Analysis of shock wave reflection from fixed and moving boundaries using a stabilized particle method

In the present paper, the efficiency of an enhanced formulation of the stabilized corrective smoothed particle method （CSPM） for simulation of shock wave propagation and reflection from fixed and moving solid boundaries in compressible fluids is investigated. The Lagrangian nature and its accuracy for imposing the boundary conditions are the two main reasons for adoption of CSPM. The governing equations are further modified for imposition of moving solid boundary conditions. In addition to the traditional artificial viscosity, which can remove numerically induced abnormal jumps in the field values, a velocity field smoothing technique is introduced as an efficient method for stabilizing the solution. The method has been implemented for one- and two-dimensional shock wave propagation and reflection from fixed and moving boundaries and the results have been compared with other available solutions. The method has also been adopted for simulation of shock wave propagation and reflection from infinite and finite solid boundaries.     

Efficient modelling of particle collisions using a non-linear viscoelastic contact force

In this paper the normal collision of spherical particles is investigated. The particle interaction is modelled in a macroscopic way using the Hertzian contact force with additional linear damping. The goal of the work is to develop an efficient approximate solution of sufficient accuracy for this problem which can be used in soft-sphere collision models for Discrete Element Methods and for particle transport in viscous fluids. First, by the choice of appropriate units, the number of governing parameters of the collision process is reduced to one, which is a simple combination of known material parameters as well as initial conditions. It provides a dimensionless parameter that characterizes all such collisions up to dynamic similitude. Next, a rigorous calculation of the collision time and restitution coefficient from the governing equations, in the form of a series expansion in this parameter is provided. Such a calculation based on first principles is particularly interesting from a theoretical perspective. Since the governing equations present some technical difficulties, the methods employed are also of interest from the point of view of the analytical technique. Using further approximations, compact expressions for the restitution coefficient and the collision time are then provided. These are used to implement an approximate algebraic rule for computing the desired stiffness and damping in the framework of the adaptive collision model (Kempe and Fröhlich, J. Fluid Mech. 709: 445–489, 2012). Numerical tests with binary as well as multiple particle collisions are reported to illustrate the accuracy of the proposed method and its superiority in terms of numerical efficiency.     

A laser induced fluorescence technique for quantifying transient liquid fuel films utilising total internal reflection

This paper describes the development of a laser induced fluorescence (LIF) technique to quantify the thickness and spatial distribution of transient liquid fuel films formed as a result of spray–wall interaction. The LIF technique relies on the principle that upon excitation by laser radiation the intensity of the fluorescent signal from a tracer like 3-pentanone is proportional to the film thickness. A binary solution of 10% (v/v) of 3-pentanone in iso-octane is used as a test fuel with a Nd:YAG laser as the excitation light source (utilising the fourth harmonic at wavelength 266 nm) and an intensified CCD camera is used to record the results as fluorescent images. The propagation of the excitation laser beam through the optical piston is carefully controlled by total internal reflection so that only the fuel film is excited and not the airborne droplets above the film, which had been previously shown to induce significant error. Other known sources of error are also carefully minimised. Calibrated temporally resolved benchmark results of a transient spray from a gasoline direct injector impinging on a flat quartz crown under atmospheric conditions are presented, with observations and discussion of the transient development of the fuel film. The calibrated measurements are consistent with previous studies of this event and demonstrate the applicability of the technique particularly for appraisal of CFD predictions. The potential utilisation of the technique under typical elevated ambient conditions is commented upon.     

An optical study of thin interfacial liquid films using total reflection of light

The light totally reflected at the interface between a glass prism and a liquid (water) of lower index can be partly transmitted as a droplet of liquid of larger index (oil) approaches this interface. By using the variation of the reflected intensity, one can study the static structure and the thickness variation of the intermediate water film in a range of thickness of a few 10 Å to 10² Å. A preliminary experiment is presented together with the optical technique.     

Near-wall hindered Brownian diffusion of nanoparticles examined by three-dimensional ratiometric total internal reflection fluorescence microscopy (3-D R-TIRFM)

A three-dimensional nanoparticle tracking technique using ratiometric total internal reflection fluorescence microscopy (R-TIRFM) is presented to experimentally examine the classic theory on the near-wall hindered Brownian diffusive motion. An evanescent wave field from the total internal reflection of a 488-nm bandwidth argon-ion laser is used to provide a thin illumination field on the order of a few hundred nanometers from the wall. Fluorescence-coated polystyrene spheres of 200±20 nm diameter (specific gravity=1.05) are used as tracers and a novel ratiometric analysis of their images allows the determination of fully three-dimensional particle locations and velocities. The experimental results show good agreement with the lateral hindrance theory, but show discrepancies from the normal hindrance theory. It is conjectured that the discrepancies can be attributed to the additional hindering effects, including electrostatic and electro-osmotic interactions between the negatively charged tracer particles and the glass surface.

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Numerical simulations of shock wave reflection phenomena in non-stationary flows using regularized smoothed particle hydrodynamics (RSPH)

In this paper we wish to demonstrate to what extent the numerical method regularized smoothed particle hydrodynamics (RSPH) is capable of modelling shocks and shock reflection patterns in a satisfactory manner. The use of SPH based methods to model shock wave problems has been relatively sparse, both due to historical reasons, as the method was originally developed for studies of astrophysical gas dynamics, but also due to the fact that boundary treatment in Lagrangian methods may be a difficult task. The boundary conditions have therefore been given special attention in this paper. Results presented for one quasi-stationary and three non-stationary flow tests reveal a high degree of similarity, when compared to published numerical and experimental data. The difference is found to be below 5, in the case where experimental data was found tabulated. The transition from regular reflection (RR) to Mach reflection (MR) and the opposite transition from MR to RR are studied. The results are found to be in close agreement with the results obtained from various empirical and semi-empirical formulas published in the literature. A convergence test shows a convergence rate slightly steeper than linear, comparable to what is found for other numerical methods when shocks are involved.     

The total reflection of a sound pulse of arbitrary form

The problem of a sound pulse of arbitrary form incident on a half space with an angle of incidence greater than the critical angle is discussed. Formulae are obtained for the transmitted and reflected pressure fields. An expression is obtained for the energy flux across the interface, and it is shown that the net energy flow per unit area over all time is zero.     

Evaluation of effervescent atomizer internal design on the spray unsteadiness using a phase/Doppler particle analyzer

The purpose of this research was to investigate the dependence of effervescent spray unsteadiness on operational conditions and atomizer internal design by the ideal spray theory of Edwards and Marx. The convergent–divergent effervescent atomizer spraying water with air as atomizing medium in the “outside-in” gas injection was used in this study. Results demonstrated that droplet formation process at various air to liquid ratio (ALR) led to the spray unsteadiness and all droplet size classes exhibited unsteadiness behavior in spray. The spray unsteadiness reduced quickly at ALR of 3% and decreased moderately at ALR of other values as the axial distance increased. When the axial distance was 200 mm, the spray unsteadiness reduced dramatically with the increase in radial distance, but lower spray unsteadiness at the center of spray and higher spray unsteadiness at the edge of spray were shown as the axial distance increased. The spray unsteadiness at the center region of spray increased with the injection pressure. Low spray unsteadiness and good atomization performance can be obtained when the diameter of incline aeration holes increased at ALR of 10%. Although short mixing chamber with large discharge orifice diameter for convergent–divergent effervescent atomizer produced good atomization, the center region of spay showed high spray unsteadiness and maybe formed the droplet clustering.     

The effect of total reflection in PLIF imaging of annular thin films

Planar laser-induced fluorescence (PLIF) imaging techniques are increasingly used to study wavy annular flows in vertical and horizontal pipes. We present a ray-tracing study that analyzes the imaging properties of the PLIF technique for uniform and wavy annular films. Part of the emitted fluorescence will hit the water–air interface at angles greater than the critical angle of total reflection. As a consequence, PLIF imaging probes the film twice: From bottom to top and then again from top to bottom. Deflected fluorescence widens PLIF images of uniform films by about 30%. Surface waves further increase the contribution of deflected rays to the overall signal. At the steep slopes of large amplitude axial waves, total reflection might widen PLIF signals by up to a factor of two.     

A critical overview of internal and external cylinder contact force models

Most of the analytical models found in the literature, to study the contact between cylindrical bodies, are based on the Hertz pressure distribution. The major shortcomings associated with these cylindrical models concern their nonlinearity. Firstly, the indentation is expressed as an implicit function of the contact force, thus a numerical iterative technique is required to evaluate the contact force for a given indentation. In a dynamic analysis code, it is implied that at each integration time step, the iterative process for the solution of the nonlinear equations has to be solved. Secondly, the current cylindrical contact models include logarithmic functions, which impose mathematical and physical limitations on their application, particularly for conformal contact conditions with lower clearance values. The validity domain of each contact model is identified in this work with relation to the clearance value and material properties of the contacting cylinders. A comparative assessment of the performance of each model is performed calculating the relative difference of each one in relation to Johnson’s model. The results show that, in general, different models exhibit distinct behavior for both the internal and external contact between cylinders. The load limit of each model and the restrictions on its application is identified using two simple examples of mechanical engineering practice in which internal contacting cylinders are involved and analyzed to include: journal bearings and roller chain drives.     

Hydrodynamic resistance of a spheroidal particle with uniform internal heat release

The Stokes approximation is used to describe the stationary motion of a heated hydrosol spheroidal particle in a viscous incompressible liquid in which internal, uniformly distributed heat sources (sinks) of constant capacity act. It was assumed that the average particle surface temperature could differ significantly from the temperature of the ambient liquid. An analytical expression for the hydrodynamic force acting on the uniformly heated spheroidal particle was obtained by solving hydrodynamic equations with the temperature dependence of the viscosity represented as an exponential power series.     

Modified smoothed particle hydrodynamics approach for modelling dynamic contact angle hysteresis

Dynamic wetting plays an important role in the physics of multiphase flow, and has a significant influence on many industrial and geotechnical applications. In this work, a modified smoothed particle hydrodynamics (SPH) model is employed to simulate surface tension, contact angle and dynamic wetting effects at meso-scale. The wetting and dewetting phenomena are simulated in a capillary tube, where the liquid particles are raised or withdrawn by a shifting substrate. The SPH model is modified by introducing a newly developed viscous force formulation at the liquid-solid interface to reproduce the rate-dependent behaviour of the moving contact line. Dynamic contact angle simulations with the interfacial viscous force are conducted to verify the effectiveness and accuracy of this new formulation. In addition, the influence of interfacial viscous forces with different magnitude on the contact angle dynamics is examined by empirical power-law correlations;the derived constants suggest that the dynamic contact angle changes monotonically with the interfacial viscous force. The simulation results are consistent with experimental observations and theoretical predictions, implying that the interfacial viscous force can be associated with the slip length of flow and the microscopic surface roughness. This work demonstrates that the modified SPH model can successfully account for the rate-dependent effects of a moving contact line, and can be used for realistic multiphase flow simulations under dynamic conditions.     

Two-color particle image velocimetry technique for an internal combustion engine

A two-color particle image velocimetry (PIV) technique has been applied to a single-cylinder motored research engine. Two-color PIV is a quantitative planar velocity measurement technique that can unambiguously determine the velocity magnitude and direction.

The work includes the development of an interrogation system, a series of computer simulations to determine the performance of the technique under various conditions, the comparison of these results to similar ones obtained for an autocorrelation PIV system, and a test of the technique by reconstructing the velocity field of a uniform jet flow.

The technique was then applied to the in-cylinder flow field of a motored single-cylinder, cup-in-head, research engine. A total of 27 instantaneous velocity fields were obtained at a single measurement plane for a single operating condition of the engine. The data were analyzed to yield ensemble-averaged velocity and velocity fluctuation.     

Analysis of the adhesive contact of confined layers by using a Green's function approach

The authors develop a numerical procedure to analyze the adhesive contact between a soft elastic layer and a rough rigid substrate. The solution of the problem, which belongs to the class of the free boundary problems, is obtained by calculating the Green's function which links the pressure distribution to the normal displacements at the interface. The problem is then formulated in the form of a Fredholm integral equation of the first kind with a logarithmic kernel, and the boundaries of the contact area are calculated by requiring that the energy of the system is stationary. The methodology is relatively simple and easy to implement in a numerical code. It has been utilized to analyze the adhesive properties of a confined layer in contact with a wavy rigid substrate as a function of thickness, applied stress or penetration. It is shown that reducing the thickness of the slab reduces the effective energy of adhesion, i.e. the work needed to separate the bodies, but nevertheless increases the adherence force between the slab and the substrate. However, thinning the slab also increases the confinement of the system and therefore increases the negative hydrostatic pressure in the layer. This, in turn, may produce cavitation. When this happens the rupture of the adhesive bond does not occur through interfacial crack propagation but, by the growth of new interfacial voids or cavities.     

新型声子晶体全反射贯穿效应的滤波特性

利用转移矩阵法计算了弹性波在大于全反射角入射一维声子晶体的透射率,结果发现：在入射角岛为0．33rad、0．4rad、0．9rad、1．3rad附近都出现了明显的透射峰带,即在透射波中出现了全反射贯穿效应;其中在0．4rad附近的这个透射峰带的频率范围小、峰值细密,可以利用它来实现多通道滤波。同时研究了贯穿效应随介质厚度和周期数的变化特征,发现贯穿效应具有优良的滤波特性。利用这些特性可以设计出结构简单、控制方便的新型一维声子晶体的滤波器。     

Analysis of the flow in inhomogeneous particle beds using the spatially averaged two-fluid equations

The drag force term appearing in two-fluid models for fluid–particle flows is commonly closed by expressing it as a function of the local quantities, such as the local particle volume fraction, the local slip velocity between the particle and fluid phases, and the local mean-squared fluctuating velocity of the particles. The adequacy of such closures for inhomogeneous suspensions has been debated in the literature and some researchers have suggested the need for additional terms involving spatial gradients in these quantities. To test this proposition, simulations of flow in inhomogeneous steady beds of particles have been performed using the lattice-Boltzmann method. The particle beds consisted of disordered assemblies with a density profile on a scale much larger than the particle radius. Inhomogeneous beds with a controlled density profile were generated in three different ways, (i) by inhomogeneous stretching of the particle bed in one direction, (ii) by applying an inhomogeneous force to the particle phase during random motion of the particles, and (iii) by taking snapshots of a direct simulation of a traveling wave in a fluidization simulation. The global structure of the three beds was comparable, while assessment of the radial distribution functions showed that the three beds exhibited clearly different microscopic structures.