Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “multiple shocks”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2

MAGNETIC-RECONNECTION GENERATED SHOCK WAVES AS A DRIVER OF SOLAR SURGES

We found that a surge consists of multiple shock features. In our high-spatiotemporal spectroscopic observation of the surge, each shock is identified with the sudden appearance of an absorption feature at the blue wings of the Ca II 8542 Å line and Hα line that gradually shifts to the red wings. The shock features overlap with one another with the time interval of 110 s, which is much shorter than the duration of each shock feature, 300-400 s. This finding suggests that the multiple shocks might not have originated from a train of sinusoidal waves generated by oscillations and flows in the photosphere. As we found the signature of the magnetic flux cancelations at the base of the surge, we conclude that the multiple shock waves in charge of the surge were generated by the magnetic reconnection that occurred in the low atmosphere in association with the flux cancelation.

79 ASTRONOMY AND ASTROPHYSICS↗

Amplification of turbulence through multiple planar shocks

We study the amplification of isotropic, incompressible turbulence through multiple planar, collisional shocks, using analytical linear theory. There are two limiting cases we explore. The first assumes shocks occur rapidly in time such that the turbulence does not evolve between shocks. Whereas the second case allows enough time for turbulence to isotropize between each shock. For the latter case, through a quasi-equation-of-state, we show that the weak multishock limit is agnostic to the distinction between thermal and vortical turbulent pressures, like an isotropic volumetric compression. When turbulence does not return to isotropy between shocks, the generated anisotropy—itself a function of shock strength—can feedback on amplification by further shocks, altering choices for maximal or minimal amplification. In addition for this case, we find that amplification is sensitive to the shock ordering. As a result, we map how choices of shock strength can impact these amplification differences due to ordering, finding, for example, shock pairs which lead to identical mean postshock fields (density, temperature, pressure) but maximally distinct turbulent amplification.

Astrophysical fluid dynamics↗

RADIO AND X-RAY SHOCKS IN CLUSTERS OF GALAXIES

Radio relics detected in the outskirts of galaxy clusters are thought to trace radio-emitting relativistic electrons accelerated at cosmological shocks. In this study, using the cosmological hydrodynamic simulation data for the large-scale structure formation and adopting a diffusive shock acceleration (DSA) model for the production of cosmic-ray (CR) electrons, we construct mock radio and X-ray maps of simulated galaxy clusters that are projected in the sky plane. Various properties of shocks and radio relics, including the shock Mach number, radio spectral index, and luminosity, are extracted from the synthetic maps and compared with observations. A substantial fraction of radio and X-ray shocks identified in these maps involve multiple shock surfaces along lines of sight (LOSs), and the morphology of shock distributions in the maps depends on the projection direction. Among multiple shocks in a given LOS, radio observations tend to pick up stronger shocks with flatter radio spectra, while X-ray observations preferentially select weaker shocks with larger kinetic energy flux. As a result, in some cases the shock Mach numbers and locations derived from radio and X-ray observations could differ from each other. We also find that the distributions of the spectral index and radio power of the synthetic radio relics are somewhat inconsistent with those of observed real relics; a bit more radio relics have been observed closer to the cluster core and with steeper spectral indices. We suggest that the inconsistency could be explained if very weak shocks with M{sub s} ≲ 2 accelerate CR electrons more efficiently, compared with the DSA model adopted here.

79 ASTRONOMY AND ASTROPHYSICS↗

The Advanced Composition Explorer Shock Database and Application to Particle Acceleration Theory

The theory of particle acceleration via diffusive shock acceleration (DSA) has been studied in depth by Gosling et al. (1981), van Nes et al. (1984), Mason (2000), Desai et al. (2003), Zank et al. (2006), among many others. Recently, Parker and Zank (2012, 2014) and Parker et al. (2014) using the Advanced Composition Explorer (ACE) shock database at 1 AU explored two questions: does the upstream distribution alone have enough particles to account for the accelerated downstream distribution and can the slope of the downstream accelerated spectrum be explained using DSA? As was shown in this research, diffusive shock acceleration can account for a large population of the shocks. However, Parker and Zank (2012, 2014) and Parker et al. (2014) used a subset of the larger ACE database. Recently, work has successfully been completed that allows for the entire ACE database to be considered in a larger statistical analysis. We explain DSA as it applies to single and multiple shocks and the shock criteria used in this statistical analysis. We calculate the expected injection energy via diffusive shock acceleration given upstream parameters defined from the ACE Solar Wind Electron, Proton, and Alpha Monitor (SWEPAM) data to construct the theoretical upstream distribution. We show the comparison of shock strength derived from diffusive shock acceleration theory to observations in the 50 keV to 5 MeV range from an instrument on ACE. Parameters such as shock velocity, shock obliquity, particle number, and time between shocks are considered. This study is further divided into single and multiple shock categories, with an additional emphasis on forward-forward multiple shock pairs. Finally with regard to forwardforward shock pairs, results comparing injection energies of the first shock, second shock, and second shock with previous energetic population will be given.

Parker, L. Neergaard↗

The Advanced Composition Explorer Shock Database and Application to Particle Acceleration Theory

The theory of particle acceleration via diffusive shock acceleration (DSA) has been studied in depth by Gosling et al. (1981), van Nes et al. (1984), Mason (2000), Desai et al. (2003), Zank et al. (2006), among many others. Recently, Parker and Zank (2012, 2014) and Parker et al. (2014) using the Advanced Composition Explorer (ACE) shock database at 1 AU explored two questions: does the upstream distribution alone have enough particles to account for the accelerated downstream distribution and can the slope of the downstream accelerated spectrum be explained using DSA? As was shown in this research, diffusive shock acceleration can account for a large population of the shocks. However, Parker and Zank (2012, 2014) and Parker et al. (2014) used a subset of the larger ACE database. Recently, work has successfully been completed that allows for the entire ACE database to be considered in a larger statistical analysis. We explain DSA as it applies to single and multiple shocks and the shock criteria used in this statistical analysis. We calculate the expected injection energy via diffusive shock acceleration given upstream parameters defined from the ACE Solar Wind Electron, Proton, and Alpha Monitor (SWEPAM) data to construct the theoretical upstream distribution. We show the comparison of shock strength derived from diffusive shock acceleration theory to observations in the 50 keV to 5 MeV range from an instrument on ACE. Parameters such as shock velocity, shock obliquity, particle number, and time between shocks are considered. This study is further divided into single and multiple shock categories, with an additional emphasis on forward-forward multiple shock pairs. Finally with regard to forward-forward shock pairs, results comparing injection energies of the first shock, second shock, and second shock with previous energetic population will be given.

Parker, L. Neergaard↗

Ion pre-acceleration in fully self-consistent particle-in-cell simulations of supercritical perpendicular reforming shocks in multiple ion species plasmas

Supernova remnant and heliopause termination shock plasmas may contain significant populations of minority heavy ions, with relative number densities n{sub α}/n{sub i} up to 50%. Preliminary kinetic simulations of collisionless shocks in these environments showed that the reformation cycle and acceleration mechanisms at quasi-perpendicular shocks can depend on the value of n{sub α}/n{sub i} . Shock reformation unfolds on ion spatio-temporal scales, requiring fully kinetic simulations of particle dynamics, together with the self-consistent electric and magnetic fields. This paper presents the first set of particle-in-cell simulations for two ion species, protons (n{sub p} ) and α-particles (n{sub α}), with differing mass and charge-to-mass ratios, that spans the entire range of n{sub α}/n{sub i} from 0% to 100%. The interplay between the differing gyro length scales and timescales of the ion species is crucial to the time-evolving phenomenology of the shocks, the downstream turbulence, and the particle acceleration at different n{sub α}/n{sub i} . We show how the overall energization changes with n{sub α}/n{sub i} , and relate this to the processes individual ions undergo in the shock region and in the downstream turbulence, and to the power spectra of magnetic field fluctuations. The crossover between shocks dominated by the respective ion species happens when n{sub α}/n{sub i} = 25%, and minority ion energization is strongest in this regime. Energization of the majority ion species scales with injection energy. The power spectrum of the downstream turbulence includes peaks at sequential ion cyclotron harmonics, suggestive of ion ring-beam collective instability.

79 ASTRONOMY AND ASTROPHYSICS↗

Non-Richtmyer–Meshkov instability ejecta production based on shallow bubble collapse

The study of shock-driven ejecta production has focused on Richtmyer–Meshkov instability (RMI) growth from geometric features of the material surface. Extensive study of this mechanism under both single- and multiple-shock conditions has found that the ejected mass tends to be closely associated with the shocked surface phase, and its temperature is not dramatically greater than the hydrodynamic shock temperature of the bulk. In this work, we propose and demonstrate a new ejecta production mechanism that can occur under multiple-shock conditions based on the collapse of bubbles near the free surface of the material. This mechanism produces ejected mass that is much greater in quantity than observed in the RMI case. The particles are much hotter than predicted by the shock Hugoniot state, and the ejected mass does not appear to be strongly dependent upon initial surface finish. The ejecta source extends into the material with no clear remaining free surface. We name this mechanism Shallow Bubble Collapse (SBC) and discuss the conditions under which it activates. We demonstrate resolved modeling methods that enable the calculation, design, and study of SBC as a mechanism and perform a series of experiments to compare with the models. Under some multiple-shock conditions, SBC ejection produces ten times more ejected mass than RMI growth.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

WHEN SHOCK WAVES COLLIDE

Supersonic outflows from objects as varied as stellar jets, massive stars, and novae often exhibit multiple shock waves that overlap one another. When the intersection angle between two shock waves exceeds a critical value, the system reconfigures its geometry to create a normal shock known as a Mach stem where the shocks meet. Mach stems are important for interpreting emission-line images of shocked gas because a normal shock produces higher postshock temperatures, and therefore a higher-excitation spectrum than does an oblique shock. In this paper, we summarize the results of a series of numerical simulations and laboratory experiments designed to quantify how Mach stems behave in supersonic plasmas that are the norm in astrophysical flows. The experiments test analytical predictions for critical angles where Mach stems should form, and quantify how Mach stems grow and decay as intersection angles between the incident shock and a surface change. While small Mach stems are destroyed by surface irregularities and subcritical angles, larger ones persist in these situations and can regrow if the intersection angle changes to become more favorable. The experimental and numerical results show that although Mach stems occur only over a limited range of intersection angles and size scales, within these ranges they are relatively robust, and hence are a viable explanation for variable bright knots observed in Hubble Space Telescope images at the intersections of some bow shocks in stellar jets.

79 ASTRONOMY AND ASTROPHYSICS↗

Incorporation of coupled nonequilibrium chemistry into a two-dimensional nozzle code (SEAGULL)

A two-dimensional multiple shock nozzle code (SEAGULL) was extended to include the effects of finite rate chemistry. The basic code that treats multiple shocks and contact surfaces was fully coupled with a generalized finite rate chemistry and vibrational energy exchange package. The modified code retains all of the original SEAGULL features plus the capability to treat chemical and vibrational nonequilibrium reactions. Any chemical and/or vibrational energy exchange mechanism can be handled as long as thermodynamic data and rate constants are available for all participating species.

Ratliff, A. W.↗

Heat Pipe Vapor Dynamics

The dynamic behavior of the vapor flow in heat pipes is investigated at startup and during operational transients. The vapor is modeled as two-dimensional, compressible viscous flow in an enclosure with inflow and outflow boundary conditions. For steady-state and operating transients, the SIMPLER method is used. In this method a control volume approach is employed on a staggered grid which makes the scheme very stable. It is shown that for relatively low input heat fluxes the compressibility of the vapor flow is low and the SIMPLER scheme is suitable for the study of transient vapor dynamics. When the input heat flux is high or the process under a startup operation starts at very low pressures and temperatures, the vapor is highly compressible and a shock wave is created in the evaporator. It is shown that for a wide range of input heat fluxes, the standard methods, including the SIMPLER scheme, are not suitable. A nonlinear filtering technique, along with the centered difference scheme, are then used for shock capturing as well as for the solution of the cell Reynolds-number problem. For high heat flux, the startup transient phase involves multiple shock reflections in the evaporator region. Each shock reflection causes a significant increase in the local pressure and a large pressure drop along the heat pipe. Furthermore, shock reflections cause flow reversal in the evaporation region and flow circulations in the adiabatic region. The maximum and maximum-averaged pressure drops in different sections of the heat pipe oscillate periodically with time because of multiple shock reflections. The pressure drop converges to a constant value at steady state. However, it is significantly higher than its steady-state value at the initiation of the startup transient. The time for the vapor core to reach steady-state condition depends on the input heat flux, the heat pipe geometry, the working fluid, and the condenser conditions. However, the vapor transient time, for an Na-filled heat pipe is on the order of seconds. Depending on the time constant for the overall system, the vapor transient time may be very short. Therefore, the vapor core may be assumed to be quasi-steady in the transient analysis of a heat pipe operation.

Issacci, Farrokh↗

Free energy models for ice VII and liquid water derived from pressure, entropy, and heat capacity relations

Here, we present equations of state relevant to conditions encountered in ramp and multiple-shock compression experiments of water. These experiments compress water from ambient conditions to pressures as high as about 14 GPa and temperatures of up to several hundreds of Kelvin. Water may freeze into ice VII during this process. Although there are several studies on the thermodynamic properties of ice VII, an accurate and analytic free energy model from which all other properties may be derived in a thermodynamically consistent manner has not been previously determined. We have developed such a free energy model for ice VII that is calibrated with pressure-volume-temperature measurements and melt curve data. Furthermore, we show that liquid water in the pressure and temperature range of interest is well-represented by a simple Mie-Grüneisen equation of state. Our liquid water and ice VII equations of state are validated by comparing to sound speed and Hugoniot data. Although they are targeted towards ramp and multiple-shock compression experiments, we demonstrate that our equations of state also behave reasonably well at pressures and temperatures that lie somewhat beyond those found in the experiments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Flame acceleration and transition to detonation in a pre-/main-chamber combustion system

Numerical simulations are performed to study the mechanism of deflagration to detonation transition (DDT) in a pre-/main-chamber combustion system with a stoichiometric ethylene–oxygen mixture. A Godunov algorithm, fifth-order in space, and third-order in time, is used to solve the fully compressible Navier–Stokes equations on a dynamically adapting mesh. A single-step, calibrated chemical diffusive model described by Arrhenius kinetics is used for energy release and conservation between the fuel and the product. The two-dimensional simulation shows that a laminar flame grows in the pre-chamber and then develops into a jet flame as it passes through the orifice. A strong shock forms immediately ahead of the flame, reflecting off the walls and interacting with the flame front. The shock–flame interactions are crucial for the development of flame instabilities, which trigger the subsequent flame development. The DDT arises due to a shock-focusing mechanism, where multiple shocks collide at the flame front. A chemical explosive mode analysis (CEMA) criterion is developed to study the DDT ignition mode. Preliminary one-dimensional computations for a laminar propagating flame, a fast flame deflagration, and a Chapman–Jouguet detonation are conducted to demonstrate the validity of CEMA on the chemical-diffusive model, as well as to determine the proper conditioning value for CEMA diagnostic. The two-dimensional analysis with CEMA indicates that the DDT initiated by the shock-focusing mechanism can form a strong thermal expansion region at the flame front that features large positive eigenvalues for the chemical explosive mode and dominance of the local autoignition mode. Thus, the CEMA criterion proposed in this study provides a robust diagnostic for identifying autoignition-supported DDT, of which the emergence of excessive local autoignition mode is found to be a precursor. The effect of grid size, initial temperature, and orifice size are then evaluated, and results show that although the close-chamber DDT is highly stochastic, the detonation initiation mechanism remains robust.

42 ENGINEERING↗

The acceleration of electrons at collisionless shocks moving through a turbulent magnetic field

We perform a numerical-simulation study of the acceleration of electrons at shocks that propagate through a prespecified, kinematically defined turbulent magnetic field. The turbulence consists of broadband magnetic fluctuations that are embedded in the plasma and cover a range of wavelengths, the smallest of which is larger than the gyroradii of electrons that are initially injected into the system. We find that when the variance of the turbulent component of the upstream magnetic field is sufficiently large—σ{sup 2} ∼ 10 B{sub 0}{sup 2}, where B{sub 0} is the strength of the background magnetic field—electrons can be efficiently accelerated at a collisionless shock regardless of the orientation of the mean upstream magnetic field relative to the shock-normal direction. Since the local angle between the incident magnetic-field vector and the shock-normal vector can be quite large, electrons can be accelerated through shock-drift acceleration at the shock front. In the upstream region, electrons are mirrored back to the shock front leading to multiple shock encounters. Eventually the accelerated electrons are energetic enough that their gyroradii are of the same order as the wavelength of waves that are included in our description of the turbulent magnetic field. Our results are consistent with recent in situ observations at Saturn’s bow shock. This study may help us to understand the acceleration of electrons at shocks in space and astrophysical systems.

79 ASTRONOMY AND ASTROPHYSICS↗

Numerical studies of multiple-encounter shock drift acceleration

Test particle simulation is performed to examine the mechanism previously proposed by Chiueh for particle acceleration by a nearly perpendicular shock where only downstream MHD turbulence is present. A nonnegligible fraction of low-energy particles is observed gaining energy by more than three orders of magnitude in a few hundred cyclotron periods. Criteria for effective acceleration given previously are examined and confirmed. The numerical results suggest that in the nonrelativistic energy range, a power-law particle energy spectrum, with the power index determined by the degree to which the criteria are satisfied, may form.

Chiueh, Tzihong↗

Multiple shock-shock interference on a cylindrical leading edge

The details of an experimental study of shock wave interference heating on a cylindrical leading edge representative of the cowl of a rectangular hypersonic engine inlet are presented. This Mach 8 study has provided the first detailed pressure and heat transfer rate distributions on a cylinder resulting from a two-dimensional shockwave interference pattern created by two incident oblique shock waves intersecting the cylinder bow shock wave. The peak heat transfer rate was 38 times the undisturbed flow stagnation point level and occurred when the two oblique shock waves coalesced prior to intersecting the cylinder bow shock wave. Development of pressure deflection diagrams identified a new interference pattern consisting of concomitant supersonic jets separated from each other by a shear layer and submerged in the subsonic region between the bow shock wave and body.

Wieting, Allan R.↗