Evaluation of unsteadiness in effervescent sprays by analysis of droplet arrival statistics - The influence of fluids properties and atomizer internal design

The ideal spray theory of Edwards and Marx was used to investigate the dependence of effervescent spray unsteadiness on fluid properties and atomizer internal design. Results demonstrate that fluid properties and internal design of atomizer directly affect the two-phase flow pattern inside the atomizer which consequently affects the spray unsteadiness of the atomizer. Water sprays are more unsteady when the air to liquid ratio (ALR) increases, whereas, more unsteady is observed for using glycerol/water mixture (high-viscosity Newtonian fluid) or glycerol/water/xanthan (non-Newtonian fluid) mixture as ALR reduces. In addition, sprays using low-viscosity or strong non-Newtonian fluids usually are more unsteady, regardless of ALR.A short mixing chamber results in less unsteady for water but has no effect on spray unsteadiness for high-viscosity or non-Newtonian fluids at ALR of 0.15. Otherwise, the influence of mixing chamber distance on the spray quality is weak at ALR of 0.15. Large diameter of inclined aeration holes shows the low spray unsteadiness and good spray quality for water but causes more unsteady for glycerol/water/xanthan mixture at ALR of 0.15. Furthermore, the diameter of the inclined aeration holes has little influence on spray unsteadiness for glycerol/water mixture. Spray unsteadiness and quality are not affected by the angle of aeration holes for three fluids at ALR of 0.15.     

A comprehensive analysis of the viscous incompressible flow in quasi-three-dimensional aerofoil cascades

A rigorous model of the fully elliptic flow over the blade-to-blade stream surface in an annular aerofoil cascade is developed. The model accuracy stems from its precise simulation of the meridional hub-to-casing flow effects, including those of the shear stress components that are created by the spanwise velocity gradients. These stresses are unprecedentedly introduced in the flow-governing equations in the form of source terms and are modelled as such. The final set of flow-governing equations are solved using the Galerkin weighted residual method coupled with a biquadratic finite element of the Lagrangian type. The flow solution is verified against the numerical results of a fully three-dimensional flow model and a set of experimental data, both concerning a low-aspect-ratio stator of an axial flow turbine under a low Reynolds number and subsonic flow operation mode. The numerical results in this case show well predicted aerofoil loading and pitch-averaged exit flow conditions. Also evident is a substantial capability of the analysis in modelling such critical regions as the wake subdomain. It is further proven that the new terms in the governing equations enhance the quality of the numerical predictions in this class of flow problems.     

Certain hydrodynamic characteristics of the evolution of a solitary spherical bubble in the finite compression regime

The characteristics of unsteady incompressible fluid flow around a gas or vapor bubble compressed to a finite size are theoretically investigated. The velocity on the bubble boundary, the integral flow-rate and kinetic energy, and the form of the pressure distribution in the fluid are analyzed. Certain general qualitative regularities independent of viscosity, surface tension, and the intensity of the heat and mass transfer processes are revealed. The general results obtained are illustrated and specified with reference to a simplified polytropic model.     

Symmetry of a periodic array of particles and a viscous fluid flow in the stokes approximation

A suspension in which rigid spherical particles of the same radius form a periodic array is considered. A general solution of the Stokes equations periodic with respect to this array is obtained. With reference to a fluid flow through a fixed array and a shear flow with frozen-in particles it is shown that taking the array structure and the symmetry of the conditions on the particle surface into account leads to a considerable simplification of the problem and makes it possible to determine the velocity and pressure distributions over the fluid.     

Using the perturbation method to solve the problem of separated incompressible flow past thin airfoils

A model for separated incompressible flow past thin airfoils in the neighborhood of the “shockless entrance” condition is constructed based on the averaging of the vortex shedding flow past the airfoil edges. By approximation of the vortex shedding by two vortex curves, determination of the average hydrodynamic parameters is reduced to a twofold solution of an integral singular equation equivalent to the equation describing steady-state nonseparated airfoil flow. In this case, the calculation time is two orders of magnitude smaller than the time required for the solution of the corresponding evolution problem. The results of a test calculation using the proposed method are in fair agreement with available results of calculations and experiments. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 49–63, May–June, 2006.     

Three-dimensional analysis of the flow in the cyclones

Sincethecycloneisextensivelyusedinindustry,themechanismofitsstreamhasbeeninvestigatedandanalysed.Buttheprocessofthepreviousdiscussionstaysattheleveloftwo-dimensionedmodelanalysis,withtheaddedconsiderationabouttheaxialIysymmetry.lntheseyears,somespecialistshavediscusseditinthelightofthetotalthree-dimensionview.Thispapertriestogivesystematicanddetai]edexp1anationsandtopresentacorrectresultofRef[1].I.GeneralEquationEstablishedFirstweestablishmathematicalexpressionofflowinthecyclone.Wecanimaget…     

On identification of flow separation and vortices in internal periodic flows

To permit simplified analysis of complex time-dependent flows, possible relationship between the near-wall flow, flow separation and vortices are studied numerically for a flow in a constricted two-dimensional channel. The pulsating incoming wave-form consists of a steady flow, followed by a half-sinus flow superimposed on the steady component. One pair of vortices is created in each cycle, one vortex near each wall. The vortices propagate downstream in the next cycles, promoting flow separation as they move. Existing flow separation criteria were not found to be uniformly valid. A relation between the near-wall flow and the vortical system exists only during the steady incoming flow phase of the cycle. It seems that local criteria of flow separation cannot be found for complex internal pulsating flow fields. However, the vorticity field can be utilized, even in complex time-periodic flows, for identifying vortices that have been formed by the roll-up of shear layers.     

Mathematical modeling of the sound induced in a subsonic flow around cascades in relative motion

A method of mathematical modeling of the tonal sound induced by the unsteady aerodynamic interaction of two plane airfoil cascades in a subsonic flow and in uniform relative motion in the direction of their fronts is developed. The method is based on the numerical integration of the unsteady flow equations using a simplified model for the periodic system of edge wakes shed from the airfoils of the first (leading) cascade in the viscous flow and acting on the second (trailing) cascade. An analysis of the distinctive features of the flow under consideration demonstrates the efficiency of the model proposed.     

Unsteady flow of a fourth-grade fluid due to an oscillating plate

The governing non-linear high-order, sixth-order in space and third-order in time, differential equation is constructed for the unsteady flow of an incompressible conducting fourth-grade fluid in a semi-infinite domain. The unsteady flow is induced by a periodically oscillating two-dimensional infinite porous plate with suction/blowing, located in a uniform magnetic field. It is shown that by augmenting additional boundary conditions at infinity based on asymptotic structures and transforming the semi-infinite physical space to a bounded computational domain by means of a coordinate transformation, it is possible to obtain numerical solutions of the non-linear magnetohydrodynamic equation. In particular, due to the unsymmetry of the boundary conditions, in numerical simulations non-central difference schemes are constructed and employed to approximate the emerging higher-order spatial derivatives. Effects of material parameters, uniform suction or blowing past the porous plate, exerted magnetic field and oscillation frequency of the plate on the time-dependent flow, especially on the boundary layer structure near the plate, are numerically analysed and discussed. The flow behaviour of the fourth-grade non-Newtonian fluid is also compared with those of the Newtonian fluid.     

On the theory of stability of a cylindrical hydrodynamic suspension

The stability of a cylindrical hydrodynamic suspension is investigated with complete account for the dependence of the fluid velocity distribution profile on the radial coordinate in the supporting layer without an a priori representation of the inertial terms in the fluid layer in terms of the velocity averaged over the clearance cross-section. It is shown that the central position of a light inner body in the cylindrical hydrodynamic suspension is asymptotically stable. The suspension remains asymptotically stable for a fairly long time as the light inner body is displaced from the central position along the dynamic equilibrium curve. The central position of a heavy inner body is unstable; however, as it is displaced from the central position under the action of a constant external decentering force a stability domain develops.     

Calculation of the unsteady aerodynamic parameters of a rotating cascade of oscillating blades in incompressible flow

The unsteady aerodynamic parameters of 3D blade cascades oscillating in incompressible flow are determined with account for blade geometry and the influence of the steady hydrodynamic loads acting on the blades. On the assumption of separationless flow and harmonic blade oscillations, the corresponding boundary-value problem for the amplitude function of the unsteady velocity potential component is solved in the linear formulation, using a finite-element method. Test calculation results are presented and an example of calculating the unsteady aerodynamic parameters of a hydro-turbine model is given.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 40–52. Original Russian Text Copyright © 2005 by Kurzin and Tolstukha.     

Hydromagnetic flow in a viscoelastic fluid due to the oscillatory stretching surface

An analysis is carried out to study the unsteady magnetohydrodynamic (MHD) two-dimensional boundary layer flow of a second grade viscoelastic fluid over an oscillatory stretching surface. The flow is induced due to an infinite elastic sheet which is stretched back and forth in its own plane. For the investigated problem, the governing equations are reduced to a non-linear partial differential equation by means of similarity transformations. This equation is solved both by a newly developed analytic technique, namely homotopy analysis method (HAM) and by a numerical method employing the finite difference scheme, in which a coordinate transformation is employed to transform the semi-infinite physical space to a bounded computational domain. The results obtained by means of both methods are then compared and show an excellent agreement. The effects of various parameters like visco-elastic parameter, the Hartman number and the relative frequency amplitude of the oscillatory sheet to the stretching rate on the velocity field are graphically illustrated and analysed. The values of wall shear stress for these parameters are also tabulated and discussed.     

Stokes流问题中的辛本征解方法

通过引入哈密顿体系,将二维Stokes流问题归结为哈密顿体系下的本 征值和本征解问题. 利用辛本征解空间的完备性,建立一套封闭的求解问题方法. 研究结果 表明零本征值本征解描述了基本的流动,而非零本征值本征解则显示着端部效应影响特点. 数值算例给出了辛本征值和本征解的一些规律和具体例子. 这些数值例子说明了端部非规则 流动的衰减规律. 为研究其它问题提供了一条路径.     

Development of highly accurate interpolation method for mesh‐free flow simulations II. Application of CIVA method to incompressible flow simulations

This is the second report on the development of a highly accurate interpolation method, which is called cubic interpolation with volume/area (CIVA) co‐ordinates, for mesh‐free flow simulations. In this paper, the method of determining the c‐parameter of CIVA using a constant curvature condition is first considered for the two‐ and three‐dimensional cases. A computation of a three‐dimensional passive scalar advection problem is performed for accuracy verification and for comparison with widely used methods. Then, an application algorithm of the CIVA method respecting incompressible fluid simulation is presented. As the incompressible condition based on Lagrangian approaches causes problems, in this paper we consider the condition based on the conventional Eulerian approach. The CIVA‐based incompressible flow simulation algorithm enables a highly accurate simulation of many kinds of problems that have complicated geometries and involve complicated phenomena. To confirm the facts, numerical analyzes are executed for some benchmark problems, namely flow in a square cavity, free surface sloshing and moving boundary problems in complex geometries. The results show that the method achieves high accuracy and has high flexibility, even for the flows involving high Reynolds number, complicated geometries, moving boundaries and free surfaces. Copyright © 2000 John Wiley & Sons, Ltd.     

黏性不可压缩流体流动前沿的数值模拟

提出了模拟注射成型中黏性、不可压缩流体流动前沿的新方法. 将Hele-Shaw流动应用于非 等温条件下的黏性、不可压缩流体，建立了流动分析模型，用充填因子的输运方程描述流动 前沿. 应用高阶Taylor展开式计算每一时间步长的充填因子，用Galerkin方法导出了计算 充填因子各阶导数的递推公式. 给出了时间增量的选取方法，证明了它的稳定性. 针对Han 设计的试验模具，用相同的材料及工艺条件模拟充填过程，比较了传统方法和该方法的模 拟结果与实验结果的差异. 算例分析表明，该方法可以有效地提高注射成型中流动前沿的 模拟精度和计算效率.     

On the existence of periodic solutions to higher dimensional periodic system with delay

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Exact solution of electroosmotic flow in generalized Burgers fluid

An exact solution is developed for the time periodic electroosmotic flow of a non-Newtonian fluid between the micro-parallel plates. The constitutive equations of a generalized Burgers fluid are used in the mathematical formulation. The resulting problem is solved by a Fourier transform technique. Graphs are plotted and discussed for various emerging parameters of interest.     

Non-swirling axisymmetric flow of the ω-D fluid

In this paper a constitutive equation for the extra stress tensor τ is considered, which can be used for steady axisymmetric flows when u _ϕ=0 (non-swirling). It is explicit with coefficients which, in case of incompressibility, depend only upon three invariants. As such it should prove useful in numerical calculations, especially so if used in its simplest form, namely the quasi-Newtonian fluid. Here, a purely viscous code can be used. The constitutive equation is self-consistent and receives additional justification from the fact that any constitutive equation is bound to result in the form proposed if the flow is a constant stretch history flow. Received: 30 March 1998 Accepted: 6 August 1998