymptotic expansions by approximate analytical procedures and numerical methods. It is shown that, to the leading order of approximation, the radiation slip method yields exactly the same result as the more complicated matching procedure. Both the cases of linear and nonlinear radiation have been considered, the former being of interest in developing approximate methods which are subsequently generalized to handle the nonlinear problem. Detailed results are presented for both cases.

Hypersonic stagnation‐point boundary layers with massive blowing in the presence of a magnetic field

The effect of massive blowing rates on the steady laminar hypersonic boundary‐layer flow of an electrically conducting fluid in the stagnation region of an axisymmetric body with an applied magnetic field has been studied. The governing equations have been solved numerically by combining the implicit finite‐difference scheme with the quasi‐linearization technique. It is observed that the effect of massive blowing rates is to remove the viscous layer away from the boundary, whereas the effect of the magnetic field is just the opposite. It is also found that the velocity overshoot increases with blowing rates and also with magnetic field. The effect of the variation of the density‐viscosity product across the boundary layer is strong only when the blowing rate is small, but for the massive blowing rate the effect is negligible.

Alfvén waves in inhomogeneous magnetic fields: An integrodifferential equation formulation

An integrodifferential formulation for the equation governing the Alfvén waves in inhomogeneous magnetic fields is shown to be similar to the polyvibrating equation of Mangeron. Exploiting this similarity, a time‐dependent solution for smooth initial conditions is constructed. The important feature of this solution is that it separates the parts giving the Alfvén wave oscillations of each layer of plasma and the interaction of these oscillations representing the phase mixing.

Studies on Unsteady Pressure Fields in the Region of Separating and Reattaching Flows

Experimental studies on the measurement of pressure fields in the region of separating and reattaching flows behind several two-dimensional fore-bodies and one axisymmetric body are reported. In particular, extensive measurements of mean pressure, surface pressure fluctuation, and pressure fluctuation within the flow were made for a series of two-dimensional fore-body shapes consisting of triangular nose with varying included angle. The measurements from different bodies are compared and one of the important findings is that the maximum values of rms pressure fluctuation levels in the shear layer approaching reattachment are almost equal to the maximum value of the surface fluctuation levels.

Turbulent flow computations on a hybrid cartesian point distribution using meshless solver LSFD-U

This paper may be considered as a sequel to one of our earlier works pertaining to the development of an upwind algorithm for meshless solvers. While the earlier work dealt with the development of an inviscid solution procedure, the present work focuses on its extension to viscous flows. A robust viscous discretization strategy is chosen based on positivity of a discrete Laplacian. This work projects meshless solver as a viable cartesian grid methodology. The point distribution required for the meshless solver is obtained from a hybrid cartesian gridding strategy. Particularly considering the importance of an hybrid cartesian mesh for RANS computations, the difficulties encountered in a conventional least squares based discretization strategy are highlighted. In this context, importance of discretization strategies which exploit the local structure in the grid is presented, along with a suitable point sorting strategy. Of particular interest is the proposed discretization strategies (both inviscid and viscous) within the structured grid block; a rotated update for the inviscid part and a Green-Gauss procedure based positive update for the viscous part. Both these procedures conveniently avoid the ill-conditioning associated with a conventional least squares procedure in the critical region of structured grid block. The robustness and accuracy of such a strategy is demonstrated on a number of standard test cases including a case of a multi-element airfoil. The computational efficiency of the proposed meshless solver is also demonstrated. (C) 2010 Elsevier Ltd. All rights reserved.

Non-Newtonian boundary layers on a moving cylinder

The analysis of steady laminar forced convection boundary layer of power-law non-Newtonian fluids on a continuously moving cylinder with the surface maintained at a uniform temperature or uniform heat flux is presented. Of interest were the effects of power-law viscosity index, transverse curvature, generalized Prandtl number and streamwise coordinate on the local Nusselt number as well as on the velocity and temperature profiles. The two thermal boundary conditions yield quite similar results. Comparison of the calculated results with available series expansion solutions for a Newtonian fluid shows a very good performance of the present numerical procedure.

A Numerical-Simulation Of The Gneiss-Charnockite Transformations In Southern India

This paper presents a numerical simulation of the well-documented, fluid-controlled Kabbal and Ponmudi type gneiss-chamockite transformations in southern India using a free energy minimization method. The computations have considered all the major solid phases and important fluid species in the rock - C-O-H and rock - C-O-H-N systems. Appropriate activity-composition relations for the solid solutions and equations of state for the fluids have been included in order to evaluate the mineral-fluid equilibria attending the incipient chamockite development in the gneisses. The C-O-H fluid speciation pattern in both the Kabbal and Ponmudi type systems indicates that CO2 and H2O make up the bulk of the fluid phase with CO, CH4, H-2 and O2 as minor constituents. In the graphite-buffered Ponmudi-system, the abundance of CO, CH4 and H-2 is orders of magnitude higher than that in the graphite-free Kabbal system. Simulation with C-O-H-N fluids of varying composition demonstrates the complementary role of CO2 and N2 as rather inert dilutants of H2O in the fluid phase. The simulation, carried out on available whole-rock data, has demonstrated the dependence of the transformation X(H2O) on P,T, and phase and chemical composition of the precursor gneiss.

A sufficient criterion for Kelvin–Helmholtz instability in the magnetopause boundary‐layer region

The Kelvin–Helmholtz instability has been investigated for the magnetopause boundary‐layer region by the linearized method. The plasma in magnetosheath and magnetopause is assumed to be semi‐infinitely extended homogeneous, nondissipative, and incompressible. It is observed that, if one relation of two plasma speeds on the two sides of the magnetopause, wave number, and boundary‐layer thickness exceeds a certain threshold, the instability sets in. This new analytically sufficient criterion for excitation of instability in the three‐layer plasma flow generalizes the corresponding Chandrasekhar’s instability criterion for two‐layer plasma flow. The known results have been recovered and modified, the new results have been discovered. It is proved that the velocity threshold for the onset of instability is low when the magnitude of the magnetosheath and boundary‐layer region magnetic field and the angle between them are small. Also the threshold depends on the direction of plasma flow. The following results are observed numerically. The growth of the instability is sensitive to the magnetic field direction in the magnetosheath. A slight variation in the magnetic field direction in the second region can substantially change the relative velocity threshold for instability. When the ratio of the density of the second and third layer (magnetosphere) increases or that of the first and third layer decreases, the threshold decreases. Apart from this a necessary criterion for instability is obtained for a particular case.

Blade manipulators in turbulent channel flow

We report here the results of a series of careful experiments in turbulent channel flow, using various configurations of blade manipulators suggested as optimal in earlier boundary layer studies. The mass flow in the channel could be held constant to better than 0.1%, and the uncertainties in pressure loss measurements were less than 0.1 mm of water; it was therefore possible to make accurate estimates of the global effects of blade manipulation of a kind that are difficult in boundary layer flows. The flow was fully developed at the station where the blades were mounted, and always relaxed to the same state sufficiently far downstream. It is found that, for a given mass flow, the pressure drop to any station downstream is always higher in the manipulated than in the unmanipulated flow, demonstrating that none of the blade manipulators tried reduces net duct losses. However the net increase in duct losses is less than the drag of the blade even in laminar flow, showing that there is a net reduction in the total skin friction drag experienced by the duct, but this relief is only about 20% of the manipulator drag at most.

Calorimetry In Vapor Absorption And Binary Mixture Vapor Compression Refrigeration And Heatpump Systems

The use of binary fluid systems in thermally driven vapour absorption and mechanically driven vapour compression refrigeration and heatpump cycles has provided an impetus for obtaining experimental date on caloric properties of such fluid mixtures. However, direct measurements of these properties are somewhat scarce in spite of the calorimetric techniques described in the literature being quite adequate. Most of the design data are derived through calculations using theoretical models and vapour-liquid equilibrium data. This article addresses the choice of working fluids and the current status on the data availability vis-a-vis engineering applications. Particular emphasis is on organic working fluid pairs.

Channel Volatiles Of South Indian Cordierites As Indicators Of Metamorphic Fluid Composition

The channel volatiles in cordierites of the Precambrian high-grade metapelites from southern and eastern Karnataka northern Tamil Nadu and southern Kerala were analyzed in an attempt to use them as metamorphic fluid fugacity indicators. Infrared powder absorption spectra, used to characterize the channel volatiles, showed that all the 21 analyzed cordierites have H2O and CO2 as the channel volatiles, indicating the predominantly H2O-CO2 composition of the metamorphic fluids. The H2O fraction in the metamorphic fluid was computed using a published thermodynamic method in conjunction with gravimetrically determined cordierite channel H2O content, available P - T estimates and an appropriate equation of state for the H2O - CO2 fluids. The IR data and these calculated X(H2O) values indicate an overall correlation between the variation in the relative proportion of H2O and CO2 in the fluids and the metamorphic grade. The average computed X(H2O) values are: 0.78 for the amphibolite facies eastern Karnataka pelites, 0.36 for the amphibolite facies southern Karnataka pelites, 0.19 for the southern Karnataka transitional zone rocks and 0.13 for the northern Tamil Nadu granulites. Consistently low X(H2O) values, at about 0.2, were obtained for the orthopyroxene-bearing assemblages.

Cooling of an infinite slab in a two-fluid medium

A mixed boundary-valued problem associated with the diffusion equation, that involves the physical problem of cooling of an infinite slab in a two-fluid medium, is solved completely by using the Wiener-Hopf technique. An analytical solution is derived for the temperature distribution at the quench fronts being created by two different layers of cold fluids having different cooling abilities moving on the upper surface of the slab at constant speed. Simple expressions are derived for the values of the sputtering temperatures of the slab at the points of contact with the respective layers, assuming one layer of the fluid to be of finite extent and the other of infinite extent. The main problem is solved through a three-part Wiener - Hopf problem of a special type, and the numerical results under certain special circumstances are obtained and presented in the form of a table.