Asymptotic analysis of the structure of long‐wave Görtler vortices in a hypersonic boundary layer

An asymptotic (at high Reynolds and Görtler numbers) model of nonlinear longwave Görtler vortices localized inside the boundary layer near a concave surface located in a hypersonic viscous gas flow in the regime of weak viscidinviscid interaction is constructed. The maximum wavelength is evaluated. Numerical solutions are obtained for an inviscid local limit in the linear approximation. It is shown that an increase in the freestream Mach number exerts a stabilizing effect on the vortices, and a change in the Prandtl number has no significant effect on them. For the case where the vortices form a threelayered disturbed flow structure, it is shown analytically for the first time that surface heating exerts a stabilizing action on the vortices.     

The Theory of Thin-Walled Rods of Open Profile as a Result of Asymptotic Splitting in the Problem of Deformation of a Noncircular Cylindrical Shell

A new asymptotic approach to the theory of thin-walled rods of open profile is suggested. For the problem of linear static deformation of a noncircular cylindrical shell we consider solutions, which are slowly varying along the axial coordinate. A small parameter is introduced in the equations of the modern theory of shells. Conditions of compatibility for the shell strain measures are employed. The principal terms of the series expansion of the solution are determined from the conditions of solvability for the minor terms. We conclude the procedure with the subsequent solution for the field of displacements. The analysis shows that the known equations of thin-walled rods, which were previously obtained with some approximate methods using hypotheses and approximations of displacements, are asymptotically exact. The presented semi-numerical analysis of the shell equations allows us to estimate the accuracy of the obtained solution. The results of the paper constitute a sound basis to the equations of the theory of thin-walled rods and provide trustworthy information concerning the distribution of stresses in the cross-section.     

Turbulent heat—Concentration plume in the case of high viscosity in a nonstratified medium

In this paper, an approximate self-similar solution for the structure of the heat—concentration plume produced by an instantaneous point source of heat in the presence of multicomponent admixture and when the coefficient of turbulence is large is found on the basis of the turbulent transfer equations of vorticity, energy, and matter. Analytical expressions are obtained for the propagation velocity of the buoyancy core and the toroidal vortex formed. The influence of the source parameters and of the coefficient of turbulence on the structure and dynamics of thermal lift is investigated. A comparison is made with the laminar regime of motion of similar formations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6. pp. 153–163, November–December, 1984.     

Experiments on the Flow Field and Acoustic Properties of a Mach number 0·75 Turbulent Air Jet at a Low Reynolds Number

In this paper we present the experimental results of a detailed investigation of the flow and acoustic properties of a turbulent jet with Mach number 0·75 and Reynolds number 3·5 10³. We describe the methods and experimental procedures followed during the measurements, and subsequently present the flow field and acoustic field. The experiment presented here is designed to provide accurate and reliable data for validation of Direct Numerical Simulations of the same flow. Mean Mach number surveys provide detailed information on the centreline mean Mach number distribution, radial development of the mean Mach number and the evolution of the jet mixing layer thickness both downstream and in the early stages of jet development. Exit conditions are documented by measuring the mean Mach number profile immediately above the nozzle exit. The fluctuating flow field is characterised by means of a hot-wire, which produced radial profiles of axial turbulence at several stations along the jet axis and the development of flow fluctuations through the jet mixing layer. The axial growth rate of the jet instabilities are determined as function of Strouhal number, and the axial development of several spectral components is documented. The directivity of the overall sound pressure level and several spectral components were investigated. The spectral content of the acoustic far field is shown to be compatible with findings of hot-wire experiments in the mixing layer of the jet. In addition, the measured acoustic spectra agree with Tam’s large-scale similarity and fine-scale similarity spectra (Tam et al., AIAA Pap 96, 1996).     

On a Theory of the Infusion Method of Measuring the “Opening Pressure” in the Urethra

At rest the muscles which control the urethra (urine duct) are contracted and its lumen is practically equal to zero over its entire length. To open the urethra, a mechanical effort (due, for example, to a pressure rise in the bladder) must be applied. Reduced contractile activity of the muscles may be one of the reasons for incontinence (enuresis). A widespread method of estimating the blocking capability of the urethra consists in inserting a catheter with lateral perforations near the end. The catheter enters the bladder and is then removed at a constant velocity while a fluid is constantly pumped (infused) into it by a syringe pump at a steady rate and then flows out through the gap between the catheter and the urethral wall. The pumping pressure is considered to be a local measure of the blocking capability, and its dependence on the location of the catheter is regarded as an important diagnostic characteristic.Below, we will consider the simple, longitudinally homogeneous model system formed by an elastic tube pulled over a catheter segment when the initial stresses in the tube are constant over its length. An incompressible viscous fluid flows out of the perforations and percolates in a thin layer along the catheter. In solving the model problem, we will use the lubricating layer approximation under the assumption of small layer curvature. On the basis of an analysis of the results and a comparison of the model with a practical intraurethral measurement procedure, we discuss, firstly, the relationship between the measured quantities and the real characteristics of the urethra and, secondly, the possible formulation of a more realistic model problem.     

Asymptotic Description of Solutions of the Planar Exterior Navier–Stokes Problem in a Half Space

We consider the problem of a body moving within an incompressible fluid at constant speed parallel to a wall in an otherwise unbounded domain. This situation is modeled by the incompressible Navier–Stokes equations in a planar exterior domain in a half space with appropriate boundary conditions on the wall, the body, and at infinity. We focus on the case where the size of the body is small. We prove in a very general setup that the solution of this problem is unique and we compute a sharp decay rate of the solution far from the moving body and the wall.     

On the Ellipticity of the Middle Surface of a Shell and its Application to the Asymptotic Analysis of ‘Membrane’ Shells

We consider a surface S = (), where ² is a bounded, connected, open set with a smooth boundary and : ³ is a smooth map; let () denote the components of the two-dimensional linearized strain tensor of S and let 0 with length 0 > 0. We assume the the norm ,|| ()||0, in the space V0() = { H¹() × H¹() × L²(); = 0 on 0 } is equivalent to the usual product norm on this space. We then establish that this assumption implies that the surface S is uniformly elliptic and that we necessarily have 0 = .     

Inequalities of Korn’s Type and Existence Results in the Theory of Cosserat Elastic Shells

This paper is concerned with the linear theory of anisotropic and inhomogeneous Cosserat elastic shells. We establish the inequalities of Korn’s type which hold on Cosserat surfaces. Using these inequalities, we prove the existence of the solution to the variational equations in the elastostatics of Cosserat shells. For the dynamic problems, we employ the semigroup of linear operators theory to obtain the existence, uniqueness and continuous dependence of solution.      

Asymptotic Stability of Rarefaction Wave for the Navier–Stokes Equations for a Compressible Fluid in the Half Space

This paper is concerned with the asymptotic stability towards a rarefaction wave of the solution to an outflow problem for the Navier–Stokes equations in a compressible fluid in the Eulerian coordinate in the half space. This is the second one of our series of papers on this subject. In this paper, firstly we classify completely the time-asymptotic states, according to some parameters, that is the spatial-asymptotic states and boundary conditions, for this initial boundary value problem, and some pictures for the classification of time-asymptotic states are drawn in the state space. In order to prove the stability of the rarefaction wave, we use the solution to Burgers’ equation to construct a suitably smooth approximation of the rarefaction wave and establish some time-decay estimates in L ^p -norm for the smoothed rarefaction wave. We then employ the L ²-energy method to prove that the rarefaction wave is non-linearly stable under a small perturbation, as time goes to infinity. P. Zhu was supported by JSPS postdoctoral fellowship under P99217.     

A Semilinear Schrödinger Equation in the Presence of a Magnetic Field

We consider the semilinear stationary Schrödinger equation in a magnetic field: (–i+A)² u+V(x)u=g(x,|u|)u in ^N , where V is the scalar (or electric) potential and A is the vector (or magnetic) potential. We study the existence of nontrivial solutions both in the critical and in the subcritical case (respectively g(x,|u|)=|u|^{2 * –2} and |g(x,|u|)|c(1+|u| ^{p –2}), where 2<p<2^*). The results are obtained by variational methods. For g critical we use constrained minimization and for subcritical g we employ a minimax-type argument. In the latter case we also study the existence of infinitely many geometrically distinct solutions.     

On the Propagation of Long‐Wave Perturbations in a Two‐Layer Free‐Boundary Rotational Fluid

A mathematical model for the propagation of longwave perturbations in a freeboundary shear flow of an ideal stratified twolayer fluid is considered. The characteristic equation defining the velocity of perturbation propagation in the fluid is obtained and studied. The necessary hyperbolicity conditions for the equations of motion are formulated for flows with a monotonic velocity profile over depth, and the characteristic form of the system is calculated. It is shown that the problem of deriving the sufficient hyperbolicity conditions is equivalent to solving a system of singular integral equations. The limiting cases of weak and strong stratification are studied. For these models, the necessary and sufficient hyperbolicity conditions are formulated, and the equations of motion are reduced to the Riemann integral invariants conserved along the characteristics.     

Mitigation of flow-induced pressure fluctuations in a Francis turbine operating at the design and partial load regimes—LES simulations

High-fidelity large eddy simulations (LES) were conducted to characterize the spatial and temporal structure of turbulent flows in an industrial-sized Francis turbine while the unit operated at the design point and partial load. A pressure surge with an amplitude of 8% of the turbine head was observed at partial load while the amplitude was <1% at the design point. The vortex rope precession observed in the draft tube correlated to the amplitude and frequency of the pressure surge. Central and peripheral water injections at various volumetric rates were considered to control the flow-induced pressure fluctuations. Central injection at the 4% and 6% flow rates attenuated high amplitude pressure fluctuations by 40% and 75% respectively at partial load. At the same operating conditions, peripheral injections did not have the same desired effect. Although power generation was not changed with water injection at the design point, it was reduced by about 2.5% by central injection and 0.5% by peripheral injection at partial load, showing a water injection mitigation strategy could be applied without any penalty.     

Aerosol composition,sources, and secondary processing during autumn at a regional site in the Beijing–Tianjin–Hebei region

Air pollution is serious during autumn in the Beijing–Tianjin–Hebei (BTH) region, but there are few studies that have utilized real-time observations and source apportionment of the autumn submicron aerosols in this region. In this study, a quadrupole aerosol chemical speciation monitor (Q-ACSM) was deployed for the real-time measurement of the non-refractory compositions of submicron aerosols (NR-PM₁) at a regional site (Xianghe) from October 3 to November 14, 2017. The results showed that nitrate was the largest inorganic aerosol, and the oxygenated organic aerosol (OOA) was the largest organic aerosol in Xianghe. Hydrocarbon-like OA (HOA) was the largest organic aerosol When the NR-PM₁ mass concentrations increased from the lowest to the highest bins, nitrate and biomass burning OA (BBOA) showed increasing trends in the suburban area. Enhanced nitrate formation during the pollution episodes resulted from both photochemical and aqueous processing. To reduce the particulate matter (PM_2.5) concentrations and eliminate heavy pollution episodes, control measures should focus on reducing NO_x, NH₃, and volatile organic compound (VOC_s) emissions.     

Steady Motions of Viscoelastic Fluids in Three‐Dimensional Exterior Domains. Existence, Uniqueness and Asymptotic Behaviour

. We study systems of nonlinear partial differential equations governing the steady motion of certain viscoelastic non‐Newtonian fluids around a rigid body ${\cal B}\subset\real^{3}$ . Considering the equations in a suitably decomposed form, we obtain, for small and sufficiently regular data, existence of a unique solution using a fixed‐point argument in an appropriate functional setting. This setting contains also the asymptotic decay of the solution. Our model equations include the second‐grade and the Maxwell fluid.     

Radial Solutions and Phase Separation in a System of Two Coupled Schrödinger Equations

We consider the nonlinear elliptic system

Experimental and Numerical Study of a Hypersonic Separated Flow in the Vicinity of a Cone‐Flare Model

An axisymmetric laminar separated flow in the vicinity of a coneflare model is studied experimentally and numerically for a Mach number M = 6. The distributions of pressure and Stanton numbers along the model surface and velocity profiles in the region of shock wave–boundary layer interaction are measured and compared with the calculated data. The influence of the laminar–turbulent transition on flow parameters is studied numerically.     

A study of the effect of locust bean gum on the rheological behaviour and microstructure of a β-lactoglobulin gel at pH 7

The effect of locust bean gum (LBG), a non-gelling polysaccharide, on the thermal gelation of -lactoglobulin, at 80 °C, and on the gel properties after quenching to 20 °C was studied by small deformation rheology and by confocal laser scanning microscopy (CLSM). The concentration of -lactoglobulin was kept constant at 10 wt% and that of LBG varied from 0 to 0.78 wt%. For all the concentrations studied, the presence of LBG enhanced the aggregation rate and the strength of the protein gel, but the magnitude of these effects depended on the -lactoglobulin/LBG ratio: 0.35 wt% LBG resulted only in a very slight increase of G, whereas 0.45 wt% LBG caused a ~fivefold jump; for higher LBG concentrations, the differences between the systems were quite small. The linear viscoelastic behaviour, at 20 °C, was characterized over the 10^–5 to 100 rad/s frequency range by combining the dynamic and retardation tests. Compliance data were converted from the time to the frequency domain. The viscoelastic plateau was seen to extend down in the 0.001–0.0001 rad/s range and its lower limit seemed not to vary much with LBG concentration. Its upper limit was visibly beyond 100 rad/s. The observed microstructure of the gels showed that they were two-phase and that the state of aggregation of -lactoglobulin was influenced by the -lactoglobulin/LBG ratio.This paper was presented at the first Annual European Rheology Conference (AERC) held in Guimarães, Portugal on September 11–13, 2003     

The Mechanical Properties of the Slurry and the Resistance Force of a Sphere Moving With Uniform Velocity in the Slurry

It is commonly considered that the mechanical properties of the slurryare different from that of ordinary Newtonian fluid,and can be describedby that of Bingham fluid.Hence its shearing stress should be described bythe formula of the shearing stress of Bingham fluid.But the author holdsthe contrary opinion and firmly believes that the slurry is a highly viscousfluid with very long relaxation time such as those of asphalt,glass,etc.In this article,we have discussed the mechanical properties of the slurryand the reslstance of a sphere moving with uniform veloclty in the slurry.In the process of discussion.we use Stokes solution of the vlscous fluidpassing around a sphere.When the sphere is in equilibrium under theaction of gravitational force,the force of buoyancy and the resistance,we get the velocity of sedimentation.When the velocity of sedimentationis equal to zero,we get the relation between the yield stress of Binghamfluid and the diameter of the particles which will not sink.The theoreticalresults