Some Gasdynamic Problems in the Flow of Condensing Vapors

Some Gasdynamic Problems in the Flow of Condensing Vapors. The general problem of the flow of a wet vapor, with or without an inert diluent is formulated under the assumption that the liquid phase is finely divided and dispersed throughout the gaseous component in droplets whose radii are nearly constant in any local region. The processes of momentum transfer, heat transfer between phases are assumed to take place according to Stokes law and Nusselt number of unity, respectively. The mass transfer process is treated as diffusion governed in the presence of an inert diluent and kinetic governed for two phases of a pure substance. The physical understanding of such problems, in contrast with those of conventional gas dynamics, rests largely in the role played by the relaxation times or equilibration lengths associated with these three processes. Consequently, both simple and coupled relaxation processes are examined rather carefully by specific examples. Subsequently, the problem of near-equilibrium flow in a nozzle with phase change is solved under the small-slip approximation. The structure of the normal shock in a pure substance is investigated and reveals three rather distinct zones: the gasdynamic shock, the vapor relaxation zone, and the thermal and velocity equilibration zone. The three-dimensional steady flow of the two-phase condensing continuum is formulated according to first order perturbation theory, and the structure of waves in such supersonic flow is examined. Finally, the attenuation of sound in fogs is formulated and solved accounting for the important effects of phase change as well as the viscous damping and heat transfer which have been included in previous analyses

Propagation of stall in a compressor blade row

Recent experimental observations on compressors, in particular those of Rannie and Iura, have clarified some features of the phenomenon of stall propagation. Using these observations as a guide, the process of stall in an airfoil cascade has been characterized by a static pressure loss across the cascade which increases discontinuously at the stall angle, the turning angle being affected in only a minor way. Deductions from this simple model yield the essential features of stall propagation such as dependence of the extent of stalled region upon operating conditions, the pressure loss associated with stall, and the angular velocity of stall propagation. Using two-dimensional approximation for a stationary or rotating blade row, free from interference of adjacent blade rows, extent of the stalled region, the total pressure loss and stall propagation speed are discussed in detail for a general cascade characteristic. Employing these results, the effect of stall propagation upon the performance of a single-stage axial compressor is illustrated and the mechanism of entering the regime of stall propagation is discussed. The essential points of the results seem to agree with experimental evidence

Response of a nozzle to an entropy disturbance example of thermodynamically unsteady aerodynamics

The larger number of problems that qualify as unsteady aerodynamics relate to non-uniform motion of surfaces -- such as pitching of airfoils -- or the correspondingly non-uniform motion of a fluid about a surface -- such as a gust passing over an airfoil. Experiment and analysis concerning these problems aims to determine the non-steady forces or surface stresses on the object. These may be thought of as "kinematically" non-steady problems. Another class of problems presents itself when the undisturbed gas stream temperature (or density) is non-steady although the velocity and pressure are steady; such non-uniformities are associated with entropy variations from point to point of the stream. In a locally adiabatic flow these entropy variations are transported with the stream, and when a fixed boundary -- such as an airfoil -- is encountered, the flow field undergoes a non-steady change because the density variations alter the pressure field -- or the stresses at the boundaries. This happens in spite of the fact that the undisturbed free -stream velocity field and the surface boundaries of the flow are independent of time. A gas turbine blade, for example, will experience a time-dependent load simply because of temperature fluctuations in the combustion products flowing over it, although the angle of attack is independent of time. We shall call these "thermodynamically" unsteady flows in contrast with the more familiar kinematically unsteady flows

Dynamics of a gas containing small solid particles

N/

Reply to comments by S. L. Soo

If one takes due regard for the condition under which my collision model is valid, explicitly stated by Eq. (15), Ref. 1, the difficulties experienced by Soo(2) will not arise

Droplet Agglomeration in Rocket Nozzles Caused by Particle Slip and Collision

Droplet Agglomeration in Rocket Nozzles Caused by Particle Slip and Collision. The development of the particle mass spectrum in a rocket nozzle is investigated under the assumption that droplet growth by collision and agglomeration is the dominant mechanism subsequent to initial appearance of particles in the rocket chamber. Collisions are calculated on the basis oflinearized particle slip theory and a spectral integral equation is derived describing the development of particle mass spectrum during the flow process along the nozzle. This agglomeration process continues until the droplet temperature falls below the freezing point of the material. A solution is obtained for the approximate growth in the average particle size during the expansion process. The results show that, according to this model, the particle size is strongly dependent on the initial pressure in the rocket chamber and is independent of nozzle geometry. These results suggest that the collision-agglomeration process is at least one of the critical factors that accounts for the size of solid particles in rocket exhausts

Theoretical Analysis of Nitric Oxide Production in a Methane/Air Turbulent Diffusion Flame

The coherent flame model is applied to the methane-air turbulent diffusion flame with the objective of describing the production of nitric oxide. The example of a circular jet of methane discharging into a stationary air atmosphere is used to illustrate application of the model. In the model, the chemical reactions take place in laminar flame elements which are lengthened by the turbulent fluid motion and shortened when adjacent flame segments consume intervening reactant. The rates with which methane and air are consumed and nitric oxide generated in the strained laminar flame are computed numerically in an independent calculation. The model predicts nitric oxide levels of approximately 80 parts per million at the end of the flame generated by a 30.5 cm (1 foot) diameter jet of methane issuing at 3.05 x 10^3 cm/sec (100 ft/sec). The model also predicts that this level varies directly with the fuel jet diameter and inversely with the jet velocity. A possibly important nitric oxide production mechanism, neglected in the present analysis, can be treated in a proposed extension to the model

Nozzle contours for minimum particle-lag loss

The flow of a gas-particle mixture through a rocket nozzle is analyzed under the approximation that the particle slip velocity is small compared with the average mixture velocity, using one-dimensional gasdynamics, the Stokes drag law, and corresponding approximations for the heat transfer between solid and gas phase. The variational problem defining the pressure distribution giving the minimum impulse loss due to particle lag is formulated and solved for nozzles of prescribed mass flow, length, and of given exit pressure or area. The throat section of the optimum nozzle is considerably elongated and more gradual than that of the conventional nozzle. The velocity and temperature lags were much lower (about 1/3) in the throat region than those for the conventional nozzle. The impulse loss of the optimum nozzle was, however, reduced only about 30% below that of the conventional nozzle. It is concluded that contouring of the nozzle to improve gas-particle flow performance will result in only very modest gains. As a direct consequence, the impulse losses calculated herein for optimum nozzles can be used as a rough but convenient approximation for the impulse losses in conventional nozzles having the same area ratio or pressure ratio