Theoretical and numerical results of a deterministic two-dimensional vortex method

The first part of the paper reviews results obtained in earlier work: (1) The outline of the derivation of an integral equation of Fredholm type with respect to vorticity from the Navier-Stokes equations, and (2) the analytical results for two deterministic vortex methods which are based on the corespreading model. The aim of the second part is to confirm the results of the previous analysis and to estimate the accuracy of these methods numerically. In the present paper, the model problem of a transient flow past an impulsively started circular cylinder is studied by several numerical methods. The numerical results show that (1) the Gaussian core-spreading methods are comparable with the random walk vortex method, (2) the numerical fluctuation of the deterministic methods is small, and (3) the number of panels is smaller than those in the random walk vortex method to obtain the flow with almost the same accuracy. The theoretical results in § 2–4 of the present paper are summarized from “Core-spreading vortex methods in two-dimensional viscous flows”,Computer methods in applied mechanics and engineering (in press), by Kida and Nakajima, with permission from Elsevier Science, The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK. The experimental picture is transferred from “The early stage of development of the wake behind an impulsively started cylinder for 40<Re<⁴”, by R Bouard and M Coutanceau,J. Fluid Mech. (1980) 101: 583–607.     

Recombination of two vortex filaments and jet noise

The recombination of two vortex filaments in a viscous incompressible fluid is analysed by the use of the vorticity equation. The analysis is confined to a local flow field, where the recombination process occurs, and is based on several assumptions, such as the conservation of the fluid impulse, spatial symmetry of the flow field etc. The flow field is expanded as polynomials of coordinates, and variations of their coefficients are obtained by the use of the vorticity equation. It is proved that the process is completed within a short time ofO (σ ²/Γ) and the viscous effect is essential;σ and Γ are the size and the circulation of the vortex filaments, respectively. This result is applied to predict the far-field noise of a circular jet by assuming that the main noise source is the recombination process in deformed vortex rings in the jet near field. The predicted noise intensity shows theU dependence and has an additional new factor (d/σ)⁶;U is the jet velocity andd is the average spacing between vortex rings.     

Determining wake flow parameters for two counterphase synchronized von Kármán vortex streets from configuration stability analysis

The problem of determining the parameters of near wake flow past a pair of cylindrical bluff bodies from one-point spectra of the velocity pulsation is solved in the limit of an inviscid incompressible flow. For this purpose, the stability of wake configuration with respect to infinitesimal perturbations of the equilibrium localization of the vortices is analyzed within the framework of a flow model of two counterphase synchronized von Kármán vortex streets. A necessary condition for the flow stability is determined.     

Flow visualization studies of vortices

An actual vortex in the Kármán vortex street downstream of a circular cylinder has a core of finite dimension which increases downstream. The circulation of the vortex is nearly constant. The ratiob/a which is 0.281 according to the theory of Kármán, grows from 0.2 to 0.4 in the near wake. In the flow about a circular cylinder rotating in a uniform flow, a Kármán vortex street, Görtler-type vortices and Taylor vortices are generated at the same time. In the flow about a circular cylinder impulsively started with a constant velocity, the primary twin vortices behind the cylinder induce secondary twin vortices near the separation point. At the beginning of the motion, the separation does not occur even though a reverse flow is observed in the boundary layer. Mutual slip-through of a pair of vortex rings was achieved by increasing the Reynolds number. A vortex ring rebounds from a plane surface due to the separation of the flow on the surface induced by the vortex ring, and the secondary vortex ring is formed from the separated shear layer.     

Effects of an airfoil and shock waves on vortex shedding process behind a square cylinder

Summary Effects of an airfoil and shock waves on vortex shedding process behind a square cylinder have been examined experimentally at a Mach number of about 0.91 and at a Reynolds number (based on the side lengthD of the square cylinder) of about 4.2×10⁵. The main experimental parameter is the spacing ratioL/D, and is varied from 1.125 to 5.5, whereL is the spacing between the square cylinder and the airfoil.It is found that similarly to the case at subcritical Mach numbers at the supercritical Mach number there exist three patterns of the flow around the square cylinder and airfoil arranged in tandem depending upon the spacing ratioL/D: In the first flow pattern with small spacing ratio, the downstream airfoil is enclosed completely in the vortex formation region of the square cylinder. In the second flow pattern, the shear layers separating from the square cylinder reattach to the airfoil. In the third flow pattern with large spacing the shear layers roll up upstream of the airfoil. The Strouhal number at the supercritical Mach number is higher than that at the subcritical Mach numbers. Shock waves hasten the vortex shedding behind the square cylinder by decreasing the area of asymmetrical part of the vortex formation region with respect to the wake axis, and let the streamwise length of the separating shear layers longer than otherwise.With 8 Figures     

Urania-yttria solid solution electrodes for high-temperature electrochemical applications

Measurements of total electrical conductivity on fluorite-type U₃O₈-Y₂O₃ (Sc₂O₃) solid solutions have been made as a function of temperature and U/Y(Sc) ratio. The following compositions were studied: (U_0.7Y_0.3)O_2+x , (U_0.6Y_0.4)O_2+x , (U_0.5Y_0.5)O_2+x , (U_0.45Y_0.55)O_2+x , (U_0.4Y_0.6)O_2+x , (U_0.35Y_0.65)O_2+x , (U_0.3Y_0.7)O_2−x , (U_0.5Sc_0.5)O_2+x and (U_0.38Sc_0.62)O_2+x . Preliminary measurements on the latter two compositions were carried out for comparison purposes. The maximum conductivity value occurred for the U₃O₈-Sc₂O₃ solid solutions, and for (U_0.7Y_0.3)O_2+x in the U₃O₈-Y₂O₃ system. The conductivity in these fluorite-type solid solutions is mainly electronic, the conduction mechanism being hopping-type. The energy of activation lay between 25 and 40 kJ mol⁻¹. The (U_0.3Y_0.7)O_2−x composition appeared to be an ionic conductor with an activation energy of ∼110 kJ mol⁻¹ below 800 to 850° C. The diffusion of cations of U₃O₈-Y₂O₃ into ZrO₂-Y₂O₃ was studied during passage of current: no observable diffusion occurred over the period of current passage (384 h). Attempts were made to determine the anionic contribution to the total conductivity in U₃O₈-Y₂O₃ solid solutions using the blocking electrode technique. Results indicated that complete isolation of the specimen-blocking electrode (YSZ) interface from the ambient gases is necessary if such measurements are to be reliable. The diffusion coefficients calculated from the conductivity data using the Nernst-Einstein relation were two orders of magnitude higher than those obtained by a direct method.     

Electronic computer study of separation flow features around a vibrating cylinder

The nonstationary separation flow around a circular cylinder performing harmonic vibrations across-the stream by an incompressible viscous fluid is investigated in a numerical experiment.Notation d, y, yo diameter, transverse deflection, and amplitude of cylinder vibrations - l spacing between vortices - ₁,₂ angular location of the points of separation - U_o unperturbed stream velocity - V_y velocity of transverse cylinder motion - u velocity of vortex motion - f₁ cylinder vibrations frequency - f vortex shedding frequency - t time - kinematic velocity - Sh₁=f₁d/U_o dimensionless cylinder vibrations frequency, the kinematic Strouhal number - Sh=fd/U_o Strouhal number of vortex shedding - Re=dU_o/ Reynold number - =tU_o/d dimensionless time - ¯y=y/d, ¯y_o=yo/d, ¯l=l/d; /U_o, t₁ period of cylinder vibrations - T=t₁U_o/d dimensionless period of vibrations Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 47, No. 1, pp. 41–47, July, 1984.     

Sand accumulation on a wall in flows around a near-wall circular cylinder

Summary The sand accumulation on a flat plate in flows around a near-wall circular cylinder has been mainly investigated by the method of numerical simulation at the sub-critical Reynolds number1200 (based on the diameter of the circular cylinder) and the gap ratio G/D (ratio of the gap between the circular cylinder and the plane wall to the diameter of the circular cylinder) 1.0, 0.5 and 0.25. The standard k− ε turbulent model and the vorticity-stream function formulation are adopted to analyze the wake characteristics. The lift and drag coefficients of the circular cylinder and the pressure pulsation on the wall are solved. The simulation of streak-lines for the flow visualization and PIV experiments are detailed carried out to analyze the sand accumulation phenomenon on the plane wall, and a possible mechanism has been proposed. Results of the numerical simulation indicate that the effect of the cylinder results in flow separation from the plane wall. Separations occur about 1 to 2 cylinder diameters behind the cylinder, where the particles in the flow near the plane wall accumulate gradually.     

Numerical Study of Particle Dispersion in the Wake of Two Tandem Square Cylinders Using Discrete Vortex Method

This study has been conducted to investigate numerically the particle dispersion in the wake of dilute particle-laden gas flows past two identical square cylinders in tandem arrangement at Reynolds number of 10,000,000. In the numerical method, the discrete vortex method is employed to calculate the gas flow fields, and the Lagrangian approach is applied to track individual solid particles. A dispersion function is defined to represent the lateral dispersion scale of particles. The wake vortex patterns and the distributions of particles with various Stokes numbers ranging from 0.01 to 10 are obtained. The numerical results reveal that: (1) the particles with St = 0.01 can distribute both in the vortex core and around the vortex periphery, whereas the particles with St = 1.0, 10 congregate mainly around the vortex periphery; (2) the particles with St = 0.01, 0.1 are trapped by the vortices into the gap between the two square cylinders, while very few particles with St = 1.0, 10 are distributed within the gap; (3) the particle's dispersion intensity along the lateral direction decreases greatly as St is increased from 0.01 to 10.     

High-frequency actuator control of air flow near a circular cylinder: Impact of the discharge parameters on the cylinder aerodynamic drag

The impact of capacitive high-frequency surface discharge on a flow around a circular cylinder is studied at airflow velocity of 20–100 m/s and the Reynolds numbers Re < 2.4 × 10⁵. The power of the discharge was modulated at a frequency of 10²–10⁴ Hz, corresponding to the Strouhal number St = 0.1–10. It is shown that the distribution of pressure in the wake behind the cylinder is significantly influenced by the discharge. A decrease in the average diameter of the wake is observed. The parameters of the discharge were measured: the gas temperature, heating rate in the discharge region, and velocity of discharge propagation.     

Vortex shedding suppression for laminar flow past a square cylinder near a plane wall: a two-dimensional analysis

Summary A numerical study on the uniform shear flow past a long cylinder of square cross-section placed parallel to a plane wall has been made. The cylinder is considered to be within the boundary layer of the wall. The maximum gap between the plane wall to the cylinder is taken to be 0.25 times the cylinder height. We investigated the flow when the regular vortex shedding from the cylinder is suppressed. The governing unsteady Navier-Stokes equations are discretized through the finite volume method on staggered grid system. A pressure correction based iterative algorithm, SIMPLER, has been used to compute the discretised equations iteratively. We found that the critical value of the gap height for which vortex shedding is suppressed depends on the Reynolds number, which is based on the height of the cylinder and the incident stream at the surface of the cylinder. At high Reynolds number (Re ≥ 500) however, a single row of negative vortices occurs for wall to cylinder gap height L ≥ 0.2. The shear layer that emerges from the bottom face of the cylinder reattaches to the cylinder itself at this gap hight.     

燃气单钝体绕流流场特性的数值模拟研究

应用基于有限体积法的FLUENT6.1计算软件对管道中单钝体的燃气绕流现象进行了仿真研究,即对实现管道燃气流量计量的DN200mm新型宽量程流量计的流场进行了数值模拟,就燃气计量管道中漩涡发生体的漩涡脱落频率与实测数据进行了比较。结果表明,数值计算结果与实测结果具有很好的一致性,从而提出了在新型燃气流量计的研制中可以应用数值模拟方法来优化流量计结构设计的结论。     

Flows of inelastic non-Newtonian fluids through arrays of aligned cylinders. Part 2. Inertial effects for square arrays

Numerical simulations are presented for flows of inelastic non-Newtonian fluids through periodic arrays of aligned cylinders. The truncated power-law fluid model is used for the relationship between the viscous stress and the rate-of-strain tensor. Results for the drag coefficient for creeping flows of such fluids have been presented in a companion paper [1]. In this second part the effects of finite fluid inertia are investigated for flows through square arrays. It is shown that the Reynolds-number dependence of the drag coefficient of a cylinder in the array is of the form C _d≡ F/(ηU) = k ₀ + k ₂ Re²+ .. for small values of the Reynolds number Re ≡ ρaU/η, where F is the drag force, U is the averaged velocity in the array, η = K (U/a)^n-1 is a viscosity scale with K and n the power-law coefficient and index and a the cylinder radius, and k ₀ is the drag coefficient for creeping flows. The proportionality constant k ₂ depends on the way the drag coefficient and the Reynolds number are defined. It is shown that the observed strong dependence of k ₂ on n can almost be eliminated by using length scales different from a in the viscosity scales η used in the definition of Re and in the definition of the drag coefficient. Numerical simulation results are also presented for the velocity variance components. Results for flows at moderate Reynolds number, of order 100, are also presented; these are qualitatively similar to those for Newtonian fluids. The value of the Reynolds number beyond which the flow becomes unsteady was related to the Newtonian fluid case by rescaling. These results for moderate-Reynolds-number flow are compared against previously published experimental data.     

A comparative study on effect of plain- and wavy-wall confinement on wake characteristics of flow past circular cylinder

A first attempt is made for identifying the wake characteristics of circular cylinder confined by a wavy wall at laminar flow regime. Numerical study of flow characteristics past circular cylinder with wavy-wall confinement perpendicular to cylinder axis has been carried out in the range of Reynolds number 20–100. The finite volume-based CFD solver Ansys Fluent (Version 15.0) is used for computations. The results are presented in the form of streamline plots, mean drag co-efficient, flow separation angle and recirculation length. Wavy-wall confinement leads to highly significant changes in the cylinder wake such as the evolution of strong x-plane vortices, enhanced fluid mixing, wake suppression near the crest region and vortex stretching near the trough region on the downstream of the cylinder has been observed. Flow separation angle varies significantly along the axis of the cylinder. Increased wall shear stress on rear surface of the cylinder has also been observed. The part of vorticity magnitude as compared to strain rate has been distinguished and identified using vortex identification methods such as Q-criterion and Lambda-2 criterion.     

Surface degradation behaviour of sodium borophosphate glass in aqueous media: Some studies

The degradation behaviour of phosphate glass with nominal composition, 40Na₂O-10BaO-xB₂O₃-(50-x)P₂O₅, where 0 ≤ x ≤ 20 mol%, was studied in water, HCl and NaOH solutions at room temperature to 60°C for different periods extending up to 300 h. These glasses were synthesized by conventional melt-quench technique. Dissolution rates were found to increase with B₂O₃ content in the glass. The dissolution rates for the glass having 10 mol% B₂O₃ were found to be 0·002 g/cm² and 0·015 g/cm² in distilled water and 5% NaOH solution, respectively, at room temperature after 225 h of total immersion period, whereas it increased considerably to 0·32 g/cm² in 5% NaOH at 60°C after 225 h. However, glass samples with x = 15 and 20 mol% B₂O₃ were dissolved in 5% HCl solution after 5 h immersion. The degradation behaviour has been correlated with the structural features present in the glass. The optical microscopy of the corroded surface revealed that the corrosion mechanism were different in acid and alkali media.     

Angular momentum of the fields of a few-mode fiber: I. A perturbed optical vortex

This paper presents the results of studies of the physical nature of the electrodynamic angular momentum of a stable CV ₊₁ ⁺ vortex in a few-mode fiber. It shows that the angular momentum of a CV ₊₁ ⁺ vortex can be conventionally divided into orbital and spin angular momenta. The longitudinal component of the fundamental HE ₁₁ ⁺ mode on the axis of the fiber has a pure screw dislocation with a topological charge of e=+1. The longitudinal component of a CV ₊₁ ⁺ vortex also has a pure screw dislocation on the axis of the fiber with a topological charge of e=+2. Therefore, perturbation of a CV ₊₁ ⁺ vortex by the field of the fundamental HE ₁₁ ⁺ mode removes the degeneracy of the pure screw dislocations of the longitudinal and transverse components of the field and breaks down the structural stability of the CV ₊₁ ⁺ vortex. As a result, an additional azimuthal flux of energy with an angular momentum opposite to that of the fundamental flux is induced. An analogy is drawn between the stream lines of a perturbed CV vortex and the stream lines of an inviscid liquid flowing around a rotating cylinder. Studies of the evolution of a CV vortex in a parabolic fiber show that they are structurally stable when acted on by the perturbing field of the HE ₁₁ ⁺ mode. However, perturbing a CV ₊₁ ⁺ 1 vortex of a stepped fiber with the field of the HE ₁₁ ⁺ mode destroys the structural stability of the vortex. It is found that the propagation of a circularly polarized CV vortex can be represented as a helical wavefront screwing into the medium of the fiber. The propagation of a linearly polarized vortex in free space is characterized by the translational displacement (without rotation) of a helical wavefront. Pis’ma Zh. Tekh. Fiz. 23, 74–81 (November 12, 1997)     

Estimating the energy of electric breakdown in air gap between electrolyte and metal electrode

The influence of induced electric charge (localized on the surface of a suspended copper rod) on the formation of a protrusion (Taylor cone) on the inducing liquid (aqueous solution) surface is considered. At an applied voltage of U ≤ 12 kV, the protrusion height in the interval of pre-breakdown voltages (U < U _P) is limited by the electric field strength. At U > U _P, the growth of protrusion is terminated by an electric discharge, which drives the liquid to oscillate in a broad range of applied voltages U at almost constant multiple frequencies f = f ₀ n, which are resonantly switched at certain fixed U values. By measuring the amount of evaporated liquid, the energy (27.8 × 10⁻³ J) and current (64.9 A) of single discharge were evaluated and the electric capacitance (7.6 × 10⁻¹⁰ F) of a system comprising the water surface and suspended copper electrode was estimated. Serial connection of an additional capacitor (100 μF) to the copper electrode with induced electric charge leads to a threefold increase in these parameters.     

矩形柱二维尾流的稳定性研究

采用实验和数值模拟两种方法对长宽比为3∶1的矩形柱尾流进行了稳定性研究.实验发现当雷诺数接近临界值时,未加扰动的矩形柱尾流呈二维定常状态.当在柱体上游一定位置和下游靠近柱体的位置上沿垂直于来流方向施加一个宽度很小的短时脉冲射流扰动以后,扰动随时间放大,并出现旋涡脱落现象,并且这种扰动激发的旋涡脱落可以持续很长时间,不会衰减.而在下游较远处施加同样的扰动时,扰动将会衰减,不能激发出持续的旋涡脱落.数值模拟再现了上述实验结果,并且表明,当扰动强度(脉冲射流出口速度)较小时,不会出现持续的规则旋涡脱落,只有当扰动强度达到一定阈值时,旋涡脱落才能被激发.     

Numerical simulation of planar shear flow passing a rotating cylinder at low Reynolds numbers

Two-dimensional shear flow over a rotating circular cylinder is investigated using lattice Boltzmann method. Simulations are performed at a fixed blockage ratio (B = 0.1) while the Reynolds number, nondimensional shear rate (K) and absolute rotational speed range as 80 ≤ Re ≤ 180, 0 ≤ K ≤ 0.2 and −2 ≤ β ≤ 2, respectively. To verify the simulation, the results are compared to previous experimental and numerical data. Quantitative information about the flow variables such as drag and lift coefficients, pressure coefficient and vorticity distributions on the cylinders is highlighted. It is found that, generally, with the increment in |β|, the absolute value of time average lift coefficient increases and time average drag coefficient decreases, and beyond a certain magnitude of β, the vortex shedding vanishes. It is also revealed that the drag coefficient decreases as the Reynolds number increases while the effect of the Reynolds number on lift is almost negligible. At the end, correlations for drag and lift coefficients ([`(C<sub>D</sub> )] ,[`(C_L )]){(\overline {C_D } ,\overline {C_L })} are extracted from the numerical data.     

Redox equilibrium U(IV) + 2Fe(CN) 63? ? U(VI) + 2Fe(CN) 64? in solutions of unsaturated heteropoly anions: Potentials of redox couples, stability of U(IV) complexes, reaction mechanism

The kinetics and equilibria of the reactions UO₂²⁺ + 2L + 2Fe(CN)₆⁴⁻ ⇄ UL₀ + 2Fe(CN)₆³⁻ in 0.1–1.0 M HCl solutions (ionic strength 1.0), where L is heteropoly anion of the composition P₂W₁₇O₆₁¹⁰⁻ or SiW₁₁O₃₉⁸⁻, were studied speelrophotometrically. Measurement of the redox potential of the ferri/rerrocyanide couple in acid solutions allowed estimation of the stability constants of the complxes U^IV(P₂W₁₇O₆₁)₂¹⁶⁻ and U^IV(SiW₁₁O₃₉)₂¹²⁻, equal in 1 M H⁺ solutions to 10^18.6 and 10^21.O, respectively. Accumulation of U^IVL₂ formed by reduction of UO₂²⁺ follows a first-order rate law, i.e., it involves the formation of UO₂⁺ which slowly reacts with L. The arising complex rapidly reacts with UO₂⁺. The loss of UL₂ occurs via formation of the complex of nonoxygenated U(V) with the heleropoly anion. Original Russian Text ? V.P. Shihv, A.B. Yusov. M.N. Sokolova, A.M. Fedoseev, 2008, published in Radiokhimiya, 2008, Vol. 50, No. 3, pp. 209–214.