Stagnation pressure considerations

To understand the difference in stagnation pressure losses between subsonic and supersonic combustion one must consider sonic conditions in isoergic and isentropic flows that is, one must deal with, as is done in fluid mechanics, the Fanno and Rayleigh lines. Following an early NACA report for these conditions, since the mass flow rate (puA) must remain constant, then for a constant area duct the momentum equation takes the form 

For M 1, (dPIdA) 0 and for M 1, (dPIdA) 0 that is, the pressure falls as one expands the area in supersonic flow and rises in subsonic flow. 

For adiabatic flow in a constant area duct, that is pu = constant, one has for the Fanno line 

Since T varies in the same direction as p in an isotropic change, the term in brackets is positive. 

The Rayleigh line is defined by the condition which results from heat exchange in a flow system and requires that the flow force remain constant, in essence for a constant area duct the condition can be written as 

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Specific effects on spectroscopy and photophysics induced by complexation of the D-A chromophores with various solvent molecules have been examined for all the compounds under consideration. The idea of the beam work is to generate n solute-solvent complexes and to determine thereby the relation between the solute-solvent interactions and the excited-state CT process. Kajimoto et al. [81a,c, 89], Phillips and co-workers [82], Peng et al. [83], Bernstein and co-workers [84] and others [85, 88, 90-92] have shown that solute-solvent complexes of CDMA were readily produced by varying the partial pressure of the compounds and the stagnation pressure of the carrier gas. Cyclohexane, chloroform, carbon tetrachloride, methyl fluoride, trifluoromethane, dichloromethane, acetone, acetonitrile, metha-... 

The motions of heart valves have drawn a considerable amount of auention from physicians and anatomists. One of the major reasons for this interest can be attributed to the frequent diagnosis of valvular incompetence in association with cardiopulmonary dysfunctionings. The first study exploring the nature of valve functioning, by Henderson and Johnson (1912), was a series of simple in vitro experiments, which provided a fairly accurate description of the dynamics of valve closure. Then came the Bellhouse and Bellhouse experiments (1969) and Bellhouse and Talbot (1969) analytical solution, which showed that the forces responsible for valve closure, are directly related to the stagnation pressure of the flow field behind the valve cusps. 

Another possible source of nonideal behavior and large pressure fluctuations would be boundary layer separation caused by the interaction with the reflected shock wave. Boundary layer separation and bifurcated reflected shock waves are observed under certain conditions in shock tubes with nonreactive flows. Mark formulated a simple model that predicts the occurrence of bifurcation shock bifurcation and boundary layer separation will occur when the pressure jump across the reflected shock exceeds the maximum stagnation pressure possible in the cold boundary layer fluid. Numerical calculation for the present situation reveals bifurcation would not be expected when the detonation first reflects. This is a situation peculiar to detonations and is due to the much lower reflected-shock pressure ratio relative to that which would be produced by reflecting a shock wave of comparable strength. Consideration of the reflected shock motion at later times indicates that bifurcation would not occur until after the shock had reflected from the far end of the tube. 

A new method of solution is required when the valve becomes choked. If the valve exit pressure has fallen below the value needed to produce choking, any variation below that pressure will have no effect on the flow, nor on upstream conditions. A considerable measure of decoupling occurs between upstream parameters and downstream parameters, although the two sections of pipe will carry the same flow, of course. In the calculation, the upstream conditions are determined first, and then the downstream conditions, subject to the constraint that the two pipe sections are linked by a common flow and a common stagnation enthalpy. 

The condition for the stagnant cup formation, the surface concentration variation along the bubble surface, and the adsorption saturation near the rear stagnation point is determined in terms of Marangoni niunber. If the compressive viscous shear force exceeds the characteristic linear surface pressure force, i.e. at small Marangoni numbers, the adsorption layer is compressed considerably and no saturation near the rear stagnation point can result. 

In this study we present theoretical considerations for Laval nozzle flows of a large-heat-capacity fluid at pressures and temperatures including the critical region. The corresponding experiments show phase changes close to the critical point during blowdown from supercritical stagnation conditions. 

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