A tilted pad thrust slider bearing improved by the boundary slippage

The present paper proposes a new type of hydrodynamic lubricated tilted pad thrust slider bearing which is augmented with the boundary slippage at the stationary contact surface in the inlet zone. This design is of purpose to reduce the friction coefficient but increase the load-carrying capacity of the bearing. A theoretical analysis is presented for this bearing. Computational results and design guides for this bearing are given. It is found that the most increase of the carried load of the bearing by the boundary slippage is around 30 %, while the most reduction of the friction coefficient of the bearing by the boundary slippage is more than 40 %. This advantage is reached when the boundary slippage zone occupies 80 % of the bearing lubricated area and the fluid-contact interfacial shear strength at the boundary slippage interface is very low.     

Numerical study on the oscillation of a transient bubble near a confined free surface for droplet generation

In the present work, the oscillation of a spark-created bubble near a confined water–air interface and the ensuing droplet generation and ejection are studied numerically using the boundary element method. The interface is accorded by the top opening of either one of the following symmetrical configurations, which are distinguished by the value of angle between their vertical symmetry axis and lateral wall (i.e., θ): (i) a centrally perforated horizontal flat plate (θ = 90°) and (ii) vertically placed cylinder (θ = 0°), nozzle (θ > 0°) and diffuser (θ < 0°). Furthermore, the influences of the effective parameters such as the strength parameter (i.e., the intensity of local energy input), the bubble-free surface distance (standoff distance) and the nozzle size on the bubble dynamics and droplet formation and ejection processes are investigated. It was found that the moment at which the bubble attained its maximum volume was advanced as θ increased. In addition, by decreasing θ the attraction of the bubble toward the free surface during its expansion phase and its migration from the free surface during its contraction phase became stronger. Furthermore, for the nozzle case, by increasing θ, the volume of the droplet was increased. It was also found that by increasing the strength parameter, the volume of the droplet increased and its pinch-off happened earlier. Finally, as the standoff distance was increased, the volume of the droplet increased and its pinch-off was delayed.     

Squeeze flow of a power-law fluid between non-parallel plates

Squeeze flow in the gap between non-parallel circular plates of radius R is discussed. The test material is assumed to be a power-law fluid, with a no-slip boundary condition at the plates. If the mean separation between the plates is h, and the angle of inclination between the plates is ? ? h/R, the force on the plates is perturbed only at O(?²) and is increased by less than 10% if ? < 0.35h/R. A torque O(?) tends to return the plates to a parallel configuration.     

复合表面径向滑动轴承的概念和性能预报

近年来的研究发现固液界面的滑移可以减小表面摩擦,但也会造成流体动力效应下降甚至消失.本文提出了复合表面滑动轴承的概念,轴套表面由具有不同吸附和滑移特性的复合表面组成,发现复合表面轴承比普通轴承有许多优点.通过改变轴套表面的滑移特性可以改变和优化轴承的各种性能,例如摩擦系数、承载力、润滑剂流量、承载角等.数值解表明,在轴承高压区改变轴套表面滑移特性,轴承的整体性能会有大幅度提高.例如,本文给出的初步优化设计方案使得摩擦系数降低50%以上,同时承载力可提高20%,并且承载角可以降低33%.本文提出的设计理念不但可用于设计出具有更优异特性的径向滑动轴承,而且可以设计出具有复合表面的轴向滑动轴承或滑块轴承.复合表面滑动轴承在降低轴承摩擦、提高承载能力方面有很大的空间可以探索.     

The effect of suction or injection on the boundary layer flows induced by continuous surfaces stretched with prescribed skin friction

The boundary layer flow and heat transfer on a stretched surface moving with prescribed skin friction is studied for permeable surface. Three major cases are studied for isothermal surface (n=0) stretched corresponding to different dimensional skin friction boundary conditions namely; skin friction at the surface scales as (x ^?1/2) at m=0, constant skin friction at m=1/3 and skin friction scales as (x) at m=1. The constants m and n are the indices of the power law velocity and temperature exponent respectively. Similarity solutions are obtained for the boundary layer equations subject to power law temperature and velocity variation. The effect of various governing parameters, such as Prandtl number Pr, suction/injection parameter f _w , m and n are studied. The results show that for isothermal surface increasing m enhances the dimensionless heat transfer coefficient for fixed f _w at the suction case and the reverse is true at the injection case. Furthermore, for fixed m, as f _w increases the dimensionless heat transfer coefficient increases. Large enhancements are observed in the heat transfer coefficient as the temperature boundary condition along the surface changes from uniform to linear where the dimensional skin friction is of order (x) at m=1. This enhancement decreases as the suction increases.     

Bearing capacity analysis using the method of characteristics

Using the method of characteristics,the bearing capacity for a strip footing is analyzed.The method of characteristics leads to an exact true limit load when the calculations of the three terms in the bearing capacity formula are consistent with one collapse mechanism and the soil satisfies the associated flow rule.At the same time,the method of characteristics avoids the assumption of arbitrary slip surfaces,and produces zones within which equilibrium and plastic yield are simultaneously satisfied for given boundary stresses.The exact solution without superposition approximation can still be expressed by Terzaghi's equation of bearing capacity,in which the bearing capacity factor N γλ is dependent on the dimensionless parameter λ and the friction angle φ.The influence of groundwater on the bearing capacity of the shallow strip footing is considered,which indicates that when the groundwater effect is taken into account,the error induced by the superposition approximation can be reduced as compared with dry soil condition.The results are presented in the form of charts which give the modified value(Nwγλc /Nγλc) of bearing capacity factor.Finally,an approximated analytical expression,which provides results in close agreement with those obtained by numerical analysis in this paper,has been suggested for practical application purposes.     

Measurement of local forcing on a turbulent boundary layer using PIV

An experimental study was carried out to investigate the effect of periodic blowing and suction on a turbulent boundary layer. Particle image velocimetry (PIV) was used to probe the characteristics of the flow. Local forcing was introduced to the boundary layer via a sinusoidally-oscillating jet issuing from a thin spanwise slot. Three forcing frequencies (f⁺=0.44, 0.66 and 0.88) with a fixed forcing amplitude (A⁺=0.6) were employed at Re _θ =690. The effect of three different forcing angles (α=60°, 90° and l20°) was investigated under a fixed forcing frequency (f⁺=0.088). The PIV results showed that the wall-region velocity decreases on imposition of the local forcing. Inspection of the phase-averaged velocity profiles revealed that spanwise large-scale vortices are generated downstream of the slot and persist farther downstream. The highest reduction in skin friction was achieved at the highest forcing frequency (f⁺=0.088) and a forcing angle of α=120°. The spatial fraction of the vortices was examined to analyze the skin friction reduction.     

Squeeze flow of Bingham fluids under slip with friction boundary condition

This paper develops a theoretical analysis of a Bingham fluid in slipping squeeze flow. The flow field decomposition consists in combining a central extensional flow zone in the plane of symmetry and shear flow zones near the plates. It is also considered that the slipping zone is located around a central sticking zone as previously shown from experiments. It is assumed that the shear stress at the plates is constant in the slipping zone and equals a fixed friction yield value. The squeeze force required to compress a Bingham fluid under the slipping behaviour as well as the radial evolution of the transition point between both sticking and slipping zones are finally determined.     

The influence of confinement on the bearing capacity of strip footingsEffet du confinement sur la capacité portante d'une fondation superficielle

The bearing capacity for a strip footing acting on a soil foundation with rigid boundaries at a finite distance is investigated within the framework of the Yield design theory both for a purely cohesive soil and for a frictional soil. It is shown that the analysis can be performed simply by referring to already existing results concerning the bearing capacity of a strip footing on a soil layer with limited thickness. Each bearing capacity factor in Terzaghi formula is increased by a factor that increases when the distance of the rigid boundary to the edge of the footing decreases. The bearing capacity is proved to be the more sensitive to this confining effect as the friction angle of the soil increases. From a physical point of view this theoretical analysis would show that, when effective, confinement reduces the depth of the soil layer involved in the collapse mechanism. To cite this article: J. Salençon, C. R. Mecanique 330 (2002) 319–326.     

Flow characteristics and flow-induced forces of a stationary and rotating triangular cylinder with different incidence angles at low Reynolds numbers

In this paper, the problem of two-dimensional fluid flow past a stationary and rotationally oscillating equilateral triangular cylinder with a variable incident angle, Reynolds number, oscillating amplitude, and oscillating frequency is numerically investigated. The computations are carried out by using a two-step Taylor-characteristic-based Galerkin (TCBG) algorithm. For the stationary cases, simulations are conducted at various incident angles of α=0.0–60.0° and Reynolds numbers of Re=50–160. For the oscillation cases, the investigations are done at various oscillating amplitudes of θ_max=7.5–30.0° and oscillating frequencies of F_s/F_o=0.5–3.0 considering two different incidence angles (α=0.0°, 60.0°) and three different Reynolds numbers (Re=50, 100, 150). The results show that the influences of key parameters (incidence angle, Reynolds number, oscillating amplitude, and oscillating frequency) are significant on the flow pattern and hydrodynamic forces. For the stationary cases, at smaller angle of incidence (α≤30.0°), Reynolds number has a large impact on the position of the separation points. When α is between 30.0° and 60.0°, it was found that the separation points are located at the rear corners. From a topological point of view, the diagram of flow pattern is summarized, including two distinct patterns, namely, main separation and vortex merging. A deep analysis of the influence of Reynolds number and incidence angles on the mean pressure coefficient along the triangular cylinder surface is presented. Additionally, for the oscillating cases, the lock-on phenomenon is captured. The dominant flow patterns are 2S mode and P+S mode in lock-on region at α=0.0°. It is found at α=60.0°, however, that the flow pattern is predominantly 2S mode. Furthermore, except for the case of F_s/F_o=2.0, the mean drag decreases as the oscillating amplitude increases for each Reynolds number at α=0.0°. At α=60.0°, the minimum mean drag for F_s/F_o=1.5 is lower than that for stationary case, and occurs at θ_max=15.0° (Re=100) and θ_max=22.5° (Re=150), respectively. Finally, the effect of Reynolds number on a rotational oscillation cylinder is elucidated.     

Friction coefficient and error test via micro-rotation mechanics model

An air pressure-loading mode incorporated into the friction apparatus is firstly applied to coatings tribology involving large load, automation, stepless and continuous loading processes. A novel measurement principle is proposed and a micro-rotation mechanics model was developed for high precision measurement of friction coefficient. By properly designing and locating two sensors real-time monitoring the normal and friction forces, the troublesome influences in friction measurement is considerably relieved which come from surface characteristics of coatings of the samples in traditional friction test processes. By calculation and analysis, the max rotation angle θ_max = 0.0018° is gained, which indicates that the measurement error of the apparatus is greatly reduced. The whole system error is about 1.15% given by finite element method and indication error of the least square fitting of measurements.     

Coherent structure in the turbulent wake behind a circular cylinder 2. numerical simulation using the vortex filament model

In the previous paper the authors reported observing the formation of a spoon-shaped vortex chain in a wake behind a circular cylinder as a coherent structure in turbulence. In this report numerical simulation is carried out based on the assumption that the structure is formed by deformation of the Kánnán vortices. The basic equation is the localized induction equation for a single vortex filament with an influence of the background mean flow. The vortex filament is given an initial deformation within a plane at an angle θ to the x−z plane (x is the mean flow direct and z the spanwise direction) with the width Z_w, and the further deformation process of the filament is numerically traced. The first calculation is made with fixed Z_w and various values of θ. The result shows that the vortex filament finally reaches a structure lying on a plane with a constant angle of 30° ~ 45° to the x-z plane irrespective of the initial values of θ. The second calculation is made with fixed θ and various values of Z_w. In this case the final spanwise scale of the deformed region of the filament has almost constant values of about 4d−6d (d is diameter of the cylinder). These results indicate that the final structure of the vortex filament is stable and definite irrespective of the initial disturbances.     

Multiple scattering of flexural waves in a semi-infinite thin plate with a cutout

The multiple scattering of flexural waves and dynamic stress concentration in a semi-infinite thin plate with a cutout are investigated, and the expressions of this problem are obtained. The analytical solutions of wave fields are expressed by employing the wave function expansion method and the expanded mode coefficients are solved by satisfying the boundary condition of the cutout. The image method is used to satisfy the traction free boundary condition of the plate. As an example, the numerical results of dynamic stress concentration factors are graphically presented and discussed. Numerical results show that the analytical results of the scattered waves and dynamic stress in semi-infinite plates are significantly different from those in infinite plates when the ratio of distance b/a is relatively little. In the region of low frequency and long wavelength, the maximum dynamic stress concentration factors occur on the illuminated side of the scattering body with θ = π, but not at the edge of the cutout with θ = π/2. As the incidence frequency increases (the wavelength becomes short), the dynamic stress on the illuminated side of the cutout decreases, however, the dynamic stress on the shadow side increases.     

Numerical study of large amplitude,nonsinusoidal motion and camber effects on pitching airfoil propulsion

The effects of large amplitude and nonsinusoidal motion on pitching airfoil aerodynamics for thrust generation were numerically studied with a 2-D NACA0012 airfoil used, and various 2-D NACA asymmetric airfoils were applied for camber effect study. The large amplitude effect study has been undertaken over a wide range of reduced frequency k (from 6 to 18) and pitching amplitude θ (from 5° to 30°) at Re=1.35×10⁴ with sinusoidal pitching profile used. It is shown that the large pitching amplitude results in much more thrust generated than that at low pitching amplitude and the increase of thrust with amplitude becomes slow when the amplitude reaches some degree. However, the propulsive efficiency noticeably decreases with the increase of θ at a fixed k.An adjustable parameter K was employed to realize various nonsinusoidal motions and the effect of nonsinusoidal motion was investigated with various unsteady parameters (θ, k) applied. The results reveal that nonsinusoidal motion has a noticeable effect on the aerodynamic performance, as it affects the instantaneous force coefficients, maximum thrust coefficients and flow structures. An increase in K results in a better thrust generation performance at fixed θ and k, especially for K>0. It is also shown that the larger K noticeably influences the wake pattern and induces a stronger reverse von Karman vortex street in the wake, which in turn leads to the increased thrust. The camber study was performed on various 2-D NACA airfoils with different cambers and camber locations undergoing sinusoidal pitching motion at θ=5° and Re=1.35×10⁴. It is found that varying camber offers little improvement in thrust generation performance.     

Effect of gravity on the mechanical properties of lunar regolith tested using a low gravity simulation device

Simulations of the bearing capacity and shear strength of regolith under Earth’s gravity produce different results from those under low gravity. A low-gravity simulation device was developed in this study, and an internal stress model of regolith simulant was established to correct the errors. The model revealed additional force on both shear plane in the shear test and the press plate area in the pressure–sinkage test. The sinkage and shear test results showed that low gravity decreased the deformable index n, frictional modulus k_φ and cohesion c, whereas there were no obvious changes to the cohesive modulus k_c and internal friction angle φ. The sinkage generally increased as the gravity decreased under a consistent normal load larger than 50 N, but when the wheel load was lower than 50 N, the sinkage of the TYII-1 simulant was larger under 1 G than 1/6 G. Gravity had little effect on the shear strength of the regolith. However, the tractive thrust of the TYII-1 simulant was lower under 1/6 G than 1 G. The smaller difference was due to differences in the way the soils responded to changes in the gravity level for the TYII-2 simulant.     

Influence of the nutation angle in gravitational settling of particles near vortices and in turbulence

The knowledge of the conditions in which particles denser than fluid settle is important in many areas of engineering, environmental sciences, meteorology, etc.For particle flows influenced by vortices, research mainly related to steady horizontal vortices has been undertaken. In this paper we determine the influence of the inclination of the vortex axis in the gravitational settling of particles.The results obtained, in relation to the trajectories, are qualitatively similar to previous ones for horizontal vortices. The main difference is this: in a horizontal vortex particles always remain in a plane perpendicular to the vortex axis and in an inclined vortex (angle θ) particles do not remain on that plane because there is a component v_tcosθ that takes them out.The average fall velocity 〈v_z〉 has an asymptote to the dimensionless terminal velocity v_t; this tendency is faster as the Stokes Number St increases and as v_t decreases. A fundamental result is the following: as θ decreases, v_t is reached faster because the component of the velocity u of the Rankine vortex over the Oz direction is small and because the v_t component that tries to keep the particles in a plane perpendicular to the vortex axis is small, so the vortex takes action over the particles for a small period of time.     

Experimental investigation of the onsets of gas and liquid entrainment from a small branch mounted on an inclined wall

The phenomena of the onsets of liquid entrainment and gas entrainment were investigated experimentally for the case of a flat plane with a circular outlet branch of diameter d (=6.35 mm) at the plane centre. This flat plane was situated in a large tank containing a stratified mixture of air and water under pressure (317 kPa for most experiments and 520 kPa for a few experiments) and at room temperature. The plane was inclined through various angles (θ) in increments of 30°, from the outlet branch orientation being vertically upward through the horizontal to vertically downward. For both onsets the vertical distance between the centre of the outlet branch and the undisturbed gas–liquid interface (h) was measured for various angles of inclination and Froude numbers. Both onsets were observed visually through a large viewing part of the test section. It was found that for both onsets there is a range of inclination angles where the onset h depended on θ and a range where the onset h essentially did not depend on θ. The data were correlated in terms of onset h/d, Froude number, and θ where there was dependence of onset h on the angle of inclination.     

Generation of tones due to flow past a deep cavity: Effect of streamwise length

Shear flow past a deep cavity can generate self-sustained oscillations, including locked-on flow tones, due to coupling between the inherent instability of the separated shear layer and an acoustic mode of the cavity resonator. This investigation focuses on the dimensionless pressure amplitude response within a deep cavity, as a function of the streamwise length of the cavity opening; for each length, the pressure response is characterized over a wide range of dimensionless inflow velocity. Criteria for locked-on flow tones are assessed. They include a measure of the strength of lock-on, SoL and the quality factor Q. All self-excited oscillations are assessed using both of these criteria, in order to interpret dimensionless forms of the fluctuation pressure amplitude. The dimensionless pressure amplitude response of the cavity involves several successive regimes, due to variations of streamwise length L of the cavity opening. These regimes are defined in relation to L/θ, where θ is the momentum thickness of the inflow boundary layer. Below a minimum value of L/θ, flow tones cannot be generated. Furthermore, these regimes are defined in terms of the possible hydrodynamic modes (stages) of the unsteady shear layer and the acoustic modes of the deep cavity.     

Numerical and experimental studies of natural convective heat transfer from vertical and inclined narrow isothermal flat plates

Natural convective heat transfer from an isothermal narrow flat plate embedded in a plane adiabatic surface and inclined at moderate positive and negative angles to the vertical has been numerically and experimentally studied. The solution has the Rayleigh number, the dimensionless plate width, the angle of inclination, and the Prandtl number as parameters. Attention was restricted to a Prandtl number of 0.7. The numerical results have been obtained for Rayleigh numbers between 10³ and 10⁷ for dimensionless plate widths of between 0.3 and 1.2 and for angles of inclination between +45° and −45°. In the experimental study, results have been obtained for Rayleigh numbers between 4 × 10² and 10⁵ for dimensionless plate widths of 0.4 and 2.5 and for angles of inclination between +45° and −45° to the vertical. Empirical equations for the heat transfer rate have been derived.     

Flow and mixing characteristics of a forward-inclined stack-issued jet in crossflow

The flow and mixing characteristics of a forward-inclined stack-issued jet at various inclination angles (θ) and jet-to-crossflow momentum flux ratios (R) were experimentally studied in an open-loop wind tunnel. Flow behaviors were examined using the laser-assisted smoke flow visualization technique. The instantaneous velocities of the upwind-side shear-layer were digitized by a hot-wire anemometer using a high-speed data acquisition system. The instability frequencies in the upwind-side shear-layer vortices were obtained by the fast Fourier transform method. Long-exposure flow images were processed using the binary edge-detection technique to obtain the jet spread width. Transverse dispersion of jet fluids was determined using tracer gas concentration detection. The upwind-side shear-layer vortices revealed four characteristic flow modes: the High impingement-crossflow dominated mode (about θ < 15° and low R), the High impingement-jet flow dominated mode (about θ < 25° and high R), the Low impingement-crossflow dominated mode (about θ > 15° and low R), and the Low impingement-jet flow dominated mode (about θ > 25° and high R). Increasing θ in the crossflow dominated regimes eliminated the upwind-side shear-layer vortices, while increasing θ in the jet flow dominated regimes emphasized the upwind-side shear-layer vortices. Increasing θ at a fixed value of R increased jet spread width in the far field in all modes. In the near field, at x/d < 5 in the High impingement-crossflow dominated regime, the jet spread width was greater than in the Low impingement-crossflow dominated regime. In the jet flow dominated regimes, higher θ values led to greater jet spread width. Transverse dispersion of the jet fluids approached the jet spread width results. In the Low impingement-jet flow dominated regime, transverse dispersion of the jet fluids was significantly increased compared to the other regimes. In addition, the maximum tracer gas concentration was severely reduced at all axial stages, which implied better dispersion of the jet fluids in this regime.