Finite-length Pulse Research Articles

Global thermoacoustic oscillations in a thermally driven pulse tube

We obtain linearized, BiGlobal thermoacoustic solutions in a pulse tube driven via an imposed mean temperature gradient. Here, the pulse tube is treated as a key unit of a thermoacoustic heat engine, in which the conversion of thermal energy to useful acoustic fluctuations occurs. A primary goal of this work is to understand the hydrodynamic efficiency of the energy conversion process and how it depends upon some of the important operating parameters, including the geometry of the device which in the limit of long length-to-diameter ratio approaches the so-called narrow tube approximation. As this limit is frequently imposed in the wave propagation analyses of thermoacoustic devices, it is critical to investigate the physical connections of such a model to more realistic finite-length pulse tube configurations, which we do here. The mean flow is quiescent with an analytic mean temperature profile that still models the necessary physical details of the hot heat exchanger and regenerator. The computed thermoacoustic oscillations are found to be globally stable, approaching neutral stability conditions at the narrow tube limit. In finite-length tubes, three distinct types of modes are identified and analyzed. Here, within a linear framework, radial modes do appear to act as key enablers for longitudinal modes to be the primary carriers of acoustic energy from the pulse tube section, while the identified boundary modes, essentially numerical constructs, are ignored in the analysis. Further, a disturbance energy-based efficiency metric is constructed that provides mechanistic understanding of some of the key parameters in pulse tube operation. For finite-length tubes, it shows oscillations of the first asymmetric mode to be the most efficient, while the axisymmetric perturbations dominate for longer tubes that eventually lead to the idealized plane wave propagation.

Transient reflection from mud during molecular diffusion of salt

Harbor basins and estuarine environments experience drastic salinity fluctuations in the water near the water-sediment interface, which can significantly affect how sound interacts with a low-velocity mud bottom. This presents challenges in applications including mine detection, port protection and shallow water sonar. In a previous investigation of this system, a mud sample that was saturated with fresh water was instantaneously exposed to salt water. Laboratory measurements of plane wave reflection from the water-mud interface were obtained using a time-gated broadband impulse as time evolved. Results suggested molecular diffusion of salt into the sample had altered the reflected pulse’s amplitude and caused a depth-dependent impedance profile in the mud. The sediment was discretized into layers much thinner than a wavelength and a multi-layer steady-state model was used to predict the reflection from the diffusing mud. As the effective diffusion length reached a critical value, predictions of the steady-state model began to deviate from the measurements, indicating that a transient solution was required. A model of the transient reflection of a finite-length pulse from a half space with an arbitrary impedance will be presented and model results compared with laboratory measurements. [Work supported by ONR.]

The Errors in Determining the Thermal Characteristics of Porous Structural Materials by the Laser Pulse Method

The errors in determining the thermal characteristics of a typical composite heterogeneous material – sintered aluminum powder, are analyzed. The errors are due to radiation energy transfer in the heated layer of the material when the laser pulse method is employed, due to the action on the surface of the composite of a collimated laser pulse of finite length. The effect of the porosity of the material and the radiation absorption process on this error is established.

Laser wakefield and beat-wave generation by multiple and chirped laser pulses

Generation of large amplitude plasma waves using high-power lasers in either the wakefield or beat-wave scheme is considered. We show how the nonlinear behavior of the plasma wave may make it advantageous to split the total energy into more than one pulse in the wavefield scheme. When a beat wave is generated by a pulse of finite length, we show how the final wave amplitude may be enhanced if the frequency of one or both pulses is chirped in such a way that the wavelength of the beat increases from the front to the back of the pulse.

Transient acoustic radiation from excited plates

The acoustic radiation time signature as radiated from an infinite elastic plate is obtained for transient forced excitation applied to a point on the plate. The forced excitations considered are those encountered in industrial and marine applications such as the sudden application of dead weight, an impact load, or a sinusoidal finite length pulse that could be generated by starting machinery. The solutions in these cases were idealized by use of a point force whose time history is a step function, a square pulse, or a cw pulse. The time signature for the radiated noise was obtained by convolving the approximate acoustic radiation impulse response solution for an impulsive force with the force time history.

A new approach to suppression of finite-length pulse interference using modified linear predictor

In this paper the problem of pulse interference suppression using prediction technique is considered. It is shown that the conventional predictor cannot be used to suppress a finite-length pulse interference even when the data are ideal, for example, in the absence of a background random process. A new method is presented for the design of an adaptive tapped delay line filter used for finite-length pulse suppression. The method is based on a modified form of linear prediction procedure using a set of artificial state variables given by the product of input samples and their delayed versions. The advantages of this modified linear predictor are demonstrated by two examples, using computer simulation.

Variational formulation and low-frequency approximation for Coulomb scattering in a laser field

The theory of scattering of a charged particle in the presence of a laser field is formulated variationally. If the field is slowly varying, its dominant effect over a wide range of field intensities will be to modify the asymptotic motion of the projectile. A trial function is chosen which correctly accounts for the projectile-field interaction in asymptotic states. It leads to a variational approximation for the transition amplitude which generalizes earlier versions of the low-frequency approximation in two respects. Firstly, the field is not restricted to be of the form of a monochromatic plane wave but, more realistically, is taken to be a pulse of finite length. Secondly, the target may carry a net charge. The dependence of the transition amplitude on the variable ..delta..E, which represents the energy transferred to the field, is modified by the presence of the long-range Coulomb interaction; additional terms which depend logarithmically on ..delta..E are found. The variational expression for the transition amplitude consists of two factors, one depending only on the external field and the other representing the amplitude for single-photon spontaneous bremsstrahlung. The present analysis of this bremsstrahlung amplitude is based on the assumption that ..delta..E is sufficiently small so thatmore » the dominant contribution to the spatial integration comes from the asymptotic domain. The low-energy approximation obtained in this way provides a generalization of Low's theorem on spontaneous bremsstrahlung to include the effect of the Coulomb tail.« less

Energy loss from an electron pulse in a plasma

Upper and lower bounds are presented for the rate of energy loss by a high intensity Gaussian pulse of finite length propagating in a cold dense homogeneous plasma. For sufficiently high plasma conductivity these bounds coalesce yielding an explicit expression for the dissipated power.

Measurement of thermal diffusivity of hemispherical samples (bismuth)

The temperature distribution in a hemispherical sample with a point source (sink) is obtained for the case where the heat is supplied in the form of a pulse of finite length. The results of measurement of the thermal diffusivity of solid and liquid bismuth are presented.

ON THE MINIMUM OSCILLATORY CHARACTER OF SPHERICAL SEISMIC PULSES

Compressional seismic pulses, such as originate from an explosion in a shot hole, can be discussed generally without reference to the non‐linear effect, such as heating, fracturing and other departures from Hooke’s law, in the neighborhood of the shot. A pulse of finite length from front to back is considered in the present note. It is shown that such a pulse is not as arbitrary as the general solution of the spherical wave equation would indicate, but the dilatation must change algebraic sign at least twice within the pulse. Thus the pulse must generally be, to this minimal extent, oscillatory if the front and rear regions are to be quiet.