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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
Response of a Thin Airfoil Encountering a Strong Density Discontinuity
Airfoil theory for unsteady motion has been developed extensively assuming the undisturbed medium to be of uniform density, a restriction accurate for motion in the atmosphere, Glauert (1929), Burgers (1935), Theodorsen (1935), Kussner (1936), Karman and Sears (1938), Kinney and Sears (1975). In some instances, notably for airfoils comprising fan, compressor and turbine blade rows, the undisturbed medium may carry density variations or "spots," resulting from non-uniformaties in temperature or composition, of a size comparable to the blade chord. This condition existsfor turbine blades, Marble (1975), Giles and Krouthen (1988), immediately downstream of the main burner of a gas turbine engine where the density fluctuations of the order of 50 percent may occur. Disturbances of a somewhat smaller magnitude arise from the ingestion of hot boundary layers into fans, Wortman (1975), and exhaust into hovercraft. Because these regions of non-uniform density convect with the moving medium, the airfoil experiences a time varying load and moment which we propose to calculate
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
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