Discontinuity Breakdown Research Articles

Energy conversions at shock wave interaction with pulse discharge in profiled channel

The objective of this paper is to conduct a comprehensive investigation of the thermal and gas dynamic flow fields generated during the interaction of pulsed volume discharge plasma with high-speed channel flow. A comparative visualization was carried out using high-speed infrared thermography and shadowgraphy techniques. We examined phenomena related to both plasma and gas dynamic interactions within a special test section of the gas dynamic channel. The spatial–temporal characteristics of the thermal fields associated with these plasma and gas dynamic interactions were analyzed, together with infrared radiation intensity diagrams. The dynamics of discontinuities and inhomogeneities resulting from the interaction of shock waves with the pulsed volume discharge plasma—referred to as discontinuity breakdown—were also investigated. We compared two physical mechanisms of energy conversion into infrared radiation recorded by the thermal imager in the range of 1.5–5.1 μm. These mechanisms include low-temperature plasma emission from a sub-microsecond localized volume discharge and the sub-millisecond radiation from the inner surfaces of glass walls heated due to thermal conductivity at the interface with the gas flow boundary layer.

Application of the Riemann problem with complex equations of state for modeling three-dimensional flows of real media

The paper considers the numerical simulation of spatial flows of real media in safety valves on the basis of the problem of an arbitrary discontinuity breakdown with complex equations of state. The solution is constructed by means of the developed numerical method, which is a modification of the classical scheme by S. K. Godunov and includes various complex equations of state of matter. The Van der Waals equations of state were used to model the flow of real gases, and the Mie-Grüneisen equation was used to describe the flow of a real weakly compressible fluid. It is shown that the proposed numerical schemes allow for modeling fluid and gas dynamic processes in real fluids and gases with shock waves and contact discontinuities and can be used both in areas of classical medium behavior and in areas with non-classical behavior.

Neglected culprit of nonlinear discharge characteristics in SF6: shielding effect induced by positive glow corona discharge

The discharge characteristics of SF6 dependent on gas pressure under extremely inhomogeneous electric fields are strongly nonlinear and must be carefully considered when optimizing gas-insulated equipment insulation design and defect detection. The main aim of this study was to determine the relationship between nonlinear breakdown characteristics and the pre-breakdown discharge mode transition. The breakdown model established by Niemeyer, as adapted under impulse voltage, was expanded. The images and the phase-resolved patterns of the pre-breakdown discharge as a function of gas pressure and applied voltage were analyzed to observe the relationship between them as per the spatial distribution of the spark paths. A universal model of the nonlinear breakdown phenomenon under steady-state voltage was established accordingly. Experimental results demonstrate the existence of a positive glow corona (PGC) discharge in the interval with the discontinuous breakdown voltage as well as significant interactions between the PGC discharge and leader discharge. The nonlinear characteristics can be attributed to the inception and quenching of the PGC discharge. The shielding effect induced by the PGC discharge is the neglected culprit of the strong nonlinear discharge characteristics under steady-state voltage. The nonmonotonic U–p curve in electronegative gases was also assessed in an effort to build a theoretical basis for the manufacture and condition monitoring of the gas-insulated equipment.

Monotonic derivative correction for calculation of supersonic flows with shock waves

Subject of Research. Numerical solution methods of gas dynamics problems based on exact and approximate solution of Riemann problem are considered. We have developed an approach to the solution of Euler equations describing flows of inviscid compressible gas based on finite volume method and finite difference schemes of various order of accuracy. Godunov scheme, Kolgan scheme, Roe scheme, Harten scheme and Chakravarthy-Osher scheme are used in calculations (order of accuracy of finite difference schemes varies from 1st to 3rd). Comparison of accuracy and efficiency of various finite difference schemes is demonstrated on the calculation example of inviscid compressible gas flow in Laval nozzle in the case of continuous acceleration of flow in the nozzle and in the case of nozzle shock wave presence. Conclusions about accuracy of various finite difference schemes and time required for calculations are made. Main Results. Comparative analysis of difference schemes for Euler equations integration has been carried out. These schemes are based on accurate and approximate solution for the problem of an arbitrary discontinuity breakdown. Calculation results show that monotonic derivative correction provides numerical solution uniformity in the breakdown neighbourhood. From the one hand, it prevents formation of new points of extremum, providing the monotonicity property, but from the other hand, causes smoothing of existing minimums and maximums and accuracy loss. Practical Relevance. Developed numerical calculation method gives the possibility to perform high accuracy calculations of flows with strong non-stationary shock and detonation waves. At the same time, there are no non-physical solution oscillations on the shock wave front.

Analysis of finite-difference schemes based on exact and approximate solution of Riemann problem

The Riemann problem of one-dimensional arbitrary discontinuity breakdown for parameters of unsteady gas flow is considered as applied to the design of Godunov-type numerical methods. The problem is solved in exact and approximate statements (Osher-Solomon difference scheme used in shock capturing numerical methods): the intensities (the ratio of static pressures) and flow velocities on the sides of the resulting breakdowns and waves are determined, and then the other parameters are calculated in all regions of the flow. Comparison of calculation results for model flows by exact and approximate solutions is performed. The concept of velocity function is introduced. The dependence of the velocity function on the breakdown intensity is investigated. A special intensity at which isentropic wave creates the same flow rate as the shock wave is discovered. In the vicinity of this singular intensity approximate methods provide the highest accuracy. The domain of applicability for the approximate Osher-Solomon solution is defined by performing test calculations. The results are presented in a form suitable for usage in the numerical methods. The results obtained can be used in the high-resolution numerical methods.

Definition of the Existence Region of the Solution of the Problem of an Arbitrary Gas-dynamic Discontinuity Breakdown at Interaction of Flat Supersonic Jets with Formation of Two Outgoing Compression Shocks

We have considered the modern theory of breakdown of an arbitrary gas-dynamic discontinuity for the space-time dimension equal to two. The regions of solutions existence for a one-dimensional non-stationary case and a two-dimensional stationary case have been compared. The Riemann problem of breakdown of an arbitrary discontinuity of parameters of two flat flows angle collision is considered. The problem is solved in accurate setting. The problem parameter areas where outgoing waves appear as two jumps are specified. Two depression waves solution are not covered. The special Mach numbers of interacting flows dividing the parameter plane into areas with different outgoing discontinuities are given.

An extended EPQ-based problem with a discontinuous delivery policy, scrap rate, and random breakdown.

In real supply chain environments, the discontinuous multidelivery policy is often used when finished products need to be transported to retailers or customers outside the production units. To address this real-life production-shipment situation, this study extends recent work using an economic production quantity- (EPQ-) based inventory model with a continuous inventory issuing policy, defective items, and machine breakdown by incorporating a multiple delivery policy into the model to replace the continuous policy and investigates the effect on the optimal run time decision for this specific EPQ model. Next, we further expand the scope of the problem to combine the retailer's stock holding cost into our study. This enhanced EPQ-based model can be used to reflect the situation found in contemporary manufacturing firms in which finished products are delivered to the producer's own retail stores and stocked there for sale. A second model is developed and studied. With the help of mathematical modeling and optimization techniques, the optimal run times that minimize the expected total system costs comprising costs incurred in production units, transportation, and retail stores are derived, for both models. Numerical examples are provided to demonstrate the applicability of our research results.

Three-dimensional magnetohydrodynamic model of the interaction between the solar wind and cometary atmospheres

A magnetohydrodynamic (MHD) model of the interaction between the solar wind and an expanding gas flow issuing from a comet nucleus is presented. The processes of photoionization of the neutral component of the comet matter and the resonance charge exchange between charged and neutral particles are taken into account, together with the interplanetary magnetic field effect. The adequacy of the single-fluid MHD approximation in describing the plasma flow with different temperatures of the components is shown. The model is numerically realized on the basis of the higher-order Godunov method using an approximate solution of the arbitrary MHD discontinuity breakdown problem. The results of a numerical investigation of the plasma and magnetic field parameters in the vicinity of a comet are presented for the conditions corresponding to the flyby of several spacecraft near comet Halley in March 1986 and the expected fly-round of comet Churyumov-Gerasimenko by the Rosetta spacecraft in 2015.

Inducing effect on the percolation transition in complex networks

Percolation theory concerns the emergence of connected clusters that percolate through a networked system. Previous studies ignored the effect that a node outside the percolating cluster may actively induce its inside neighbours to exit the percolating cluster. Here we study this inducing effect on the classical site percolation and K-core percolation, showing that the inducing effect always causes a discontinuous percolation transition. We precisely predict the percolation threshold and core size for uncorrelated random networks with arbitrary degree distributions. For low-dimensional lattices the percolation threshold fluctuates considerably over realizations, yet we can still predict the core size once the percolation occurs. The core sizes of real-world networks can also be well predicted using degree distribution as the only input. Our work therefore provides a theoretical framework for quantitatively understanding discontinuous breakdown phenomena in various complex systems.

Numerical study of shock wave dynamics in a gas suspension

We describe a process of pressure discontinuity breakdown in a gas suspension, dynamics of which is simulated by a system of equations of motion for a two-temperature two-speed monodisperse medium without phase transition and coagulation. The carrying medium is described by the Navier-Stokes equation system. A disperse phase is simulated by equations of mass, momentum and internal energy conservation. The system is reduced to a dimensionless form, it is written in the generalized coordinates and is solved by the explicit MacCormack method with a conservative correction scheme applied to each phase to obtain a monotonous solution. We describe an effect of decreasing the time intensity of a shock wave when its attitude is retained. The time of the pressure differential value relaxation at the direct shock wave front depends on the volumetric content and dispersion degree of the gas suspension.

Unsteady rarefied-gas expansion on evaporation of a condensed material from its overheated surface

The problem of sudden unsteady one-dimensional expansion of the vapors of a material, whose surface is heated to a given temperature under the action of, for example, suddenly applied intense irradiation, is considered. The structure of the plane Knudsen wall layer and the conditions under which a steady state of this layer is achieved are revealed. The calculations are carried out using direct statistical Monte Carlo simulation. The results are compared with the solution of a similar discontinuity breakdown problem governed by Euler equations.

Calculation of viscous and inviscid gas flows on unstructured grids using the AUSM scheme

An approach to the solution of the two-dimensional Navier-Stokes equations on triangular unstructured grids is considered. The method is based on the key idea of the Godunov scheme, namely, the advisability of solving the Riemann problem of arbitrary discontinuity breakdown. In the calculations the derivatives with respect to space are approximated with both the first and the second order. However, as distinct from the conventional Godunov method, in calculating the fluxes across the cell boundaries the Riemann problem is solved using the Advection Upstream Splitting Method (AUSM). The concepts involved in the AUSM scheme are discussed. The solution of the discontinuity breakdown problem obtained within the framework of this approach is compared with the results obtained using the Godunov method. Numerical solutions of some problems of viscous and inviscid perfect-gas flows obtained on unstructured grids of different fineness and those obtained on structured grids are also compared. The effect of the spatial approximation order on the accuracy of numerical solutions is studied.

Difference method for solving the gasdynamics equations based on the relations at discontinuities

Numerical, Godunov-type schemes for calculating time-dependent and steady supersonic flows are presented. They are based on the approximation of the flow parameters at the boundaries of the difference grid cells using approximate solutions of the corresponding problems of the gasdynamic discontinuity breakdown and the interaction between uniform supersonic flows. The solution of these problems is obtained from the relations that express the mass, momentum, and energy conservation laws for the gasdynamic equations in the mass variables when the wave velocities are taken in accordance with the upper bound. The schemes are economical, have a wide range of applicability, and ensure the calculation of expansion zones, the “smooth” passage through the sonic point at the change of sign of the characteristics, and the absence of oscillations on intense shocks.

Correlation of plume morphologies on joint surfaces with their fracture mechanic implications

AbstractThe fractography and conditions of propagation of joints that cut Devonian siltstones in the Appalachian Plateau, New York, and Eocene chalks from the Beer Sheva Syncline, Israel, are investigated. The joints cutting the siltstones are marked by S-type and C-type plumes, and the joints cutting the Lower Eocene and Middle Eocene chalks are marked by coarse and delicate plumes, respectively. The four plume types propagated under sub-critical (slow propagation) conditions. On the semi-quantitative fracture velocity (v) versus the tensile stress intensity (KI) curves, the S and C plume types fall in the KI=0.073–0.79 MPa m1/2 and v=2×10−4–10−2 m/s and KI=0.073–0.79 MPa m1/2 and v=10−6–10−4 m/s ranges respectively. The coarse and delicate plumes fall in the KI=0.03–0.17 MPa m1/2 and v=10−6–4×10−5 m/s and KI=0.03–0.17 MPa m1/2 and v=10−4–5×10−3 m/s ranges, respectively. Generally, slow plumes are relatively short, show periodicity, and typically exhibit superposition of arrest marks. On the other hand, faster plumes are longer and continuous, occur particularly in thinner layers, and show no superposition of arrest marks. There is a clear distinction between two en échelon segmentation end-members in the joint fringe, the ‘discontinuous breakdown type’ and the ‘continuous breakdown type’. There are also ‘transitional’ variations between the end-members. Only curved ‘discontinuous breakdown type’ boundaries of en échelon fringes can be equated with mirror boundaries.

Experimental realization of the two-dimensional problem of plane discontinuity breakdown at pulsed ionization of a flow with a shock

Experimental realization of the two-dimensional problem of plane discontinuity breakdown at pulsed ionization of a flow with a shock

Discontinuity breakdown on shock wave interaction with nanosecond discharge

Discontinuity breakdown conditions were experimentally realized by instant energy input in front of a plane shock wave. A shock tube and a special type of transversal nanosecond electric discharge with plasma electrodes were used for this research. A two-dimensional (2D) numerical simulation under experimental conditions has been undertaken. The pressure, density, temperature, and velocity fields have been examined. A comparison of numerical data and shadow images of a 2D flow after shock wave interaction with the discharge area was conducted. The geometry of the disturbed flowfield was found to be in good correspondence with one from numerical calculations. The results of the investigation also showed that, by using the described experimental setup, it is possible to achieve a special type of Richtmyer–Meshkov instability without applying an additional curved diaphragm.

On the Water Depth in the Breach during a Partial Dam Break

Theoretical and experimental data which make it possible to find the flow-rate, momentum and energy of the fluid that enters the lower pool after a discontinuity breakdown (dam break) in a rectangular channel with an even bottom, a step (sharp downstream rise in the bottom), a shelf (sharp drop in the bottom), and a threshold on the bottom are presented.

Problem of Oil Displacement by Gas Mixtures

The system of equations of one-dimensional flow of a multicomponent mixture with phase transitions through a porous medium is considered. In particular, this system describes the processes of enhanced oil recovery by injection of gases. For this system self-similar solutions of the Riemann problem of discontinuity breakdown are constructed by splitting the problem into "physicochemical" and "hydrodynamic" problems. Main elements of the procedure for constructing the solution are illustrated with reference to a four- component system with constant distribution coefficients and the solutions obtained by different methods are compared. It is shown that the approach proposed is also effective for a system with a greater number of components.

Slot diffraction of waves generated by an underwater explosion on the axis of a circular cylindrical shell

The problem of diffraction of a cylindrical shock wave generated by an electrical explosion in water on a longitudinal slot in a cylindrical rigid shell is considered. The numerical method of discontinuity breakdown is modified in relation to the polar coordinates used, which simplifies significantly the technical aspect of the solution. In the calculations pressure fields with diffraction maxima and minima are obtained and the evolution of the minima into “ruptures” is traced.

Effect of low hydrostatic pressure on migration of interphase boundaries in discontinuous breakdown

Effect of low hydrostatic pressure on migration of interphase boundaries in discontinuous breakdown