Diffusion in neutral and ionized gases with extreme pressure gradients

Diffusion in vortex flows is considered as a simple case of the more general problem of diffusion in flows with large pressure gradients normal to the principal flow direction. Two examples are considered. In the first the two gases are assumed electrically neutral, and pressure and concentration diffusion are equally important. In the second, diffusion of the electrons of an ionized gas is studied. Diffusion due to electromagnetic body forces is of equal importance with pres sure diffusion in this case, while concentration diffusion is negligible. It is found in the first example that the ratio of the radial mass flow of one species to the total radial mass flow is a characteristic value of the diffusion equation. The rates of diffusion are such that significant separation of the isotopes of uranium should be possible in vortices with supersonic tangential velocities. The radial pressure gradient leads to a radial electric field in the second example. A solution is obtained for the case of zero currents. By means of a perturbation technique, the solution is then extended to the case of small currents and induced fields

Electrode boundary layers in direct-current plasma accelerators

One of the problems that must be faced in the development of direct-current plasma accelerators is that of boundary-layer growth on the electrode surfaces. These surfaces must be maintained at a somewhat lower temperature than is desirable in the bulk of the gas flow. The associated reduction in electrical conductivity near the electrode surface, together with the continuous current through the boundary layer, may result in greatly augmented Joule heating near the surface, and increased heat transfer. This phenomenon is treated within the framework of boundary layer theory. It is found that similar solutions for the thermal and viscous boundary layers exist for a certain class of accelerated flows in which the velocity varies as a power of the streamwise coordinate. The solutions show that the heat-transfer rate at Mach numbers near unity may be as much as ten times that which would be expected for a normal boundary layer. At higher Mach numbers, the similarity is not precisely valid; however, the analysis indicates qualitatively that a stagnation enthalpy overshoot may occur in the high-temperature portion of the boundary layer as a result of the electromagnetic acceleration

Flow instability in particle-bed nuclear reactors

The particle-bed core offers mitigation of some of the problems of solid-core nuclear rocket reactors. Dividing the fuel elements into small spherical particles contained in a cylindrical bed through which the propellant flows radially, may reduce the thermal stress in the fuel elements, allowing higher propellant temperatures to be reached. The high temperature regions of the reactor are confined to the interior of cylindrical fuel assemblies, so most of the reactor can be relatively cool. This enables the use of structural and moderating materials which reduce the minimum critical size and mass of the reactor. One of the unresolved questions about this concept is whether the flow through the particle-bed will be well behaved, or will be subject to destructive flow instabilities. Most of the recent analyses of the stability of the particle-bed reactor have been extensions of the approach of Bussard and Delauer, where the bed is essentially treated as an array of parallel passages, so that the mass flow is continuous from inlet to outlet through any one passage. A more general three dimensional model of the bed is adopted, in which the fluid has mobility in three dimensions. Comparison of results of the earlier approach to the present one shows that the former does not accurately represent the stability at low Re. The more complete model presented should be capable of meeting this deficiency while accurately representing the effects of the cold and hot frits, and of heat conduction and radiation in the particle-bed. It can be extended to apply to the cylindrical geometry of particle-bed reactors without difficulty. From the exemplary calculations which were carried out, it can be concluded that a particle-bed without a cold frit would be subject to instability if operated at the high temperatures desired for nuclear rockets, and at power densities below about 4 megawatts per liter. Since the desired power density is about 40 megawatts per liter, it can be concluded that operation at design exit temperature but at reduced power could be hazardous for such a reactor. But the calculations also show that an appropriate cold frit could very likely cure the instability. More definite conclusions must await calculations for specific designs

Small disturbances in compressor annuli with swirl, throughflow and entropy variation

October 1970Includes bibliographical references (leaf 25)Introduction: Control of the radiation of sound from the compressors and turbines of jet engines depends to a great extent on understanding of the propagation of acoustical modes in the ducting, the general design approach being to choose the numbers of blades in interacting rows so that no propagating mode will be strongly excited. The conditions for non-propagation or "cutoff" are therefore critical to this procedure. Another application of modal analysis is found in the linear three dimensional flow theory of turbomachinery. Here the complete isentropic flow field of the compressor rotor is represented as a superposition of normal modes. To date, most such modal treatments have either neglected the effect of average flow velocity in the turbomachine duct, or considered the acoustical disturbances to propagate in a gas at rest in a coordinate system moving with the average flow velocity.This approach is correct if the resulting (moving) coordinate system is inertial, but in general is not correct for rotating coordinate systems. In the context of compressor analyses, it is valid for uniform axial flow, as applied by McCune, for example, but incorrect for swirl, as applied by Morfey.Indeed, as we shall show, the classical technique of dividing small disturbances into the three classes of vorticity, entropy, and sound fluctuations, which do not interact to first order, is not valid in rotating flows. Thus, a generalization of the concepts of sound and turbulence is needea. Such a generalization will not be achieved in the present work, but it is hoped that a few steps will be made in this direction. The general equations for pressure disturbances in an inhomogeneous swirling gas have been given by Blokhintsev, who also obtained the general equation for an isentropic gas.Apparently the only other analyses of pressure wave behavior in rotating fluids are those of Salant and Sozou. The former considered the effects of a solid body rotation on the symmetric normal modes, i.e., modes with no tangential nonuniformity. The latter treated the same type of disturbance in a Rankine vortex. The main purpose of the present analysis is to provide a consistent modal acoustic treatment for compressor annuli with large swirl and throughflow, and with radial variations of entropy. The mean flow will be assumed uniform in the axial and tangential directions, so that the results are applicable only sufficiently far upstream and downstream of blading that the first order variations in these directions have died out. As might be expected, the analysis is nevertheless somewhat complex.While a general treatment will be given, for arbitrary radial variations of entropy and tangential and axial velocity, analytical solutions for the radial eigenfunctions are available only for some special cases. These do include three important cases, namely, 1) isentropic flow with solid body rotation and constant axial velocity, 2) isentropic flow with free vortex rotation and constant axial velocity, and 3) flow with negligible mean velocity but with radial entropy variation. The first of these represents the conditions behind inlet guide vanes, though not with complete consistency, as will be noted below. The second represents quite accurately the conditions behind high-work fan rotors, except for the effects of entropy variation. The last case gives some insight into the effects of such variations.This Research was Carried Out in the Gas Turbine Laboratory, M.I.T., with the Support of Pratt Whitney Division, United Aircraft Corporatio

Vortex containment for the gaseous-fission rocket

The nuclear rocket is potentially capable of much higher specific impulse than any chemically fueled rocket, because of the high energy content per unit mass of the fissionable material. While a part of this potential can be realized by use of a low molecular weight propellant heated by solid fuel plates, it seems clear that the full potential can be realized only if the fissionable material can be retained in gaseous form, and its fission energy transferred directly to the propellant

[Assessment of the Space Station Program]

This letter report by the National Research Council's (NRC's) Aeronautics and Space Engineering Board addresses comments on NASA's response to the Board's 1993 letter report, NASA's response to technical and management recommendations from previous NRC technical reports on the Space Station, and an assessment of the current International Space Station Alpha (ISSA) program

Rotor wake transport in turbomachine stators

February 1971Includes bibliographical references (leaf 12)The mechanism of rotor wake interaction with stators has been examined experimentally by using helium, injected into the rotor wakes, as a tracer for the wake fluid. Time averaged helium Drofiles downstream of the stator, measured with a thermal conductivity cell, indicate the time averaged distribution of rotor wake fluid at the stator exit. The results are in qualitative agreement with the wake transport theory of Kerrebrock and Mikolajczak, but indicate the need for accounting for differential radial drifts of the wake fluid which encounters the motion and pressure sides of the stator blades. They also indicate that the wake transport theory is valid only when the stators flow is not separated.This Research Carried Out in the Gas Turbine Laboratory, M.I.T., Supported in Part by Pratt & Whitney Aircraft, Division of United Aircraft Corporation, and in Part by the General Electric Compan

Exit flow from a transonic compressor rotor

September 1975Includes bibliographical references (page 6-8)Summary: The three dimensional unsteady flow field behind a transonic compressor rotor with a design pressure ratio of 1.6 at a tip Mach number of 1.2 has been resolved on the blade-passing time scale, using the M.I.T. Blowdown Compressor Facility. Quantities determined were total and static pressures, tangential flow angle and radial flow angle. The spatial and temporal resolution achieved was sufficient to determine velocity components inside individual blade wakes and in the surrounding flow. From these measurements the flow structure is described at stations immediately behind the rotor and one chord downstream. Some dominant features of the flow just behind the rotor are large radial velocity components, large static pressure fluctuations near the blade wakes, and definite unsteadiness (in rotor coordinates) of the wakes. The wake behavior one chord downstream is described in terms of the effect of the strong mean swirl on the behavior of shear disturbances. In the outer portion of the annulus, where the mean flow approximates a solid body rotation, a strong, persistent oscillatory flow is found with 16 periods in the circumference as roughly predicted by theory. In the inner portion of the annulus the disturbances attenuate axially.This research was supported in part by the NASA Lewis Research Center under Grant NGL 22-009-383Supported in part by the Pratt & Whitney Aircraft Division, United Technology Corporation, and the General Electric Compan

Similar solutions for boundary layers in constant-temperature magneto-gasdynamic channel flow

One of the problems that must be faced in the development of plasma accelerators is the growth of boundary layers upon the accelerator walls. The boundary-layer effects may be important not only from a heat-transfer standpoint, but because of the displacement effect on the main flow. For the steady-flow accelerator utilizing crossed electric and magnetic fields, such as that discussed by Resler and Sears, a very interesting situation may develop upon the walls that are perpendicular to the current flow. Since the wall must generally be cool, there is a tendency for the plasma conductivity near the wall to be lower than that in the relatively hot free stream. Consequently, the Joule heating associated with the continuous current will be highest in the neighborhood of the wall. This increased heating may produce an abnormal thermal boundary layer and, quite possibly, a severe heat-transfer condition

Constant-temperature magneto-gasdynamic channel flow

In the course of investigating boundary-layer flow in continuous plasma accelerators with crossed electric and magnetic fields, it was found advantageous to have at hand simple closed-form solutions for the magneto-gas dynamic flow in the duct which could serve as free-stream conditions for the boundary layers. Nontrivial solutions of this sort are not available at present. and in fact, as in the work of Resler and Sears, the variation of conditions along the flow axis must be obtained through numerical integration. Consequently, some simple solutions of magneto-gasdynamic channel flow were sought, possessing sufficient algebraic simplicity to serve as free-stream boundary conditions for analytic investigations of the boundary layer in a physically reasonable accelerator. In particular, since the cooling of the accelerator tube is likely to be an important physical problem because of the high gas temperatures required to provide sufficient gaseous conductivity, channel flow with constant temperature appears interesting. Some simple algebraic solutions for the case of a constant temperature plasma are developed in the following paragraphs