A formulation of the mixed finite element method is proposed in this paper which may be suitable for analysis of the instability problems of plates and shells. A plane triangular element is applied to the problems of a large deflection of square plates with initial deflection, a snap-through of shallow square caps, a large deflection of circular plates and a compression buckling of square plates with the results obtained by previous workers. And it can be concluded that, although the expression of the obtained stiffness matrix is quite simple sufficiently accurate results can be obtained by using the present method.

View full abstract

Numerical solutions of the unsteady Navier-Stokes equations are presented for a two-dimensional flow past a circular cylinder immersed in a uniform shear flow. Several values of the shear parameter K defined as Ga/U_∞ is the oncoming velocity at the center of the cylinder. The Reynolds number Re based on 2a and U_∞ is assumed to be 40 and 80. Although a pair of steady standing vortices is formed in a uniform flow when Re=40, it is found that a periodic vortex shedding occurs at the same Reynolds number in the case of a shear flow with a shear parameter K=0.2, however, the vortex shedding is suppressed even in the case of a shear flow revealing a clearly asymmetric flow pattern with respect to the geometrical center line of the cylinder. The same tendency is also observed in the flow of the Reynolds number Re=80. The time-averaged lift force acts in the direction towards the high-velocity side of the shear flow and its magnitude is approximately proportional to the shear parameter.

View full abstract

A discrete-vortex model is used to simulate a turbulent plane mixing layer. The vorticity in the mixing layer is partitioned into a number of vorticity blods which are again replaced by inviscid discrete vortices with an inner structure. It is found that random walks of appropriate variance should be superposed on the motion of the vortices in order to obtain the time-averaged velocity and turbulent quantities consistent with experiments. The random walks are assumed to simulate very roughly the diffusion of vorticity by turbulent transport. The potential field of application of the present model and its limitations are also discussed.

View full abstract

This paper presents theoretical and experimental analyses of turbulent boundary layer velocity profiles and the boundary layer parameters. This work clarifies the influence of adverse pressure gradients and the effect of the boundary layer control by uniform suction on the boundary layer. A continuous velocity profile from a sublayer to an inner layer is obtained by developing the damping factor of a mixing length to the boundary layer with suction. The velocity profile in an outer layer is determined theoretically by extending a theory on the assumption of intermittency phenomena at the outer layer with adverse pressure gradient and uniform suction. The results of theoretical calculation are in good agreement with the experimental data.

View full abstract

The starting process of a supersonic wind tunnel with a diffuser with contraction has been studied in detail by schlieren optical observations and pressure measurements. As the result, it has been shown that the wind tunnel starts when the flow is even sonic but not choked at the second throat. Based on this fact, the flow in the starting process has been classified into three patterns according to the area ratio of the second throat to the test section. Furthermore, the differences between the theoretical values and the experimental results of the starting pressure ratio and the minimum starting area at the second throat have been well explained, taking into consideration the fact that a normal shock wave assumed in the previous one-dimensional theory becomes a pseudo-shock wave due to the interaction with the wall boundary layer.

View full abstract

The behavior of a shock wave in a supersonic outflow at a sudden enlargement of a duct has been clarified experimentally by a schlieren optical system and static pressure measurements. A self-excited oscillation of flow with a shock wave has been observed at the downstream duct at a particular range of supply pressures in which range the outflowing jet is underexpanded at the sudden enlargement and furthermore the jet does not reattach in the downstream duct. In the oscillating flow, compression and expansion waves propagate back and forth between the sudden enlargement section and thickset of the duct, and the base-pressure in the dead-air region downstream of the sudden enlargement and the width of the outflowing jet oscillate periodically.

View full abstract

Oscillatory and pulsating flows through a rigid, circular tube are experimentally analyzed in the region of fully developed laminar flow. Transitions of the velocity distribution with respect to time are measured by a flow-visualization method. Aluminium powder is suspended in the fluid for the measurement, and many particle tracks (path lines) are photographed for a certain period of time. The velocity distribution is obtained by measuring the length of path lines. The experimental data are compared with the results of theoretical analysis, the validity of which is thus ascertained.

View full abstract

The effect of compressibility at subsonic speed in piping systems with bends or elbows is studied in this report. Experiments are carried out with varying deflection angle, relative radius of curvature, inner surface roughness as well as the flow Mach number. The effect of compressibility on Kt, the loss coefficient of bends or elbows, is expressed by the following empirical formulas, Kt/Kti=1.0+αM³, where the subscript i refers to an incompressible flow, and α, β are constants dependent of configurations of bends or elbows. Furthermore, flow patterns around curved parts are visualized by Finally, a practical computing method of flow losses of high speed piping system is summarized.

View full abstract

Flow characteristics of piping systems with sudden enlargement at high subsonic region is studied in this in this report. Experiments are carried out with the area ratio as well as the flow Mach number varied. The effect of a change in the face pressure on loss characteristics is studied, and the following empirical formulas are obtained P_f/P₁=1.0-M₁^β, where P_f denotes the pressure at the face of the step, and the subscript 1 refers to the inlet value of the enlarged section, and α, β are constants dependent on the area ratio of enlarged parts. Flow patterns around the sudden enlargement parts are visualized applying the Schlieren method and the flow asymmetry or vibration down-stream of the enlarged part is discussed. Finally, a practical method of computing flow losses of high speed piping system is described.

View full abstract

Pulsating turbulent pipe flow was measured at the time - averaged Reynolds number of about 5.7×1-⁴ and over wide ranges of both frequency and velocity amplitude ratio. The flow pattern in an incompressible turbulent pipe flow was found to be described by four characteristic parameters and not to be affected so much by four characteristic parameters and not to be affected so much by velocity amplitude ratio. Further, the flow patterns were classified into three types, i.e., quasi-steady, intermediate, and inertia dominant ones with respect to the dimensionless frequency ω'. The values of ω' representing the limits between three regions were proposed.

View full abstract

The effect of frequency on frictional losses in a pulsating turbulent pipe flow is investigated. The frictional losses estimated from flow pattern diagrams agree well with those obtained experimentally at the time-averaged Reynolds number of about 5.7×10⁴ and over wide ranges of both frequency and velocity amplitude ratio A₁. As is expected, the instantaneous friction factor λ_u(t) and the quasi-steady friction factor λ_q are almost equal in the quasi-steady region indicated in a previous paper. With an increasing dimensionless frequency ω', however, λ_u(t)⪌λ_q in both accelerating and decelerating zones of a pulse cycle. The time average friction factor λ_u, ta, which is a function of ω' and A₁, is always larger than the friction factor λ_s for a steady flow with equivalent mean Reynolds number and increases monotonically with ω' and A₁.

View full abstract

The characteristic parameters Φ_t, n, Φ_z, n, α_t, n, and α_z, n describing the flow pattern in a pulsating turbulent pipe flow are introduced as functions ofω'/Re^3/4_ta from quasi-steady analysis, where ω' is the dimensionless frequency, R_e ta the time-averaged Reynolds number and the validity of these parameters is confirmed experimentally. In the range of time-averaged Reynolds numbers larger than 1×10⁵, where Blasius' 1/4 power frictional law is not valid, ω'/(λ_s R_e ta). Then λ_s is calculated from another friction law. The values of ω'/Re^3/4_ta corresponding to the limits between quasi-steady, intermediate, and inertia dominant regions are also proposed.

View full abstract

The two-dimensional flow of a viscous fluid caused by a velocity distribution given on a plane boundary is investigated theoretically using Stoke's approximation. A general formula for the velocity components of the flow in a hail-space bounded by a plane wall with a given velocity is obtained from the superposition of the solution of the viscous flow due to a source on a plane wall. Several problems for the slow motion of the viscous fluid of this kind are solved by making use of this formula. It is supposed that the formula for velocity components is an expedient for solving the problems of a viscous flow associated with the ventilation in a room and the ground water

View full abstract

A theoretical study is made of two-dimensional flows of a viscous incompressible fluid in a narrow channel with a simple-harmonic wavy wall. The main object is to study the effect of the wave length and amplitude of the wavy wall on the leakage of the fluid through the channel. The decreasing rate of the discharge is proportional to the square of the ratio of the amplitude to the width of the channel. In case of a long wave, the problem can be solved analytically by the perturbation procedure; then the discharge decreases due to the wavy wall. In case of a medium wave length, the discharge decreases monotonically and makes the wave shorten. However, if the Reynolds number increases, the decreasing rate of the discharge first decreases and then increases, i.e., there is a minimum decreasing rate.

View full abstract

The influences of the machine elements of regenerative type blowers on the performance and inner flow are investigated experimentally. In addition, the results are discussed from a view point of viscous effects on the pump performance and inner flow. It is concluded that relations between the machine elements and inner flow are in a similar tendency between pumps and blowers. Performance parameters of the pump and the blower are systematically arranged by using the same dimensionless parameter. Inner flows in the cross section and along the longitudinal direction of the flow channel are observed in blowers which have different vane angles. The performance curves are closely related with the back flow.

View full abstract

In order to reveal the calorimetric behavior of gases, an apparatus for the absolute determination of the isobaric specific heat capacity (Cp) of gases was carefully designed and constructed based on the flow calorimetry. Experimental results of Cp for gaseous carbon dioxide were obtained for temperatures from 245 K to 345 K and pressures up to 3.7 MPa including those near the saturation line. The overall experimental error of the Cp measurements was estimated to be less than 0.52%, and the reproducibility of these results was also confirmed to be less than 0.1%. The reported results were in good agreement with the available literature data within their experimental errors.

View full abstract

A one-dimensional analysis of subsonic radial turbines in terms of non-dimensional velocity λis developed introducing a new incidence loss model. Based on this theory a performance prediction of radial turbine of a tip diameter d₃=228 mm is conducted. The predicted performance is compared with experimental results, and is considered to be of a sufficiently good coincidence. Comparison with incidence loss models, one due to Wallace and the other to NASA, is also presented.

View full abstract

The effects of the interaction between two burning identical fuel droplets are analyzed exactly in the Schvab-Zeldovich formulation. The expression for the evaporation rate of each droplet is obtained in an explicit form, which shows that the interaction reduces the evaporation rate compared with that of an isolated droplet. The criterion which divides two possible types of flame surfaces, i, e., two separate flames or one coalescent flame, is derived, which will be of interest in connection with the prediction of the combustion modes in spray.

View full abstract

A stochastic model of a turbulent diffusion flame in a confined space has been developed by assuming that each fluid particle behaves as an ideal batch in which a chemical equilibrium holds at any instant, and that the particle undergoes random binary collision and redispersion immediately to produce two equal particles having the average thermodynamic state. This model may afford not only the descriptions of macroscopic quantities such as pressure and average temperature but also those of nonuniformities in composition and temperature. Results of computation performed for constant-volume cases suggest that the model characterizes the main part of diesel combustion in which initial segregation of fuel and air is disintegrated from time to time reaching a final uniform state, by forming flames of a highly turbulent nature. Some considerations are made regarding the mixing rate parameter that determines overall rate of the process.

View full abstract

Based on the stochastic model developed in the first report, description of the combustion process occurring in a diesel engine has been made. The model has been revised to include several factors such as volume change caused by piston motion, an air purity in the cylinder charge. The results show that the measured pressure-time relations in a direct-injection engine may well be reproduced for a range of operational conditions through a proper selection of two empirical parameters that describe initial segregation of fuel and air and the rate of turbulent mixing. The capability of the model to describe the diesel combustion phenomena is finally suggested by the model prediction carried out for nitric oxide formation. The comparison of the prediction with the experimental data shows that the correlation between predicted and exhaust measured concentration is fairly good.

View full abstract

In order to the unsteady flow problems in engine cylinders, the heat transfer from hot-wires, a length-diameter ratio of which is about 400, has been measured with a constant-temperature anemometer. Gas temperatures and wire temperatures were varied independently of each other from 306 to 351°K respectively. After corrections for the heat conduction to the wire supports and the temperature jump at the wire surface by taking the temperature dependence of the thermal accommodation coefficient into consideration, the continuum Nusselt number can be related to the Reynolds number and the temperature loading factor by the expression N_μm{(Tf/Ta)(300/Ta)}^<0.08 = a+0.68 Re⁰.5_f where the values of gas properties are taken at the film temperature and the value of gas properties are taken at the film temperature and the value of gas properties are taken at the film temperature and the value of a varies between 0.28 and 0.34 for respective wires. The procedures for calculating the gas velocities and temperatures from the relation above and the heat-balance equations for two wires, one of which is operated at the constant-temperature mode and the other at the constant-current mode, are shown also.

View full abstract

In this paper a balancing method of flexible rotor is systematically defined and the relation between a modal balance and an influence coefficient method is described. Then the least square method, a kind of the influence coefficient method is discussed in detail, that is, on the balancing quality, performance index, weighting function and the relation between the weighting function and measuring errors of the influence coefficients. As the result, it is known that the balancing quality is greatly different between the use of amplitude of rotor and bearing force as an object function, and it is necessary to discuss on the balancing also from the viewpoint of error analysis.

View full abstract

This paper studies the nonstationary vibration of a rotating shaft on flexible supports in passing through the critical speed. In particular the interaction or the coupling effect caused by near critical speeds in continuous passing through 1st and 2nd critical speeds has been studied. For the case of a rotor system on damped flexible supports, its approximate equation in transition through the critical speed has been derived by the asymptotic method as in the former report. Moreover, observing nonstationary maximum amplitudes, the analytical results have been considered. The experiments support the analysis.

View full abstract

Coupled torsional-flexural vibration of a shaft in a spur geared system is investigated. Equation of motion which contain the terms of geometrical eccentricity of gears and mass unbalance are introduced. The coupling between torsional and flexural displacements is considered in the equations which assume that surfaces of tooth of meshed gears are always in contact during the rotation. By solving the equation, it is possible to get natural frequencies, mode shapes, and frequency response of the system. It is usual to ignore the effect of the coupling between torsional and flexural vibrations. But comparing the result with them, some new phenomena were revealed. They are: (1) shifts of the critical speeds (2) transformations of the mode shapes (3) a forced vibration which is caused by geometrical eccentricity of a gear.

View full abstract

In this paper, we investigated a frictional noise produced when a long steel cantilever was pressed in the radial direction on a rotating thick disk. The results obtained are summarized as follows: (1) With a longer rod, both fundamental and higher mode squeal noises occur. These squeal frequencies are coincident with the lateral natural frequencies of the rod. The squeal frequencies of higher modes are equal to the lateral natural frequency near the longitudinal natural frequency of the rod. (2) Squeal noise of higher modes occurs in two cases. The first case is when contact surface between the rod and the disk is relatively large and the longitudinal vibration increases after a squeal noise of the fundamental mode damps. The second one is when the longitudinal vibration increases in rubbing noise. (3) however, a complete squeal noise of higher modes does not occur without damping of a squeal noise of fundamental mode, even if longitudinal vibration of the rod increases.

View full abstract

A new nondestructive test method using the mechanical impedance was developed for nondestructively detecting damages, such as a crack, flaw, etc. in the structural member. This method consists of comparing mechanical impedance measurements of a sound structure before use with those of the same structure in service. In order to verify the utility of the method, bending vibration tests were carried out on a clamped rectangular steel plate model with two parallel stiffeners, measuring its mechanical impedance in the course of cutting away one of the stiffeners gradually, which meant to simulate the growth of a crack in the root of the stiffener. Basic knowledges for judging the existence, size and location of a damage could be obtained from the model tests and the hardware as well as the software for a damage detecting equipment could be designed, based on the experience of the tests.

View full abstract

Following the previous paper the effect of surface roughness on scoring was investigated using a two-disc machine. Unlike in the previous investigation with an annealed carbon steel of high work-hardening ability, in the present investigation the disc material was a hardened carbon steel with high surface hardness and little ability of work-hardening. The anti-scoring performance of the discs with small roughness showed duality. Whereas scoring occurred when the surface temperature reached a critical value of about 180 °C, it did not occur even when the surface temperature exceeded the critical one, and the anti-scoring performance represented by fPVs at scoring (f: coefficient of friction, P: applied load per unit contact width, Vs: sliding speed) increased proportionally with an increase in concentration of oxygen on the disc surfaces. The formation of oxide film on the surface of the high speed disc promoted the anti-scoring performance, that is, it is benefical for prevention of scoring to use a disc with smaller roughness than the mating disc as the high speed disc.

View full abstract

Some overconstrained mechanisms in which the number of the independent closure equations of rotation or translation is smaller than 3 are analyzed and the displacements, velocities and accelerations are obtained with use of coordinate transformation matrices, and a dimensional synthesis of a spatial path generator is carried out. Moreover the dynamic characteristics of the above mechanism are analyzed theoretically considering the stiffness of each member, and the results are confirmed experimentally.

View full abstract

A 2-dimensional periodic elastohydrodynamic squeeze film between a rigid plane and an elastomer of uniform thickness attached on a rigid substrate is theoretically analyzed. Time-dependent film shape and pressure distribution through each period are calculated about a 2-dimensional model, and an elastic periodic squeeze film with an incompressible lubricant is found to be able to keep hydrodynamic lubrication condition under positive load. It is explained about this new lubrication mechanism that the lubricant is pumped inside the film by periodic deformation of the wall just like flapping flight, and consequently average film pressure takes positive value. A squeeze thrust bearing with silicone rubber lubricated with mineral oil was vibrated with electric power under constant load and experimentally investigated. The changes in floating gap and film pressure were measured and the experimental result verified the theory on the whole.

View full abstract