Milos Stanic

Tendency of spherically imploding plasma liners formed by merging plasma jets to evolve toward spherical symmetry

We have performed three-dimensional (3D) simulations using smoothed particle hydrodynamics (SPH) in order to study the effects of discrete plasma jets on the processes of plasma liner formation, implosion on vacuum, and expansion. It was found that the pressure histories of the inner portion of the liner from 3D SPH simulations with a uniform liner and with 30 discrete plasma jets were qualitatively and quantitatively similar from peak compression through the complete stagnation of the liner. The 3D simulations with a uniform liner were first benchmarked against results from one-dimensional radiation-hydrodynamic simulations [T. J. Awe et al., Phys. Plasmas 18, 072705 (2011)]. Two-dimensional plots of the pressure field show that the discrete jet SPH case evolves towards a profile that is almost indistinguishable from the SPH case with a uniform liner, thus indicating that non-uniformities due to discrete jets are smeared out by late stages of the implosion. The processes of plasma liner formation and implosion on vacuum were shown to be robust against Rayleigh-Taylor instability growth. Finally, interparticle mixing for a liner imploding on vacuum was investigated. The mixing rate was found to be very small until after the peak compression for the 30 jet simulations.

Case and Development Path for Fusion Propulsion

This paper discusses the importance of fusion propulsion for interplanetary space travel, illustrates why the magnetoinertial fusion parameter space may facilitate the most rapid, economic path for development, justifies the choice of pulsed Z pinch, and provides a potential development path leading up to a technical readiness level 9 system. Round trips of less than one year to Mars are only possible using fusion propulsion systems. Such a system will require an onboard nuclear fission reactor for reliable startups, and so fission and fusion developments for space are mutually beneficial. The paper reviews the more than 50 year history of fusion research and summarizes results from a recent study of the fusion parameter space for terrestrial power, which suggests magnetoinertial fusion can provide the smallest, most economical approach for a fusion propulsion system. Emerging experimental data and theory show pulsed Z-pinch fusion solves some of the most deleterious instabilities and scales to fusion bre...

Ideal hydrodynamic scaling relations for a stagnated imploding spherical plasma liner formed by an array of merging plasma jets

This work presents scaling relations for the peak thermal pressure and stagnation time (over which peak pressure is sustained) for an imploding spherical plasma liner formed by an array of merging plasma jets. Results were derived from three-dimensional (3D) ideal hydrodynamic simulation results obtained using the smoothed particle hydrodynamics code SPHC. The 3D results were compared to equivalent one-dimensional (1D) simulation results. It is found that peak thermal pressure scales linearly with the number of jets and initial jet density and Mach number, quadratically with initial jet radius and velocity, and inversely with the initial jet length and the square of the chamber wall radius. The stagnation time scales approximately as the initial jet length divided by the initial jet velocity. Differences between the 3D and 1D results are attributed to the inclusion of thermal transport, ionization, and perfect symmetry in the 1D simulations. A subset of the results reported here formed the initial design basis for the Plasma Liner Experiment [S. C. Hsu et al., Phys. Plasmas 19, 123514 (2012)].

Scale coupling in Richtmyer-Meshkov flows induced by strong shocks

We perform the first systematic study of the nonlinear evolution and scale coupling in Richtmyer-Meshkov (RM) flows induced by strong shocks. The smoothed particle hydrodynamics code (SPHC) is employed to ensure accurate shock capturing, interface tracking and accounting for the dissipation processes. We find that in strong-shock-driven RMI the background motion is supersonic. The amplitude of the initial perturbation strongly influences the flow evolution and the interfacial mixing that can be sub-sonic or supersonic. At late times the flow remains laminar rather than turbulent, and RM bubbles flatten and decelerate. In the fluid bulk, reverse cumulative jets appear and “hot spots” are formed—local heterogeneous microstructures with temperature substantially higher than that in the ambient. Our numerical simulations agree with the zero-order, linear, weakly nonlinear, and highly nonlinear theoretical analyses as well as with the experiments and suggest that the evolution of RMI is a multi-scale and heter...

Non-uniform volumetric structures in Richtmyer-Meshkov flows

We perform an integrated study of volumetric structures in Richtmyer-Meshkov (RM) flows induced by moderate shocks. Experiments, theoretical analyses, Smoothed Particle Hydrodynamics simulations, and ARES Arbitrary Lagrange Eulerian simulations are employed to analyze RM evolution for fluids with contrast densities in case of moderately small amplitude initial perturbation at the fluid interface. After the shock passage the dynamics of the fluids is a superposition of the background motion and the interfacial mixing, and only a small part of the shock energy is available for interfacial mixing. We find that in the fluid bulk the flow fields are non-uniform at small scales, and the heterogeneous volumetric structures include reverse jets, shock-focusing effects, and local hot spots with the temperature substantially higher than that in the ambient.

Characteristics-based sectional modeling of aerosol nucleation and condensation

A new numerical method for the solution of an internally mixed spatially homogeneous sectional model for aerosol nucleation and condensation is proposed. The characteristics method is used to predict droplet sizes within a discrete time step. The method is designed such that 1) a pre-specified number of moments of the droplet size distribution may be preserved, 2) there exists no time step stability restriction related to the condensation rate and section size, 3) highly skewed fixed sectional distributions may be used and 4) it is straightforward to extend to spatially inhomogeneous settings and to incorporate droplet coagulation and break-up. We derive, starting from mass conservation, a consistent internally mixed multi-species aerosol model. For certain condensational growth laws analytical solutions exist, against which the method is validated. Using two-moment and four-moment-preserving schemes, we find first order convergence of the numerical solution to the analytical result, as a function of the number of sections. As the four-moment-preserving scheme does not guarantee positivity of the solution, a hybrid scheme is proposed, which, when needed, locally reverts back to two-moment preservation, to prevent negativity. As an illustration, the method is applied to a complete multi-species homogeneous nucleation and condensation problem.

Improved PISO algorithms for modeling density varying flow in conjugate fluid-porous domains

Two modified segregated PISO algorithms are proposed, which are constructed to avoid the development of spurious oscillations in the computed flow near sharp interfaces of conjugate fluid-porous domains. The new collocated finite volume algorithms modify the Rhie-Chow interpolation to maintain a correct pressure-velocity coupling when large discontinuous momentum sources associated with jumps in the local permeability and porosity are present. The Re-Distributed Resistivity (RDR) algorithm is based on spreading flow resistivity over the grid cells neighboring a discontinuity in material properties of the porous medium. The Face Consistent Pressure (FCP) approach derives an auxiliary pressure value at the fluid-porous interface using momentum balance around the interface. Such derived pressure correction is designed to avoid spurious oscillations as would otherwise arise with a strictly central discretization. The proposed algorithms are successfully compared against published data for the velocity and pressure for two reference cases of viscous flow. The robustness of the proposed algorithms is additionally demonstrated for strongly reduced viscosity, i.e., higher Reynolds number flows and low Darcy numbers, i.e., low permeability of the porous regions in the domain, for which solutions without unphysical oscillations are computed. Both RDR and FCP are found to accurately represent porous media flow near discontinuities in material properties on structured grids. Two modified segregated PISO algorithms are proposed.The Rhie-Chow interpolation is modified to maintain a correct pressure-velocity coupling when large discontinuous momentum sources are present.The proposed algorithms are successfully compared against published data for the velocity and pressure for two reference cases of viscous flow.The robustness of the proposed algorithms is additionally demonstrated for high Reynolds number flows and low Darcy numbers.

Maximum initial growth-rate of strong-shock-driven Richtmyer-Meshkov instability

We focus on the classical problem of the dependence on the initial conditions of the initial growth-rate of strong shock driven Richtmyer-Meshkov instability (RMI) by developing a novel empirical model and by employing rigorous theories and Smoothed Particle Hydrodynamics simulations to describe the simulation data with statistical confidence in a broad parameter regime. For the given values of the shock strength, fluid density ratio, and wavelength of the initial perturbation of the fluid interface, we find the maximum value of the RMI initial growth-rate, the corresponding amplitude scale of the initial perturbation, and the maximum fraction of interfacial energy. This amplitude scale is independent of the shock strength and density ratio and is characteristic quantity of RMI dynamics. We discover the exponential decay of the ratio of the initial and linear growth-rates of RMI with the initial perturbation amplitude that excellently agrees with available data.

Scaling Laws for Merging and Implosion of Discrete Plasma Jets

High pressures and temperatures may be generated at the center an imploding plasma liner with applications in thermonuclear fusion, laboratory scale astrophysics, and high energy density physics. These phenomena are being studied on the Plasma Liner Experiment (PLX) in which a spherical liner is formed via the merging of plasma jets. The basic physical processes include pulsed plasma acceleration, plasma jet propagation in a vacuum, plasma jet merging, liner formation, liner implosion, stagnation, and rarefaction. A summary of PLX, some preliminary theory and modeling results, and scaling laws based on 3D hydrodynamic modeling are presented. We will emphasize our recent 3D hydro modeling, which provides insights into liner formation, implosion, and effects of initial jet parameters on scaling of peak pressure.

Validation of SPHC and CRASH codes in modeling of linear and non-linear Richtmyer-Meshkov instabilities

Richtmyer-Meshkov instability (RMI) plays an important role in a broad variety of phenomena in nature and technology and is of special interest in the fields of shockturbulence interaction, supersonic aerodynamic flows, and inertial and magneto-inertial fusion. The instability develops when a shock refracts an interface between two fluids with different values of the acoustic impedance, and RMI dynamics is defined primarily by the flow Mach number and the Atwood number for the two fluids. For continuous fluid dynamic (CFD) codes, numerical modeling of RMI is a severe task, which imposes high requirements on the resolution, accuracy and spatio-temporal dynamic range of the simulations. Modeling of high-Atwood and high-Mach flows, which are of interest in practical applications, is even more challenging, as it requires shock capturing, interface tracking and accurate accounting for the dissipation processes. We used Smooth Particle Hydrodynamics Code (SPHC) and Center for RAdiative Shock Hydrodynamics (CRASH) codes to mutually evaluate the codes and compare their results against the analytical RMI theory. The numerical and theoretical results are in good qualitative and quantitative agreement with one another. These results indicate that at large scales the nonlinear dynamics of RMI is a multi-scale processes; at small scale the flow field is heterogeneous and is characterized by appearance of local microscopic structures; the coupling between the scales has a complicated character.