摘要:

The Lagrangian equations of hydrodynamics are transformed to general coordinates. Since they involve two sets of variables (dependent and independent) two transformations are involved. The independent coordinates are usually taken to be the time and the initial positions of the particles of the fluid. Other kinds of independent variables are often useful. If they are chosen so that they describe the motion of a second fluid, the Lagrangian equations become a tool for comparing the motion of the two fluids. If the second fluid obeys the same laws as the first, the comparison is between two modes of motion of the same fluid. The study of this problem leads to a new derivation of the Eulerian equations from the Lagrangian. If the two modes of motion differ only slightly, the perturbation equations are obtained in generalized coordinates. They satisfy a variation principle. This can be transformed so as to exhibit the general form of a pseudo potential energy function that is useful in the study of stability problems.

ISSN:0031-9171    

DOI:10.1063/1.1706859

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

L. N. Howard proved an inequality concerning the complex velocity of the propagation of waves disturbing the laminar, unidirectional flow of an incompressible stratified fluid. It is shown that this theorem is closely related to the virial theorem of hydrodynamics. It can be generalized for the steady motion of a compressible fluid, provided the streamlines are either parallel straight lines or coaxial circles. The connection of the circle and virial theorems provides an interpretation of the former in terms of the energy of the perturbation. A positive potential energy always exerts a stabilizing influence, as does the angular velocity in the case of circular streamlines. This latter is diminished for short waves; it is also complicated by the fact that radial variations of the angular velocity may contribute negative terms to the potential energy. Zonal flow, such as the jet stream of the Earth's atmosphere, is generally baroclinic. In the barotropic case, the potential energy of the perturbation is simply proportional to the Va¨isa¨la¨‐Brunt frequency. In the baroclinic case, this frequency cannot be usefully defined, and the more elaborate formulae are derived.

ISSN:0031-9171    

DOI:10.1063/1.1706860

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

Energy transfer from large to small eddies at three stations in turbulence behind a square mesh is determined by measuring the rates of change and viscous dissipation of the spectrum and the results are compared with a theoretical prediction. Large eddies for which viscous dissipation is negligible satisfy a similarity relation which agrees with the fact that the total energy decays as some negative power of time. Small eddies which are in approximate statistical equilibrium satisfy local similarity according to Kolmogoroff. Various terms in the vorticity equation are also determined and the quantities representative of small scale motion are universal constants when expressed in terms of Kolmogoroff parameters.

ISSN:0031-9171    

DOI:10.1063/1.1706861

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

The effect of a finite rate of chemical recombination on the structure of a Prandtl‐Meyer expansion is studied theoretically. A numerical technique, based on the method of characteristics, is used to obtain an exact solution for a representative set of initial conditions. Wall expansion angles up to and including 30° are considered. From the results it is concluded that the flow departs from that appropriate to constant composition at the corner and approaches the infinite rate equilibrium solution at very large radial distances. Subsidiary wave reflections between vortex layers (due to the thermodynamically irreversible chemical reaction) and the wall can cause pressure fluctuations in the region following the primary expansion. Finally, the flow in the vicinity of the wall is bounded by a constant pressure region at a very large distance downstream.

ISSN:0031-9171    

DOI:10.1063/1.1706862

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

A reacting flow situation is considered wherein a gas mixture initially in a state of chemical equilibrium flows over a surface having a chemical affinity for one of the components in the flowing gas. A gas‐solid reaction results which, in turn, upsets the gas phase equilibrium so that a reaction starts there also. Evolution of gaseous products of the wall reaction serves to lower skin friction and to further complicate the situation. The flow is taken to be over a flat plate, and the simplest forms for the two reactions are used. The interactions among the processes are viewed in terms of an interaction parameterG, which is the ratio of the square of the characteristic time for wall reaction processes to the product of characteristic times for the gas phase and diffusion processes, and a stoichiometric factorK¯. The latter represents the mass of wall material that can react with unit mass of the free‐stream gases. Typical results for drag show that whenG= 1 andK¯= 5, a 45% reduction occurs; whenG= 5 andK¯= 5, a 55% reduction is obtained. Even greater differences are found between values of skin friction whenK¯varies at constantG.

ISSN:0031-9171    

DOI:10.1063/1.1706863

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

The breakup of drops exposed to blasts of air is studied in a shock tube. Results are obtained for water, methyl alcohol, and three viscous oils. An acoustical drop holder has been developed in which radiation pressure is used to support the drops at rest in the shock tube. Photographs showing new details in the breakup process are presented.

ISSN:0031-9171    

DOI:10.1063/1.1706864

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

Recent investigations of idealized Navier‐Stokes detonation structure have left unresolved the existence and nature of flow solutions in the case of very fast reactions. By formulating the problem explicitly in terms of a specified initial state and a specified hot boundary mass velocitywP(relative to the unreacted explosive), it is shown that suitable ``steady'' flows exist in all cases, providing that a rarefaction wave or a slower moving shock wave is allowed to follow the detonation front.An initial‐state parameter &Ggr;0, involving the reaction‐rate ``pre‐exponential factor'' and the thermal conductivity, is defined, as well as an associated critical value &Ggr;u(CJ), which depends on the heat capacity ratio, and the enthalpy and activation energy of the reaction. If &Ggr;0< &Ggr;u(CJ), then for smallwPthe predicted flow is the Chapman‐Jouguet (CJ) detonation followed by a rarefaction. AswPis increased through the CJ mass velocitywC J, the flow changes continuously to increasingly overdriven detonations. If &Ggr;0> &Ggr;u(CJ), then for smallwPthe predicted flow is a weak detonation whose velocityDdepends on &Ggr;0, followed by a rarefaction. AswPis increased through the corresponding weak detonation mass velocityw(&Ggr;0), the flow becomes the same weak detonation followed by a slower moving shock wave. With continued increase ofwPthis shock velocity increases until, at a certain value ofwP, it becomes equal to the weak detonation velocity. At still largerwP, the flow changes continuously into an overdriven strong detonation.Both unimolecular and bimolecular kinetics are considered. So‐called ``reasonable'' values of the unimolecular parameters lead to the possibility of the flows involving weak detonations, but as noted by Hirschfelder, Curtiss,et al., the conditions are then such as to require a quasi‐unimolecular mechanism to become bimolecular, due for example to depletion of the activated state. When bimolecular kinetics are considered, reasonable parameter values appear to exclude the weak detonation flows.

ISSN:0031-9171    

DOI:10.1063/1.1706865

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

A hot‐wire apparatus of the ``potential leads'' type has been used to determine the thermal conductivities of nitrogen, oxygen, nitric oxide and nitrous oxide, and the binary mixtures: N2O&sngbnd;N2, N2O&sngbnd;O2, N2O&sngbnd;NO and NO&sngbnd;N2, over the temperature range 30° to 200°C. Corrections were made for the various possible sources of error, and the final results are accurate to within 2%. The results for single gases are discussed in terms of the original Eucken formula, the diffusion‐mechanism theory and the Mason‐Monchick theory. The mixtures are treated in terms of the general Hirschfelder equation, and also by use of the Wassiljewa‐type relation. In the latter case, the experimental Wassiljewa coefficients are compared with those calculated by the Mason‐Saxena and Lindsay‐Bromley approximate relations.

ISSN:0031-9171    

DOI:10.1063/1.1706866

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

The high temperature quantum corrections to the second virial coefficient are calculated for a square‐well repulsive core model. It is shown that the hard core correction is large for He4at all temperatures for which present measurements exist. The correction can be verified experimentally, because it leads to a 5% difference between He4and He3values at high temperatures.

ISSN:0031-9171    

DOI:10.1063/1.1706867

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

A volume source sheet plus a uniform flow is used to represent the flow field of a flame propagating in a channel. The unknown flame shape is determined by the requirement that the velocity normal and relative to it, i. e., the local flame speed is constant. The ratio of the propagation speed of the flame as a whole to the local flame speed appears as the important parameter. Five flow fields for the values 1.05, 1.20, 1.50, 2.00, and 4.00 of the parameter are computed. These give generally correct flame shapes and flow fields. The detailed results of the analysis are compared with two observed flow fields. Subject to the inherent limitations of the theory, the comparison is favorable.

ISSN:0031-9171    

DOI:10.1063/1.1706868

出版商:AIP    

年代:1963

数据来源: AIP