Numerical simulation of the noise generated by a low Mach number, low Reynolds number jet

In this paper we study the sound field produced by a turbulent round jet with a Mach number of 0.6 based on the centerline velocity and the ambient speed of sound c_∞. The turbulent flow field is found by solving the fully compressible Navier–Stokes equations with help of high-order compact finite difference schemes. It is shown that the simulated flow field is in good agreement with experiments. The corresponding sound field has been obtained with help of the Lighthill equation using two different formulations for the Lighthill stress tensor T_ij. In the first formulation of T_ij the fluctuating density is taken into account. In the second formulation the density is assumed to be constant. As an additional check we have also performed an acoustic calculation using a formulation in which a homogeneous wave equation is solved. The boundary conditions for this homogeneous wave equation are obtained from the numerical simulation of the Navier–Stokes equation. The results obtained with both formulations of the Lighthill stress tensor are nearly identical. This implies that an incompressible formulation of the conservations laws could be used to predict jet noise at low Mach numbers.     

Experimental study of liquid sloshing dynamics in a barge carrying tank

An experimental work has been carried out to study the phenomena of sloshing of liquid in partially filled tanks mounted on a barge exposed to regular beam waves. Three liquid fill levels with liquid depth, h_s to length of tank, l ratio (h_s/l) of 0.163, 0.325 and 0.488, are studied. The time histories of sloshing oscillation are measured along the length of container at predefined locations. The nonlinear behaviour of sloshing oscillation is observed for the regular wave excitation. The spectra of the sloshing oscillation and their qualitative assessment are reported. Attempts are made to evaluate the harmonics present in the sloshing oscillation and compare with the results of earlier studies. The effects of wave excitation frequency and wave height on the sloshing oscillation as well as on the response of the barge are studied.     

A study of electromechanical switching in ferroelectric single crystals

This article documents both modeling and experimental studies developed to investigate the switching behavior of ferroelectric single crystals. The theoretical model makes a priori ansatz that switching follows the evolution of a particular domain pattern. The choice of this configuration is dictated by the requirement that domains remain compatible during evolution, giving rise to a low-energy path for the overall switching. The construction of this pattern is achieved using multirank laminates. It offers an advantage of specifying different types of domain wall movements, leading to a distinction for the switching types. A loading experiment is performed on a barium titanate (BaTiO₃) single crystal with a constant compressive stress and a cyclic electric field. Both 180 and 90 coercive fields are measured as input parameters required for the theoretical framework. The simulation results show good agreement with the observed strains measured by the present and other available experiments. It is found that depolarization has a non-trivial influence on attainable actuation strains.     

Separation of variables in one problem of motion of the generalized Kowalevski top

In the problem of motion of the Kowalevski top in a double force field the new case of reduction to a Hamiltonian system with two degrees of freedom was pointed out by Kharlamov [Kharlamov, M.P., 2004. Mekh. Tverd. Tela 34, 47–58]. We show that the equations of motion in this case can be separated by the appropriate change of variables, the new variables U,V being hyperelliptic functions of time. The natural phase variables (components of the angular velocity and the direction vectors of the forces with respect to the movable basis) are expressed via U,V explicitly in elementary algebraic functions.     

On the flow in a uniformly porous pipe

This article considers fully laminar flow of an incompressible viscous fluid in a uniformly porous pipe with suction and injection. An exact solution of the Navier–Stokes equations is given. The velocity filed can be expressed in a series form in terms of the modified Bessel function of the first kind of order n. The volume flux across a plane normal to the flow, the vorticity and the stress on the boundary are presented. The flow properties depend on the cross-Reynolds number, Ua/ν, where U is the suction velocity, a is the radius of the pipe and ν is the kinematic viscosity of the fluid. It is found that for large values of the cross-Reynolds number, the flow near the region of the suction shows a boundary layer character. In this region the velocity and the vorticity vary sharply. Outside the boundary layer, the velocity and the vorticity do not show an appreciable change.     

Linear and nonlinear sloshing in a circular conical tank

Linear and nonlinear fluid sloshing problems in a circular conical tank are studied in a curvilinear coordinate system. The linear sloshing modes are approximated by a series of the solid spheric harmonics. These modes are used to derive a new nonlinear modal theory based on the Moiseyev asymptotics. The theory makes it possible to both classify steady-state waves occurring due to horizontal resonant excitation and visualise nonlinear wave patterns. Secondary (internal) resonances and shallow fluid sloshing (predicted for the semi-apex angles >60) are extensively discussed.     

Perturbation theory for the double sine-Gordon equation

This paper presents a perturbation theory for the double sine-Gordon equation. We obtain a system of differential equations that shows the soliton parameters modification under the influence of the perturbation. For the particular case λ=0 the results transform into the well-known perturbation theory for the sine-Gordon equation.     

Autoparametric quasiperiodic excitation

The dynamics of an autonomous conservative three degree of freedom system which exhibits autoparametric quasiperiodic excitation is investigated. The system is a generalization of a classical system known as the “particle in the plane”. The system exhibits a motion, the z=0 mode, whose stability is governed by a linear second order ODE with quasiperiodic coefficients. The behavior of the latter ODE is studied by using three different methods: numerical integration, harmonic balance and perturbation methods.     

A robust near-wall elliptic-relaxation eddy-viscosity turbulence model for CFD

An eddy-viscosity model based on Durbin’s elliptic relaxation concept is proposed, which solves a transport equation for the velocity scales ratio instead of , thus making the model more robust and less sensitive to grid nonuniformities. Computations of flows and heat transfer in a plane channel, behind a step and in a round impinging jet show all satisfactory results.     

Experimental investigation of the grid-generated turbulence features in a free surface flow

The present study aims to investigate the features of a grid-generated turbulence occurring in a current flow with a free surface flow. The interest is focused on the length and time scales of the turbulence. These are the macro, the micro and the Kolmogorov scales. To analyze the flow, a 2D LDV system has been used to measure , , u′ and w′. This non-intrusive and optical technique is really accurate (in terms of space and time resolution). Furthermore, it does not disturb the flow and provides a high data rate. Both horizontal and vertical velocities are recorded at the same time according to a coincidence window (τ_cw). Bias measurements are avoided by using a filtering technique during data processing. The improved homogeneity and isotropy of the turbulence downstream of the grid allows the use of the Taylor hypothesis. Thus, all length and time scales of the flow can be estimated. Results are discussed as well as the influence of the upcoming mean velocity on the turbulence properties.     

Analysis for a screw dislocation accelerating through the shear-wave speed barrier

An analysis is performed for an accelerating screw dislocation through the shear-wave speed barrier. At this instant, the function that determines the interval of the path of the dislocation motion that contributes to the wave front has roots that change from a pair of complex conjugate to a double real, which subsequently splits into two real ones. The analysis is performed at this transition to supersonic that occurs at the double root maximum of the function that defines the interval of the dislocation path that contributes to the field points. It is found that the stress has a log|ξ-ξ^*|/|ξ-ξ^*|^1/2 singularity in the coefficient of the delta function of the forming Mach front, implying that for this phenomenon the Volterra dislocation model has too strong a discontinuity (step-function) in the displacement to be meaningful. A ramp-core displacement dislocation model analysis, which removes the singularity in the stress, is presented. These results can be useful in a multiscale dislocation dynamics modeling with inertia effects.     

Heat transfer from a line source located in the periodic laminar near wake of a circular cylinder

This experimental study is devoted to the diffusion of a passive scalar downstream a line source located in a Bénard–von Kármán street. Measurements of velocity and temperature have been performed using LDA and cold wire thermometer with a phase reference. Information on the initial evolution of mean, fluctuating velocity and temperature and associated shear-stresses and heat fluxes fields are presented for two locations of the source: ( and 1). The results show that the velocity field in the wake is strongly related to the geometric structure of vortices while the temperature field is controlled by both the time scale of rotation of the vortices and the location of the heated fluid within the vortex street.     

Predicting transition in two- and three-dimensional separated flows

This paper is concerned with the numerical prediction of two- and three-dimensional transitional separated flows of turbomachinery interest. The recently proposed single-point transition model based on the use of a laminar kinetic energy transport equation is considered, insofar as it does not require to evaluate any integral parameter, such as boundary-layer thickness, and is thus directly applicable to three-dimensional flows. A well established model, combining a transition-onset correlation with an intermittency transport equation, is also used for comparison. Both models are implemented within a Reynolds-averaged Navier–Stokes solver employing a low-Reynolds-number k–ω turbulence model. The performance of the transition models have been evaluated and tested versus well-documented incompressible flows past a flat plate with semi-circular leading edge, namely: tests T3L2, T3L3, T3L5, and T3LA1 of ERCOFTAC, with different Reynolds numbers and free-stream conditions, the last one being characterized by a non-zero pressure gradient. In all computations, the first model has proven as adequate as or superior to the second one and has been then applied with success to two more complex test cases, for which detailed experimental data are available in the literature, namely: the two- and three-dimensional flows through the T106 linear turbine cascade.     

Numerical prediction of locally forced turbulent separated and reattaching flow

An unsteady numerical simulation was performed for locally forced separated and reattaching flow over a backward-facing step. The local forcing was given to the separated and reattaching flow by means of a sinusoidally oscillating jet from a separation line. A version of the k––f_μ model was employed, in which the near-wall behavior without reference to distance and the nonequilibrium effect in the recirculation region were incorporated. The Reynolds number based on the step height (H) was fixed at Re_H=33 000, and the forcing frequency was varied in the range 0St_H2. The predicted results were compared and validated with the experimental data of Chun and Chun. It was shown that the unsteady locally forced separated and reattaching flows are predicted reasonably well with the k––f_μ model. To characterize the large-scale vortex evolution due to the local forcing, numerical flow visualizations were carried out.     

Conservation laws and reduction to quadratures of the generalized time-dependent duffing equation

The field-momentum method and the method of Hamilton and Jacobi are applied for finding the conservation laws and reduction to quadratures of the non-linear time-dependent equation

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where Q_i are constant parameters and f_i(t) are supposed to be power-type functions of time, that is, f_i(t) = t^k_i.     

Direct numerical simulations of two-layer viscosity-stratified flow

Two-dimensional simulations of flow instability at the interface of a two-layer, density-matched, viscosity-stratified Poiseuille flow are performed using a front-tracking/finite difference method. We present results for the small-amplitude (linear) growth rate of the instability at small to medium Reynolds number for varying thickness ratio n, viscosity ratio m, and wavenumber. We also present results for large-amplitude non-linear evolution of the interface for varying viscosity ratio and interfacial tension. For the linear case, the interfacial mode is neutrally stable for as predicted by analysis. The growth rate is proportional to Reynolds number for small Re, and increases with viscosity ratio. The growth rate also increases when the thickness of the more viscous layer is reduced. Strong non-linear behavior is observed for relatively large initial perturbation amplitude. The higher viscosity fluid is drawn out as a finger that penetrates into the lower viscosity layer. The simulated interface shape compares well with previously reported experiments. Increasing interfacial tension retards the growth rate of the interface as expected, whereas increasing the viscosity ratio enhances it. Drop formation at the small Reynolds number considered in this study is precluded by the two-dimensional nature of the calculations.     

On the stability of solutions of a non-linear, non-autonomous equation

Sufficient conditions for the stability of solutions of the equation

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are deduced. These conditions depend on coefficient ratios a/c and b/c as well as on initial conditions. As an example the pendulum of variable length is discussed.     

A study of two alternate tangent modulus formulations and attendant implicit algorithms for creep as well as high-strain-rate plasticity

Two alternate tangent modulus formulations based on the use of material characteristics expressed as

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, respectively, are prese for the analysis of material response under conditions such as high temperature creep and high strainrate dynamic plasticity. In each formulation, implicit algorithms of generalized midpoint radial mapping are presented to compute stress histories at a material point. Several examples to illustrate the stability, accuracy, and convergence of the presented computational methodologies are included. In each instance, the two alternate tangent modulus approaches lead to results of comparable accuracy and compare excellently with each other as well as other available independent solutions.     

Flow in a cylinder driven by rotating split-disk endwalls

Flow of an incompressible viscous fluid contained in a cylindrical vessel (radius R, height H) is considered. Each of the cylinder endwalls is split into two parts which rotate steadily about the central axis with different rotation rates: the inner disk (r < r₁) rotating at Ω₁, and the outer annulus (r₁ < r < R) rotating at Ω₂. Numerical solutions to the axisymmetric Navier-Stokes equations are secured for small system Ekman numbers E ( v/(ΩH²)). In the linear regime, when the Rossby number Ro

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, the numerical results are shown to be compatible with the theoretical prediction as well as the available experimental measurements. Emphasis is placed on the results in the nonlinear regime in which Ro is finite. Details of the structures of azimuthai and meridional flows are presented by the numerical results. For a fixed Ekman number, the gross features of the flow remain qualitatively unchanged as Ro increases. The meridional flows are characterized by two circulation cells. The shear layer is a region of intense axial flow toward the endwall and of vanishing radial velocity. The thicknesses of the shear layer near r = r₁ and the Ekman layer on the endwall scale with E and E , respectively. The numerical results are consistent with these scalings.