When the rotating speed of a rotor varies periodically with a frequency νω(ω=mean rotating speed of the rotor), the rotor is governed by differential equations having variable coefficients with time. In such a system, it is usually expected that unstable vibrations take place. It is found, houwever, that there occurs no unstable vibration in rotating shaft systems with a variable rotating speed.Variable inertia terms induced by the variable rotating speed result in forced vibrations with frewuencies νω+ω₀, νω-ω₀ as well as ω₀, where ω₀ is the frequency of an external force. It follows that at resonance ω₀≒νω+p and ω₀≒p-νω (p=a natural frequency), forced vibrations of frequencies ω₀-νω and ω₀+νω occur respectively. Furthermore, the external force of frequency ω caused by unbalances of the rotor yields three forced vibrations of frequencies ω, (1+ν)ω, (1-ν)ω.

View full abstract

This paper concerns the iterative computational method for solving a large-scale nonlinear optimal control problem. The system to be optimized in this paper is formed by interconnecting a number of nonlinear dynamical subsystems. Furthermore, some of coupling parameters are assumed to be "adjustable". This assumption gives rise to new feature.In order to circumvent the computational difficulties due to high dimensionality of the system a two-level computing algorithm for solution of the problem is proposed, where optimization is performed by interchanging the necessary information between the "center" (the second level) and a number of "processing units" (the first level).At the "center" the iterative algorithm of conjugate gradient method is carried out to obtain the solution, but the calculation of gradients is not carried out directly. It is partitioned into "processing units" of the first level, which are related to each subsystem, to reduce computational difficulties.The "center's" algorithm is illustrated by making use of logic flowcharts. A simple numerical example is presented to show the procedure of the present method, which will desirably be to be extensively used for the more complex version.

View full abstract

This paper deals with an experimental study of a forced-vortex impeller in an axial flow fan without inlet vanes. The impeller used is designed such as to have a forced-vortex flow at the impeller outlet on the assumption that the axial velocity component is uniformly distributed from hub to tip. Not only velocity profiles up- and downstream of the impeller but also theoretical head, loss of head and mean effective radius of the impeller, and lift and drag coefficinets of each blade section are presented.

View full abstract

Though supersonic gas dynamics has already been introduced in the design of supersonic turbine blades, many problems are left unsolved, which were made clear by our preliminary experiment of conventional blades. The problems are summarized as follows. (1) The shock boundary layer interaction around the leading edges.(2) The introduction of the effect of boundary layer displacement in the blade design.(3) The behavior of the supersonic flow around the trailing edges of turbine blades. Special model tests concerning these problems are performed to obtain new design data, which are applicable to improve the design method. A new design method to realize given velocity triangles is proposed. Using this method a new blade is designed, manufactured and tested to confirm the superior performances.

View full abstract

In the present paper, to simplify the theoretical treatment, a workless impeller is driven at the outlet of a wing tunnel and the velocity distribution in the boundary layer on a rotating blade is measured. As the turbulent boundary layer was recognized in the experiment, we solved momentum equations of the boundary layer in both cases of the turbulent and laminar flows and compared those results with experimental ones. Moreover, experimental studies on the blade with an attack angle were performed, too. In main results of these studies, (1) the measured boundary layer thickness coincides pretty weel with the theoretical one, (2) the radial flow in the boundary layer is comparatively small but has an effect of absorption of the boundary layer. (3) The radial flow in the boundary layer on the blade with an attack angle increases considerably on the pressure side.

View full abstract

When a volute pump is operated under various off-design conditions, the impeller sufferes radial thrust due to the pressure varying around the impeller. The author analyzes the pressure distribution around the impeller under the assumption that the total pressure and the velocity of the fluid leaving the impeller depends upon the local static pressure. In the analysis the impeller periphery is replaced by a straight line, the volute by a wedge shape space, and the flow in the wedge shape space is disintegrated into potential flows and a flow with vortices so that the combined flow many satisfy the boundary conditions along the impeller periphery as well as along the volute wall.The theory predict that the pressure near the tang is contant regardless of the flow rate of pump and that the pressure variation along the periphery is little near the tang and is significant near the exit of the volute. These predictions agree well with experimental facts quoted in the literature.

View full abstract

Visual study was made of the flow and boiling pattern near critical heat flux in the horizontal square ducts, and the critical heat flux was measured at the top or the bottom of the duct heated separately by high pressure steam.Two types of dryout were observed. For large quality region, the flow pattern is annular and the dryout occurs due to extinction of the annular liquid film. In this case, the difference between the top and the bottom is not remarkable. The other type of dryout occurs due to the defect of liquid at the top of the duct by phase separation. This phase separation is more liable to occur when the flow velocity is smaller and the duct height is larger. In this case, the critical heat flux at the top is significantly small as compared with that at the bottom.

View full abstract