This paper presents an experimental study of the flow field behind the shock waves propagating into a two-dimensional convergent channel. The experiments were made in a conventional shock tube having a cross section of 12×8cmcm2, with initial shock Mach numbers varying from 1.30 to 2.51 in air. During each run density distributions of the flow field were measured using a MACH-ZEHNDER interferometer. Also previous experimental results were used to calculate temperature distributions. It is shown that the density gradient is normal to the direction of the propagation of imploding shocks, but it is in the same direction in the case of exploding shocks. Furthermore in the vicinity of the channel vertex, the temperature distribution is nearly uniform over the range of 2x/h <1.0, irrespective of channel shape.
Two (one and a modified) of the simple methods for calculating the inverse problems of stationary laminar boundary layer of an incompressible fluid are presented. They belong to the so-called method of moments and are developed on the basis of the approximation procedure which is a generalization of the KÄRMÄN-POH-LHAUSEN's method, and has been applied to the standard problems. The first method is adequate for calculating the velocity distribution outside the boundary layer under the condition of prescribed wall shear, and is applied to BLASIUS' flow and HoWARTH's flow up to the separation point. The accuracy is found to be satisfactory. The modified method is suitable for analyzing the flow including separation, and is applied to a tentative to proceed beyond the separation point as a continuation of HOWARTH'S flow. A flow pattern after the separation is worked out. Finally, HORTON's problem concerning the separating and reattaching boundary layer is recalculated through the first method. It is clarified that our present method, much less laborious than-HORTON's, yields the accuracy almost comparable with the original solution.
In numerical methods of unsteady subsonic lifting surface theories, several chordwise quadratures are required each of which contains a unique singularity of kernel function. Suitable treatment of these quadratures often improves considerably convergence of the whole solutions. In this paper two kinds of kernel function[1+x0/√x0x02+YY2] (Part I) and ln |x0| (Part II) are investigated through as many methods as possible, and as systematic as possible. The results of Part I show that the ALWAY's method is extremely superior to all of other methods for most of the cases investigated and that individually restricted applicability of each remaining method is clarified. The results of Part II show that the method developed by us is drastically excellent.
The dynamic behavior of parametrically excited pin-ended thin columns is analyzed. For the past some two decades, considerable efforts have been mainly paid to define the boundaries of unstable regions of parametric instability phenomena, and the detailed behavior of structural components in unstable regions has not yet been made clear. In the present paper, the nonlinear equation of motion is solved first using the KRYLOFF-BOGOLIUBOFF method where the effect of longitudinal inertia is reduced to that of nonlinear transversal restoring force. And the properties of beat phenomena are discussed in detail in both the stable and unstable regions. Next, employing the direct numerical integration method, the influence of initial condition upon the stability and the behavior of columns at large values of excitation parameter are shown.