Small Nonuniformity Research Articles

The wall-pressure spectrum in turbulent flow over a randomly inhomogeneous elastic solid

The characteristics of the low-wave-number and acoustic domains of the turbulent boundary layer wall-pressure spectrum are critically dependent on the structural properties of the wall. This dependence is examined in this paper in terms of a theoretical model of turbulent flow of water over an elastomeric material containing a random distribution of rigid (but movable) filaments. The interaction of hydrodynamic, convective boundary layer pressure fluctuations with the filaments generates a secondary pressure field by scattering. The intensities of the secondary pressures are negligible compared to the convective pressures responsible for their generation, but may nonetheless be large enough to produce significant changes in the relatively weak, low-wave-number region of the wall pressure. The magnitude of the changes depends on the relative mass density of the material of the filaments, on their diameters relative to the boundary layer thickness, and on their fractional volume density. Numerical results indicate that increases of the order of 10–20 dB (compared to theoretical estimates for the homogeneous elastomer) can be produced by filaments occupying only 1% by volume of the elastomer. Predictions of this kind suggest that experimental data relating to the low-wave-number and acoustic domains are easily contaminated by the presence of relatively small nonuniformities in wall properties.

Criticality in reactors under domain or external temperature perturbations

The conditions for the onset of thermal runaway in reactors with small non-uniformities is investigated. The reaction is modelled by an Arrhenius heat generation term with a finite activation energy and the dimensionless temperature,u0, is taken to satisfy a nonlinear equation of the form Δu0+λ0F(u0) = 0,x∈D; ∂vu0+bu0= 0.xϵ∂D. We investigate three classes of perturbations of this problem. First, we treat a small temperature variation maintained on the boundary of the domain. Secondly, we consider a small distortion of the boundary of a circular cylindrical domain, and thirdly, we analyse the effect of a small hole in the domain. In each case we derive asymptotic expansions for the critical Frank-Kamenetskii parameter,λc(ϵ), whereϵis a measure of the size of the perturbation. A numerical scheme is then used to determine numerical values for the coefficients in the asymptotic expansion ofλc. Finally, some of the asymptotic results are compared with corresponding numerical results obtained from a full numerical solution of the perturbed problem.

Critical examination of the uniformity requirements for single‐photon emission computed tomography

It is generally recognized that single-photon emission computed tomography (SPECT) imposes very stringent requirements on gamma camera uniformity to prevent the occurrence of ring artifacts. The purpose of this study was to examine the relationship between nonuniformities in the planar data and the magnitude of the consequential ring artifacts in the transaxial data, and how the perception of these artifacts is influenced by factors such as reconstruction matrix size, reconstruction filter, and image noise. The study indicates that the relationship between ring artifact magnitude and image noise is essentially independent of the acquisition or reconstruction matrix sizes, but is strongly dependent upon the type of smoothing filter applied during the reconstruction process. Furthermore, the degree to which a ring artifact can be perceived above image noise is dependent on the size and location of the nonuniformity in the planar data, with small nonuniformities (1-2 pixels wide) close to the center of rotation being less perceptible than those further out (8-20 pixels). Small defects or nonuniformities close to the center of rotation are thought to cause the greatest potential corruption to tomographic data. The study indicates that such may not be the case. Hence the uniformity requirements for SPECT may be less demanding than was previously thought.

Differential thermal analysis of individual specimens by thermal EMF measurement

The thermal electromotive force (EMF) generated across a specimen owing to a small nonuniformity in the sample’s temperature is used to follow phase transitions in the specimen. As the temperature is scanned, a first-order phase transition yields a sharp S-shaped peak in the EMF versus time, t, and temperature, T(t), curves. A transition to a superconducting state exhibits a sharp drop in EMF as was observed during measurements on YBa2Cu3O7. The dependence of the EMF on time and temperature is calculated for a first-order phase transition. Predictions are confirmed by experiment. This method is therefore useful for detecting phase transition temperatures. A practical feature of this measurement is the ability to precisely calibrate, in situ, the temperature measuring element, e.g., thermometer or thermocouple, when the transition temperature is already known.

Experimental Investigation of Morel’s Method for Wind Tunnel Contractions

Based on a numerical study of the potential flow through contractions of chosen geometry, Morel (1975) has given a method to obtain the shape of contraction which gives small adverse pressure gradients and low nonuniformity in the velocity distribution at the exit. Two contractions with area ratios of 12 and 3.464 designed using this method are investigated experimentally. It is found that there is no separation of flow, the thickness of the boundary layer at the exit is small and the nonuniformity in velocity at the exit is smaller than the predicted value.

Dose distributions in regions containing beta sources: small scale nonuniformities.

An analytic model for the calculation of dose in regions containing slightly nonuniform distributions of beta sources, and a solution for the dose distribution in an infinite, homogeneous medium with a uniform, monoenergetic source distribution and a sinusoidal perturbation of the source are presented.

Study of the two-domain processing structure in the superfluid3He-B

The systematic experimental and theoretical investigation of the longlived induction signal, known to exist in the3He-B, has shown that even very small nonuniformity of a steady magnetic fieldH0 changes qualitatively the precession pattern arising in the pulsed NMR experiments after tipping of the magnetization. The spin supercurrents redistribute magnetization within the experimental cell to produce the precessing structure, consisting of two domains. In one-domain, situated in the higher field region, magnetizationM has its equilibrium value and is parallel toH0. In the other domain the angle betweenM andH0 is slightly larger thanϑ0=arc cos (−1/4). The structure precesses with frequency, equal to the Larmor frequency at the site of the wall, separating the domains. The relaxation of this structure goes via the growth of the equilibrium domain at the expense of the precessing domain; therefore in the course of the relaxation the frequency of the precession has to decrease with time. The calculated rate decrease agrees with the observed value. Experiments were carried out directly demonstrating the existence of the two-domain structure.

Heat transfer in an unevenly heated porous layer

For a uniform saturated porous layer heated from below, the dependence of the quantity of heat transferred on the distribution of the heat source is investigated. It is found, using perturbation methods and numerical techniques, that very small nonuniformities in the heat source having the same wavelength as the preferred convection mode significantly reinforce natural convection.

Effects of Ambient Pressure on the Instability of a Liquid Boiling Explosively at the Superheat Limit

The effect of ambient pressure on the intrinsic instability of rapid vaporization in single droplets boiling explosively at the limit of superheat has been studied experimentally and theoretically. The instability that distorts the evaporating interface and substantially enhances the mass flux at atmospheric pressure is suppressed at high pressure. The radiated pressure field is two orders of magnitude smaller from stabilized bubbles than from unstable. At intermediate pressures bubble growth occurs in two stages, first stable, then unstable. The Landau–Darrieus instability theory predicts absolute stability at atmospheric pressure for a spherical bubble, whereas the theory for planar interfaces yields results in general agreement with observation. The sensitivity of the instability to temperature suggests that small temperature nonuniformities may be responsible for quantitative departures of the behavior from predictions.

The convergent effect of the annealing temperatures of electron irradiated defects in FZ silicon grown in hydrogen : Qin Guogang and Hua Zonglu. Solid St. Commun.53 (11) 975 (1985)

A third generation industrial high current ion implanter, Series III, has been produced for the uniform implantation of milliampere-beams with total acceleration voltages up to 200 kV. Magnetic analysis of the beam with initial acceleration voltages variable up to 40 kV is carried out in the accelerator terminal followed by post-acceleration across a single gap up to a maximum total acceleration voltage of 200 kV into a grounded processor chamber.The ion source is a Freeman type capable of delivering milliampere beams of most elements. The source feed materials for the three main ion species required by the semiconductor industry, i.e. B, P and As, can all be pumped by surfaces with temperatures down to liquid nitrogen temperature. Consequently large liquid nitrogen cryopump/traps are used as the primary pumping system with diffusion pumps having a secondary role for non-cryopumpable gases. Three stages of differential pumping are provided in the accelerator together with a 12″ pumping system for the processor.The large processor takes a maximum load of 108 2″ silicon wafers or 54 3″ silicon wafers. Mechanical scanning is used because of the need to maintain space charge neutralisation in the beam which rules out electrostatic scanning and also because of the need to distribute the heat dissipation over a large number of wafers in order to prevent an excessive temperature rise in the wafers during high dose implants (>1015ions/cm2). The carousel which carries the wafers is shaped so that the wafers pass through the beam in a straight line and at a constant speed. A stepper motor driven vane unit in the terminal controls the ion beam current. In order to achieve high implantation uniformities the processor dose control system controls the ratio ion current/carousel speed and therefore any small non-uniformities in the carousel rotation speed can be compensated by the vane unit.The various functions in the terminal are controlled from ground potential using fibre optics. The system is highly automated and unskilled operators can be used.

Single wafer high rate RIE employing magnetron discharge : Steve Schultheis. Solid St. Technol. 233 (April 1985)

A third generation industrial high current ion implanter, Series III, has been produced for the uniform implantation of milliampere-beams with total acceleration voltages up to 200 kV. Magnetic analysis of the beam with initial acceleration voltages variable up to 40 kV is carried out in the accelerator terminal followed by post-acceleration across a single gap up to a maximum total acceleration voltage of 200 kV into a grounded processor chamber.The ion source is a Freeman type capable of delivering milliampere beams of most elements. The source feed materials for the three main ion species required by the semiconductor industry, i.e. B, P and As, can all be pumped by surfaces with temperatures down to liquid nitrogen temperature. Consequently large liquid nitrogen cryopump/traps are used as the primary pumping system with diffusion pumps having a secondary role for non-cryopumpable gases. Three stages of differential pumping are provided in the accelerator together with a 12″ pumping system for the processor.The large processor takes a maximum load of 108 2″ silicon wafers or 54 3″ silicon wafers. Mechanical scanning is used because of the need to maintain space charge neutralisation in the beam which rules out electrostatic scanning and also because of the need to distribute the heat dissipation over a large number of wafers in order to prevent an excessive temperature rise in the wafers during high dose implants (>1015ions/cm2). The carousel which carries the wafers is shaped so that the wafers pass through the beam in a straight line and at a constant speed. A stepper motor driven vane unit in the terminal controls the ion beam current. In order to achieve high implantation uniformities the processor dose control system controls the ratio ion current/carousel speed and therefore any small non-uniformities in the carousel rotation speed can be compensated by the vane unit.The various functions in the terminal are controlled from ground potential using fibre optics. The system is highly automated and unskilled operators can be used.

Gain uniformity of InP/InGaAsP/InGaAs avalanche photodiodes with separate absorption, grading, and multiplication regions

We report on the spatial uniformity of the gain <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> of InP/ InGaAsP/InGaAs avalanche photodiodes with separate absorption, grading, and multiplication regions (SAGM-APD's). Typically, these APD's exhibit less than 10 percent variation in the gain (for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M \leq 10</tex> ) over the entire photosensitive area. The small nonuniformity which is observed shows a one-to-one correspondence with inhomogeneities in the epitaxial layers of the SAGM-APD structure. We also observe a reduction in the effective photosensitive diameter with increasing bias voltage.

Crystallographic slip in GaAs wafers annealed using incoherent radiation

Reflection x-ray topography has been used to show that incoherent radiation annealing of complete 2-in.-diam GaAs wafers results in extensive crystallographic slip networks. These slip lines are believed to be due to small temperature nonuniformities induced during the anneal by both edge radiation and thermal mass effects. The use of a series of annular guard rings around the wafer during the anneal is shown to reduce both the severity and the number of slip lines.

Improved Field Stability in RFQ Structures with Vane Coupling Rings

The small apertures common in many RFQ linac designs lead to tuning difficulties, primarily because asymmetries in the quadrant fields can arise as a result of small non-uniformities in the vane to vane capacitances. Sensitivity to such capacitance or other tuning variation in the quadrants is greatly reduced by the introduction of pairs of vane coupling rings that provide periodic electrical connections between diametrically opposite vanes. Results of measurements on a cold model RFQ structure with and without vane coupling rings are presented. The number of rings required for field stabilization and the effect of rings on mode frequencies are discussed.

The Effect of Internal Solidification on Turbulent Flow Heat Transfer and Pressure Drop in a Horizontal Tube

A simple analysis of the steady-state heat transfer and pressure drop in turbulent flow in a tube is presented for the case involving a “thin”, steady-state frozen deposit on the inside tube wall. Sparrow-Hallman-Siegel type internal flow convective heat transfer expressions and Blasius type pressure drop expressions are employed while neglecting second order interface curvature effects. Experimental heat transfer and pressure drop data are presented for comparison. It is shown that simple analyses of the type developed can be used to predict heat transfer and pressure drop in tube flow under freezing conditions and that, for the experimental conditions tested, basic agreement between theory and experiment was obtained. It is also shown experimentally that small nonuniformities in wall temperature can produce wide variations in pressure drop when a frozen layer exists within a tube.

The design philosophy for a 200 kV industrial high current ion implanter

A third generation industrial high current ion implanter, Series III, has been produced for the uniform implantation of milliampere-beams with total acceleration voltages up to 200 kV. Magnetic analysis of the beam with initial acceleration voltages variable up to 40 kV is carried out in the accelerator terminal followed by post-acceleration across a single gap up to a maximum total acceleration voltage of 200 kV into a grounded processor chamber. The ion source is a Freeman type capable of delivering milliampere beams of most elements. The source feed materials for the three main ion species required by the semiconductor industry, i.e. B, P and As, can all be pumped by surfaces with temperatures down to liquid nitrogen temperature. Consequently large liquid nitrogen cryopump/traps are used as the primary pumping system with diffusion pumps having a secondary role for non-cryopumpable gases. Three stages of differential pumping are provided in the accelerator together with a 12″ pumping system for the processor. The large processor takes a maximum load of 108 2″ silicon wafers or 54 3″ silicon wafers. Mechanical scanning is used because of the need to maintain space charge neutralisation in the beam which rules out electrostatic scanning and also because of the need to distribute the heat dissipation over a large number of wafers in order to prevent an excessive temperature rise in the wafers during high dose implants (>10 15 ions/ cm 2). The carousel which carries the wafers is shaped so that the wafers pass through the beam in a straight line and at a constant speed. A stepper motor driven vane unit in the terminal controls the ion beam current. In order to achieve high implantation uniformities the processor dose control system controls the ratio ion current/carousel speed and therefore any small non-uniformities in the carousel rotation speed can be compensated by the vane unit. The various functions in the terminal are controlled from ground potential using fibre optics. The system is highly automated and unskilled operators can be used.

Effect of perturbations in loudspeaker directivity patterns on localization

Because localization cues probably occur during the first millisecond after the radiation of a sound toward a listener, the presence of reflections within this period, having higher intensity than the direct sound, can confuse localization. While such a phenomenon is rare in nature, it may be common in multichannel sound reproduction systems where transducers have frequency-variant nonuniformities in their directivity patterns. In this paper, numerical ratings of localization error, based on directivity equations of the forms p(θ) = 2J1F(θ)/F(θ)2 for a single source and p(θ) = sin[nπmf sinθ/c)]/[n sin(πmf sinθ/c)] for an array; and on empirical relationships of arrival time and intensity, are computed for various combinations of listening positions, room configurations, and transducer configurations. Data suggest that small nonuniformities can produce significant localization error.

On the stability of dilatant hardening for saturated rock masses

Fissured rock masses tend to dilate as they are deformed inelastically toward failure. When the rock is fluid saturated and the time scale does not allow drainage, suctions are induced in the pore fluid, and by the effective stress principle the rock is dilatantly hardened over the resistance that it would show to a corresponding increment of drained deformation. This paper considers a compressed layer of saturated rock deformed in shear. Inelastic stress-strain relations are formulated, and these relations illustrate dilatant hardening when the layer is sheared without drainage at its boundaries. Parameters governing the slope of the hardened stress-strain curve are identified; these parameters predict a rising slope even when that presumed for homogeneous deformation under drained conditions is unstably falling. However, it is shown that the amount of dilatant strengthening that can actually be realized is limited by an instability. In particular, when the corresponding drained stress-strain curve has become unstable, small nonuniformities in the deformation field are shown to grow by local diffusive fluxes of pore fluid, and this is taken as the inception of localized shearing in a fault zone.

The modified Enskog equation

Arguments are presented for a modified form of the nonlinear Enskog equation, which describes the time dependence of the single-particle distribution function in a dense gas of hard spheres. Unlike the usual Enskog equation it is not restricted to small spatial non-uniformities, and may thus be used to derive Burnett and higher-order hydrodynamic equations. In a single-component system both equations are equivalent at the level of the Navier-Stokes equations. The main importance of the modified Enskog equation becomes manifest when it is extended to mixtures of hard spheres. It is shown that the existing versions of Enskog's theory for mixtures lead to results which are in conflict with irreversible thermodynamics (more specifically, the Onsager symmetry relations do not hold), whereas the present modified Enskog theory gives results in complete agreement with irreversible thermodynamics.

Application of holographic interferometry for visual observation of small non-uniformities in gas flows.: A N Berezkin et al, Zh Tekh Fiz, 42 (1), Jan 1972, 219–221 ( in Russian)

Application of holographic interferometry for visual observation of small non-uniformities in gas flows.: A N Berezkin et al, Zh Tekh Fiz, 42 (1), Jan 1972, 219–221 ( in Russian)