Continuous Line Source Research Articles

The second-order moment structure of dispersing plumes and puffs

A description of the behaviour of the second-order moments of concentration for a variety of source types is derived within the context of the classical phenomenology of isotropic turbulence. The sources considered include instantaneous area, line and point sources and can also be interpreted as relating to plumes from continuous point sources and continuous crosswind line sources in a strong uniform mean flow. A large number of different regimes are identified corresponding to different relative sizes of the many length scales involved. Perhaps the most interesting result is the identification of an ‘Inertial–meander’ subrange when the inertial-subrange eddies contribute to the meandering of the plume.

A contaminant‐dilution heuristic model

AbstractThe sheet‐strand texture of a contaminant concentration field in turbulent flows is the basis of a simple model of the dilution process in contaminant clouds and plumes. The model is used to explain qualitative observations on kurtosis, skewness and probability density functions near the source in continuous line and point source plumes in grid turbulence.

Fundamental solution in thermoelasticity with two relaxation times for cylindrical regions

The solution of the problem of determining stress and temperature distributions with a continuous line source of heat in an infinite elastic body governed by the equations of generalized thermoelasticity with two relaxation times are obtained by using the Hankel and Laplace transform techniques. Inverse transforms are obtained in an approximate manner for small values of time. Numerical results for a particular case are given.

The Use of Lagrangian Methods To Describe Turbulent Transport of Heat from a Wall

Tracking of heat markers released instantaneously from a point source on a wall boundary in a numerically simulated turbulent channel flow is used to describe the transfer of heat. The trajectories of 16 129 heat markers are monitored in time and space. These results are used to calculate temperature fields generated by continuous line or planar sources and the temperature profile in a channel with a heated bottom wall and a cooled top wall. The good agreement between the calculated fully-developed profile and the profile generated by a direct numerical simulation illustrates the equivalence of the Lagrangian and Eulerian approaches. The main point to be made is that dispersion from an instantaneous point source is a basic element. Its understanding could provide a better foundation for establishing the physics of wall heat transfer than is supplied by Eulerian analyses.

A simple representation of a developing contaminant concentration field

Chatwin & Sullivan (1990) have demonstrated that, for a wide range of self-similar scalar fields, the moments of the probability density function of concentration have a very simple form. Here, an extension to this simple form which takes account of the source distribution is developed. This extension has two effects. Firstly it modifies the values of the two parameters appearing in the original theory and in particular explains the observed behaviour of these parameters very near to a line source of heat in grid tubulence. Secondly, it introduces an additional parameter in the description of each moment beyond the second. It is shown that these additional parameters are necessary in order to describe measurements of the first four central moments throughout the concentration field from a continuous line source of heat in grid-generated turbulence.

On the synthesis of fractal radiation patterns

The fundamental relationship between self‐similar, that is, fractal, arrays and their ability to generate radiation patterns which possess fractal features is examined in this paper. The theoretical foundation and design procedures are developed for using fractal arrays to synthesize fractal radiation patterns having certain desired characteristics. A family of functions, known as generalized Weierstrass functions, are shown to play a pivotal role in the theory of fractal radiation pattern synthesis. These functions are everywhere continuous but nowhere differentiable and exhibit fractal behavior at all scales. It will be demonstrated that the array factor for a nonuniformly but symmetrically spaced linear array can be expressed in terms of a Weierstrass partial sum (band‐limited Weierstrass function) for an appropriate choice of array element spacings and excitations. The resulting fractal radiation patterns from these arrays possess structure over a finite range of scales. This range of scales can be controlled by the number of elements in the array. For a fixed array geometry, the fractal dimension of the radiation pattern may be varied by changing the array current distribution. A general and highly flexible synthesis technique is introduced which is based on the theory of Fourier‐Weierstrass expansions. One of the appealing attributes of this synthesis technique is that it provides the freedom to select an appropriate generating function, in addition to the dimension, for a desired fractal radiation pattern. It is shown that this synthesis procedure results in fractal arrays which are composed of a sequence of self‐similar uniformly spaced linear subarrays. Finally, a synthesis technique for application to continuous line sources is presented which also makes use of Fourier‐Weierstrass expansions.

A MODEL OF NEAR-SOURCE TURBULENT MIXING

A simple, physical model is developed to represent mixing between host and contaminant fluid near a source in a turbulent flow. Advantage is taken of recent theoretical developments to compare the model results with those of experiments from continuous point and line sources in grid generated turbulence.

A method of generation of sum and sls‐type difference patterns

AbstractThe article presents a method of realization of useful sum and sidelobe‐suppressed difference patterns using only one array antenna. The method involves the synthesis of phase functions required for the generation of desired patterns. Computed results on radiation patterns are presented both for a continuous line source and an array of radiators © 1994 John Wiley & Sons, Inc.

Temperature-rate-dependent thermoelastic interactions due to a line heat source

Temperature-rate-dependent thermoelasticity theory is employed to study thermoelastic interactions due to a continuous line source in a linear, homogeneous and isotropic unbounded solid. Laplace and Hankel transforms are employed to solve the problem. Explicit expressions for temperature and stress fields are obtained for small time approximation. Numerical results for a copper material are presented.

Particle mixing and diffusion in the turbulent wake of cylinder arrays

The collection of 10 μ DOP droplets from an aerosol flow around an array of five circular cylinders in a turbulent air stream was measured. Axial and angled alignments of the target array, normal to the flow, were examined. Cylinder Reynolds numbers ranged from 1,300 to 5,100, and effective Stokes numbers from 0.50 to 1.58. A continuous line source turbulent diffusion model was used with the centerline velocity and concentration distributions to derive the eddy diffusion coefficients for momentum and particle concentration in the near wake of the cyinders. Angled collection results showed an optimal target alignment at the edge of the momentum wake of the lead cylinder. Further examination with an LDA system suggests the peak in collection is due to a particle velocity surplus in the wake.

Two‐Dimensional Mixing in Rivers with Unsteady Pollutant Source

A numerical model, the mixing analysis based on the Concept of Stream Tubes (MABOCOST), has been developed for the analysis of two‐dimensional, transient mixing of nonconservative substances in natural streams. The model can be applied to steady flows in sinuous, nonprismatic channels. A curvilinear coordinate system is used to account for variations in velocity, depth, and channel curvature. By dividing the stream tubes into variable length elements so that the Courant number for the grid space is always equal to unity, the problem of numerical diffusion and dispersion in the computation of streamwise advection is avoided. The model has been verified with analytical solutions for the cases of simple advection, continuous line source and instantaneous injection. Dispersion experiments were carried out in a sinuous channel with irregular bottom topography, using both slug injection and a variable rate injection of tracer. Measured time‐concentration data agree quite well with predictions using MABOCOST.

Designing MLS Arrays with Specified Individual Sidelobes

Multipath errors caused by the sidelobes radiation reflected by an obstacle around the airport area are of great concern for antenna designer. This paper presents a modified Taylor's pattern synthesis method for the determination of continuous line sources to yield narrow beam pattern with sidelobes having individual heights that can be adjusted to any arbitrary specifications. Four examples pertaining to MLS arrays are presented, two for symmetric and the other two for asymmetric case.

Measurements of heat diffusion from a continuous line source in a uniformly sheared turbulent flow

The diffusion of a passive scalar (heat) from a continuous line source placed in a uniformly sheared, nearly homogeneous, turbulent shear flow is examined. Measurements indicate that the mean temperature profile is approximately Gaussian near the source but, further downstream, it becomes asymmetric and its peak shifts towards the region of lower velocity. The r.m.s. temperature fluctuation profile is double peaked close to the source, it is single peaked at intermediate distances and it demonstrates a re-emergence of double peaks which grow in relative magnitude far away from the source. In comparison to similar experiments in isotropic turbulence, the centreline mean temperature appears to have a comparable decay rate, whereas the centreline mean-square temperature fluctuations appear to decay at a faster rate. The spread of the plume is faster than that in isotropic turbulence. The measured turbulent heat fluxes and triple temperature-velocity correlations demonstrate self-similar features. The development of temperature integral lengthscales and microscales is comparable to that in other heated, uniformly sheared flows, while the temperature p.d.f. and the temperature-velocity joint p.d.f. are distinctly non-Gaussian, especially away from the centreline. The relative magnitudes of the two measured components of the turbulent diffusivity tensor are in agreement with earlier measurements.

Generalised Villeneuve n̄ distribution

In this paper, a generalised Villeneuve type linear array distribution is developed, which permits the direct synthesis of discrete array distributions for high efficiency sum patterns of arbitrary sidelobe level and envelope taper. With the Dolph–Chebyshev distribution as the parent space factor, and the correct perturbation of these space factor zeros, the excitation efficiency and beamwidths are kept as close to their optimum values as is possible under the given sidelobe ratio and envelope taper conditions. The method is the discrete analogue of the generalised Taylor n-distribution, used for continuous line source synthesis. Examples are given to illustrate the principal features of the distribution.

Equivalence of optimal slope-sum product discrete and continuous linear electromagnetic radiators

The discrete distributions which provide maximum slope-sum product, analogous to that derived earlier for continuous line sources, are considered and some comparisons made.

Brachytherapy Implants with Differently Spaced IR-192 Seeds: A Dosimetric Study: Radiology, Vol. 165, No. 1, October 1987, pp. 271–274

Brachytherapy implantations traditionally have been carried out with continuous line sources of radium. With the popularity of afterloading implantations, iridium-192 seeds in plastic ribbons have replaced radium in the United States, although continuous sources, such as iridium wires, are widely used in Europe. The authors analyzed the impact of the use of noncontinuous sources in brachytherapy implants. Computer simulations and film dosimetry of a two-planar implant were carried out. Seeds at standard spacing (1 seed/cm), nonstandard spacing (1 seed/6mm), and continuously arranged seeds were studied.

A new reduction algorithm for marine heat flow measurements

Multiple penetration heat flow surveys that employ “violin bow” multithermistor array instruments generate large quantities of high‐quality data. To cope with the problems associated with the reduction of these data, an algorithm has been developed which can be used to reduce the data automatically on a microcomputer. The algorithm is designed for use with a pulsed line source method of conductivity measurement, although it could be modified easily for use with the continuous line source method. The multiply iterative algorithm deals, on a sensor by sensor basis, with errors associated with nonideal probe construction and sediment entry, factors that affect the determination of both in situ temperatures and thermal conductivities. Numerical tests of the algorithm show that it is accurate and stable and fast enough for post‐real‐time reduction of data at sea. Practical tests on high‐quality data from the western Pacific show that accuracies are limited by the instrumental resolution; in these cases, the reduction algorithm provided determinations of undisturbed in situ temperatures to better than 1 mK and of in situ conductivities to within 1%.

Excitations providing maximum directivity for difference arrays of discrete elements

The discrete distributions which provide maximum difference directivity, analogous to that derived previously for continuous line sources, are considered, and some general results given.

Maximisation of normalised boresight slope of a difference array of discrete elements

The discrete distributions which provide maximum normalised boresight slope, analogous to that derived earlier for continuous line-sources, are considered and some general conclusions reached.

Heat pulse line-source method to determine thermal conductivity of consolidated rocks

An instrument designed to measure thermal conductivity of consolidated rocks, dry or saturated, using a transient method is presented. The instrument measures relative values of the thermal conductivity, and it needs calibration to obtain absolute values. The device can be used as heat pulse line source and as continuous heat line source. Two parameters to determine thermal conductivity are proposed: TMAX, in heat pulse line source, and SLOPE, in continuous heat line source. Its performance is better, and the operation simpler, in heat pulse line-source mode with a measuring time of 170 s and a reproducibility better than 2.5%. The sample preparation is very simple on both modes. The performance has been tested with a set of ten rocks with thermal conductivity values between 1.4 and 5.2 W m−1 K−1 which covers the usual range for consolidated rocks.