Oblique Shock Front Research Articles

Structure of rotating detonation in mixtures of natural gas and oxygen

The rotating detonation combustor is investigated as a potential implementation of pressure-gain combustion. Achieving net pressure-gain has proven to be extremely challenging in most combustors reported in the literature, regardless of their operating parameters. The performance losses observed in rotating detonation, compared to ideal predictions, can be attributed to mechanisms such as vitiation by residual burnt gases, partial detonation, and pre-combustion of reactants. The literature frequently discusses the impact of these mechanisms on measurable properties such as thrust and wave speed, but their effects on the front structure have not been fully understood. This study proposes using the rotating detonation structure for the first time to evaluate the vitiation quantitatively. The front structure of a compressed natural gas — oxygen-fueled rotating detonation is characterized using broadband chemiluminescence, and properties such as oblique shock angle, expansion angle, and front height are reported. The experimental values are then compared to the ideal predictions derived based on mass flow rates. The experimental front heights are found to be much higher than their ideal predicted counterparts. Analytical calculations that include pre-burning and vitiation show an increase in front height and a reduction in expansion angle, consistent with the chemiluminescence levels observed. The vitiated mass fraction is then deduced from the experimental front height, and the remaining velocity deficit is then used to evaluate the partial detonation mass fraction. Vitiated front angles compare favorably to the predicted values.Novelty and SignificanceThis study reports high-quality chemiluminescence imaging of natural gas/oxygen rotating detonation front enabling the measurement of critical geometrical front features such as the front height, oblique shock angle, and expansion angle. The conventional front mass flow rate balance is extended to account for the re-circulation of burnt gases effects and is used to estimate the experimental vitiation. Most notably, vitiation of the fresh mixture, which was already known to reduce front speed and pressure rise, is also shown to strongly decrease the expansion angle resulting in further losses of axial thrust.

A simple electrometric method for parametric determination of Jones-Wilkins-Lee equation of state from underwater explosion test

The parametric determination of the Jones-Wilkins-Lee equation of state (JWL-EOS) of condensed explosives was mostly dependent on a cylinder test using a high-speed photography technique. In the present work, a simple electrometric method based on the underwater explosion test was developed with a novel pressure-conducted velocity probe permitting recording the detonation and shock wave velocity in a single test. Specifically, a velocity probe-based testing setup for the underwater explosion was designed at first to measure the oblique shock wave front of the cylinder charge. We carried out four tests using powdery cyclotrimethylenetrinitramine (RDX) and obtained the curves of detonation-shock front position versus time. The oblique shock wave fronts were then determined based on the analysis of two-dimensional steady flow, and some other parameters such as detonation pressure, adiabatic exponent, Mach number, and gas-water interface angle were calculated combining the Prandtl-Mayer expansion law. Excellent agreements with the calculation results of Kamlet’s semi-empirical formulas were achieved. By applying a numerical calculation and test-and-error process, we adjusted the six JWL-EOS parameters (A, B, C, R1, R2, and ω) constantly to make the error between numerical and experimental results of oblique shock front fall within ±2%. Finally, the JWL-EOS of powdery RDX in each test was determined, and the curves of adiabatic pressure versus relative volume were plotted as well to demonstrate the accuracy of the present method.

DO CLOUD-CLOUD COLLISIONS TRIGGER HIGH-MASS STAR FORMATION? I. SMALL CLOUD COLLISIONS

We performed sub-parsec (~0.06pc) scale simulations of two idealised molecular clouds with different masses undergoing a collision. Gas clumps with density greater than 1e-20 g/cm3 (0.3e4 cm-3) were identified as pre-stellar cores and tracked through the simulation. The colliding system showed a partial gas arc morphology with core formation in the oblique shock-front at the collision interface. These characteristics support NANTEN observations of objects suspected to be colliding giant molecular clouds (GMCs). We investigated the effect of turbulence and collision speed on the resulting core population and compared the cumulative mass distribution to cores in observed GMCs. Our results suggest that a faster relative velocity increases the number of cores formed but that cores grow via accretion predominately while in the shock front, leading to a slower shock being more important for core growth. The core masses obey a power law relation with index gamma = -1.6, in good agreement with observations. This suggests that core production through collisions should follow a similar mass distribution as quiescent formation, albeit at a higher mass range. If cores can be supported against collapse during their growth, the estimated ram pressure from gas infall is of the right order to counter the radiation pressure and form a star of 100Msun.

Numerical investigation of oblique shock wave/vortex interaction

The purpose of the present study was to investigate the interaction between stream-wise vortices with oblique shock fronts of various intensities. A three-dimensional, Navier–Stokes solution of the problem with an orthogonal grid incorporating a RANS approach with a RNG k–ɛ turbulence model was used to simulate earlier experimental studies of the problem. The accuracy of the computational study was examined by comparing the results to the previous experiments of oblique shock vortex interactions using three different shock wave intensities leading to weak, moderate and strong interactions as identified in our previous experimental investigations. Similar to the experimental findings, the weak and the moderate interactions did not result in vortex breakdown as the vortex was seen to deflect in the direction of the main flow downstream of the shock with lowered intensity. Computational simulation of the strong interaction case however, confirms presence of a supersonic vortex breakdown having many of the characteristics of subsonic vortex breakdown. The flow field generated by the strong interaction is characterized by the formation of a bulged forward shock structure followed by a rapid expansion of the vortex core, formation of a stagnation point on the vortex axis and appearance of a reversed flow region in a recirculation zone. The vortex was modeled by implementing the experimentally measured vortex properties at the inlet, namely total and static pressures, while constant total temperature was assumed to calculate the velocity, and components of the Mach number. Inlet values for turbulent kinetic energy and turbulent dissipation rate were calculated from assumed values of turbulence intensity.

Oblique shock structures formed during the ablation phase of aluminium wire array z-pinches

A series of experiments has been conducted in order to investigate the azimuthal structures formed by the interactions of cylindrically converging plasma flows during the ablation phase of aluminium wire array Z pinch implosions. These experiments were carried out using the 1.4 MA, 240 ns MAGPIE generator at Imperial College London. The main diagnostic used in this study was a two-colour, end-on, Mach-Zehnder imaging interferometer, sensitive to the axially integrated electron density of the plasma. The data collected in these experiments reveal the strongly collisional dynamics of the aluminium ablation streams. The structure of the flows is dominated by a dense network of oblique shock fronts, formed by supersonic collisions between adjacent ablation streams. An estimate for the range of the flow Mach number (M = 6.2-9.2) has been made based on an analysis of the observed shock geometry. Combining this measurement with previously published Thomson Scattering measurements of the plasma flow velocity by Harvey-Thompson et al. [Physics of Plasmas 19, 056303 (2012)] allowed us to place limits on the range of the Z¯Te of the plasma. The detailed and quantitative nature of the dataset lends itself well as a source for model validation and code verification exercises, as the exact shock geometry is sensitive to many of the plasma parameters. Comparison of electron density data produced through numerical modelling with the Gorgon 3D MHD code demonstrates that the code is able to reproduce the collisional dynamics observed in aluminium arrays reasonably well.

Instability of an interface between steel layers acted upon by an oblique shock wave

This paper reports results of experiments in which development of instability was observed on the interface between two identical metals in tight contact with passage of an oblique shock wave through it. Numerical modeling of experimental results was performed by a two-dimensional Lagrangian procedure using an elastoplastic model with a functional dependence of the dynamic yield point on the state variables of the material. The calculations showed that perturbations develop only in the presence of a technological microgap of several tens of micrometers between the metal layers. Unloading of the material behind the oblique shock front into the gap gives rise to a considerable short-term velocity gradient. Simultaneously, near the interface behind the wave front there is a short-term loss of strength of the material due to thermal softening and the heterogeneous nature of the deformation.

Shock formation at the magnetic collimation of relativistic jets

If the observed relativistic plasma outflows in astrophysical jets are magnetically collimated and a single-component model is adopted, consisting of a wind-type outflow from a central object, then a problem arises with the inefficiency of magnetic self-collimation to collimate a sizeable portion of the mass and magnetic fluxes in the relativistic outflow from the central object. To solve this dilemma, we have applied the mechanism of magnetic collimation to a two-component model consisting of a relativistic wind-type outflow from a central source and a non-relativistic wind from a surrounding disc. By employing a numerical code for a direct numerical solution of the steady-state problem in the zone of super-fast magnetized flow, which allows us to perform a determination of the flow with shocks, it is shown that in this two-component model it is possible to collimate into cylindrical jets all the mass and magnetic fluxes that are available from the central source. In addition, it is shown that the collimation of the plasma in this system is usually accompanied by the formation of oblique shock fronts. The non-relativistic disc-wind not only plays the role of the jet collimator, but it also induces the formation of shocks as it collides with the initially radial inner relativistic wind and also as the outflow is reflected by the system axis. Another interesting feature of this process of magnetic collimation is a sequence of damped oscillations in the width of the jet.

Influence of Flow Angularities in a Hypersonic Ramjet Diffuser on the Formation of the Shock-Wave Structure of the Real Gas Flow

We have investigated the shock‐wave structures arising at the entrance to the engine section of hypersonic aircraft and the influence on the process of their formation of the flow angularity after oblique shock fronts incident inside the diffuser with a different type of interaction (Mach or regular). To take into account the real properties of the atmosphere, we used the effective adiabatic exponent method permitting determination of the topology of shock‐wave patterns and calculation of the gas‐ and thermodynamic parameters in various flow zones between the shock fronts in a wide range of diagnostic variables for the Earth's atmosphere.

Instability of an Interface Between Steel layers Acted Upon by an Oblique Shock Wave

This paper reports results of experiments in which development of instability was observed on the interface between two identical metals in tight contact with passage of an oblique shock wave through it. Numerical modeling of experimental results was performed by a two-dimensional Lagrangian procedure using an elastoplastic model with a functional dependence of the dynamic yield point on the state variables of the material. The calculations showed that perturbations develop only in the presence of a technological microgap of several tens of micrometers between the metal layers. Unloading of the material behind the oblique shock front into the gap gives rise to a considerable short-term velocity gradient. Simultaneously, near the interface behind the wave front there is a short-term loss of strength of the material due to thermal softening and the heterogeneous nature of the deformation.

Stability of oblique shock front

Stability of oblique shock front

Stability of oblique shock front

Stability of oblique shock front

Effect of shock strength on oblique shock-wave/vortex interaction

An experimental study of the interaction between streamwise vortices and two-dimensional oblique shock waves has been conducted at Mach 2.5. The experiments involved positioning an instrumented two-dimensional wedge downstream of a semispan wing so that the trailing tip vortex from the wing interacted with the oblique shock wave formed over the wedge surface. The experiments were designed to simulate interaction of streamwise vortices with shock waves formed over aerodynamic surfaces or in supersonic inlets. The influence of oblique shock wave intensity on this inherently three-dimensional interaction was examined for vortices of variable strength. Results indicate that the interaction of a moderate strength vortex with an oblique shock wave can lead to the formation of a steady separated shock structure upstream of the oblique shock front. A significant expansion of the vortex core is observed in these cases, and the scale of the structure increases with shock wave intensity. In some instances the separated shock structure continues through the oblique shock front to strike the shock-generating wedge forming a three-dimensional shock-wave/boundary-layer interaction. The experiments indicate that significant distortion of streamwise vortices can be precipitated by oblique shock fronts with supersonic downstream conditions.

Oblique Shocks in Extragalactic Jets

In the framework of the diffusive shock acceleration of relativistic electrons in extragalactic jets, we show that it is possible to derive the speed of the jet. For this purpose, we transform continuity relations through an oblique shock front into the reference frame of the observer. We apply these calculations to knot A of the M87 jet. Measuring the deviation of the fluid through the shock front from high-resolution radio maps and the deviation of the magnetic field from optical polarization maps (Fraix-Burnet et al., 1989), we derive speeds of about 0.01 c (Fraix-Burnet and Biermann, in preparation). The compression ratio is most probably 4 and the magnetic field is nearly parallel to the shock front both upstream and downstream.

Shock‐associated energetic proton events at large heliocentric distances

Enhancements of energetic protons (≳0.5 MeV) in association with forward‐reverse shock pairs have been observed at large heliocentric distances. An interpretation of the time profiles of these events is offered in terms of a model of solar wind stream structure. Persistent sweeping of energetic particles by each shock front and their banking‐up by reflection lead to the formation of a gradient along field lines upstream of the shocks. The rise (fall) of intensity before (after) the forward (reverse) shock is explained by a gradient in particle density directed along the upstream field lines toward the shock. A marked intensity decrease between the two shocks is interpreted in the same fashion as being due to parallel density gradients directed toward the shocks. First‐order Fermi acceleration upon reflection at each highly oblique shock front offsets loss by leakage through the shock front and sustains the particle intensity in the upstream region. Other acceleration mechanisms may not be required. A simple model is explored in which the gradient profile is primarily determined by a balance between shock sweeping and diffusive flow away from the shock (it is argued that acceleration by reflection and leakage through the shock cause a secondary modification of the profile). Profiles outside the compression region in 15 observations of corotating events suggest a radial mean free path λr = 0.021 → 0.64 AU (the mean is over r = 2.6–6 AU. The model predicts an anisotropy which upstream of each shock is lower in magnitude than observations by a factor of ≈ 2. The predicted direction in the upstream region is in the direction of corotation, i.e., perpendicular to the radius vector and counterclockwise in the ecliptic plane. Although net flows in this direction are observed, observations have not generally sought to distinguish upstream from downstream regions where net flows are expected to be approximately reversed.

Separation of Gas Mixtures in a Supersonic Jet. II. Behavior of Helium-Argon Mixtures and Evidence of Shock Separation

Further experimental evidence is presented for the separation of gas mixtures in the supersonic jet formed by a Laval nozzle. The results are in agreement with a separation theory based on free-molecule kinetics. In addition, anomalies are observed which can be attributed to pressure diffusion effects generated during passage through an oblique shock front located at the exit plane of the nozzle.