Figure - available from: AIP Advances
This content is subject to copyright. Terms and conditions apply.
Source publication
In this study, a system of two equations is developed that allows the time evolution of the underwater spark channel to be calculated numerically from a given power input. The proposed mathematical model utilizes the elliptical coordinates. This approach has the advantage of considering the underwater spark as an expanding ellipsoid, which closely...
Citations
... The expanding spark channel is filled with cold high-pressure weakly ionized plasma originating from the gas of the injected bubble and evaporated water. There are numerous publications devoted to the theoretical or experimental studies of hydrodynamic phenomena induced by underwater spark discharges (see, for example, References [8,[16][17][18][19][20][21]). However, the study of plasma in the spark channel has so far received less attention. ...
... Therefore, we must conclude that the underwater spark is not a source of a black-body radiation. Nevertheless, the assumption of black-body emission by the spark is able to simplify the mathematical model in some cases and can give a reasonable result in hydrodynamic mathematical simulations of underwater spark expansion [16][17][18][19][20][21]. ...
This paper is aimed at the investigation of the acoustic and spectral characteristics of underwater electric sparks generated between two plate electrodes, using synchronized gas bubble injection. There are two purposes served by discharge initiation in the bubble. Firstly, it creates a favorable condition for electrical breakdown. Secondly, the gas bubble provides an opportunity for the direct spectroscopy of plasma light emission, avoiding water absorption. The effect of water absorption on captured spectra was studied. It was observed that the emission intensity of the Ha line and a shockwave amplitude generated by discharge strongly depend on the size of the gas bubble in the moment of the discharge initiation. It was found that the plasma in the underwater spark channel does not correspond to a source of black-body radiation. This study can be also very useful for understanding the difference between discharges produced directly in a liquid and discharges produced in gas/vapor bubbles surrounded by a liquid.
... There is continuing interest in the numerical simulation of high-voltage pulse underwater discharges, and this field has been intensively studied over the past few decades. Most prior studies have been devoted to the simulation of spark generation and the subsequent oscillation of the bubble (see for example references [1][2][3][4][5][6][7][8]). A pulsed corona discharge in water or in bubble is another type of underwater discharge in which electrical breakdown does not occur and an underwater spark is not generated [9][10][11][12][13][14][15]. ...
... In case of the spark, the deposited electrical energy can be calculated as R(t)i(t) 2 , where the resistance R(t) can be treated as a constant [3,6], or an empirical expression for the plasma channel resistance can be used [4]. Another approach is to use the measured temporal voltage u(t) and current i(t) data and to calculate the deposited energy as u(t)i(t) [6][7][8]. However, the latter method is not appropriate for calculating the corona dis- charge, as the corona resistance is connected in series with a water equivalent resistance (as shown in figure 1), and both of these vary with time. ...
... The corona is formed due to vaporisation and ionisation processes, and is an expanding cavity filled with a mixture of low-temperature plasma and water vapour. It has been shown in several studies that there are two main components of the discharge energy: the internal energy of the plasma, and the mechanical energy of expansion of the bubble in the water [1,4,6,7]. The energy losses through thermal conduction and light emission are small, and can be neglected [1]. ...
We present a study that was undertaken to calculate the resistance of low current corona discharge in saline water. A novel empirical model was obtained, based on several assumptions, which allowed us to determine the corona resistance using the measured current. This resistance could be then exploited to compute the power deposited to the corona as a function of time. The wall motion of a bubble freely oscillating in saline water was calculated using hydrodynamic equations and the calculated power function. A comparison of numerical simulations with experimental results showed that good agreement was achieved.
... That is why a two stage description was introduced, at which an earlier cylindrical geometry transforms later on into a spherical one [34,35]. A first attempt to numerically simulate the discharge channel as an expanding ellipsoid was done by Stelmashuk [36]. Nevertheless, there is still a lack of studies describing a medium power cylindrical spark expansion in compressible viscous liquid. ...
... Therefore, it is desirable to rewrite this model for spherical symmetry and to apply it to short gap geometry, where data from the fast camera are available [31] and a more reliable fitting to experiment could be done. There is still a possibility to transform this one-dimensional model with radial expansion in cylindrical/spherical geometry to two-dimensions and use an ellipsoidal geometry (similarly to how it has been done in a much simpler situation in [36]); however, in new tensor equations (39) and (40), pop-up cross-terms with partial derivatives/differences with respect to tangential ('con-focal ellipsoid') and radial ('con-focal hyperbolic') coordinates simultaneously. Development of a new computational strategy under these conditions represents a very challenging task. ...
In this study, a new finite-difference cylindrical model of long underwater spark is developed that allows us to numerically calculate the time evolution of the underwater spark channel from a given power input. A one dimensional simulation starts in the breakdown moment. The whole time development is divided into time steps of equal duration. The investigated region consists of a homogeneous cylindrical central column filled with weakly ionized vapour and its atomic fragments, and co-axial cylindrical liquid slabs of equal thickness in the beginning. In each time step, some energy (experimentally given and reduced by losses spent on dissociation, excitation, and ionization) is delivered into the central plasma column. This energy is partly irradiated, out-conducted, spent on mechanical work, and/or used for an increase of inner energy of the plasma column. This ambiguity enables us in future to fit, e.g. the plasma column diameter at the end of energy input to its experimental value. The model shows that plasma channel expansion generates a primary pressure wave propagating with supersonic velocity, and a subsequent secondary pressure wave that propagates with sound velocity. An advantage of this approach is that the present solution with constant coefficients can be relatively easily upgraded to a solution with variable coefficients.
