Injected Gas Temperature Research Articles

A description of narrow jets using a quasi-one-dimensional model. I - Jets with constant opening angle

Using a quasi-one-dimensional MHD model for narrow jets (which we develop by projecting the system of the ideal MHD equations onto the jet axis), we examine the relative importance of the combined effects of rotation and magnetic fields upon the acceleration of matter in jets. We also examine the relative importance of the gas pressure and the gravitational field of the source on the flow and the position of the three critical points (Alfven, slow, and fast magnetosonic). When the model is used for jets with constant opening angle, the results are very similar to the ones obtained in solar wind models. The model allows both a "pressure confinement" and/or a "magnetically assisted confinement," implying that the gas pressure (given by a polytropic equation of state) and the centrifugal pressure (which is the result of the rotation of the flow) are balanced by an external medium and/or the tension of the "frozen-in" magnetic field lines. For a jet with constant opening angle we find the form of the pressure of the external medium necessary to provide pressure balance. We study the analytic structure of the equations using parameters appropriate to jets emanating from black holes, neutron stars, and protostars. We confirm the results and conclusions of our previous paper in which we had set the gas pressure, gravitational field of the source, and the r-component of the velocity and magnetic field equal to zero. For all cases the flow is initially subsonic, and it accelerates only if the gravitational field is large enough to simulate the throat of a nozzle (as in the solar wind case). For the black hole and neutron star cases, the combination of magnetic fields and rotation is a very important acceleration mechanism, producing relativistic velocities far away from the source. For a typical black hole case, acceleration to v_max_ ~ 0.4c occurs over a distance of a few 100 AU from the source. The minimum resolution needed to observe such effects in this region (corresponding to Cen A, the closest extragalactic source with clear morphological jets) is a few 0.01 mas. For the solution to go through the slow magnetosonic and sonic points the value of the injection velocity and gas temperature at the origin cannot be arbitrary; instead, one determines the other (as in the solar wind case). Using "characteristic" values for the parameters of interest at the jet origin, we find that an outflow exists only if the polytropic index is 1 <= γ <~ 1.239. Unless γ = 1, the initial temperature required is so high (e.g., 3 x 10^9^ K <~ T_0_ <~ 10^12^ K for γ = 1.001) that it seems probable that the outflow originates from a high-temperature region surrounding the black hole, in much the same way as the solar wind originates from the corona surrounding the Sun. The asymptotic value of the jet Mach number is 1 <~ M_p_ <~ 5. Assuming equipartition between the magnetic and kinetic energy densities for a jet emanating from an active galactic nucleus, we find that if the flow is to be physical the plasma beta factor at the origin must satisfy β_0_ >~ (γ - 1)/γ. As a typical neutron star case we use SS 433, for which the jet reaches relativistic velocities (ν <~ c) at a distance of ~ 10^10^ cm, requiring a resolution of ~ 2 x 10^-3^ mas. The large magnetic field strength at the jet origin imposes an upper limit to the jet opening angle. The general behavior of the solution is the same as for the black hole case and requires 1 <= γ <~ 1.473. The initial temperature required is also high, and the presence of a high- temperature region surrounding the neutron star is probable. For protostar cases we find that the velocity reaches its asymptotic value of ~ 300 km s^-1^ (for γ = 1.2, and strongly dependent on γ and ν_0_) at a distance of ~ 10^-4^ pc; in these cases the gas pressure is the primary acceleration mechanism. For the solution to go through the sonic and fast magnetosonic points and using "characteristic" values for the parameters of interest, we find that 1 <= γ <~ 1.498 and T_0_ < 1.5 x 10^6^ K. The asymptotic value of the jet Mach number is 5 <~ M_p_ <~ 40, consistent with observations. From the behavior of the density and magnetic field strength at large distances we estimate that at the origin ρ_0_ ~ 10^-10^-10^-8^ g cm^-3^ and B_0_ ~ 1 G. For all cases considered the model leads naturally to a hollow jet (i.e., ρ is proportional to r^P^, where p > 0), consistent with recent observations.

Film-Cooling Effectiveness and Skin Friction in Hypersonic Turbulent Flow

Experimental equilibrium temperatures and skin friction at the surface of a flat plate cooled by two-dimensional, tangential slot injection are presented for a Mach 6 mainstream. Effects of slot height, slot mass-flow rate, injection gas temperature, and heat conduction to the slot are investigated. Experimental skin friction and effectiveness data in general agree well with predictions from a finite-difference method. Film cooling at Mach 6 was found significantly more effective than at lower speeds, with large reductions in friction drag measured downstream of the slot These results indicate the necessity for a new evaluation of film-cooling systems for hypersonic vehicles.

A Feasibility Study of an In Situ Retorting Process for Oil Shale

Abstract A heat transfer study was made of hot gas injection into oil shale through wells interconnected by vertical fractures. This analysis involved the simultaneous numerical solution of a nonlinear, second-order partial differential equation that describes two-dimensional conduction heat transfer in oil shale and a non linear first-order partial differential equation that describes convection heat transfer in the fractures. Three nonlinear, temperature-dependent coefficients were used in this work; they are thermal conductivity, thermal capacity and retorting endothermic heat losses of oil shale. Vertical fractures were considered to be of finite height. Although vertical conduction heat transfer was not considered, an estimate of the error resulting from this limitation was made. How retorting efficiency was affected by injected gas temperature, injection rate, system geometry, cyclic injection and time were investigated. Results from this study show that the rate of retorting oil shale is a direct function of both injection temperature and rate, and the theoretical producing air-oil ratio:(AOR) is an inverse function of temperature. Retorting rates are constant until "breakthrough" of the 700 F isotherm at the producing. well, assuming constant injection parameters. Retorting rates for bounded systems are higher than the analogous unbounded systems and likewise AOR's are less. The use of an alternating injection-soak routine with high injection rates is less efficient than continuous injection at lower rates. These results indicate that injection temperatures on the order of 2000 F or greater may give theoretical AOR's in the economic range. Introduction Over half of the known oil shale reserves are located in the U.S., and most of them lie in the Piceance Creek basin of Western Colorado. The Colorado oil shale outcrops on the edges of the Piceance Greek Basin. At the outcrops the shale beds are relatively thin, from 25 to 50 ft thick. In the center of the basin the oil shale is as great as 2,000 ft thick and is covered with 1,000 ft of overburden. It has been estimated that there are over 1,000 billion bbl of oil in shales having an oil content over 15 gal/ton in this basin. Oil shale does not contain free oil but an organic matter called kerogen. Kerogen yields petroleum hydrocarbons by destructive distillation. It must be heated to approximately 700 F, at which temperature it decomposes into shale oil, gases and coke. The U.S. Bureau of Mines and, more recently, oil companies have conducted considerable research on surface retorting methods to economically recover oil from this shale. Another approach to exploit the oil shale deposits, in particular that portion having 1,000 ft of overburden, is to retort the oil shale in place and produce the liquid and gaseous hydrocarbons through wells drilled into the shale. Some research has been done on this approach. There are several variations to the in situ retorting approach. These variations fall into one of two groups, depending upon the geometry of the system:retorting in a highly fractured or broken up matrix;retorting from single fractures between production and injection wells. The latter is the group studied. Several investigators, using various assumptions, have studied flow of heat through horizontal systems. The objective of this work was to make a heat transfer study of in situ retorting oil shale by hot gas injection through wells interconnected by single vertical fractures of finite height. The oil shale thermal conductivity, thermal capacity and retorting endothermic heat losses were considered to be functions of temperature. SPEJ P. 231ˆ