Modelling of time development of cylindrical underwater spark channel in compressible viscous liquid

Abstract

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.

Pressure in underwater spark discharge initiated with the help of bubble injection and its evaluation based on H-alpha line broadening

“…which for discharge (a) gives a value of ∼8000 K. For discharges (b) and (c), the higher members of the Balmer series lines are very small, and are therefore unsuitable for temperature determination. The temperature value given above is higher than indicated in the model [1], but smaller than in all other experiments (for example, Martin [17] measured a value of ∼30 000 K; Robinson et al [15] measured temperatures up to 52 000 K; and Vokurka and Plocek [18] found temperatures between 11 000 and 18 000 K). On the other hand, since discharges type (b) and (c) need to heat more particles than type (a) for the same driving circuit, we expect that they will have even lower temperatures.…”

“…[12,13]}. Our previous article [9] demonstrates (1) experimental arrangement that enables to collect visible spectra without water absorption (through ground electrode), (2) that the underwater spark in its early stage is not a black body radiator (it has a dominant hill-like region in the range from 350 to 580 nm {probably a result of substantially broadened line radiation}, and clearly pronounced H α line that broadens {undoubtedly due to increased pressure} with the gas bubble diminution), (3) that the increased pressure with gas bubble diminution is confirmed by a pressure probe that measures amplitude of the pressure wave propagating from the discharge channel. Our present paper proceeds from the same experimental data published in [9], but their interpretation is based on in-depth analysis of H α line profile (line width) that not only leads to determination of the pressure in the discharge channel, but also casts new light on other processes taking place in the early stage of underwater spark discharge initiated with gas bubble assistance.…”

“…Underwater spark discharges can serve as a source of diverging pressure waves [1]. After reflection at a suitable reflector, they can be transformed into converging shock waves [2] with a huge range of potential applications (such as extracorporeal lithotripsy {i.e.…”

An empirical resistance equation for the modelling of corona discharge in saline water

“…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.…”