A calculation method for fully developed flows in curved rectangular tubes

I.IntroductionacestudyofviscousnowincurvedtubesisoffundamentalinterestinfluidmechanicssincetheDean'spioneerwork(1928)l']oncurvedpipes.Therearenumerousapplications,whichincludetheflowsthroughturbomachinery,aircraftintakes,diffusersandheatexchangersetc.Itwa…     

Inversion for weak triclinic anisotropy from acoustic axes

Acoustic axes are directions in anisotropic elastic media, in which phase velocities of two or three plane waves (P$P$, S1$S1$ or S2$S2$ waves) coincide. Acoustic axes are important, because they can cause singularities in the field of polarization vectors and anomalies in the shape of the slowness surface. The maximum number of acoustic axes in triclinic anisotropy is 16, and their directions depend on anisotropy parameters in a complicate way. Under weak anisotropy approximation this dependence simplifies and the directions of acoustic axes can be used for the inversion for anisotropy parameters. The maximum acoustic axes under weak anisotropy is 16, the minimum number of acoustic axes is zero. In the inversion, we can retrieve 13 combinations of anisotropy parameters provided we use directions of 7 acoustic axes at least. Under weak anisotropy approximation, the directions of acoustic axes are insensitive to strength of anisotropy; hence we cannot invert for absolute values of weak anisotropy parameters, but only for their relative values. Numerical tests have shown that the inversion is applicable only to very weak anisotropy with strength of less than 5%, provided that the acoustic axes used in the inversion are determined with an accuracy of 0.1^°$0.1^{°}$ or better. In this case the inversion yields an average error for elastic parameters of less than 10%. In order to invert for the total set of 21 anisotropy parameters it is necessary to combine the measurements of the directions of the acoustic axes with measurements of other attributes of elastic waves in anisotropic media.     

Use of equivalent body forces for acoustic emission from a crack in a plate

A method to determine acoustic emission of surface waves from a crack near the free edge of a plate, is presented, in terms of the function f(t), which defines the time dependence of the crack opening process, the crack opening volume per unit thickness of the plate, and the elastic constants of the plate. The determination of the time-varying displacement is based on the use of equivalent body forces, which are shown to be two double forces. The acoustic emission of the crack, or the equivalent radiation from the double forces, has been obtained by a novel use of the elastodynamic reciprocity theorem. It is of interest that the normal surface-wave displacement at a position x₀ of the free edge comes out as depending on df/dt evaluated at x₀ for t > x₀/c_R, where c_R is the velocity of surface waves on the free edge.     

Parametric interaction of acoustic waves in micro-inhomogeneous media with hysteretic nonlinearity and relaxation

A theoretical investigation of parametric processes that arise as a result of the interaction of powerful and weak longitudinal acoustic waves in micro-inhomogeneous media with hysteretic nonlinearity and relaxation was carried out. The case of degenerate interaction between a powerful high-frequency wave and a weak low-frequency one was considered. The nonlinear damping coefficient and the carrier frequency phase delay of the weak wave propagating under the action of the powerful wave were determined.     

A discontinuous Galerkin method with plane waves and Lagrange multipliers for the solution of short wave exterior Helmholtz problems on unstructured meshes

Recently, a discontinuous Galerkin method with plane wave basis functions and Lagrange multiplier degrees of freedom was proposed for the efficient solution of the Helmholtz equation in the mid-frequency regime. This method was fully developed however only for regular meshes, and demonstrated only for interior Helmholtz problems. In this paper, we extend it to irregular meshes and exterior Helmholtz problems in order to expand its scope to practical acoustic scattering problems. We report preliminary results for two-dimensional short wave problems that highlight the superior performance of this discontinuous Galerkin method over the standard finite element method.     

A remedy for numerical oscillations in weakly compressible smoothed particle hydrodynamics

Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) can lead to non‐physical oscillations in the pressure and density fields when simulating incompressible flow problems. This in turn may result in tensile instability and sometimes divergence. In this paper, it is shown that this difficulty originates from the specific form of spatial discretization used for the pressure term when solving the mass conservation equation. After describing the pressure–velocity decoupling problem associated with the so‐called colocated grid methods, a modified approach is presented that overcomes this problem using a different discretization scheme for the second derivative of pressure. The modified scheme is employed for solving a number of benchmark problems including both single‐phase and two‐phase test cases. Copyright © 2010 John Wiley & Sons, Ltd.     

Measurements of the dynamic lift force acting on a circular cylinder in cross-flow and exposed to acoustic resonance

A piezoelectric transducer is developed to perform direct measurements of the dynamic lift force acting on a circular cylinder in cross-flow, in the presence and absence of acoustic resonance. Details of the force transducer design are presented in the paper. The dynamic lift force is measured for a single cylinder with two different diameters, D=12.7 and 15.8 mm. During the tests, the first transverse acoustic mode of the duct housing the cylinder is self-excited. The fluctuating pressure on the top wall of the duct is measured simultaneously with the dynamic lift force. In the absence of acoustic resonance, the measured dynamic lift coefficients agree favorably with those reported in the literature. However, when the acoustic resonance is initiated, the dynamic lift experiences a drastic increase in amplitude associated with abrupt changes in the phase between the lift force and the acoustic pressure. A methodology to extract the hydrodynamic lift component from the total lift measured during acoustic resonance is also proposed. The hydrodynamic lift force is then decomposed into in-phase and out-of-phase components, with respect to the resonant sound pressure. This decomposition procedure provides new insights into the nature of the aeroacoustic sources in the cylinder wake. The proposed methodology, together with the test results provide a general design approach to assess the increase in the dynamic fluid loading on bluff bodies in cross-flow due to the excitation of acoustic resonance.     

Characteristic fast marching method on triangular grids for the generalized eikonal equation in moving media

The governing equation of the first arrival time of a monotonically propagating front (wavefront or shock front) in an inhomogeneous moving medium is an anisotropic eikonal equation, called the generalized eikonal equation in moving media. When the ambient medium is at rest, this equation reduces to the well-known (isotropic) eikonal equation in which the characteristic direction coincides with the normal direction of the propagating front. The fast marching method is an efficient method for computing the first arrival time of a propagating front as the approximate solution of the isotropic eikonal equation. The fast marching method inherits the property that the characteristic direction coincides with the normal direction at every point on the propagating wavefront and therefore is well suited for the eikonal equation. Due to anisotropic nature, this property does not hold in the case of front propagation in a moving medium. Thus, the fast marching method cannot be directly used for the generalized eikonal equation and needs some suitable modifications. We recently proposed a characteristic fast marching method on a rectangular grid for the generalized eikonal equation (Dahiya et al., 2013) and shown numerically that this method is stable, accurate, and easy to update to second order approximations. In the present work, we generalize the method on structured triangular grids. We compare the numerical solution obtained using our method with the ray theory solution to show that the method captures accurately the viscosity solution of the generalized eikonal equation. We use the method to study some interesting geometrical features of an initially planar wavefront propagating in a medium with Taylor–Green type vortices.     

A general numerical method for solution of gravity wave problems. Part 2: Steady nonlinear gravity waves

A type of numerical scheme for 2D and 3D steady non-linear water wave problems is described. It is based on the finite process method and is insensitive to initial solutions. The relationship between the finite process method and iterative techniques is discussed. As a numerical example the flow past a submerged vortex is solved and the results are compared with those of other authors.     

A consistent boundary element method for free surface hydrodynamic calculations

Free surface phenomena are described by equations that exhibit two types of non-linearities. The first is inherent to the equations themselves and the second is caused by the application of boundary conditions at a free surface at an unknown location. Numerical calculations usually do not specifically recognize the second non-linearity, nor treat it in a fashion consistent with the more obvious non-linearities in the boundary conditions. A consistent formulation is introduced in the present paper. The field equation is integrated and the free surface boundary conditions are applied on the unknown geometry by means of appropriate series expansions. The consistent formulation introduces improvements in accuracy and computing speed. The method is demonstrated on several hydrodynamic free surface problems and an error analysis is included.     

A numerical method for coupling three dimensional nonlinear finite elements with elastic boundary elements

This paper systematically deals with the following three problems: (1) Some numerical schemes in coupling FEM- and BEM: including condensation of the boundary integral equation, symmetrization of equivalent stiffness matrix and treatment of traction discontinuity, (2) Coupling of elastoplastic finite elements to elastic boundary elements, (3) Coupling of elasto-viscoplastic finite elements to elastic boundary elements and numerical stability condition.     

大型复杂圆柱壳中高频振动噪声仿真计算方法研究

建立大型复杂圆柱壳中高频振动噪声仿真计算方法,对于解决船舶和飞机等大型复杂结构的辐射噪声预报问题具有重要意义。介绍了完美匹配层流固耦合计算方法,并成功应用于大型复杂双层圆柱壳的水下辐射噪声预报,相对于传统的声学流固耦合有限元和边界元计算方法,使外部流场域模型至少缩小了11/15。探讨了环频率和阻尼对圆柱壳结构振动传递的影响,提出了求解中高频声学问题时大型圆柱壳复杂结构仿真建模处理方法。数值算例表明,发展的PML方法和模型简化方法是合理的,可应用工程问题研究。     

A numerical approach based on the meshless collocation method in elastodynamics

In this paper, a collocation technique with the modified equilibrium on line method （ELM） for imposition of Neumann （natural） boundary conditions is presented for solving the two-dimensional problems of linear elastic body vibrations. In the modified ELM, equilibrium over the lines on the natural boundary is satisfied as Neumann boundary condition equations. In other words, the natural boundary conditions are satisfied naturally by using the weak formulation. The performance of the modified version of the ELM is studied for collocation methods based on two different ways to construct meshless shape functions： moving least squares approximation and radial basis point interpolation. Numerical examples of two-dimensional free and forced vibration analyses show that by using the modified ELM, more stable and accurate results would be obtained in comparison with the direct collocation method.     

A general numerical method for the solution of gravity wave problems. Part 1: 2D steep gravity waves in shallow water

In this paper, 2D steep gravity waves in shallow water are used to introduce and examine a new kind of numerical method for the solution of non-linear problems called the finite process method (FPM). On the basis of the velocity potential function and the FPM, a numerical method for 2D non-linear gravity waves in shallow water is described which can be applied to solve 3D problems, e.g. the wave resistance of a ship moving in deep or shallow water. The convergence is examined and a comparison with the results of other authors is made. The FPM can successfully avoid the use of iterative methods and therefore can overcome the disadvantages and limitations of such methods. In contrast to iterative methods, the FPM is insensitive to the selection of the initial solution and the number of unknowns. The basic idea of the FPM can be used to solve other non-linear problems. Its disadvantage is that much more CPU time is needed to obtain a sufficiently accurate result.     

A numerical method for the determination of weakly non‐hydrostatic non‐linear free surface wave propagation

A numerical method is described that may be used to determine the propagation characteristics of weakly non‐hydrostatic non‐linear free surface waves over a general, bottom topography. In shallow water of constant undisturbed depth, such waves are equivalent to the familiar cnoidal waves characterized by sharp crests and relatively flat troughs. For a certain range of parameters, these propagate without change of form by virtue of the weakly non‐hydrostatic balance in the vertical momentum equation. Effectively, this counters the tendency for the non‐linearity in a purely hydrostatic theory to lead to a continuously deforming surface wave profile. The realistic representation furnished by cnoidal wave theory of free surface waves in the shallow near‐shore zone has led to its utilization in evaluating their propagation characteristics. Nonetheless, the classic analytical theory is inapplicable to the case of wave propagation over a sloping beach or off‐shore sand bar topography. Under these conditions, a local change in form of the surface wave profile is anticipated before the waves break and knowing this is required in order to evaluate fully the propagation process. The efficacy of the numerical method is first demonstrated by comparing the solution for water of constant depth with the evaluation of the analytical solution expressed in terms of the Jacobian elliptic function cn. The general method described in the paper is then illustrated by experiments to determine the change in profile of weakly non‐hydrostatic non‐linear surface waves propagating over bed forms representative of those found in shallow coastal seas. Copyright © 2001 John Wiley & Sons, Ltd.     

New numerical schemes based on a criterion for constructing essentially stable and accurate numerical schemes for convection-dominated equations

In order to obtain stable and accurate numerical solutions for the convection-dominated steady transport equations, we propose a criterion for constructing numerical schemes for the convection term that the roots of the characteristic equation of the resulting difference equation have poles. By imposing this criterion on the difference coefficients of the convection term, we construct two numerical schemes for the convection-dominated equations. One is based on polynomial differencing and the other on locally exact differencing. The former scheme coincides with the QUICK scheme when the mesh Reynolds number (Rm) is $\mathop \[{\textstyle{{\rm 8} \over {\rm 3}}}\] $, which is the critical value for its stability, while it approaches the second-order upwind scheme as Rm goes to infinity. Hence the former scheme interpolates a stable scheme between the QUICK scheme at Rm = $\mathop \[{\textstyle{{\rm 8} \over {\rm 3}}}\] $ and the second-order upwind scheme at Rm = ∞. Numerical solutions with the present new schemes for the one-dimensional, linear, steady convection-diffusion equations showed good results.     

General formalism for plane guided waves in transversely inhomogeneous anisotropic plates

The sextic approach to plane waves in infinite (visco)elastic plates of arbitrary anisotropy and transverse inhomogeneity is outlined. A particular thrust is set on continuous inhomogeneity when the propagator is defined by the Peano expansion. Despite underlying explicit intricacy, the basic framework of the pursued formalism is little affected by a through-plate variation of material. To make it evident, the principal algebraic symmetry of the propagator for unattenuated waves and the ensuing arrangement of the impedance as a Hermitian matrix with specific traits are inferred directly from energy considerations. Staying the same as for homogeneous plates, those features yield useful developments in the broader context of inhomogeneity. The formalism may be expressed in either pair picked among velocity, frequency and wavenumber, but different choices of a dispersion variable are shown to entail analytical dissimilarities. In addition, the impact of the profile symmetry and of the horizontal plane of crystallographic symmetry is examined. The surface-impedance method and some other aspects of the numerical treatment are discussed.     

一类非线性发展方程的交替分段显隐并行数值方法

给出了一类非线性发展方程的交替分段显隐并行数值方法 ,得到了方法的无条件稳定性和并行性兼顾的结果。数值例子说明理论分析的正确性和格式的有效性