One-dimensional Plane Research Articles

Acoustic flowmeter for the measurement of the mean flow velocity in pipes.

This paper proposes a new technique for measuring the gas flow velocity averaged along the finite length of a pipe as well as over its cross-sectional area. Unlike the conventional gas flowmeters, the proposed technique exploits the one-dimensional plane waves that propagate uniformly across the pipe cross-sectional area. When a fluid flows along the pipe, the plane waves are superposed with the flow field such that the positive-going and negative-going plane wave components undergo the change of their wave numbers. Such wave number variation due to the mean flow velocity has provided a major motivation for developing a new way of measuring the mean flow velocity in the pipe, which is referred to as the acoustic flowmeter. To examine the feasibility of the developed flow velocity measurement method, including its theoretical backgrounds, experimental setups are illustrated in this paper. Detailed experimental data for the flow velocity range of 2-27 m/s reveal the linearity of the proposed acoustic flowmeter and its salient environmental robustness for the different acoustic pressure patterns in the pipe and, furthermore, for different velocity profiles over the pipe cross-section area.

Fundamental Research on Multiresolution Time Domain Scheme and Its Applications

In this paper, we have made fundamental investigation on a generalized multiresolution time domain (MRTD) scheme on the basis of the cubic spline Battle?Lemarie scaling and high-level resolution wavelet function expansions for electromagnetic applications. Focusing on a one-dimensional electromagnetic plane wave propagation problem, we summarize generalized orthogonal and semiorthogonal relations used for deriving MRTD updating equations. In this research, we employ high-level wavelets only in the extended discontinuity subregions where electromagnetic fields vary dramatically, while utilizing a scaling function in the entire computational region. It is found that the computed data is in good agreement with the analytic results and the finite difference time domain (FDTD) solutions for all cases investigated.

Neutron transport problems in anisotropic media

In nuclear reactor physics, neutron transport in media having anisotropic properties is of interest in modelling largely voided configurations, such as boiling-water and gas-cooled reactors. In order to treat such problems, neutronic methods need to be extended and adapted. The present work is devoted to the solution of transport problems for materials in which cross-sections are dependent on the direction of motion of the neutrons. A simple one-dimensional plane configuration is assumed, in order to be able to obtain analytical solutions and to gain physical insight into the transport phenomenon. Results can thus be considered as benchmarks for numerical algorithms employed in realistic cases.

Aluminum foam integral armor: a new dimension in armor design

Closed-cell aluminum foam offers a unique combination of properties such as low density, high stiffness, strength and energy absorption that can be tailored through design of the microstructure. During ballistic impact, the foam exhibits significant non-linear deformation and stress wave attenuation. Composite structural armor panels containing closed-cell aluminum foam are impacted with 20-mm fragment-simulating projectiles (FSP). One-dimensional plane strain finite element analysis (FEA) of stress wave propagation is performed to understand the dynamic response and deformation mechanisms. The FEA results correlate well with the experimental observation that aluminum foam can delay and attenuate stress waves. It is identified that the aluminum foam transmits an insignificant amount of stress pulse before complete densification. The ballistic performance of aluminum foam-based composite integral armor (CIA) is compared with the baseline integral armor of equivalent areal-density by impacting panels with 20-mm FSP. A comparative damage study reveals that the aluminum foam armor has finer ceramic fracture and less volumetric delamination of the composite backing plate as compared to the baseline. The aluminum foam armors also showed less dynamic deflection of the backing plate than the baseline. These attributes of the aluminum foam in integral armor system add a new dimension in the design of lightweight armor for the future armored vehicles.

Fourier-space properties of photon-limited noise in focal plane array data, calculated with the discrete Fourier transform

The Fourier-space statistical properties of one-dimensional or two-dimensional focal plane array data subject only to photon-counting noise are investigated theoretically by using the discrete Fourier transform. Signal-to-noise ratios and probability density functions for the noise and for the components of the Fourier transform are presented for two cases: when the Fourier transform itself is considered to be the signal and when the power spectrum is considered to be the signal.

BRAKE VIBRATION ANALYSIS WITH THREE-DIMENSIONAL PULSED ESPI

The measurement of brake squeal vibrations is a serious problem, because the rotating disc does not allow any physical contact with the sample during measurement. When using non contact scanning techniques (e.g. vibrometers) still problems occur if non steady vibrations are present. Furthermore, the recent interest of researchers has focused not only on the onedimensional out-of plane deformation, but on the determination of the three-dimensional vibration behavior, especially the analysis of the in-plane component of the vibration. PulsESPI has already been presented as non contact and full tield measuring technique, which provides complete maps of the vibration of any component of the brake during test. Brake discs, drums, calipers, pads have been measured with this technique. The component under investigation -e.g. a rotating brake disc with engaged caliper is illuminated by two very short laser pulses with a predetermined time separation. The images at these two laser illuminations are recorded with a special high speed camera (PulsESPI camera) and analyzed in a computer. The calculated result is a deformation map of each point of the brake disc and caliper which describes the movement of the individual points of the brake between these two laser pulses. Therefore, this technique literally freezes two moments of the movement of the brake and gives an instantaneous view of the overall deformation. Recent developments have produced 3D-PulsESPI systems, which provide the complete three-dimensional vibration map of the brake. Special algorithms are used in order to separate the rotation component of the brake disc from the in-plane vibrations. Using this 3D-PulsESPI technique completely automatic brake squeal inspection systems have been designed, which capture the squealing signal, automatically fire the laser and provide the complete deformation map of the component under test. In this paper, we describe this promising new PulsESPI technique and give examples of recent applications in the field of brake squeal analysis.

Finite parts of singular and hypersingular integrals with irregular boundary source points

The subject of this paper is the evaluation of finite parts (FPs) of certain singular and hypersingular integrals, that appear in boundary integral equations (BIEs), when the source point is an irregular boundary point (situated at a corner on a one-dimensional plane curve or at a corner or edge on a two-dimensional surface). Two issues addressed in this paper are: an unified, consistent and practical definition of a FP with an irregular boundary source point, and numerical evaluation of such integrals together with solution strategies for hypersingular BIEs (HBIEs). The proposed formulation is compared with others that are available in the literature and interesting connections are made between this formulation and those of other researchers.

An Integral Formulation of Transient Radiative Transfer

A time-dependent integral formulation is developed for modeling transient radiative transfer. The development is based on a rigorous analysis of the wave propagation process inside the participating media. The physical significance of the present integral formulation is the consideration of the time-dependent domain of computation, which is different from the domain disturbed by radiation (i.e., the wave front envelope). Numerical computations are performed for the medium that is an absorbing and isotropically scattering one-dimensional plane slab geometry. The spatial and temporal incident radiation and radiative flux distributions are presented for different boundary conditions and for uniform and nonuniform property distribution. The transient results at large time step are compared with steady-state solutions by the finite volume and quadrature methods and show excellent agreement. The solutions of reflecting boundary condition exhibit distinctive behavior from that of the non-reflecting boundary.

A boundary-element analysis for transient viscoelastic blade coating flow

The one-dimensional plane Couette flow is first determined for a large class of Oldroyd fluids with added viscosity, which typically represent polymer solutions composed of a Newtonian solvent and a polymeric solute. Next, the determined channel velocity profile is used as the boundary condition at the channel exit for the blade coating flow. The free-surface evolution of the flow at the channel exit is simulated using the boundary element method. It is argued that the free surface flow can be assumed to be Newtonian. For the channel flow, the problem is reduced to a non-linear dynamical system using the Galerkin projection method. Stability analysis indicates that the velocity profile at the inlet may be linear or non-linear depending on the range of the Weissenberg number.

On the Spectral Problems for the Discrete Boltzmann Models

The discrete Boltzmann models are used to study the spectral problems related to the one-dimensional plane wave propagation in monatomic gases which are fundamental in the nonequilibrium statistical thermodynamics. The results show that the 8-velocity model can only describe the propagation of the diffusion mode (entropy wave) in the intermediate Knudsen number regime. The 4- and 6-velocity models, instead, can describe the propagation of sound modes quite well, after comparison with the continuum-mechanical results.

Time resolved friction during dry sliding of metal on metal

In the present study, plate impact pressure–shear friction experiments are conducted to provide insight into time-resolved dry sliding characteristics of metal on metal at normal pressures of approximately 1.5 GPa, slip speeds up to 60 m/s and interfacial temperatures as high as 800°C. The plate impact friction experiments represent a significant improvement over conventional dynamic friction experiments by allowing control of interfacial tractions with the use of combined pressure–shear loading waves instead of manipulating actuator motion. Also, by measuring the combined normal and transverse motion of the rear surface of the target plate, critical frictional parameters such as the applied normal pressure, the interfacial slip resistance, and the interfacial slip speeds can be interpreted by using the framework of one-dimensional plane wave analysis. The experiments are conducted on a Carpentor Hampden tool-steel (D3)/Ti–6Al–4V tribo-pair. The frictional state at the tribo-pair interface is varied by varying the impact velocity and/or the surface roughness of the impacting surfaces. Moreover, by appropriate selection of flyer and target plate thickness the tribo-pair interface is subjected to step changes in normal pressure and step changes in applied shear stress. The results of these experiments provide new insights into the evolution of interfacial sliding resistance with accumulated interfacial slip, and its dependence on surface roughness, slip velocity, normal pressure and interfacial temperature.

A mechanism for extrusion instabilities in polymer melts

AbstractA mechanism for explaining some of the instabilities observed during the extrusion of polymer melts is further explored. This is based on the combination of non‐monotonic slip and elasticity, which permits the existence of periodic solutions in viscometric flows. The time‐dependent, incompressible, one‐dimensional plane Poiseuille flow of an Oldroyd‐B fluid with slip along the wall is studied using a non‐monotonic slip equation relating the shear stress to the velocity at the wall. The stability of the steady‐state solutions to one‐dimensional perturbations at fixed volumetric flow rateis analyzed by means of a linear stability analysis and finite element calculations. Self‐sustained periodic oscillations of the pressure gradient are obtained when an unstable steady‐state is perturbed, in direct analogy with experimental observations.

Numerical study of initial pulsed motion of a powder layer in a duct under the action of a compressed gas

One-dimensional plane pulsed joint motion of a gas phase and a disperse phase in the presence of friction of the latter against the duct walls are studied numerically using the model of a heterogeneous medium. It is established that two qualitatively different regimes of motion are possible, depending on the initial conditions in a high-pressure chamber and the value of the friction factor. It is found that the powder exit velocity is self-similar with respect to friction.

Finite-Amplitude Elastic Instability of Plane-Poiseuille Flow of Viscoelastic Fluids

The purely elastic stability and bifurcation of the one-dimensional plane Poiseuille flow is determined for a large class of Oldroyd fluids with added viscosity, which typically represent polymer solutions composed of a Newtonian solvent and a polymeric solute. The problem is reduced to a nonlinear dynamical system using the Galerkin projection method. It is shown that elastic normal stress effects can be solely responsible for the destabilization of the base (Poiseuille) flow. It is found that the stability and bifurcation picture is dramatically influenced by the solvent-to-solute viscosity ratio, ε. As the flow deviates from the Newtonian limit and ε decreases below a critical value, the base flow loses its stability. Two static bifurcations emerge at two critical Weissenberg numbers, forming a closed diagram that widens as the level of elasticity increases. [S0021-8936(00)00703-0]

Simulation of shock waves in ferrite-loaded coaxial transmission lines with axial bias

A novel model is presented for shock wave development in axially-biased ferrite-loaded coaxial lines. The one-dimensional transverse electromagnetic plane wave equations for the coaxial line are linked to the three-dimensional Landau-Gilbert gyromagnetic equation describing the coherent ferrite magnetization process. The effects of demagnetization field terms imposed by the ferrite and coaxial line geometry are identified. Numerical time-stepping solution gives the predicted transmission line waveforms directly in the time domain. Simulated and experimental waveforms are compared for a nickel-zinc ferrite-loaded coaxial pulse-sharpening line. The model is shown to give generally good results for the shock front waveform, rise time and propagation characteristics, except that predicted and measured rise times diverge increasingly at very low pulse amplitudes.

Photorefractive two-beam coupling equations with multiple spatial-temporal features: an SVD approach

We analyze the evolution of multi-feature two-beam coupling, wherein each beam contains several spatial–temporal features (spatial patterns modulated by different signals), using a one-dimensional plane wave model to describe the evolution of paired components. This general scenario is of interest for analyzing signal-processing applications of photorefractives, such as source-separation by orthogonalization of source-modulated spatial patterns. We use singular-value decomposition (SVD) to express each beam as a simple superposition of modes that are both temporally uncorrelated and spatially orthogonal. We find a solution that is a natural matrix generalization of the scalar solution for simple two-beam coupling, and a test for its validity: the two operators that give the spatial overlap associated with the temporal basis signals in the two beams must commute. Equivalently, this means that the same set of signals must be modulating the SVD modes in the two beams. Then the SVD modes are preserved in the two-beam coupling evolution, with only their amplitudes changing.

A one-dimensional CMOS focal plane array for Gabor-type image filtering

We describe the design, implementation, and test results from an analog complementary metal-oxide-semiconductor very large scale integration (CMOS VLSI) chip which combines photosensing and an image filtering operation similar to Gabor filtering. The chip contains a one-dimensional (1-D) 27-pixel array and generates three outputs at every pixel; the input image intensity and the real and imaginary parts of the filter output. These results validate experimentally a recently presented theoretical framework for the design of cellular neural network (CNN) templates for Gabor-type spatial image filtering.

Frictional Response of Sliding Interfaces Subjected to Time Varying Normal Pressures

In the present investigation a plate-impact pressure shear loading device is employed to study frictional characteristics of sliding interfaces subjected to step changes in normal pressure. The present experimental configuration represents a significant improvement over the conventional tribology experiments by allowing the control of interfacial tractions through the use of pressure-shear loading waves instead of manipulating actuator motion. Moreover, the experimental configuration allows critical frictional parameters such as the applied normal pressure, the interfacial slip resistance, and the interfacial slip velocity to be interpreted by using the framework of one-dimensional plane wave analysis. The experimental results, deduced from the response to step changes imposed on the normal pressure at the frictional interface, reinforce the importance of including frictional memory in the development of the rate-dependent state variable friction models. The scope of the above experiments include technologically important combinations of workpiece materials such as 4340VAR structural steel and a commercially available titanium alloy (Ti-6Al-4V), and tool materials such as tungsten based tool cermets (WC-Co alloys).

Time-Resolved Friction with Applications to High-Speed Machining: Experimental Observations

Pressure-shear plate impact experiments are conducted to study the kinetics of friction on a submicrosecond time scale. The configuration offers the simplicity of allowing the interpretation of the experimental results by using the framework of one-dimensional plane wave analysis. To address the problem of high-speed machining, one of the impacting plates is chosen to correspond to a wear-resistant grade of tungsten-carbide tool material and the other to a commercial-grade titanium alloy (Ti-6Al-4V). The interfacial conditions are varied from sticking to slipping by varying the angle of impact and/or the surface roughness. Also, within a single experiment, transitions from conditions of fully sticking to intermittent, to full sliding are introduced by subjecting the interface to step changes in normal pressure. The experimentally obtained time-resolved frictional response of the interface is used to examine the role of the interfacial normal pressure, slip velocity, slip distance, and surface roughness in governing the interfacial slip resistance. Presented at the 52nd Annual Meeting In Kansas City, Missouri May 18–22, 1997

Self-focusing and solitonlike structures in materials with competing quadratic and cubic nonlinearities

We study the mutual influence of quadratic and cubic nonlinearities on the propagation of the coupled fundamental and second harmonic waves in asymmetric optical media. For attractive potentials with positive coupling parameters, it is shown that, in systems with two and three transverse dimensions, mutually trapped waves can self-focus until collapse whenever their respective powers exceed some thresholds. On the contrary, coupled waves diffracting in a one-dimensional plane never collapse and may evolve towards stable solitonlike structures. For higher transverse dimension numbers, we investigate the question of forming two-component solitons and determine criteria for their stability.