Logarithmic Spiral Surface Research Articles

Flow Characteristics and Hydraulic Lift of Coandă Effect-Based Pick-Up Method for Polymetallic Nodule

The deep-sea mining vehicle is the main component of the undersea exploitation system, which gathers polymetallic nodules with its professionally designed seabed collector. The Coandă effect-based collecting method is an improved hydraulic method that forms an adverse pressure gradient over the nodules by performing wall jet flow over a rounded convex surface. In comparison to the circular cylinder surface, the effect of wall jet over the logarithmic spiral surface has a self-preserving nature, which can be advantageous to the nodule collecting. However, this effect on lift capability has seldom been studied before. In the present investigation, a reduced form modelling jet flows over logarithmic spiral surfaces was performed to study the flow characteristics and lift ability of the newly designed Coandă effect-based collector. The jet-half width has been optimized to study the influence of wall curvature on the growth rate. The lift ability was found to be stronger with larger jet exit velocity, local curvature, or non-dimensional jet slot height. The growth rate, which represents the width of the main jet flow, went up in proportion to the downstream distance. The lift capability of jet flow in logarithmical spiral of x/R = 1 is significantly better than that of x/R = 2/3.

A compact-rigid multi-analyser for energy and angle filtering of high-resolution X-ray experiments. Part 1. Principles and implementation

Diffraction and spectroscopy instruments using a filtering process with several analyser crystals have existed for about 30 years at synchrotron radiation sources, but they are difficult to use on laboratory sources. Several diffraction multi-filtering systems for powder diffraction experiments have been studied and optimized, in order to show the relevance, simplicity and efficiency of their implementation. Optical filter systems containing one or many diffracting elements, precisely positioned in a rigid manner on a logarithmic spiral surface and having a stability that allows high resolution and high sensitivity to powder diffraction experiments, have been developed. After having tested prototypes with various geometries, we present in particular the realization of a small rigid-compact multi-analyser comb that allows 20-50 measurements on synchrotron radiation sources to be filtered in parallel, but also and especially that can be adapted on laboratory X-ray sources (Ag Kα1) to increase by an order of magnitude the intensities and resolutions of the measurements. Such a rigid-compact multi-analyser block can advantageously be associated with `photon-counting' 1D and 2D detectors in order to drastically improve the detection thresholds of powder diffraction measurements to better than 0.1%, which allows the detection/quantification/analysis of minor phases in studies of `real' complex materials.

Stability Analysis of Pile-Supported Embankments over Soft Clay Considering Soil Failure between Piles Based on Upper Bound Theorem

Most analytical methods used to analyze the stability of pile-supported embankments are based on shear and bending failure of piles. However, the centrifuge test and practical engineering show that rigid pile-supported embankments have a failure mode of soil sliding around piles. Therefore, the stability analysis method of the pile-supported embankment under the failure mode of the soil sliding around piles based on the upper bound theorem is given in this study. First, the failure mechanism is assumed to be a rigid body and slide along two logarithmic spiral surfaces in the embankment and soft soil. The rate of external work and internal energy dissipation of the failure mechanism are further obtained, wherein the internal energy dissipation rate of piles is obtained based on the limit state of soil sliding around piles. Secondly, according to the equation formed by the upper bound theorem, the optimization model of the safety factor function when the potential slip surface is passing through different pile rows is obtained. Then, the algorithm of solving the model is given and the overall safety factor of the pile-supported embankment is obtained. Compared with other methods, the advantage of this method is that it considers the influence of embankment soil property and the width perpendicular to the two-dimensional plane on the pile load and the influence of the soil internal friction angle on the slip surface. Finally, it can be concluded from parametric analysis that: with the increase of the horizontal distance from piles to the slope toe, the reinforcement effect of piles first increases and then decreases; with the decrease of the embankment height and the increase of the soft soil cohesion and internal friction angle, the overall safety factor of the embankment increases.

Numerical investigation on Coanda flow over a logarithmic surface

The Coanda effect has been introduced into lift generation designs. In this paper, a logarithmic spiral surface is introduced as a curvature shape to evaluate the development of jet flow along the Coanda curvature. Moreover, 2D computational fluid dynamics numerical simulation is adopted to measure velocity profile, jet width growth, maximum velocity decay, and surface static pressure along the curvature surface. A parametric study on the effect of varying exit jet heights on the Coanda effect is also presented. Results show that jet width grows proportionally along the curved surface, and the proportional decay of maximum velocity and surface pressure is lower than the atmospheric pressure. A wider exit jet height produces lower static pressure on the unmanned aerial vehicle surface and a slower maximum velocity decay. Overall parametric analysis of varying exit jet heights shows that the effective range of d/R is 0.1 to 0.14.

Design of Logarithmic Spiral Surface Wedge Block Backstop and Dynamic Simulation

A new contact backstop with logarithmic spiral surface wedge block is pointed out.Based on the existing eccentric circle surface wedge block,the logarithmic spiral surface wedge block is designed by the curve fitting method.The simulation model of the backstop is established with the Pro/E software.The three-dimensional model is imported into ANSYS/LS-DYNA software for dynamic simulation analysis to obtain the stress characteristics during the backstop process.By comparing the contact stress of the two wedge block,results show that the new backstop has much smaller stress,smoother process and better performance than the traditional backstop with eccentric circle surface wedge block,which will offer theoretical basis for the production of the new backstop.

Research on Applying Image Processing Technology to Determine Center of Parts

The precision detection of machine parts is an important part of manufacturing, which guarantees the quality for products. Image processing technology is a new testing method of precision which opens a new way for the non-contact detection. Its application is more widely with the continuous development of image processing technology. You need a comparative basic point if it needs a comparative analysis with the ideal conditions parts when it’s necessary to detect a part. In this paper, it mainly analyzes the determination of logarithmic spiral surface couplings center points.

Calculation of curved shear layers with two-equation turbulence models

Three extensions of the k-ε turbulence model were tested for shear-layer flows with streamline curvature. The first version is an algebraic-stress model which was derived by simplification of modeled Reynolds-stress equations and does not contain curvature-specific empiricism. The other two versions use a modified form of the dissipation-rate equation. The test cases considered are a convexly curved boundary layer, a curved mixing layer, and wall jets on logarithmic spiral surfaces. The results show that the algebraic-stress model gives the best overall agreement in the curved part of the flow but predicts too fast a recovery after the removal of curvature.

On Slip Surface and Slope Stability Analysis

ABSTRACT The method of variational calculus is applied to obtain the shape of slip surface and the corresponding normal stress distribution. For a horizontal slope of uniform soil, a logarithmic spiral surface of angle φ is found to be the most critical surface. This contradicts the report made earlier by Spencer (1969). The results also emphasize the correctness of the log-spiral failure mechanism assumed in the upper bound method of limit analysis.

Investigation of Turbulent Wall Jets over Logarithmic Spiral Surfaces : 2nd Report, Properties of Flow near Wall

In fully developed turbulent wall jets over logarithmic spiral surfaces, temporal mean velocity, turbulence intensity and friction stress were measured, and limit of the logarithmic spiral surface over which a fully developed turbulent wall jet can be obtained, was analytically discussed, and it was found that; (1) the values of friction stress on the wall surface which were measured by Preston tubes were different from those obtained from the inclination of linear velocity profile near the wall surface; (2) for any logarithmic spiral wall surfaces, there were unique logarithmic and defect laws in wall region, which differ from those of general turbulent boundary layer or pipe-flow; and (3) existence of limit of the logarithmic spiral surface was made clear analytically, and this result agreed with the experimental observation.

Investigation of Turbulent Wall Jets over Logarithmic Spiral Surfaces : 1st Report, Development of Jets and Similarity of Velocity Profile

In fully developed turbulent wall jets over logarithmic spiral surfaces, the similarity of velocity profile is discussed analytically and equation of motion for jet region is numerically solved. These results are compared with experimental results, and it is concluded that : (1) for any logarithmic spiral surface, non-dimensional velocity profiles of jet region are strictly similar to those of a two-dimensional free jet; (2) non-dimensional velocity profiles of wall region are similar to one another in a certain renge of Reynolds numbers, and these are not expressed by 1/n-power law; (3) the growth of jet width, the decrease of maximum velocity and the thickness ratio of wall region to jet region vary with the characteristic value of logarithmic spiral ; and (4) there is limitation of the logarithmic spiral surface over which a fully developed wall jet can be obtained.

Investigation of Turbulent Wall Jets over Logarithmic Spiral Surfaces : 1st Report, Development of Jets and Similarity of Velocity Profile

Investigation of Turbulent Wall Jets over Logarithmic Spiral Surfaces : 1st Report, Development of Jets and Similarity of Velocity Profile

The prediction of the force needed to move blades through a bed of cohesionless granules

A previous paper described the measurement of the force required to move a plane vertical blade horizontally close to the surface of a level bed. This paper discusses methods of predicting those blade forces using modified techniques of theoretical soil mechanics. For blades close to the surface of the granular bed the shape of the material profile must be taken into account. It is demonstrated for steel blades in ballotini that force calculations employing a kinematic model of material failure lead to predictions of force above the experimental values. Such models are therefore preferable for design purposes to calculations based on assumed stress distributions which predicted forces less than experimental. It is concluded that an assumption that the granular material fails in a logarithmic spiral surface leads to the prediction of forces close to the experimental. Difficulties arise, however, because solutions are not always unique and because of doubt as to boundary conditions at the blade face.