Eric Johnsen

Implementation of WENO schemes in compressible multicomponent flow problems

High-order accurate shock-capturing schemes are capable of properly resolving discontinuities with correct wave speeds in single-fluid Riemann problems. However, when different fluids are present, oscillations develop at interfaces. A class of existing interface-capturing methods that suppress these oscillations is based on first- and second-order accurate reconstructions with Roe solvers. In this paper, we extend these methods to high-order accurate WENO schemes and the HLLC approximate Riemann solver. In particular, we show that a finite volume formulation where the appropriately averaged primitive variables are reconstructed leads to the oscillation-free advection of an isolated interface. Furthermore, numerical experiments show no spurious oscillations for problems where shockwaves and interfaces interact. We solve the Euler equations supplemented by a stiffened equation of state to model flows of gas and liquid components. Our method is high-order accurate, quasi-conservative, shock-capturing and interface-capturing; these properties are additionally verified by considering one-dimensional multicomponent Riemann problems and a two-dimensional shock-bubble interaction.

Numerical simulations of non-spherical bubble collapse.

A high-order accurate shock- and interface-capturing scheme is used to simulate the collapse of a gas bubble in water. In order to better understand the damage caused by collapsing bubbles, the dynamics of the shock-induced and Rayleigh collapse of a bubble near a planar rigid surface and in a free field are analysed. Collapse times, bubble displacements, interfacial velocities and surface pressures are quantified as a function of the pressure ratio driving the collapse and of the initial bubble stand-off distance from the wall; these quantities are compared to the available theory and experiments and show good agreement with the data for both the bubble dynamics and the propagation of the shock emitted upon the collapse. Non-spherical collapse involves the formation of a re-entrant jet directed towards the wall or in the direction of propagation of the incoming shock. In shock-induced collapse, very high jet velocities can be achieved, and the finite time for shock propagation through the bubble may be non-negligible compared to the collapse time for the pressure ratios of interest. Several types of shock waves are generated during the collapse, including precursor and water-hammer shocks that arise from the re-entrant jet formation and its impact upon the distal side of the bubble, respectively. The water-hammer shock can generate very high pressures on the wall, far exceeding those from the incident shock. The potential damage to the neighbouring surface is quantified by measuring the wall pressure. The range of stand-off distances and the surface area for which amplification of the incident shock due to bubble collapse occurs is determined.

Shock-induced collapse of a gas bubble in shockwave lithotripsy

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.

Atmospheric pressure plasma jets interacting with liquid covered tissue: Touching and not-touching the liquid

In the use of atmospheric pressure plasma jets in biological applications, the plasma-produced charged and neutral species in the plume of the jet often interact with a thin layer of liquid covering the tissue being treated. The plasma-produced reactivity must then penetrate through the liquid layer to reach the tissue. In this computational investigation, a plasma jet created by a single discharge pulse at three different voltages was directed onto a 200 µm water layer covering tissue followed by a 10 s afterglow. The magnitude of the voltage and its pulse length determined if the ionization wave producing the plasma plume reached the surface of the liquid. When the ionization wave touches the surface, significantly more charged species were created in the water layer with H3O+aq, O3−aq, and O2−aq being the dominant terminal species. More aqueous OHaq, H2O2aq, and O3aq were also formed when the plasma plume touches the surface. The single pulse examined here corresponds to a low repetition rate plasma jet where reactive species would be blown out of the volume between pulses and there is not recirculation of flow or turbulence. For these conditions, NxOy species do not accumulate in the volume. As a result, aqueous nitrites, nitrates, and peroxynitrite, and the HNO3aq and HOONOaq, which trace their origin to solvated NxOy, have low densities.

Helium atmospheric pressure plasma jets touching dielectric and metal surfaces

Atmospheric pressure plasma jets (APPJs) are being investigated in the context plasma medicine and biotechnology applications, and surface functionalization. The composition of the surface being treated ranges from plastics, liquids, and biological tissue, to metals. The dielectric constant of these materials ranges from as low as 1.5 for plastics to near 80 for liquids, and essentially infinite for metals. The electrical properties of the surface are not independent variables as the permittivity of the material being treated has an effect on the dynamics of the incident APPJ. In this paper, results are discussed from a computational investigation of the interaction of an APPJ incident onto materials of varying permittivity, and their impact on the discharge dynamics of the plasma jet. The computer model used in this investigation solves Poissons equation, transport equations for charged and neutral species, the electron energy equation, and the Navier-Stokes equations for the neutral gas flow. The APPJ ...

Preventing numerical errors generated by interface-capturing schemes in compressible multi-material flows

In the present work, errors generated in computations of compressible multi-material flows using shock-capturing schemes are examined, specifically pressure oscillations (when the specific heats ratio is variable), but also temperature spikes and species conservation errors. These numerical errors are generated at material discontinuities due to an inconsistent treatment of the convective terms. Though temperature errors are irrelevant to solutions to the Euler equations, it is shown that they have the potential to lead to problems when physical diffusion is included, i.e., for the Navier-Stokes equations. These errors are studied analytically and numerically by considering the one-dimensional advection of isolated material discontinuities. A methodology preventing such errors for weighted essentially non-oscillatory (WENO) schemes is presented, in which modified WENO weights are used to solve the transport equation for mass fraction in conservative form to prevent temperature and species conservation errors. Pressure errors are prevented by solving an additional transport equation for a given function of the ratio of specific heats. Several multi-dimensional problems with various discontinuities (shocks, material interfaces and contact discontinuities), including the single-mode Richtmyer-Meshkov instability, and turbulence are considered to test the method.

Formation of reactive oxygen and nitrogen species by repetitive negatively pulsed helium atmospheric pressure plasma jets propagating into humid air

Atmospheric pressure plasma jets have many beneficial effects in their use in surface treatment and, in particular, plasma medicine. One of these benefits is the controlled production of reactive oxygen and nitrogen species (RONS) in the active discharge through the molecular gases added to the primary noble gas in the input mixture, and through the interaction of reactive species in the plasma effluent with the ambient air. In this computational investigation, a parametric study was performed on the production of RONS in a multiply pulsed atmospheric pressure plasma jet sustained in a He/O2 mixture and flowing into ambient humid air. The consequences of flow rate, O2 fraction, voltage, and repetition rate on reactant densities after a single discharge pulse, after 30 pulses, and after the same total elapsed time were investigated. At the end of the first discharge pulse, voltage has the greatest influence on RONS production. However, the systematic trends for production of RONS depend on repetition rate and flow rate in large part due to the residence time of RONS in the plasma zone. Short residence times result in reactive species produced by the previous pulse still being in the discharge tube or in the path of the ionization wave at the next pulse. The RONS therefore accumulate in the tube and in the near effluent on a pulse-to-pulse basis. This accumulation enables species requiring multiple reactions among the primary RONS species to be produced in greater numbers.

Histotripsy-induced cavitation cloud initiation thresholds in tissues of different mechanical properties

Histotripsy is an ultrasound ablation method that depends on the initiation and maintenance of a cavitation bubble cloud to fractionate soft tissue. This paper studies how tissue properties impact the pressure threshold to initiate the cavitation bubble cloud. Our previous study showed that shock scattering off one or more initial bubbles, expanded to sufficient size in the focus, plays an important role in initiating a dense cavitation cloud. In this process, the shock scattering causes the positive pressure phase to be inverted, resulting in a scattered wave that has the opposite polarity of the incident shock. The inverted shock is superimposed on the incident negative pressure phase to form extremely high negative pressures, resulting in a dense cavitation cloud growing toward the transducer. We hypothesize that increased tissue stiffness impedes the expansion of initial bubbles, reducing the scattered tensile pressure, and thus requiring higher initial intensities for cloud initiation. To test this hypothesis, 5-cycle histotripsy pulses at pulse repetition frequencies (PRFs) of 10, 100, or 1000 Hz were applied by a 1-MHz transducer focused inside mechanically tunable tissue-mimicking agarose phantoms and various ex vivo porcine tissues covering a range of Youngs moduli. The threshold to initiate a cavitation cloud and resulting bubble expansion were recorded using acoustic backscatter detection and optical imaging. In both phantoms and ex vivo tissue, results demonstrated a higher cavitation cloud initiation threshold for tissues of higher Youngs modulus. Results also demonstrated a decrease in bubble expansion in phantoms of higher Youngs modulus. These results support our hypothesis, improve our understanding of the effect of histotripsy in tissues with different mechanical properties, and provide a rational basis to tailor acoustic parameters for fractionation of specific tissues.

Effects of tissue stiffness, ultrasound frequency, and pressure on histotripsy-induced cavitation bubble behavior.

Histotripsy is an ultrasound ablation method that controls cavitation to fractionate soft tissue. In order to effectively fractionate tissue, histotripsy requires cavitation bubbles to rapidly expand from nanometer-sized initial nuclei into bubbles often larger than 50 µm. Using a negative pressure high enough to initiate a bubble cloud and expand bubbles to a sufficient size, histotripsy has been shown capable of completely fractionating soft tissue into acelluar debris resulting in effective tissue removal. Previous work has shown that the histotripsy process is affected by tissue mechanical properties with stiffer tissues showing increased resistance to histotripsy fractionation, which we hypothesize to be caused by impeded bubble expansion in stiffer tissues. In this study, the hypothesis that increases in tissue stiffness cause a reduction in bubble expansion was investigated both theoretically and experimentally. High speed optical imaging was used to capture a series of time delayed images of bubbles produced inside mechanically tunable agarose tissue phantoms using histotripsy pulses produced by 345 kHz, 500 kHz, 1.5 MHz, and 3 MHz histotripsy transducers. The results demonstrated a significant decrease in maximum bubble radius (Rmax) and collapse time (tc) with both increasing Youngs modulus and increasing frequency. Furthermore, results showed that Rmax was not increased by raising the pressure above the intrinsic threshold. Finally, this work demonstrated the potential of using a dual-frequency strategy to modulate the expansion of histotripsy bubbles. Overall, the results of this study improve our understanding of how tissue stiffness and ultrasound parameters affect histotripsy-induced bubble behavior and provide a rational basis to tailor acoustic parameters for treatment of the specific tissues of interest.

Propagation mechanisms of guided streamers in plasma jets: the influence of electronegativity of the surrounding gas

Atmospheric pressure plasma jets for biomedical applications are often sustained in He with small amounts of, for example, O2 impurities and typically propagate into ambient air. The resulting poorly controlled generation of reactive species has motivated the use of gas shields to control the interaction of the plasma plume with the ambient gas. The use of different gases in the shield yields different behavior in the plasma plume. In this paper, we discuss results from experimental and computational investigations of He plasma jets having attaching and non-attaching gas shields. We found that negative ion formation in the He-air mixing region significantly affects the ionization wave dynamics and promotes the propagation of negative guided streamers through an electrostatic focusing mechanism. Results from standard and phase resolved optical emission spectroscopy ratios of emission from states of N2 and He imply different electric fields in the plasma plume depending on the composition of the shielding gas. These effects are attributed to the conductivity in the transition region between the plasma plume and the shield gas, and the immobile charge represented by negative ions. The lower conductivity in the attaching mixtures enables more extended penetration of the electric field whereas the negative ions aid in focusing the electrons towards the axis.