Asymptotic behavior of high-Reynolds-number flow through an array of blunt bodies

A previously developed theory of high-Reynolds-number flow around a body is extended to the case of flow through an array of bodies. An asymptotic expansion suitable for H1 and Re1, where 2H is the spacing of the array and Re is the Reynolds number, is constructed. The results are compared to numerical calculations. The structure of the asymptotic solution for H=O(1) is discussed.Institute of Mechanics, Moscow State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 30–52, April, 1993.     

Convective flows in a layer of a viscous liquid with the uniformly charged free surface

It is found theoretically that the critical conditions under which a charged liquid surface becomes unstable against the electric charge relax as a result of interaction between capillary-gravitational and convective flows in the liquid. As the surface charge density approaches a value critical in terms of development of Tonks-Frenkel instability, convection in the liquid arises at a temperature gradient however small, this effect depending on the liquid layer thickness.     

Numerical study of shock wave interaction in steady flows of a viscous heat-conducting gas with a low ratio of specific heats

Specific features of shock wave interaction in a viscous heat-conducting gas with a low ratio of specific heats are numerically studied. The case of the Mach reflection of shock waves with a negative angle of the reflected wave with respect to the free-stream velocity vector is considered, and the influence of viscosity on the flow structure is analyzed. Various issues of nonuniqueness of the shock wave configuration for different Reynolds numbers are discussed. Depending on the initial conditions and Reynolds numbers, two different shock wave configurations may exist: regular configuration interacting with an expansion fan and Mach configuration. In the dual solution domain, a possibility of the transition from regular to the Mach reflection of shock waves is considered.     

MHD mixed convection flow near the stagnation-point on a vertical permeable surface

The steady magnetohydrodynamic (MHD) mixed convection boundary layer flow of a viscous and electrically conducting fluid near the stagnation-point on a vertical permeable surface is investigated in this study. The velocity of the external flow and the temperature of the plate surface are assumed to vary linearly with the distance from the stagnation-point. The governing partial differential equations are first transformed into ordinary differential equations, before being solved numerically by a finite-difference method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. It is found that dual solutions exist for both cases, and the range of the mixed convection parameter for which the solution exists increases with suction.     

Spin correlations near the surface of a three-dimensional Heisenberg antiferromagnet

Nearest-neighbor spin correlations are considered near the surface of a semi-infinite spin- Heisenberg antiferromagnet on a simple cubic lattice. In the spin-wave approximation, the excitation spectrum of this model involves bulk modes – standing spin waves and a quasi-two-dimensional mode of surface spin waves. These latter excitations eject the bulk excitations from the surface region thus dividing the antiferromagnet into two parts with different excitations. As a result absolute values of the spin correlations near the surface exceed the bulk value. In the surface region, the pattern of spin correlations resembles the comb structure recently obtained for the two-dimensional case.     

Acoustic scattering by a three-dimensional elastic object near a rough surface

The ensemble-averaged field scattered by a smooth, bounded, elastic object near a penetrable surface with small-scale random roughness is formulated. The formulation consists of combining a perturbative solution for modeling propagation through the rough surface with a transition (T-) matrix solution for scattering by the object near a planar surface. All media bounding the rough surface are assumed to be fluids. By applying the results to a spherical steel shell buried within a rough sediment bottom, it is demonstrated that the ensemble-averaged "incoherent" intensity backscattered by buried objects illuminated with shallow-grazing-angle acoustic sources can be well enhanced at high frequencies over field predictions based on scattering models where all environmental surfaces are planar. However, this intensity must compete with the incoherent intensity scattered back from the interface itself, which can defeat detection attempts. The averaged "coherent" component of the field maintains the strong evanescent spectral decay exhibited by flat interface predictions of shallow-angle measurements but with small deviations. Nevertheless, bistatic calculations of the coherent field suggest useful strategies for improving long-range detection and identification of buried objects.     

Asymptotic analysis of a viscous cochlear model

A model of cochlear macromechanics, involving a viscous cochlear fluid, is analyzed asymptotically for slowly varying membranes. The results exhibit the effect of viscosity on the amplitude, wavelength, and damping rate, and confirm the conclusion that viscosity is not important. However the method can be used on other models, such as those of cochlear micromechanics, where viscosity is more important.     

Analysis of supersonic flow around two bodies of revolution near a surface

The results of experimental and numerical investigations of the peculiarities of flow around two identical cylindrical bodies of revolution of diameter D = 50 mm and the body aspect ratio λ = 5 with conical forebodies whose apex angles are θ = 40° and 60°, which are located above a horizontal surface in parallel with one another and with the flow, are presented for the Mach numbers M_∞ = 4.03, Reynolds numbers Re₁ ≈ 55·10⁶ m⁻¹, fixed distance from the surface Y = Δy/D = 0.96, and the gaps between their axes Z = Δz/D = 1.06−2.4. The peculiarities of three-dimensional turbulent separated flows realizing on the bodies and on the plate as well as the possibilities of predicting the aerodynamic forces and moments acting on the bodies on the basis of numerical computations within the framework of the Euler equations are considered.     

Series solution of non-similarity natural convection boundary-layer flows over permeable vertical surface

The non-similarity solution for natural convection from a permeable isothermal vertical wall is considered. The governing boundary-layer equations for non-similarity flow and temperature fields are solved using the homotopy analysis method. The homotopy-Pade' technique is applied to accelerate the convergence of the homotopy-series solution. The influence of physical parameters on the non-similarity flows is investigated in detail. Different from the previous analytic results,the homotopy-series solutions a...     

Pressure based finite volume method for calculation of compressible viscous gas flows

A pressure based, iterative finite volume method is developed for calculation of compressible, viscous, heat conductive gas flows at all speeds. The method does not need the use of under-relaxation coefficient in order to ensure a convergence of the iterative process. The method is derived from a general form of system of equations describing the motion of compressible, viscous gas. An emphasis is done on the calculation of gaseous microfluidic problems. A fast transient process of gas wave propagation in a two-dimensional microchannel is used as a benchmark problem. The results obtained by using the new method are compared with the numerical solution obtained by using SIMPLE (iterative) and PISO (non-iterative) methods. It is shown that the new iterative method is faster than SIMPLE. For the considered problem the new method is slightly faster than PISO as well. Calculated are also some typical microfluidic subsonic and supersonic flows, and the Rayleigh–Bénard convection of a rarefied gas in continuum limit. The numerical results are compared with other analytical and numerical solutions.     

Rotational friction coefficient of a permeable cylinder in a viscous fluid

An exact expression is derived for the rotational friction coefficient of a cylinder of infinite length and constant permeability immersed in an incompressible viscous fluid. An asymptotic expression for the translational friction coefficient of a permeable cylinder moving in a sheet of viscous fluid embedded on both sides in a fluid of much lower viscosity is also given.     

Exchange energy density of inhomogeneous electron gas near a metal surface

Using the first-order density matrix of an infinite barrier model of a metal surface, the exchange energy density can be evaluated exactly as a function of the distance z from the barrier. This result is compared with the local approximation $\text{?}\text{3}\text{4}\text{e}{}^2\text{(}\text{3}\text{π}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{[?(z)]}{}^{\mathrm{<mtext>4</mtext><mtext>3</mtext>}}$ where the electron density in the model. The local approximation follows the exact result quite closely at all z but leads to a large percentual error in the integrated surface exchange energy.     

Entrapment of inert gas ions near molybdenum surface

The thermal desorption spectra of inert gas ions (neon, argon and krypton) injected with various energies (430–1950 eV) into a polycrystalline molybdenum target with various dosages (6.4×10¹²−3.9×10¹⁴ ions/cm²) are reported. At least four different states of binding of the trapped atoms corresponding to the activation energies for desorption have been observed from the spectra. The activation energies are found to be relatively insensitive to the species of the bombarding ion, incident ion energy and the dosage. The shapes of the spectra are strongly influenced by the depth of penetration of the ions into the solid. The activation energies deduced are in good agreement with those reported for the migration of atoms and defects in molybdenum.     

Filamentary actuation on the surface of bodies contoured by high-speed flows

In this study, we focus our attention on the ability of a filamentary discharge to affect the shock waves patterns generated by a test model of diamond shape placed in a high-speed airflow. Our results indicate that no significant changes could be detected at moderate supersonic regimes (Ma≈1.8) or at transonic conditions (Ma≈0.8) even when the filament traversed the shock.     

Asymptotic behavior of the correlation functions for a Brownian oscillator with viscous aftereffects

Correlation functions are derived in explicit form for the asymptotic behavior at for a Brownian oscillator with viscous aftereffects.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 22–25, April, 1973.I am indebted to D. I. Polishchuk and I. Z. Fisher for discussions.     

Limiting conditions for the combustion of a rich gas mixture on the surface of a permeable matrix

The limit of the surface combustion of rich methane-air mixtures on a planar and a volumetric permeable matrix is theoretically and experimentally determined. The influence of a radiation screen on the expansion of the region of stable surface combustion at a heightened specific thermal load on the matrix is examined. The possibility of a substantial expansion of the lower limit of surface combustion in passing from a planar to a volumetric matrix is demonstrated. It is shown that heat recovery allows stable surface combustion of natural gas-air mixtures at air-to-fuel ratios of up to α = 0.35.