Numerical simulation of stress waves in water : Application to lithotripsy and decontamination of waterway.

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1 Numerical simulation of stress waves in water : Application to lithotripsy and decontamination of waterway. M. Arrigoni 1, J.-P. Cuq Lelandais 2, M. Boustie 2, H. Zastawny 3, H. Romat 3, Y. Chauveau 4 1 Laboratoire Brestois de Mécanique et des Systèmes, ENSIETA, 2 rue François Verny, Brest, Cedex 9, France. 2 Laboratoire de Combustion et de Détonique - UPR CNRS ENSMA - BP Futuroscope, France. 3 Laboratoire d'etudes Aérodynamiques, CNRS UMR 6609, SP2MI - Téléport 2, Boulevard Marie et Pierre Curie, BP 30179, Futuroscope Chasseneuil cedex, France. 4 Expertise in Multiphysics & Analysis, 53 rue des chirons longs, La Rochelle, France. Abstract : Stress wave propagation generated by electrical discharge in fluid is a phenomenon used in many applications. This paper presents Altair Hypermesh Radioss simulations for two of these applications. The first one deals with the waterway bacteria decontamination. During its lifespan, the waterway inner wall is covered by bacteria. This agglomeration of bacteria forms a biofilm that might lead to not drinkable water and even epidemic. Electrical discharges engendering stress waves is coming out as an innovative technique for preventing biofilm formation. Experiments were performed and results were compared with numerical simulation. The second application taken from the medical field presents the wave propagation occurring in a lithotripter. Lithotripter is a medical equipment used for eliminating kidney stones by provoking convergence of compressive waves at a chosen location. Simulations were performed with Altair Hypermesh Radioss in Arbitrary Lagrangian Eulerian configuration and results allow a first interpretation of experiments. Keywords : underwater shock wave, lithotripsy, decontamination, electrical discharge, biofilms, kidney stone 1

2 INTRODUCTION The use of compression wave induced by high power electrical discharges presents convenience for many applications. Among them, the water pipe decontamination and the lithotripsy are of a high interest for the health of human beings. For both applications, the approach is the same : an underwater compressive wave is induced by a high voltage discharge between two electrodes. This compressive wave propagates through the water environment and is reflected at wall interfaces. Two studies were carried out for each of these applications. The waterway decontamination study was originally supported by Electricité de France (EDF) and the characterization of the lithotripsy was performed in connection with the University Hospital of Poitiers (CHU Poitiers). Firstly, this study defines the two situations : waterway decontamination technique and lithotripsy. Then for each case experimental results and numerical simulation made with Altair Hypermesh Radioss are analyzed. A discussion follows the analysis and states significance of this work is given as a conclusion. PROBLEMS DEFINITION Decontamination of waterway Situation On Earth, about 1385 millions of km 3 of water may be available and 0.02 % is used as drinkable water. In most cases, water has to be treated before being drinkable and it also must be treated once spoiled by daily home uses. Since the Roman Empire, water is transported through aqueducts and waterway pipes. During their lifespan, waterway pipes may be contaminated by biological films composed of microorganisms called biofilms. These biofilms may induce a degradation of the water quality and even allow the proliferation of pathogens microorganisms causing diseases like the legionnaire s disease. A possible curative technique applicable on waterways relies on the use of pulsed arc discharges [1]. Underwater electrodes separated by a small gap and undergoing a high electrical potential generate a pulsed arc. The discharge induces a pressure wave, which may be the main bactericidal mechanism [2,3] as they propagate in the duct. An experimental setup consisting on a hydraulic closed circuit was designed within the framework of Zastawny s PhD thesis [1] (fig. 1). Three pressure sensors P 1, P 2 and P 3 were respectively placed along the pipe at 0.3, 4.3 and 9 meters of the electrical arc generator. Experimental results linking generated pressure with electrical parameters and the inter electrodes distance were obtained [4]. In order to characterize the pressure pulse thus generated, an inverse approach using numerical simulation performed with Altair Hypermesh Radioss was attempted. 2

3 Model In order to simplify this study, only a part of the hydraulic circuit is meshed in 3D and a symmetric plane has even been used. This part is a 70 cm cylindrical pipe of 1.6 cm of inner diameter ended by a 90 bend of 10 cm going down (fig. 2). The compression wave generator located at the straight extremity and the other extremity is supposed to be endless (ends with SILENT BOUNDARY elements [5]). The gap between electrodes is 3 mm and the electrode section is 1 cm². The Arbitrary Lagrangian Eulerian (ALE) configuration has been used. The size element is nearly constant and the mesh consists of cells. Cells has been attributed Law 26 (SESAME JOHNSON-COOK) [5] with the following coefficients set for the water : The density ρ init = 0, g.mm -3, the Young modulus E= 0, GPa, the Poisson coefficient ν= 0 and the Yield limit Y 0 = 0, GPa. The volume of water undergoing the electrical discharge is considered as water in which the internal energy varies. By imposing energy and density, SESAME tabulated Equation of State allows deducing temperature and pressure within the ionized water. The volume between electrodes is about 235 mm 3. By supposing that 50 % of the electrical energy brought by the discharge is absorbed, thus 170 J, the internal energy of the ionized water can be set to 700 mj/mm 3, which corresponds to water at 100 Bars and 311 C. Lithotripsy Situation Lithotripter is a medical device used in urology that is able to fragment kidney stones without surgery. This recent technology has emerged in Quebec in the middle eighties. It relies on the generation of a pulsed compressive wave, by electrical discharge that propagates through the patient body and, once focused, reaches the stone and fragments it. Among different existing geometrical designs, one that was used at CHU Poitiers was composed of a half elliptical basin filled with water in which electrodes are placed at one focus and the kidney stone in the patient body is positioned at the other focus (image focus). Once the compressive wave generated, it propagates through the water until the wall of the ellipsoid basin and is then reflected towards the other focus (image focus) where the stone is waiting for being fragmented (fig. 3). This method has provided good results and is becoming more and more popular. However, pressures generated by this kind of equipment are not well known and may present some fluctuations that might inconvenience patients. It was thus necessary to characterize pressure loads generated by electrical discharges. Firstly, in order to characterize the stress undergone by the kidney stone, pressure measurements were performed around the renal stone. Thus, PVDF sensors (PolyVinyliDene Fluoride, a piezoelectric polymer) were placed at the patient place in order to obtain experimental data of the pressure pulse delivered by the lithotripter [6]. Sensors were composed of 250 µm aluminium substrate whose front face were coated with a 25 µm PVDF layer. These sensors were placed at the image focus. It has been measured that the peak 3

4 pressure from one pulse to another ranges from 500 to 800 Bars, the pulse duration at half maximum is around 1 µs and the pressure rise time to maximum is about ns. These observations confirmed fluctuations that can inconvenience patients. A numerical study will allow a more accurate and optimal use of the lithotripter and a better understanding of the underwater stress generation-propagation. It relies on the same approach than the one done for the decontamination study. In this intention, a study with Altair Hypermesh Radioss was attempted. ANALYSIS Decontamination of waterway Calculations were performed for three densities corresponding to particular states of the water: the water vapor at 1 atm and 100 C, the water vapor at 100 bars and 311 C, and the water at 1 atm and 20 C. According to the literature, temperature and pressure of the plasma generated by the breakdown are respectively of the order of 10 4 K and 10 8 Pa [7]. Table 1 gives the results computed by Altair Hypermesh Radioss, obtained with three densities and for different energies per volume unit. Table 1 shows that whatever the density, for energy per volume unit of 700 mj.mm -3, the pressure has the same order as the literature s one. The temperature varies as a function of the load density and its order of magnitude was obtained similar to the literature s one when the density was the water vapour s one at 100 bars and 311 C. Thus, this last density may be suitable for characterizing the load medium. Figure 5 shows waves propagation in the pipe on which can be seen the growth of the spherical compressive wave until it reaches the wall. Afterward, the front wave is slightly spherical and propagates towards the open extremity. In red color, pressure is compression; in blue color the pressure is a tensile. Figure 6 shows the decrease of the pressure peak as a function of distance to the load, for water density at 100 bars and 300 C. The same results were obtained for other load densities. The calculated pressure values are compared with the measured ones at 30 cm to the discharge. Figure 7 shows the temporal pressure evolution for different load energies (% of 345 J), when the electrode gap medium at the breakdown moment is considered as water vapour (100 bars, 311 C). These evolutions are compared to the measured pressure one obtained for an applied electrical energy of 345 J. Lithotripsy Computation shows that the early propagation of the under water compressive wave is spherical (fig. 8). Obviously, the upper spherical front wave goes through the upper basin without being focused and thus it is a loss of pressure. Then, a part of the spherical wave 4

5 rebounds against the elliptic basin and is then reflected towards the upper part of the basin. At this stage, these reflected waves interact with the bubble created by vaporized water due to the electrical discharge (Fig. 8, t = 49 µs). The pressure at the image focus (in the upper part of the basin) is recorded. Its maximum reaches 500 Bars and its duration at half maximum is about 7 µs (fig. 8, t = 206 µs) It takes about 200 µs for the upper spherical wave to reach the ceiling (upper limit of the mesh), which represents about 330 mm. Thus the wave velocity is about 1650 m/s, which is around the acoustic velocity in water (1580 m/s at 20 C, 1 Bar). DISCUSSIONS Decontamination of waterway Computation shows that the pressure peak value increases with the load energy and it is quickly attenuated close to the load. This observation (fig. 5) makes a physical sense due to hydrodynamic decay occurring during wave propagation and also in reality due to pressure loss caused by the wall roughness that is not taken into account in the simulation. Computed and measured pressure peaks are within the same range (the order of some hundred bars, fig. 6). However, signal width at half maximum is different (160 µs for the measured signal vs 100 µs for the computed one) and the shock front is steeper for the computed case. These differences may be due to the non-consideration of the roughness walls that is supposed to increase attenuation. Furthermore in the computed case, the load energy is released instantaneously in all the electrode gap volume while in reality, the electrical discharge occurs according to a longer temporal function. Lithotripsy This study is still at its beginning but computation offers a good way of observing the propagation of underwater compressive wave. It is able to reproduce the early stage of the propagation, which is spherical and moreover, it also reproduces the wave convergence towards the image focus after rebounding against the elliptic wall. Furthermore, the wave velocity seems to be correct. However, the pressure peak duration computed at the image focus is much larger than the one observed experimentally (7 µs by computation versus 1 µs by experiments). One first comment about this discrepancy is that the experimental peak pressure was determined by an intrusive method corresponding to the signal collected by a 25 µm PVDF layer on a 250 µm aluminium substrate. That is to say the peak measurement might depend on the PVDF sensor geometry. Moreover, the electrical discharge is simplified; a more complete model would provide better results. STATES SIGNIFICANCE OF YOUR WORK Through two topics involving underwater compression wave, we have approached 5

6 experimental results by numerical simulation performed with Altair Hypermesh Radioss. The first topic concerned a technique able to decontaminate waterway of contaminants deposited against the inner wall of the pipe during its lifespan. Computation performed seems to be in good accordance with experimental observations. They deserve to be deepened by complementary experiments that could be justly adjusted by computation. But results given by this study allow estimating pressure fields by inverse approach in more complex tubular structure in order to develop this decontamination technique using underwater electrical discharges. In the same physical base of underwater wave generation and propagation, the study has been transposed to a medical application for lithotripsy. Thus, geometrical optimisations and a better accuracy concerning the aimed area in side the patient are likely reasonable objectives. ACKNOWLEDGEMENTS We are very grateful to Altaïr Engineering for kindly providing the Hyperworks suite to ENSMA and ENSIETA, and to Y. Chauveau from EMA-Multiphysics Company ( for building the model of electrical discharges into pipes. REFERENCES 1 H. Zastawny, «Étude des décharges d arc électrique pulsées dans l eau. Application à la destruction des biofilms dans les conduites». PhD thesis, Université de POITIERS, J. S. Chang, P.C.Looy and K.Urashima Pulsed arc discharge in water: mechanism of current conduction and pressure wave formation in IEEE Conference on Electrical Insulation and Dielectric Phenomena, vol. 10, 2000, pp N.-M. Efremov et al., Experimental investigation of the action of pulsed electrical discharges in liquids on biological objects. IEEE Transactions on Plasma Science, vol.28, February H. Zastawny, H. Romat, M. Boustie, Experimental and numerical study on the pressure waves generated by the pulsed arcs in water pipes, International Symposium on Electrohydrodynamics - Buenos Aires, 4 th -6 th December Altair Hypermesh Radioss Starter User's Manual, Version 4.4, 2 rue de la renaissance, Antony Cedex France. 6 S. Couturier, «Capteurs PVDF : Mesures de pression induite par choc laser et par lithotriteur», Master thesis, Université de POITIERS, M.Mikula, J.Panak and V.Dvonka, The destruction effect of a pulse discharge in water suspensions, Plasma Sources Sci. Technol., 6 (1997),

7 FIGURES AND PLOTS Pulsed arc generator High voltage sensor Current sensor Pump Hot water tank Figure 1. Hydraulic closed circuit equipped of a compressive wave generator by high voltage discharge. Figure 2. Meshed part of the hydraulic closed circuit.. Stone Calcul Positioning tray-table Plateau de positionnement 0 Patient Électrodes Electrodes Figure 3. Principle of lithotripsy. 7

8 Kommentar: 1) Enlever les zigzags rouges 2) Pour «computation zone : en français, j avais marqué «zone du calcul» en parlant des calculs rénaux et non des calculs numériques lol peut être on peut trouver mieux comme nom : «Patient body zone» par exemple. Figure 4. Geometry and Mesh of the lithotripter 8

9 t = ms t = ms t = ms t = ms t = ms t = ms t = 2.11 ms t =2.722 ms t =3.414 ms t =4.05 ms Figure 5. Simulation of compression wave propagation in a waterway of 16 mm of diameter. 9

10 E(mJ.mm -3 ) T (K) P (Pa) Water vapour 700 0, , (1 atm, 100 C) ρ= 0,1303 kg.m , , Water vapour 700 0, , (100 bars, 311 C) ρ= 55 kg.m , , , , Water (1 atm, 20 C) ρ= 1000 kg.m , , , , , , Table 1. Pressure and temperature of the load as a function of its density and the applied energy. Figure 6. Pressure peak as a function of the distance to the load for different load energies. 10

11 Figure 7. Pressure in the numerical case for different load energies (% of 345 J) and the experimental case (345 J) [4]. t = 1.14 µs t = 13.2 µs t = 33.1 µs t = 49.0 µs image Focus primary Focus t = 92.2 µs t = 133 µs t = 206 µs t = 236 µs Figure 8. Propagation of an underwater compressive wave induced by electrical discharge. 11