Bondi accretion in the finite luminous region of elliptical galaxies

The classical Bondi model is adopted to study accretion onto the finite luminous region around the central massive black hole (MBH) in an elliptical galaxy. Unlike Bondi (1952), we define the boundary conditions at a certain finite radius (rf) instead of at the infinity and examine the variation of solutions for a simple case. In the following, we consider the special case of a MBH at the center of a Hernquist galaxy and involve the gravity and luminosity of its own galaxy. Our results in the first part show that kinitic energy at the final radius is ignorable even for not so far away from the center. Moreover, the mass accretion rate will be approximately equal to its Bondi value if the final radius (rf) becomes about 2-3 orders of magnitude larger than semi-Bondi radius, i.e. $GM/c_{sf}^2$ (where M and csf are the mass of the central object and the sound speed at rf). In the second part, adding the two extra forces of gravity and radiation in the momentum equation let us know that the maximum possible of accretion rate increases with greater characteristic linear density of galaxy and lower radiation.

Spray and Flame Structure in Diesel Combustion

The diesel combustion process in direct-injection diesel engines consists of four distinct stages: an ignition delay, a premixed phase, a mixing-controlled phase, and a late combustion phase. This paper uses geometric information from high-speed direct and shadowgraph movies and corresponding combustion chamber pressure histories, taken in a rapid compression machine study of direct-injection diesel combustion, for a coupled analysis of the diesel flame geometry and energy or heat release to develop our understanding of the diesel spray and flame structure during the ignition delay period and premixed combustion phase. It is shown that each fuel spray from a multihole fuel-injector nozzle consists of a narrow liquid-containing core centered within a much larger fuel-vapor air region, which has a distinct boundary. The liquid core does not penetrate to the chamber periphery, while the vapor containing spray interacts strongly with the boundary. Ignition occurs part way along each growing spray. Once combustion starts, the outer boundary of the fuel-vapor-containing region expands more rapidly due to the combustion energy release. Very high initial spreading rates of the luminous region boundary are observed. A comparison of enflamed areas and volumes, and burned gas volumes, indicates that the luminous region during the early stages of combustion (assumed stoichiometric) is around 1 cm thick and does not fill the full height of the chamber. During the premixed combustion phase, the burned gas volume is one-half the enflamed volume, indicating the presence of a substantial unburned (rich) fuel-vapor/air core within the luminous region of each fuel spray. A close correspondence of flame geometry to spray geometry is evident throughout the combustion process.