Potential for Shock-Wave Generation at Diesel Engine Conditions and Its Influence on Spray Characteristics

Increasing the fuel injection pressure is currently the most effective way to achieve a better fuel–air mixing quality in modern engines. Systems capable of delivering fuels at a pressure of over 250 MPa have been widely adopted in diesel engines. At such high injection pressures, the shock-wave generation during fuel injection has been noticed. Investigations can be found widely discussing on how the shock-wave generation during fuel injection would affect the spray dynamics. However, the argument remains whether the shock wave can occur at diesel engine conditions since the diesel engine is operated at very high ambient temperature and density. Even if it could occur, how significantly the spray-induced shock wave affects the spray characteristics is rarely known. To address these concerns, this study was proposed. First, experiments were conducted to obtain the detailed spray dynamics from the nozzle exit to spray downstream field by taking advantage of the X-ray phase-contrast imaging (XPCI) and schlieren imaging techniques. It is found that supersonic and subsonic ligaments coexist in one spray. Increasing the injection pressure or reducing the ambient density would extend the supersonic part in the spray. Multiple shock waves occur subsequently from the nozzle exit, where the spray has the highest local velocity. Shock-wave generation during fuel injection could enhance spray penetration, whereas this effect depends on the length of the supersonic part in the spray. Finally, a diagram was proposed to predict the potential for the shock-wave generation and discuss the possible effect on spray characteristics at diesel engine conditions.

On Construction of the External Frankl Nozzle Contour Using Quadratic Curvature

The aim of the article is to develop a method, an algorithm, and appropriate software for constructing the external contour of the Frankl nozzle in the supersonic part using S-shape curves. The method is based on the problem of constructing a curve with the natural parameterization. The curve passes through two given points with the given inclination angles of the tangents and provides the given inclination angle of the tangent at the point with the given abscissa [4]. To control the inflection point of the S-shaped curve, the inclination angle of the tangent at a point with the known abscissa is used. In the case, when the curvature is given by a quadratic function, the system of five nonlinear equations is formulated, among which three equations are integral. The system has five unknown variables – three coefficients of the quadratic function, the total length of the curve and the length of the curve to the point with a known abscissa. The lemma on the relation between solutions of the original and the scalable systems, in which the coordinates of the points are multiplied by the same value, is proved. Due to this lemma, it becomes possible, using the obtained solution of the well-scalable system, to find easily the corresponding solution of a bad-scalable (singular) system. To find a solution to the system, we suggest to use the modification of the r-algorithm [5] solving special problem on minimization of the nonsmooth function (the sum of the modules of the residuals of the system), under controlling of the constraints on unknown lengths, in order to guarantee their feasible values. The algorithm is implemented using the multistart method and the ralgb5a octave function [6]. It finds the best local minimum of nonsmooth function by starting the modification of the r-algorithm from a given number of starting points. The algorithm uses an analytical computation of generalized gradients of the objective function and the trapezoid rule to calculate the integrals. The computational experiment was carried out to design the fragment of supersonic part in the external contour of a Frankl-type nozzle. The efficiency of the algorithm, developed for constructing S-shape curves, is shown.

Subsonic structure and optically thick winds from Wolf–Rayet stars

Mass loss by stellar wind is a key agent in the evolution and spectroscopic appearance of massive main sequence and post-main sequence stars. In Wolf–Rayet stars the winds can be so dense and so optically thick that the photosphere appears in the highly supersonic part of the outflow, veiling the underlying subsonic part of the star, and leaving the initial acceleration of the wind inaccessible to observations. Here we investigate the conditions and the structure of the subsonic part of the outflow of Galactic Wolf–Rayet stars, in particular of the WNE subclass; our focus is on the conditions at the sonic point of their winds. We compute 1D hydrodynamic stellar structure models for massive helium stars adopting outer boundaries at the sonic point. We find that the outflows of our models are accelerated to supersonic velocities by the radiative force from opacity bumps either at temperatures of the order of 200 kK by the iron opacity bump or of the order of 50 kK by the helium-II opacity bump. For a given mass-loss rate, the diffusion approximation for radiative energy transport allows us to define the temperature gradient based purely on the local thermodynamic conditions. For a given mass-loss rate, this implies that the conditions in the subsonic part of the outflow are independent from the detailed physical conditions in the supersonic part. Stellar atmosphere calculations can therefore adopt our hydrodynamic models as ab initio input for the subsonic structure. The close proximity to the Eddington limit at the sonic point allows us to construct a sonic HR diagram, relating the sonic point temperature to the luminosity-to-mass ratio and the stellar mass-loss rate, thereby constraining the sonic point conditions, the subsonic structure, and the stellar wind mass-loss rates of WNE stars from observations. The minimum stellar wind mass-loss rate necessary to have the flow accelerated to supersonic velocities by the iron opacity bump is derived. A comparison of the observed parameters of Galactic WNE stars to this minimum mass-loss rate indicates that these stars have their winds launched to supersonic velocities by the radiation pressure arising from the iron opacity bump. Conversely, stellar models which do not show transonic flows from the iron opacity bump form low-density extended envelopes. We derive an analytic criterion for the appearance of envelope inflation and of a density inversion in the outer sub-photospheric layers.

Application of an Analytical Method to Locate a Mixing Plane in a Supersonic Compressor

In order to achieve greater pressure ratios, compressor designers have the opportunity to use transonic configurations. In the supersonic part of the incoming flow, shock waves appear in the front part of the blades and propagate in the upstream direction. In case of multiple blade rows, steady simulations have to impose an azimutal averaging (mixing plane) which prevents these shock waves to extend upstream. In the present paper, several mixing plane locations are numerically tested and compared in a supersonic configuration. An analytical method is used to describe the shock pattern. It enables to take a critical look at the CFD steady results. Based on this method, the shock losses are also evaluated. The good agreement between analytical and numerical values shows that this method can be useful to wisely forecast the mixing plane location and to evaluate the shift in performances due to the presence of the mixing plane.