No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Propagation of Pressure Waves in Compression System Prototype for Magnetized Target Fusion Reactor in General Fusion Inc.
Abstract
A scaled prototype of a magnetized target fusion compression system has been designed and built in General Fusion Inc. to test full-size pistons and their synchronization algorithms. In the current prototype, 14 pistons are mounted on the steel sphere with inner radius of 0.5 m (staggered rings of seven pistons above and below the equator) as shown in Fig. 1a. The interior of the sphere is filled with tangentially pumped molten lead (Pb) such that an evacuated cavity (vortex) is formed in the middle of the sphere (Fig. 1b). Each piston consists of two main parts: “hammer” piston and floating “anvil” piston. A 100 kg hammer piston (accelerated by compressed air to velocities up to 50 m/s) impacts the “floating” anvil that is in contact with the liquid lead. As a result of this impact, the pressure wave propagates through the anvil and reaches the interface between steel and liquid lead. Due to the close acoustic match between steel and lead, most of the pressure wave is transmitted into the liquid lead. Discrete pressure waves produced by the individual pistons merge into a converging pressure wave as they propagate toward the evacuated cavity. When a combined converging wave hits the lead-vacuum interface, it is almost entirely reflected because of the severe mismatch between the acoustic impedances. This interaction results in a rapid inward acceleration of the interface. In the final design of the reactor, a magnetized plasma target (trapped inside evacuated cavity) is compressed as the interface moves and accelerates inward. At the same time, a wave reflected from the interface puts the liquid into tension and initiates formation of cavitation regions in the liquid lead.
... Thus one can use pneumatic pistons mounted outside the reactor to send compression waves through the spinning liquid metal that will in turn compress the plasma (Suponitsky et al 2014). However, this method introduces new challenges such as the energy efficiency of the liquid compression and the complex dynamics of liquid-gas interface (Suponitsky et al 2015). In this study we research an alternative compression system that can potentially achieve the goal of effective compression in time scale of milliseconds by releasing highly pressurized gas into a closed enclosure of very low pressure. ...
An innovative gas compression system is proposed and computationally researched to achieve a short time response as needed in engineering applications such as hydrogen fusion energy reactors and high speed hammers. The system consists of a reservoir containing high pressure gas connected to a straight tube which in turn is connected to a spherical duct, where at the sphere's centre plasma resides in the case of a fusion reactor. Diaphragm located inside the straight tube separates the reservoir's high pressure gas from the rest of the plenum. Once the diaphragm is breached the high pressure gas enters the plenum to drive pistons located on the inner wall of the spherical duct that will eventually end compressing the plasma. Quasi-1D and axisymmetric flow formulations are used to design and analyse the flow dynamics. A spike is designed for the interface between the straight tube and the spherical duct to provide a smooth geometry transition for the flow. Flow simulations show high supersonic flow hitting the end of the spherical duct, generating a return shock wave propagating upstream and raising the pressure above the reservoir pressure as in the hammer wave problem, potentially giving temporary pressure boost to the pistons. Good agreement is revealed between the two flow formulations pointing to the usefulness of the quasi-1D formulation as a rapid solver. Nevertheless, a mild time delay in the axisymmetric flow simulation occurred due to moderate two-dimensionality effects. The compression system is settled down in a few milliseconds for a spherical duct of 0.8 m diameter using Helium gas and a uniform duct cross-section area. Various system geometries are analysed using instantaneous and time history flow plots. © 2017 The Japan Society of Fluid Mechanics and IOP Publishing Ltd.
This paper presents a numerical study of an aperiodic cavitation pocket
developing in a Venturi flow. The mass transfer between phases is driven
by a void ratio transport equation model. A new free-parameter closure
relation is proposed and compared with other formulations. The re-entrant
jet development, void ratio profiles and pressure fluctuations are analyzed to
discern results accuracy. Comparisons with available experimental data are
done and good agreement is achieved.
Discontinua simulations are becoming an important part of computational mechanics to the extent that computational mechanics of discontinua is becoming a separate sub-discipline of computational mechanics. Among the most widely used methods of computational mechanics of discontinua are discrete-element methods, combined finite-discrete-element methods and discontinuum deformation analysis methods. A range of key algorithmic procedures is common to most of these methods. These include contact detection, explicit solvers, fracture and fragmentation models, handling of complex geometric considerations when processing interaction in three dimensions (contact kinematics) and fluid coupling. In recent years, there have been major breakthroughs in almost all of these key algorithmic aspects. These include linear contact-detection procedures (NBS, C-grid), discretized contact solutions, fracture and fragmentation solutions, together with fluid pressure driven fracture process and three-dimensional explicit solvers incorporating finite rotations. Many of these breakthroughs have not yet been applied across the full range of relevant discontinuum problems. The major reason for this is that discrete-element method, discontinuum deformation analysis and combined finite-discrete-element method publications are spread over a wide range of specialist journals and conferences. Thus in this paper, the main features of a selection of algorithmic breakthroughs are reviewed for the first time, enabling researchers in different fields to apply these compatible developments to their specific applications.
Novel techniques are introduced to render the classical split Hopkinson
bar apparatus suitable for dynamic recovery experiments, where samples
can be subjected to a single pulse of pre-assigned shape and duration,
and then recovered without any additional loading, for post-test
characterization; i.e., techniques for fully controlled unloading in
Hopkinson bar experiments. For compression dynamic recovery tests, the
new design generates a compressive pulse trailed by a tensile pulse
(stress reversal), travelling toward the sample. Furthermore, all
subsequent pulses which reflect off the free ends of the two bars
(incident and transmission) are rendered tensile, so that the sample is
subjected to a single compressive pulse whose shape and duration can
also be controlled. For tension recovery experiments, the new design
provides for trapping the compression pulse reflected off the sample,
and the tensile pulse transmitted through the sample. In addition, a
sample can be subjected to compression followed by tension, and then
recovered, allowing the study of, e.g. the dynamic Bauschinger effect in
materials.
The performance of the open source multiphase flow solver, interFoam, is evaluated in this work. The solver is based on a modified volume of fluid (VoF) approach, which incorporates an interfacial compression flux term to mitigate the effects of numerical smearing of the interface. It forms a part of the C + + libraries and utilities of OpenFOAM and is gaining popularity in the multiphase flow research community. However, to the best of our knowledge, the evaluation of this solver is confined to the validation tests of specific interest to the users of the code and the extent of its applicability to a wide range of multiphase flow situations remains to be explored. In this work, we have performed a thorough investigation of the solver performance using a variety of verification and validation test cases, which include (i) verification tests for pure advection (kinematics), (ii) dynamics in the high Weber number limit and (iii) dynamics of surface tension-dominated flows. With respect to (i), the kinematics tests show that the performance of interFoam is generally comparable with the recent algebraic VoF algorithms; however, it is noticeably worse than the geometric reconstruction schemes. For (ii), the simulations of inertia-dominated flows with large density ratios yielded excellent agreement with analytical and experimental results. In regime (iii), where surface tension is important, consistency of pressure–surface tension formulation and accuracy of curvature are important, as established by Francois et al (2006 J. Comput. Phys.
213 141–73). Several verification tests were performed along these lines and the main findings are: (a) the algorithm of interFoam ensures a consistent formulation of pressure and surface tension; (b) the curvatures computed by the solver converge to a value slightly (10%) different from the analytical value and a scope for improvement exists in this respect. To reduce the disruptive effects of spurious currents, we followed the analysis of Galusinski and Vigneaux (2008 J. Comput. Phys.
227 6140–64) and arrived at the following criterion for stable capillary simulations for interFoam: where . Finally, some capillary flows relevant to atomization were simulated, resulting in good agreement with the results from the literature.
Non-linear sound propagation is investigated computationally by simulating compressible time-developing mixing layers using the Large Eddy Simulation (LES) approach and solving the viscous Burgers Equation. The mixing layers are of convective Mach numbers of 0.4, 0.8 and 1.2. The LES results agree qualitatively with known flow behavior. Mach waves are observed in the near sound field of the supersonic mixing layer computed by the LES. These waves show steepening typical to non-linear propagation. Further calculations using the Burgers equation support this finding, where the initial wave slope has a role in kicking them. No visible non-linear propagation effects were found for the subsonic mixing layers. The effects of geometrical spreading and viscosity are also considered.
1] A shallow explosion in a fluid is one of the fundamental processes of airwave generation in volcanic eruptions. To better understand the mechanism of the airwave generation, underwater explosion experiments were conducted. Although the underwater explosions have been intensely studied over the last century, airwaves have received little attention. In this study, pressure waves were measured in air and under water, and the corresponding motion of the water surface was captured by a high-speed video camera. Airwaves and associated styles of the surface motion show similarities determined by the scaled depth, defined as the depth divided by the cubic root of the explosion energy. The air waveforms are quite different from the pressure waves measured in the water and cannot be completely explained by linear transmission of pressure waves from water to air. The mechanism of airwave generation is a combination of wave transmission and dynamics of the interface boundary. The first mechanism directly reflects the explosion source, and the same source is also observed as the underwater pressure waves. On the other hand, the second is not necessarily visible in the underwater pressure waves but will provide information on the mechanical properties and behavior of the material above the explosion source. Each mechanism is analyzed in the experiments.
The seaward slope of many breakwaters consists of thousands of interlocking units of rock or concrete comprising a massive granular system of large elements each weighing tens of tonnes. The dumped quarry materials in the core are protected by progressively coarser particulates. The outer armour layer of freely placed units is intended to both dissipate wave energy and remain structurally stable as strong flows are drawn in and out of the particulate core. Design guidance on the mass and shape of these units is based on empirical equations derived from scaled physical model tests. The main failure mode for armour layers exposed to severe storms is hydraulic instability where the armour units of concrete or rock are subjected to uplift and drag forces which can in turn lead to rocking, displacement and collisions sufficient to cause breakage of units. Recently invented armour unit designs making up such granular layered system owe much of their success to the desirable emergent properties of interlock and porosity and how these combine with individual unit structural strength and inertial mass. Fundamental understanding of the forces governing such wave–structure interaction remains poor. We use discrete element and combined finite-discrete element methods to model the granular solid skeleton of randomly packed units coupled to a CFD code which resolves the wave dynamics through an interface tracking technique. The CFD code exploits several methods including a compressive advection scheme, node movement, and general mesh optimization. We provide the engineering context and report progress towards the numerical modelling of instability in these massive granular systems.
The shock-induced collapse of a pre-existing nucleus near a solid surface in the focal region of a lithotripter is investigated. The entire flow field of the collapse of a single gas bubble subjected to a lithotripter pulse is simulated using a high-order accurate shock- and interface-capturing scheme, and the wall pressure is considered as an indication of potential damage. Results from the computations show the same qualitative behavior as that observed in experiments: a re-entrant jet forms in the direction of propagation of the pulse and penetrates the bubble during collapse, ultimately hitting the distal side and generating a water-hammer shock. As a result of the propagation of this wave, wall pressures on the order of 1 GPa may be achieved for bubbles collapsing close to the wall. The wall pressure decreases with initial stand-off distance and pulse width and increases with pulse amplitude. For the stand-off distances considered in the present work, the wall pressure due to bubble collapse is larger than that due to the incoming shockwave; the region over which this holds may extend to ten initial radii. The present results indicate that shock-induced collapse is a mechanism with high potential for damage in shockwave lithotripsy.
The combined finite discrete element method is a relatively new computational tool aimed at problems involving static and / or dynamic behaviour of systems involving a large number of solid deformable bodies. Such problems include fragmentation using explosives (e.g rock blasting), impacts, demolition (collapsing buildings), blast loads, digging and loading processes, and powder technology. The combined finite-discrete element method - a natural extension of both discrete and finite element methods - allows researchers to model problems involving the deformability of either one solid body, a large number of bodies, or a solid body which fragments (e.g. in rock blasting applications a more or less intact rock mass is transformed into a pile of solid rock fragments of different sizes, which interact with each other). The topic is gaining in importance, and is at the forefront of some of the current efforts in computational modeling of the failure of solids. * Accompanying source codes plus input and output files available on the Internet * Important applications such as mining engineering, rock blasting and petroleum engineering * Includes practical examples of applications areas Essential reading for postgraduates, researchers and software engineers working in mechanical engineering.
Underwater noise pollution is a by-product of marine industrial operations. In particular, the noise generated when a foundation pile is driven into the soil with an impact hammer is considered to be harmful for the aquatic species. In an attempt to reduce the ecological footprint, several noise mitigation techniques have been investigated. Among the various solutions proposed, the air-bubble curtain is often applied due to its efficacy in noise reduction. In this paper, a model is proposed for the investigation of the sound reduction during marine piling when an air-bubble curtain is placed around the pile. The model consists of the pile, the surrounding water and soil media, and the air-bubble curtain which is positioned at a certain distance from the pile surface. The solution approach is semi-analytical and is based on the dynamic sub-structuring technique and the modal decomposition method. Two main results of the paper can be distinguished. First, a new model is proposed that can be used for predictions of the noise levels in a computationally efficient manner. Second, an analysis is presented of the principal mechanisms that are responsible for the noise reduction due to the application of the air-bubble curtain in marine piling. The understanding of these mechanisms turns to be crucial for the exploitation of the maximum efficiency of the system. It is shown that the principal mechanism of noise reduction depends strongly on the frequency content of the radiated sound and the characteristics of the bubbly medium. For piles of large diameter which radiate most of the acoustic energy at relatively low frequencies, the noise reduction is mainly attributed to the mismatch of the acoustic impedances between the seawater and the bubbly layer. On the contrary, for smaller piles and when the radiated acoustic energy is concentrated at frequencies close to, or higher than, the resonance frequency of the air bubbles, the sound absorption within the bubbly layer becomes critical.
We present results of a solution to longitudinal impact of thick bars, obtained via an exact three-dimensional theory. Detailed investigation of the behavior of the solution has been carried out, including a number of subsidiary calculations. The results obtained made it possible to improve on the knowledge of the physical nature of the problem investigated. By comparing the exact theory with calculations performed in terms of an elementary bar theory, the successive transition from a three-dimensional (3D) description to a one-dimensional (ID) one could be demonstrated. The obtained dependences of displacements and stresses have been compared with Skalak's asymptotic solution and with results of experiments by Miklowitz.
Jet's sound-field emitted by a large scale source modeled as a wave packet is considered. Attention is given to nonlinear propagation effects caused by the source's supersonic Mach number and high amplitude. The approach of the Westervelt equation is adapted to derive a new set of weakly nonlinear sound propagation equations. An optimized Lax–Wendorff scheme is proposed for the newly derived equations. It is shown that these equations can be simulated using a time step close to the CFL limit even for high amplitudes unlike the conventional finite-difference simulation approach of the Westervelt equation. Two- and three-dimensional sound propagations were simulated for symmetric and asymmetric supersonic wave packets. It is seen that nonlinearity in the sound field is affected by the wave packet form, an effect that cannot be captured by a 1D propagation equation. High skewness in the pressure fluctuation and its time derivative were found near the Mach direction, showing crackle-like features. Pressure time history and frequency spectra are also investigated.
A full-scale 3D analysis of a Split Hopkinson Pressure Bar experiment on granite material using a 3D combined Finite-Discrete Element Method (FDEM) is shown. Previous efforts to simulate Split Hopkinson Pressure Bar experiments using the 2D FDEM had obtained a very good match for the loading portion of the experiment. This work extends those efforts by modeling the entire 3D Split Hopkinson Pressure Bar experimental setup, and reproducing the softening behavior of the sample after breakage. This modeling effort introduces the effect of a compliant interface between the bars and the sample.
The book presents the research results for the problems of underwater explosions and
contains a detailed analysis of the structure and the parameters of the wave fields
generated by explosions of cord and spiral charges, a description of the formation
mechanisms for a wide range of cumulative flows at underwater explosions near the
free surface, and the relevant mathematical models. Shock-wave transformation in
bubbly liquids, shock-wave amplification due to collision and focusing, and the
formation of bubble detonation waves in reactive bubbly liquids are studied in
detail. Particular emphasis is placed on the investigation of wave processes in
cavitating liquids, which incorporates the concepts of the strength of real liquids
containing natural microinhomogeneities, the relaxation of tensile stresses, and the
cavitation fracture of a liquid as the inversion of its two-phase state under
impulsive (explosive) loading.
The problems are classed among essentially nonlinear processes that occur under
shock loading of liquids and may be of interest to researchers in physical
acoustics, mechanics of multiphase media, shock-wave processes in condensed media,
explosive hydroacoustics, and cumulation.
The compression of a cylindrical gas bubble by an imploding molten lead (Pb)
shell may be accompanied by the development of the Richtmyer-Meshkov (RM)
instability at the liquid-gas interface due to the initial imperfection of the
interface. A converging pressure wave impinging upon the interface causes a
shell of liquid to detach and continue to travel inwards, compressing the gas
bubble. The efficiency of compression and collapse evolution can be affected by
development of the RM instability. Investigations have been performed in the
regime of extreme Atwood number with the additional complexity of
modeling liquid cavitation in the working fluid. Simulations have been carried
out using the open source CFD software OpenFOAM on a set of parameters relevant
to the prototype compression system under development at General Fusion Inc.
for use as a Magnetized Target Fusion (MTF) driver.
After validating the numerical setup in planar geometry, simulations have
been carried out in 2D cylindrical geometry for both initially smooth and
perturbed interfaces. Where possible, results have been validated against
existing theoretical models and very good agreement has been found. While our
main focus is on the effects of initial perturbation amplitude and azimuthal
mode number, we also address differences between this problem and those usually
considered, such as RM instability at an interface between two gases with a
moderate density ratio. One important difference is the formation of narrow
molten lead jets rapidly propagating inwards during the final stages of the
collapse. Jet behaviour has been observed for a range of azimuthal mode numbers
and perturbation amplitudes.
Large-scale discrete element simulations, the combined finite–discrete element method, DDA as well as a whole range of related methods, involve contact of a large number of separate bodies. In the context of the combined finite–discrete element method, each of these bodies is represented by a single discrete element which is then discretized into finite elements. The combined finite–discrete element method thus also involves algorithms dealing with fracture and fragmentation of individual discrete elements which result in ever changing topology and size of the problem. All these require complex algorithmic procedures and significant computational resources, especially in terms of CPU time. In this context, it is also necessary to have an efficient and robust algorithm for handling mechanical contact. In this work, a contact algorithm based on the penalty function method and incorporating contact kinematics preserving energy balance, is proposed and implemented into the combined finite element code. Copyright © 2000 John Wiley & Sons, Ltd.
This paper describes a summary of a research project for the development of extracorporeal shock wave lithotripsy (ESWL), which has been carried out, under close collaboration between the Shock Wave Research Center of Tohoku University and the School of Medicine, Tohoku University. The ESWL is a noninvasive clinical treatment of disintegrating human calculi and one of the most peaceful applications of shock waves. Underwater spherical shock waves were generated by explosion of microexplosives. Characteristics of the underwater shock waves and of ultrasound focusing were studied by means of holographic interferometric flow visualization and polyvinyliden-difluoride (PVDF) pressure transducers. These focused pressures, when applied to clinical treatments, could effectively and noninvasively disintegrate urinary tract stones or gallbladder stones. However, despite clincal success, tissue damage occurs during ESWL treatments, and the possible mechanism of tissue damage is briefly described.
General Fusion is planning to form an FRC or spheromak of 1017cm−3, 100eV, 40cm diameter by merging two spheromaks with reverse or co-helicity. This target will be further compressed in
a 3m diameter tank filled with liquid PbLi with the plasma in the center. The tank is surrounded with pneumatically powered
impact pistons that will send a convergent shock wave in the liquid to compress the plasma to 1020cm−3, 10keV, 4cm diameter for 7μs. General Fusion has built a 500kJ, 80μs, 6GW pneumatic impact piston capable of developing
2GPa (300kpsi). In this paper we will present the performances achieved to date.
The combined finite-discrete method
- A Munijza
Computational and Experimental Investigation of Supersonic Flow and their Controls
- S S Deshpande
- L Anumolu
- M F Trujillo
- V Don
- E J Avital
- F Motallebi
Deshpande, S. S., Anumolu, L. and Trujillo, M. F. [2012] "Evaluating the performance of the two-phase flow solver interFoam," Comput. Sci. Disc. 5, 014016.
Don, V., Avital, E. J. and Motallebi, F. [2013] "Computational and Experimental
Investigation of Supersonic Flow and their Controls," Proc World Academy Sci,
Eng Tech 73, 1181-1187.
- J H Ferziger
- M Peric
Ferziger, J. H., Peric, M. [1997] Computational Methods for Fluid Dynamics
(Springer-Verlag, Berlin Heidelberg, Germany).
Imploding Shock-Driven Cavitation in Cylindrical Cavities
- J Huneault
- A Higgins
Huneault, J. and Higgins, A. [2015] "Imploding Shock-Driven Cavitation in Cylindrical Cavities," In Proceedings of the 30th International Symposium on Shock
Waves, Tel-Aviv, Israel, July 19-24.
Status of Progress Towards Acoustic Magnetized Target Fusion at General Fusion
- D Richardson
- A Froese
- V Suponitsky
- M Reynolds
- D Plant
Richardson, D., Froese, A., Suponitsky, V., Reynolds, M. and Plant, D. [2013] "Status of Progress Towards Acoustic Magnetized Target Fusion at General Fusion,"
In Proceedings of the 34th Annual Conference of the Canadian Nuclear Society,
Toronto, Canada, June 9-12.
Computational fluid dynamics of dispersed two-phase flows at high phase fractions
- H Rusche
Rusche, H. [2002] "Computational fluid dynamics of dispersed two-phase flows at
high phase fractions," Imperial college of science. London. UK: Technology &
Medicine.
Sound propagation in liquid metal for a nuclear fusion applications
- E Salvatore
Salvatore, E. [2015] "Sound propagation in liquid metal for a nuclear fusion applications," M.Sc. Thesis, School of Engineering and Material Science, Queen Mary
University of London, London, UK.
Propagation of Pressure Waves in Compression System Prototype for Magnetized Target Fusion Reactor in General Fusion Inc
- V Suponitsky
- D Plant
- E J Avital
- A Munjiza
Suponitsky, V., Plant, D., Avital, E. J. and Munjiza, A. [2015] "Propagation of
Pressure Waves in Compression System Prototype for Magnetized Target Fusion Reactor in General Fusion Inc.," In Proceedings of the 30th International
Symposium on Shock Waves, Tel-Aviv, Israel, July 19-24.