scholarly journals Waves in the gas centrifuge: asymptotic theory and similarities with the atmosphere

2021 ◽  
Vol 928 ◽  
Author(s):  
Marie Rodal ◽  
Mark Schlutow
Keyword(s):  
Internal Waves ◽  
Acoustic Waves ◽  
Asymptotic Theory ◽  
Constant Pressure ◽  
Rotational Frequency ◽  
Working Fluid ◽  
Leading Order ◽  
Scale Separation ◽  
Gas Centrifuge ◽  
Lower Heat

We study the stratified gas in a rapidly rotating centrifuge as a model for the Earth's atmosphere. Based on methods of perturbation theory, it is shown that in certain regimes, internal waves in the gas centrifuge have the same dispersion relation to leading order as their atmospheric siblings. Assuming an air filled centrifuge with a radius of around 50 cm, the optimal rotational frequency for realistic atmosphere-like waves is around 10 000 revolutions per minute. Using gases of lower heat capacities at constant pressure, such as xenon, the rotational frequencies can be even halved to obtain the same results. Similar to the atmosphere, it is feasible in the gas centrifuge to generate a clear scale separation of wave frequencies and therefore phase speeds between acoustic waves and internal waves. In addition to the centrifugal force, the Coriolis force acts in the same plane. However, its influence on axially homogeneous internal waves appears only as a higher-order correction. We conclude that the gas centrifuge provides an unprecedented opportunity to investigate atmospheric internal waves experimentally with a compressible working fluid.

Mathematical methods for the characterization of ultrasound in anisotropic materials

2000 ◽  
Vol 78 (9) ◽  
pp. 803-821 ◽  
Author(s):  
B O'Neill ◽  
R Gr. Maev
Keyword(s):  
Wave Propagation ◽  
Acoustic Waves ◽  
Asymptotic Theory ◽  
Anisotropic Materials ◽  
Bulk Wave ◽  
Mathematical Methods ◽  
Theoretical Methods ◽  
The Past ◽  
Fundamental Equations

Although the fundamental equations for the propagation of elastic and acoustic waves in anisotropic materials have not changed in more than a 100 years, the last few decades have seen a surge in interest in the topic. Much of this interest stems from the growing need for characterization of an increasing number of exotic materials. The intent of this paper is to review, for the benefit of beginning researchers in acoustics and ultrasonics, the fundamental phenomena related to elastic wave propagation in anisotropic media. We also present the most common and interesting theoretical methods developed over the past 20 years to model bulk wave propagation in such media. The methods discussed include plane wave superpositions, ray asymptotic theory, paraxial beams, and Green's functions. More peripheral issues, including anisotropic effects combined with various other exotic effects, are dealt with in the bibliography. PACS No.: 43.90

Closed-Cycle OTEC Systems

1994 ◽  
Author(s):  
William H. Avery ◽  
Chih Wu
Keyword(s):  
Thermal Equilibrium ◽  
Constant Pressure ◽  
Cold Water ◽  
Heat Engine ◽  
Heat Removal ◽  
Working Fluid ◽  
Closed Cycle ◽  
Work Done ◽  
Heat Engine Cycle ◽  
Design Pressure

The Rankine closed cycle is a process in which beat is used to evaporate a fluid at constant pressure in a “boiler” or evaporator, from which the vapor enters a piston engine or turbine and expands doing work. The vapor exhaust then enters a vessel where heat is transferred from the vapor to a cooling fluid, causing the vapor to condense to a liquid, which is pumped back to the evaporator to complete the cycle. A layout of the plantship shown in Fig. 1-2. The basic cycle comprises four steps, as shown in the pressure-volume (p—V) diagram of Fig. 4-1. 1. Starting at point a, heat is added to the working fluid in the boiler until the temperature reaches the boiling point at the design pressure, represented by point b. 2. With further heat addition, the liquid vaporizes at constant temperature and pressure, increasing in volume to point c. 3. The high-pressure vapor enters the piston or turbine and expands adiabatically to point d. 4. The low-pressure vapor enters the condenser and, with heat removal at constant pressure, is cooled and liquefied, returning to its original volume at point a. The work done by the cycle is the area enclosed by the points a,b,c,d,a. This is equal to Hc–Hd, where H is the enthalpy of the fluid at the indicated point. The heat transferred in the process is Hc–Ha Thus the efficiency, defined as the ratio of work to heat used, is: . . . efficiency(η)=Hc–Hd/Hc–Ha (4.1.1) . . . Carnot showed that if the heat-engine cycle was conducted so that equilibrium conditions were maintained in the process, that the efficiency was determined solely by the ratio of the temperatures of the working fluid in the evaporator and the condenser. . . . η=TE–Tc/TE (4.1.2) . . . The maximum Carnot efficiency can be attained only for a cycle in which thermal equilibrium exists in each phase of the process; however, for power to be generated a temperature difference must exist between the working fluid in the evaporator and the warm-water heat source, and between the working fluid in the condenser and the cold-water heat sink.

New model for acoustic waves propagating through a vortical flow

2017 ◽  
Vol 823 ◽  
pp. 658-674 ◽  
Author(s):  
Jim Thomas
Keyword(s):  
Asymptotic Analysis ◽  
Wave Field ◽  
Time Scale ◽  
Acoustic Waves ◽  
High Frequency ◽  
Spatial Scales ◽  
Amplitude Equation ◽  
Vortical Flow ◽  
Reduced Model ◽  
Scale Separation

A new amplitude equation is derived for high-frequency acoustic waves propagating through an incompressible vortical flow using multi-time-scale asymptotic analysis. The reduced model is derived without an explicit spatial-scale separation ansatz between the wave and vortical fields. As a consequence, the model is seen to capture very well the features of the wave field in the regime where the spatial scales of the wave and vortical fields are comparable, a regime for which an optimal reduced model does not seem to be available.

scholarly journals Time-Dependent Propagation of Tsunami-Generated Acoustic–Gravity Waves in the Atmosphere

2020 ◽  
Vol 77 (4) ◽  
pp. 1233-1244 ◽  
Author(s):  
Yue Wu ◽  
Stefan G. Llewellyn Smith ◽  
James W. Rottman ◽  
Dave Broutman ◽  
Jean-Bernard H. Minster
Keyword(s):  
Internal Waves ◽  
Gravity Waves ◽  
Acoustic Waves ◽  
Early Stage ◽  
Vertical Displacement ◽  
Inverse Laplace Transform ◽  
Acoustic Gravity Waves ◽  
Numerical Inverse Laplace Transform ◽  
Wave Development

Abstract Tsunami-generated linear acoustic–gravity waves in the atmosphere with altitude-dependent vertical stratification and horizontal background winds are studied with the long-term goal of real-time tsunami warning. The initial-value problem is examined using Fourier–Laplace transforms to investigate the time dependence and to compare the cases of anelastic and compressible atmospheres. The approach includes formulating the linear propagation of acoustic–gravity waves in the vertical, solving the vertical displacement of waves and pressure perturbations numerically as a set of coupled ODEs in the Fourier–Laplace domain, and employing den Iseger’s algorithm to carry out a fast and accurate numerical inverse Laplace transform. Results are presented for three cases with different atmospheric and tsunami profiles. Horizontal background winds enhance wave advection in the horizontal but hinder the vertical transmission of internal waves through the whole atmosphere. The effect of compressibility is significant. The rescaled vertical displacement of internal waves at 100-km altitude shows an arrival at the early stage of wave development due to the acoustic branch that is not present in the anelastic case. The long-term displacement also shows an O(1) difference between the compressible and anelastic results for the cases with uniform and realistic stratification. Compressibility hence affects both the speed and amplitude of energy transmitted to the upper atmosphere because of fast acoustic waves.

Multidimensional stability analysis of gaseous detonations near Chapman–Jouguet conditions for small heat release

2009 ◽  
Vol 624 ◽  
pp. 125-150 ◽  
Author(s):  
PAUL CLAVIN ◽  
FORMAN A. WILLIAMS
Keyword(s):  
Heat Release ◽  
Acoustic Waves ◽  
Realistic Model ◽  
Cellular Structures ◽  
Bifurcation Parameter ◽  
Leading Order ◽  
Instability Mechanism ◽  
Gaseous Detonations ◽  
Detonation Structure ◽  
Rate Of Heat Release

Multidimensional instability of planar detonations, leading to cellular structures, is studied analytically near Chapman–Jouguet conditions, in the limit of small heat release, with small (Newtonian) differences between heat capacities, by using an expansion in a small parameter representing the ratio of the heat release to the thermal enthalpy of the fresh mixture. In this limit, the dynamics of detonations is governed by the interaction between the acoustic waves and the heat-release rate inside the inner detonation structure, the entropy–vorticity wave playing a negligible role at leading order. This situation is just opposite from that considered in our 1997 study of strongly overdriven detonations. The present analysis offers a step towards improving our understanding of the cellular structures of ordinary detonations, for which both the entropy–vorticity waves and the acoustic waves are involved in the instability mechanism. The relevant bifurcation parameter is identified, involving the degree of overdrive and the sensitivity of the rate of heat release to temperature at the Neumann state, and the onset of the instability is studied analytically for a realistic model of the inner structure of gaseous detonations.

Hypersonic compression corner flow with large separated regions

2019 ◽  
Vol 877 ◽  
pp. 471-494 ◽  
Author(s):  
Sudhir L. Gai ◽  
Amna Khraibut
Keyword(s):  
Large Scale ◽  
Asymptotic Theory ◽  
Reverse Flow ◽  
Boundary Layer Separation ◽  
Recirculation Region ◽  
Hypersonic Boundary Layer ◽  
Temperature Ratio ◽  
Scale Separation ◽  
Compression Corner ◽  
Corner Flow

The structure of large-scale hypersonic boundary layer separation and reattachment is studied numerically using a flat plate/compression corner geometry. Apart from verifying the large scale separation characteristics in hypersonic flow, a detailed discussion of secondary separation and fragmentation into multiple vortices embedded within the main recirculation region is presented. The unique relation between the second minimum in shear stress and the scaled angle is highlighted in the context of the reverse flow singularity of Smith (Proc. R. Soc. Lond. A, vol. A420, 1988, pp. 21–52) and it appears that for a small wall temperature ratio, such a singularity is unlikely. It is shown that the size of the separation can be estimated in terms of Burggraf’s expression based on asymptotic theory.

scholarly journals Scattering of acoustic waves by a vortex

1999 ◽  
Vol 386 ◽  
pp. 305-328 ◽  
Author(s):  
RUPERT FORD ◽  
STEFAN G. LLEWELLYN SMITH
Keyword(s):  
Mach Number ◽  
Acoustic Waves ◽  
Scattering Amplitude ◽  
Polar Angle ◽  
Scattered Wave ◽  
Two Dimensions ◽  
Far Field ◽  
Leading Order ◽  
Axisymmetric Vortex ◽  
Wave Region

We investigate the scattering of a plane acoustic wave by an axisymmetric vortex in two dimensions. We consider vortices with localized vorticity, arbitrary circulation and small Mach number. The wavelength of the acoustic waves is assumed to be much longer than the scale of the vortex. This enables us to define two asymptotic regions: an inner, vortical region, and an outer, wave region. The solution is then developed in the two regions using matched asymptotic expansions, with the Mach number as the expansion parameter. The leading-order scattered wave field consists of two components. One component arises from the interaction in the vortical region, and takes the form of a dipolar wave. The other component arises from the interaction in the wave region. For an incident wave with wavenumber k propagating in the positive X-direction, a steepest descents analysis shows that, in the far-field limit, the leading-order scattered field takes the form i(π−θ)eikX+½cosθcot(½θ) (2π/kR)1/2ei(kR−π/4), where θ is the usual polar angle. This expression is not valid in a parabolic region centred on the positive X-axis, where kRθ2=O(1). A different asymptotic solution is appropriate in this region. The two solutions match onto each other to give a leading-order scattering amplitude that is finite and single-valued everywhere, and that vanishes along the X-axis. The next term in the expansion in Mach number has a non-zero far-field response along the X-axis.

ELASTIC THIN SHELLS: ASYMPTOTIC THEORY IN THE ANISOTROPIC AND HETEROGENEOUS CASES

1995 ◽  
Vol 05 (04) ◽  
pp. 473-496 ◽  
Author(s):  
D. CAILLERIE ◽  
E. SANCHEZ-PALENCIA
Keyword(s):  
Shell Theory ◽  
Asymptotic Theory ◽  
Order Term ◽  
Three Dimensional ◽  
Leading Order ◽  
Three Dimensional Elasticity ◽  
Thin Shell Theory ◽  
Variational Formulations ◽  
Natural Way

Asymptotic (two-scale) methods are used to derive thin shell theory from three-dimensional elasticity. The asymptotic process is done directly for the variational formulations, and existence and uniqueness theorems are given for the shell problem. The asymptotic behavior is the same as that recently derived by the authors using classical hypotheses of shell theory. The role of the subspace G of pure bendings (inextensional motions) appears in a natural way. The asymptotic is basically described by a leading order term contained in G and a lower order term contained in the orthogonal to G. As in anisotropic heterogeneous plates, which exhibit a coupling between flexion and traction, in heterogeneous shells there is coupling between the terms in G and in its orthogonal.

The Brayton Cycle Using Real Air and Polytropic Component Efficiencies

2011 ◽  
Vol 133 (11) ◽  
Author(s):  
W. H. Heiser ◽  
T. Huxley ◽  
J. W. Bucey
Keyword(s):  
Constant Pressure ◽  
Adiabatic Compression ◽  
Design Parameters ◽  
Working Fluid ◽  
High Fidelity ◽  
Brayton Cycle ◽  
Closed Cycle ◽  
Perfect Gas ◽  
Power Cycle ◽  
Compression And Expansion

This paper presents the results of a fundamental, comprehensive, and rigorous analytical and computational examination of the performance of the Brayton propulsion and power cycle employing real air as the working fluid. This approach capitalizes on the benefits inherent in closed cycle thermodynamic reasoning and the behavior of the thermally perfect gas to facilitate analysis. The analysis uses a high fidelity correlation to represent the specific heat at constant pressure of air as a function of temperature and the polytropic efficiency to evaluate the overall efficiency of the adiabatic compression and expansion processes. The analytical results are algebraic, transparent, and easily manipulated, and the computational results present a useful guidance for designers and users. The operating range of design parameters considered covers any current and foreseeable application. The results include some important comparisons with more simplified conventional analyses.

Experimental Investigation of a Flat-Plate Oscillating Heat Pipe With Modified Evaporator and Condenser

2014 ◽  
Author(s):  
M. J. Rhodes ◽  
M. R. Taylor ◽  
J. G. Monroe ◽  
S. M. Thompson
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Flat Plate ◽  
Thermal Performance ◽  
High Heat ◽  
Working Fluid ◽  
High Heat Flux ◽  
Oscillating Heat Pipe ◽  
Lower Heat ◽  
Operating Temperatures

The thermal performance of a flat-plate oscillating heat pipe (FP-OHP) - with modified evaporator and condenser was experimentally investigated during high heat flux conditions. The copper FP-OHP (101.6 × 101.6 × 3.18 mm3) possessed two inter-connected layers of 1.02 mm2 square channels with the evaporator and condenser possessing two parallel, 0.25 × 0.51 mm2 square microchannels. The microchannels were integrated to enhance evaporation and condensation heat transfer to improve the FP-OHP’s ability to transport high heat flux. The FP-OHP was oriented vertically and locally heated with a 14.52 cm2 heating block at its base and cooled with a water block that provided either: 20 °C, 40 °C, or 60 °C operating temperatures. A FP-OHP without embedded microchannels was also investigated for baseline performance comparison. Both FP-OHPs were filled with Novec HFE-7200 (3M) working fluid at a filling ratio of approximately 80% by volume. The maximum temperature of each FP-OHP was recorded versus time for various heat inputs for the investigated operating temperatures. The results indicate that the integrated microchannels enhance the FP-OHP’s thermal performance for all operating temperatures. At 20 °C, 40 °C, and 60 °C, the microchannel-embedded evaporator and condenser dissipated 80 W, 65 W, and 55 W more than the baseline control with a minimum thermal resistance of 0.219 °C/W, 0.205 °C/W, and 0.170 °C/W, respectively — corresponding to a percent enhancement on-the-order of 25%. This percent enhancement increased with operating temperature. It has also been shown that Novec HFE-7200 allows the FP-OHP to start at relatively lower heat inputs — as low as 35 W, demonstrating that this working fluid can enhance heat transfer even at lower heat flux applications.

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