LES and analyses on the vortex structure behind supersonic MVG with turbulent inflow

In this paper, an implicitly implemented high order large eddy simulation by using the fifth order bandwidth-optimized WENO scheme is applied to make comprehensive studies on ramp flows with and without control at Mach 2.5 and Re_θ = 5760. Flow control in the form of microramp vortex generators (MVG) is applied. The mechanism of vortex ring generation behind MVG has been studied in detail and shear layer instability has been studied and found as the mechanism of K–H vortex ring generation. A series of new observations on the flow around supersonic MVG have been made including inflection points (surface in 3-D), vorticity conservation, interaction of the primary vortex and new generated K–H vortex rings, and the K–H vortex ring structure. The numerical observations have been confirmed by the experimental work.     

Existence and numerical modelling of vortex rings with elliptic boundaries

We revisit in this paper the theory of axisymmetric vortex rings in an ideal fluid. The boundary separating the vortex ring from the external (potential) flow is assumed of elliptic shape. For a given distribution of vorticity in the vortex core, we theoretically put into evidence the critical parameter for the existence of non-trivial solutions, thus confirming the numerical observation of Durst et al. [ZAMP 32 (1981) 156]. A sharp estimation of the critical threshold is analytically derived. Theoretical predictions are confirmed by numerical simulations using finite elements. A new numerical algorithm is presented and shown to display better performances compared to previous published algorithms using finite differences. The convergence of the iterative algorithm is proved using the theory of elliptic partial differential equations with discontinuous nonlinearities.     

Hydrodynamics of a particle impact on a wall

The problem of a particle impacting on a wall, a common phenomenon in particle-laden flows in the minerals and process industries, is investigated computationally using a spectral-element method with the grid adjusting to the movement of the particle towards the wall. Remeshing is required at regular intervals to avoid problems associated with mesh distortion and the constantly reducing maximum time-step associated with integration of the non-linear convective terms of the Navier–Stokes equations. Accurate interpolation between meshes is achieved using the same high-order interpolation employed by the spectral-element flow solver. This approach allows the full flow evolution to be followed from the initial approach, through impact and afterwards as the flow relaxes. The method is applied to the generic two-dimensional and three-dimensional bluff body geometries, the circular cylinder and the sphere. The principal case reported here is that of a particle colliding normally with a wall and sticking. For the circular cylinder, non-normal collisions are also considered. The impacts are studied for moderate Reynolds numbers up to approximately 1200. A cylindrical body impacting on a wall produces two vortices from its wake that convect away from the cylinder along the wall before stalling while lifting induced wall vorticity into the main flow. The situation for a sphere impact is similar, except in this case a vortex ring is formed from the wake vorticity. Again, secondary vorticity from the wall and particle plays a role. At higher Reynolds number, the secondary vorticity tends to form a semi-annular structure encircling the primary vortex core. At even higher Reynolds numbers, the secondary annular structure fragments into semi-discrete structures, which again encircle and orbit the primary core. Vorticity fields and passive tracer particles are used to characterize the interaction of the vortical structures. The evolution of the pressure and viscous drag coefficients during a collision are provided for a typical sphere impact. For a Reynolds number greater than approximately 1000 for a sphere and 400 for a cylinder, the primary vortex core produced by the impacting body undergoes a short-wavelength instability in the azimuthal/spanwise direction. Experimental visualisation using dye carried out in water is presented to validate the predictions.     

Large Eddy Simulation of the vortex end in reverse-flow centrifugal separators

The present work is a study of the gas-flow phenomenon known as the “end of the vortex” (EoV), which spontaneously occurs at the lower end, or under, reverse-flow centrifugal separators such as cyclones or swirl tubes. Different CFD models of swirl tubes have been built to study and analyse this phenomenon in detail. The present numerical work is based on—and compared with—previous experimental observations of this phenomenon. The numerical models were built in complete agreement with the geometrical configurations and operating conditions used in these earlier experimental studies [1]. Two different configurations of swirl tubes were analyzed. One configuration was an in principle long tube with variable length in which the dependence on the vessel length of the behaviour of the vortex core in a simple, well-defined geometry was studied. The other configuration was equipped with a wide “dust collection vessel” at the bottom, the depth of which was varied, to study the behaviour of the vortex core in a widely-used geometry. 3-D LES simulations were carried out using the commercial CFD package Star-CD. The bending of the vortex core to the wall of the vessel and its precessional motion, constituting the phenomenon of the EoV, was seen in both configurations, and the obtained results are in very good agreement, both qualitatively and to an extent quantitatively, with previous experimental results [1].     

Numerical simulation of the interaction between vortex ring and bubble plume

In present paper a three-dimensional Vortex-In-Cell method with two-way coupling effect was developed to study the bubble plume entrainment by a vortex ring. In this method the continuous flow was calculated by the three-dimensional Vortex-In-Cell method and the bubbles are tracked through bubble motion equation. Two-way coupling effect between continuous flow and dispersed bubbles is considered by introducing a vorticity source term, which is induced by the change of void fraction gradient in each computational cell. After validated by the comparison between experimental measurements and simulation results for the motion of vortex rings and the rising velocity of bubble plume, present method is implemented to simulate the interaction between an evolving vortex ring and a rising bubble plume. It was found that there is little effect of the bubble entrainment to the total circulation of vortex ring while the effect of bubble entrainment to the vortex ring structure is quite obvious. The bubble entrainment by the vortex ring not only changed the vorticity distribution in the vortex structure, but also displaced the positions of the vortex cores. The vorticity in the lower vortex core of the vortex ring decreases more than that in the upper vortex core of the vortex ring while the vortex core in the upper part of the vortex ring is displaced to the center of vortex ring by the entrained bubbles. Smaller bubbles are easier to be entrained by the large scale vortex structure and the transportation distance is in inverse proportion to bubble diameter.     

Near-field fluctuations and far-field noise of a three-element airfoil system by a discrete vortex method

A circulation-based discrete vortex method is used on a three-element airfoil system. Kutta conditions and Kelvin’s circulation theorem are additional conditions required for this method to determine the circulation distributions on each element and to determine vortex shedding. Discrete shed vortices are introduced near the four sharp edges to represent the sharp-edge vortex shedding caused by unsteady flow separation. The computational procedure warrants neutrally stable solutions of the self-sustained fluctuating flowfield that can provide broad-band spectral information for far-field noise predictions. The near-field vortex method directly calculates the parameters used in an asymptotic formula for far-field sound computation that attributes the noise sources to vortex interactions among the shed vortices and the surface circulations of the three-element airfoil system. The far-field noise characters are then analyzed and compared to the experimental data in the literature.     

Finite generation of canonical ring by analytic method

An overview of the analytic proof of the theorem on the finite generation of the canonical ring for the projective algebraic manifold of general type is given.     

Numerical approximation of Turing patterns in electrodeposition by ADI methods

In this paper we study the numerical approximation of Turing patterns corresponding to steady state solutions of a PDE system of reaction–diffusion equations modeling an electrodeposition process. We apply the Method of Lines (MOL) and describe the semi-discretization by high order finite differences in space given by the Extended Central Difference Formulas (ECDFs) that approximate Neumann boundary conditions (BCs) with the same accuracy. We introduce a test equation to describe the interplay between the diffusion and the reaction time scales. We present a stability analysis of a selection of time-integrators (IMEX 2-SBDF method, Crank–Nicolson (CN), Alternating Direction Implicit (ADI) method) for the test equation as well as for the Schnakenberg model, prototype of nonlinear reaction–diffusion systems with Turing patterns. Eventually, we apply the ADI-ECDF schemes to solve the electrodeposition model until the stationary patterns (spots & worms and only spots) are reached. We validate the model by comparison with experiments on Cu film growth by electrodeposition.     

Approximate general and explicit solutions of nonlinear BBMB equations by Exp-Function method

In this work, we implement a relatively new analytical technique, the Exp-Function method, for solving special form of generalized nonlinear Benjamin–Bona–Mahony–Burgers equation (BBMB) which may contain high nonlinear terms.     

结构振动诱导流场及附加质量的数值分析

将大型柔性结构低速振动诱导流体流场的问题, 归结为无粘性不可压缩无旋流动平面问题．在偶极子配置法基础上,发展了一种在结构和流体接触面上混合配置源汇和偶极子的奇点配置法,能够计算翼型、柱型等结构在流体中低速振动时诱导的流体流场并推导出流场的动能表达式,最终得到流体附加质量．给出了几个具有解析解的算例验证了此方法的可靠性．     

Numerical modelling and analysis of external gear pumps by applying generalized control volumes

Components in gear pumps usually involve complex geometrical arrangements in order to achieve the desired performance. The use of lumped parametric models is considered the most accurate and effective method for investigation of the associated design issues. In this study, the numerical modelling approach based on the lumped parameters and control volume concepts is reviewed, especially for gear teeth within the meshing zone. To apply the approach to the entire gear pump, control volume concepts are generalized to all gear pockets and flow orifices with some reasonable assumptions. The assumptions include instantaneous angular positions, orifice transitions and imagined control volumes with internal flows. The fluid dynamics and pump performance, which even have the measurement difficulties, can be estimated to investigate and optimize the design parameters of gears by the model. A simulation example and its experimental results of a gear machine are presented to validate the proposed approach in this article.     

On the variety of triangles for a hyper-Kähler fourfold constructed by Debarre and Voisin

We study the similarities between the Fano varieties of lines on a cubic fourfold, a hyper-Kähler fourfold studied by Beauville and Donagi, and the hyper-Kähler fourfold constructed by Debarre and Voisin in [3]. We exhibit an analog of the notion of “triangle” for these varieties and prove that the 6-dimensional variety of “triangles” is a Lagrangian subvariety in the cube of the constructed hyper-Kähler fourfold.     

Numerical simulation of pollution and oil spill spreading by the stochastic discrete particle method

The features of the stochastic discrete particle method are discussed as applied to the simulation of pollutant advection and diffusion in a turbulent flow and to the spread of a thin film of a viscous substance (oil) on the surface of water. The diffusion tensor in the former problem depends on the scale of the pollution cloud, and the diffusivity in the latter problem depends nonlinearly on the desired function. For pollution dispersion by a turbulent flow, a stochastic discrete particle algorithm is constructed in the case when the diffusion tensor corresponds to the Richardson 4/3 law. The numerical and analytical results are shown to agree well. The problem of oil film spreading is described by a quasilinear advection-diffusion equation. For this problem, a random walking algorithm is constructed in which the variance of the walking particle step depends on the desired function. For both instantaneous and time-continuous sources of pollutants, the solution produced by the stochastic discrete particle method agrees well with the analytical and/or numerical solutions to the test problems under consideration.     

Numerical solution of the nonstationary Stokes system by methods of adjoint-equation theory and optimal control theory

Methods in optimal control and the adjoint-equation theory are applied to the design of iterative algorithms for the numerical solution of the nonstationary Stokes system perturbed by a skew-symmetric operator. A general scheme is presented for constructing algorithms of this kind as applied to a broad class of problems. The scheme is applied to the nonstationary Stokes equations, and the convergence rate of the corresponding iterative algorithm is examined. Some numerical results are given.     

Numerical and empirical approach in predicting the penetration of a concrete target by an ogive-nosed projectile

This paper demonstrates the application of both numerical simulation and empirical equation in predicting the penetration of a concrete target by an ogive-nosed projectile. The results from the experiment performed by Gran and Frew [In-target radial stress measurements from penetration experiments into concrete by ogive-nose steel projectiles, Int. J. Impact Eng. 19 (8) (1997) 715–726] are used as a benchmark for comparison. In the numerical simulations a 3.0-caliber radius-head steel ogival-nose projectile with a mass of 2.3 kg is fired against cylindrical concrete target with a striking velocity of 315 m/s. The simulation, performed using AUTODYN 2-D, assesses three numerical schemes, namely Langrange, Euler–Lagrange coupling and smooth particles hydrodynamics SPH–Lagrange coupling, in predicting the maximum depth of penetration and the radial stress–time response of the concrete target. When assessing the three solution techniques we hypothesize that the effect of strain rate on strength for the concrete target does not adversely affect the prediction on the maximum depth of penetration and the radial stress–time response of the concrete target. In the empirical approach the penetration equation developed by Forrestal et al. [An empirical equation for penetration depth of ogive-nose projectiles into concrete targets, Int. J. Impact Eng. 15 (4) (1994) 395–405] is used to determine the maximum depth of penetration and the deceleration–time response. The deceleration–time response for the projectile using the empirical approach is compared with those obtained from the numerical simulations. Results from both the numerical and empirical approaches are consistent. The calculated depth of penetration from both approaches yield relatively good agreement with that obtained from the experiment. The numerical simulations using each of the three numerical schemes are also able to reproduce the profiles from the radial stress measurements. Simulations using the SPH numerical scheme give the best overall agreement. The good overall agreement with the experimental radial stress measurements and consistent results between both empirical and numerical approach, enhanced the confidence in engineers and ballisticians when using these two approaches in complementing full-scale testing.     

Hochschild cohomology ring modulo nilpotence of a one point extension of a quiver algebra defined by two cycles and a quantum-like relation

We consider a one point extension algebra B of a quiver algebra A _q over a field k defined by two cycles and a quantum-like relation depending on a nonzero element q in k. We determine the Hochschild cohomology ring of B modulo nilpotence and show that if q is a root of unity, then B is a counterexample to Snashall-Solberg’s conjecture.     

自由来流湍流与三维壁面局部粗糙诱导平板边界层不稳定T-S波的数值研究

采用直接数值模拟（DNS）方法,研究了在自由来流湍流与三维壁面局部粗糙作用下平板边界层内诱导产生不稳定T-S波的物理问题.数值结果可知,在平板边界层内发现了二维和三维T-S波组成的波包空间序列以及求得了波包向前传播的群速度大小,从而证明了自由来流湍流与三维壁面局部粗糙作用是激励平板边界层内诱导产生不稳定T-S波的一种机制.随后,建立了平板边界层内被激发的二维和三维T S波的初始幅值与自由来流湍流度,三维壁面局部粗糙的流向长度、展向宽度及法向高度之间的关系.这一问题的深入研究,进一步完善了流动稳定性与湍流理论.