A Windows bitmap-based numerically controlled sculpture method and its application

Bitmap （BMP） is a widely used format in image processing. With the combination of the digital image processing and computer numerically controlled （NC） techniques, we developed a bitmap-based NC single-step and multi-dot method. An example was provided to illustrate the application and principle of this bitmap-based method in our newly innovated sandblasting glass NC sculpture system.

Three-Variable Shifted Jacobi Polynomials Approach for Numerically Solving Three-Dimensional Multi-Term Fractional-Order PDEs with Variable Coefficients

In this paper,the three-variable shifted Jacobi operational matrix of fractional derivatives is used together with the collocation method for numerical solution of threedimensional multi-term fractional-order PDEs with variable coefficients.The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplifying the problem.The approximate solutions of nonlinear fractional PDEs with variable coefficients thus obtained by threevariable shifted Jacobi polynomials are compared with the exact solutions.Furthermore some theorems and lemmas are introduced to verify the convergence results of our algorithm.Lastly,several numerical examples are presented to test the superiority and efficiency of the proposed method.

Analysis of disagreement between numerically predicted and experimental heat transfer data of impinging jet

The method of numerical simulation was applied to investigate the effects of jet impinging plate thickness and its thermal conductivity on the local heat flux distribution along the impinging plate. The results show that the two factors have great effects on the heat flux distribution. The non-uniformity of the local heat-flux on the impinging plate surface gets more profound as the plate becomes thicker and thermal conductivity gets larger. When Reynolds number is 5000, the ratio of nozzle-to-plate spacing to nozzle diameter is 5 and thermal conductivity is 16W/(m·K), and even for the plate with only 25μm in thickness, the non-uniformity of the heat flux cannot be neglected. When the plate thickness is 50 μm, only when thermal conductivity is as small as 1W/(m·K), the heat flux curve can be approximately treated as an iso-heat-flux boundary. In the experimental research, a real non-iso-heat-flux boundary is treated as an iso-heat-flux boundary, which would result in under-estimated Nusselt number value in the stagnation zone and an over-estimated value outside. Such an experimental Nusselt number distribution is taken to evaluate turbulent model, and the conclusion would be drawn that the turbulent model over-predicts the stagnation heat transfer. This is one of the important reasons why many literatures reported that k-ε turbulent model dramatically over-predicts the impinging jet heat transfer in the stagnation region.

Predicting numerically the large increases in extra pressure drop when boger fluids flow through

Recent numerical studies on pressure-drops in contraction flows have introduced a variety of constitutive models to compare and contrast the competing influences of extensional vis-cosity, normal stress and shear-thinning. Early work on pressure-drops employed the constant viscosity Oldroyd-B and Upper Convected Max- well (UCM) models to represent the behavior of so-called Boger fluids in axisymmetric contrac-tion flows, in (unsuccessful) attempts to predict the very large enhancements that were ob-served experimentally. In more recent studies, other constitutive models have been employed to interpret observed behavior and some pro-gress has been made, although finding a (re-spectable) model to describe observed contrac-tion-flow behavior, even qualitatively, has been frustratingly difficult. With this in mind, the present study discusses the ability of a well- known FENE type model (the so-called FENE- CR model) to describe observed behavior. For various reasons, an axisymmetric (4:1:4) con-traction/expansion geometry, with rounded corners, is singled out for special attention, and a new hybrid finite element/volume algo-rithm is utilized to conduct the modeling, which reflects an incremental pressure-correction time-stepping structure. New to this algo-rithmic formulation are techniques in time discretization, discrete treatment of pressure terms, and compatible stress/velocity-gradient representation. We shall argue that the current simulations for the FENE-CR model have re-sulted in a major improvement in the sort-for agreement between theory and experiment in this important bench-mark problem.

Workflow to numerically reproduce laboratory ultrasonic datasets

The risks and uncertainties related to the storage of high-level radioactive waste （HLRW） can be reducedthanks to focused studies and investigations. HLRWs are going to be placed in deep geological repositories,enveloped in an engineered bentonite barrier, whose physical conditions are subjected tochange throughout the lifespan of the infrastructure. Seismic tomography can be employed to monitor itsphysical state and integrity. The design of the seismic monitoring system can be optimized via conductingand analyzing numerical simulations of wave propagation in representative repository geometry.However, the quality of the numerical results relies on their initial calibration. The main aim of this paperis to provide a workflow to calibrate numerical tools employing laboratory ultrasonic datasets. The finitedifference code SOFI2D was employed to model ultrasonic waves propagating through a laboratorysample. Specifically, the input velocity model was calibrated to achieve a best match between experimentaland numerical ultrasonic traces. Likely due to the imperfections of the contact surfaces, theresultant velocities of P- and S-wave propagation tend to be noticeably lower than those a prioriassigned. Then, the calibrated model was employed to estimate the attenuation in a montmorillonitesample. The obtained low quality factors （Q） suggest that pronounced inelastic behavior of the clay has tobe taken into account in geophysical modeling and analysis. Consequently, this contribution should beconsidered as a first step towards the creation of a numerical tool to evaluate wave propagation innuclear waste repositories. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

Numerically investigation of particle distribution in industrial-scale DTB crystallizer based on CFD modelling

The suspension state of crystals in the crystallizer is one of the important indicators for evaluating the adaptability of the crystallizer.This study adopted the Euler-Eulerian two-fluid model to simulate and analyze the fluid motion of solid-liquid two-phase flow in the industrial-grade DTB crystallization kettle,as well as the phase suspension distribution of crystal particles.The main influencing factors investigated are:the heat transfer effect,the height of the bottom of the crystallizer,the number and position of the stirring paddle,crystal size and crystal volume fraction.Based on the research of Euler-Eulerian method to simulate fluids,the Euler-Lagrangian method was further used to simulate the motion state of particle phases with different particle sizes in the crystallizer.It was found that the designed DTB crystallizer has good recycle mixing effect.The particles can be mixed evenly during the operation,which can fully realize the solid-liquid mixing and suspension effect of the drug under study.

Numerically investigating the crushing of sandstone by a tooth hob

To investigate the mechanical process that occurs between rocks and tooth hobs,the crushing of sandstone with a tooth hob was simulated using reconstructed multi-mineral mesoscopic numerical models of various grain-sized sandstone samples.When a piece of sandstone is crushed by the tooth of a hob rolling at a constant speed,the resultant reaction forces of the sandstone on the tooth first hinder and then contribute to the rolling of the hob.The absolute value of the longitudinal reaction force is significantly higher than that of the lateral reaction force.Because the tooth was subjected to reaction forces from the sandstone,forces and moments were applied to the hob in order to keep the hob rolling.The applied forces were equal in value and opposite in direction to the reaction forces of the sandstone on the tooth.Three typical curves of the work done by the applied forces and moment were obtained,and the contribution of the applied lateral force and moment to the total work done for crushing sandstones was variable;however,no work was done by the applied longitudinal force.Moreover,the applied longitudinal force and total work were positively correlated with the strength of sandstone samples.The total work,applied forces,and moment increased with the maximum penetration depth of the tooth in the sandstone.

State-of-the-art on the anchorage performance of rock bolts subjected to shear load

Rock bolts are extensively utilized in underground engineering as a means of offering support and stability to rock masses in tunnels,mines,and other underground structures.In environments of high ground stress,faults or weak zones can frequently arise in rock formations,presenting a significant challenge for engineering and potentially leading to underground engineering collapse.Rock bolts serve as a crucial structural element for the transmission of tensile stress and are capable of withstanding shear loads to prevent sliding of weak zones within rock mass.Therefore,a complete understanding of the behavior of rock bolts subjected to shear loads is essential.This paper presents a state-of-the-art review of the research progress of rock bolts subjected to shear load in three categories:experiment,numerical simulation,and analytical model.The review focuses on the research studies and developments in this area since the 1970s,providing a comprehensive overview of numerous factors that influence the anchorage performance of rock bolts.These factors include the diameter and angle of the rock bolt installation,rock strength,grouting material,bolt material,borehole diameter,rock bolt preload,normal stress,joint surface roughness and joint expansion angle.The paper reviews the improvement of mechanical parameter setting in numerical simulation of rock bolt shear.Furthermore,it delves into the optimization of the analytical model concerning rock bolt shear theory,approached from the perspectives of both Elastic foundation beam theory coupled with Elastoplasticity theory and Structural mechanic methods.The significance of this review lies in its ability to provide insights into the mechanical behavior of rock bolts.The paper also highlights the limitations of current research and guidelines for further research of rock bolts.

Recent progresses in the development of tubular segmented-in-series solid oxide fuel cells:Experimental and numerical study

Solid oxide fuel cells(SOFCs)have attracted a great deal of interest because they have the highest efficiency without using any noble metal as catalysts among all the fuel cell technologies.However,traditional SOFCs suffer from having a higher volume,current leakage,complex connections,and difficulty in gas sealing.To solve these problems,Rolls-Royce has fabricated a simple design by stacking cells in series on an insulating porous support,resulting in the tubular segmented-in-series solid oxide fuel cells(SIS-SOFCs),which achieved higher output voltage.This work systematically reviews recent advances in the structures,preparation methods,perform-ances,and stability of tubular SIS-SOFCs in experimental and numerical studies.Finally,the challenges and future development of tubular SIS-SOFCs are also discussed.The findings of this work can help guide the direction and inspire innovation of future development in this field.

Influence of water coupling coefficient on the blasting effect of red sandstone specimens

This study investigates the impact of different water coupling coefficients on the blasting effect of red sandstone.The analysis is based on the theories of detonation wave and elastic wave,focusing on the variation in wall pressure of the blasting holes.Using DDNP explosive as the explosive load,blasting tests were conducted on red sandstone specimens with four different water coupling coefficients:1.20,1.33,1.50,and 2.00.The study examines the morphologies of the rock specimens after blasting under these different water coupling coefficients.Additionally,the fractal dimensions of the surface cracks resulting from the blasting were calculated to provide a quantitative evaluation of the extent of rock damage.CT scanning and 3D reconstruction were performed on the post-blasting specimens to visually depict the extent of damage and fractures within the rock.Additionally,the volume fractal dimension and damage degree of the post-blasting specimens are calculated.The findings are then combined with numerical simulation to facilitate auxiliary analysis.The results demonstrate that an increase in the water coupling coefficient leads to a reduction in the peak pressure on the hole wall and the crushing zone,enabling more of the explosion energy to be utilized for crack propagation following the explosion.The specimens exhibited distinct failure patterns,resulting in corresponding changes in fractal dimensions.The simulated pore wall pressure–time curve validated the derived theoretical results,whereas the stress cloud map and explosion energy-time curve demonstrated the buffering effect of the water medium.As the water coupling coefficient increases,the buffering effect of the water medium becomes increasingly prominent.

Hybrid-Vlasov simulation of soft X-ray emissions at the Earth’s dayside magnetospheric boundaries

Solar wind charge exchange produces emissions in the soft X-ray energy range which can enable the study of near-Earth space regions such as the magnetopause,the magnetosheath and the polar cusps by remote sensing techniques.The Solar wind Magnetosphere Ionosphere Link Explorer(SMILE)and Lunar Environment heliospheric X-ray Imager(LEXI)missions aim to obtain soft Xray images of near-Earth space thanks to their Soft X-ray Imager(SXI)instruments.While earlier modeling works have already simulated soft X-ray images as might be obtained by SMILE SXI during its mission,the numerical models used so far are all based on the magnetohydrodynamics description of the space plasma.To investigate the possible signatures of ion-kinetic-scale processes in soft Xray images,we use for the first time a global hybrid-Vlasov simulation of the geospace from the Vlasiator model.The simulation is driven by fast and tenuous solar wind conditions and purely southward interplanetary magnetic field.We first produce global X-ray images of the dayside near-Earth space by placing a virtual imaging satellite at two different locations,providing meridional and equatorial views.We then analyze regional features present in the images and show that they correspond to signatures in soft X-ray emissions of mirrormode wave structures in the magnetosheath and flux transfer events(FTEs)at the magnetopause.Our results suggest that,although the time scales associated with the motion of those transient phenomena will likely be significantly smaller than the integration time of the SMILE and LEXI imagers,mirror-mode structures and FTEs can cumulatively produce detectable signatures in the soft X-ray images.For instance,a local increase by 30%in the proton density at the dayside magnetopause resulting from the transit of multiple FTEs leads to a 12%enhancement in the line-of-sight-and time-integrated soft X-ray emissivity originating from this region.Likewise,a proton density increase by 14%in the magnetosheath associated with mirror-mode structures can result in an enhancement in the soft X-ray signal by 4%.These are likely conservative estimates,given that the solar wind conditions used in the Vlasiator run can be expected to generate weaker soft X-ray emissions than the more common denser solar wind.These results will contribute to the preparatory work for the SMILE and LEXI missions by providing the community with quantitative estimates of the effects of small-scale,transient phenomena occurring on the dayside.

Effects of seepage pressure on the mechanical behaviors and microstructure of sandstone

Surrounding rocks of underground engineering are subjected to long-term seepage pressure,which can deteriorate the mechanical properties and cause serious disasters.In order to understand the impact of seepage pressure on the mechanical property of sandstone,uniaxial compression tests,P-wave velocity measurements,and nuclear magnetic resonance(NMR)tests were conducted on saturated sandstone samples with varied seepage pressures(i.e.0 MPa,3 MPa,4 MPa,5 MPa,6 MPa,7 MPa).The results demonstrate that the mechanical parameters(uniaxial compressive strength,peak strain,elastic modulus,and brittleness index),total energy,elastic strain energy,as well as elastic strain energy ratio,decrease with increasing seepage pressure,while the dissipation energy and dissipation energy ratio increase.Moreover,as seepage pressure increases,the micro-pores gradually transform into meso-pores and macro-pores.This increases the cumulative porosity of sandstone and decreases P-wave velocity.The numerical results indicate that as seepage pressure rises,the number of tensile cracks increases progressively,the angle range of microcracks is basically from 50-120to 80-100,and as a result,the failure mode transforms to the tensile-shear mixed failure mode.Finally,the effects of seepage pressure on mechanical properties were discussed.The results show that decrease in the effective stress and cohesion under the action of seepage pressure could lead to deterioration of strength behaviors of sandstone.

Research on the influences of motion characteristics of jetting projectile charge under water

Shaped charge warhead is important for enhancing the damage performance of underwater weapons.This paper used finite element analysis software and based on JPC water penetration experiments to examine the influence of liner parameters(wall thickness,material),charge aspect ratio,and stand-off distance on the movement characteristics of JPC in water.The findings reveal that the head diameter of the JPC increases and experiences significant erosion after entering the water,the effective length of the JPC in water undergoes two distinct phases:a growth phase and a decrease phase,with the velocity of the JPC decaying exponentially.Increasing the liner thickness,stand-off distance and the charge aspect ratio can improve the erosion resistance and the velocity retention capacity of the JPC.The optimal ranges for liner thickness and stand-off distance are 0.0363D_(k) to 0.0545D_(k)(D_(k) is the charge diameter),the stand-off distance should be within 1.0D_(k).After the charge aspect ratio higher than 1.25,the charge structure exerts minimal influence the movement characteristics of the JPC in water.Material density plays a crucial role in the velocity decay pattern of the JPC during penetration.JPC with higher densities exhibit superior velocity retention capabilities in water,with the velocity decay pattern converging if the densities are similar.Consequently,copper,tantalum and tungsten liners are deemed appropriate for underwater shaped charge warhead.Finally,the results will provide an important reference for the design of underwater shaped charge warhead.

Evaluating the stability and volumetric flowback rate of proppant packs in hydraulic fractures using the lattice Boltzmann-discrete element coupling method

The stability and mobility of proppant packs in hydraulic fractures during hydrocarbon production are numerically investigated by the lattice Boltzmann-discrete element coupling method(LB-DEM).This study starts with a preliminary proppant settling test,from which a solid volume fraction of 0.575 is calibrated for the proppant pack in the fracture.In the established workflow to investigate proppant flowback,a displacement is applied to the fracture surfaces to compact the generated proppant pack as well as further mimicking proppant embedment under closure stress.When a pressure gradient is applied to drive the fluid-particle flow,a critical aperture-to-diameter ratio of 4 is observed,above which the proppant pack would collapse.The results also show that the volumetric proppant flowback rate increases quadratically with the fracture aperture,while a linear variation between the particle flux and the pressure gradient is exhibited for a fixed fracture aperture.The research outcome contributes towards an improved understanding of proppant flowback in hydraulic fractures,which also supports an optimised proppant size selection for hydraulic fracturing operations.

Thermal safety boundary of lithium-ion battery at different state of charge

Thermal runaway(TR)is a critical issue hindering the large-scale application of lithium-ion batteries(LIBs).Understanding the thermal safety behavior of LIBs at the cell and module level under different state of charges(SOCs)has significant implications for reinforcing the thermal safety design of the lithium-ion battery module.This study first investigates the thermal safety boundary(TSB)correspondence at the cells and modules level under the guidance of a newly proposed concept,safe electric quantity boundary(SEQB).A reasonable thermal runaway propagation(TRP)judgment indicator,peak heat transfer power(PHTP),is proposed to predict whether TRP occurs.Moreover,a validated 3D model is used to quantitatively clarify the TSB at different SOCs from the perspective of PHTP,TR trigger temperature,SOC,and the full cycle life.Besides,three different TRP transfer modes are discovered.The interconversion relationship of three different TRP modes is investigated from the perspective of PHTP.This paper explores the TSB of LIBs under different SOCs at both cell and module levels for the first time,which has great significance in guiding the thermal safety design of battery systems.

Elastic-viscoplastic behaviors of polymer-blend geocell sheets:Numerical and experimental investigations

Polymer-blend geocell sheets(PBGS)have been developed as substitute materials for manufacturing geocells.Various attempts have been made to test and predict the behaviors of commonly used geogrids,geotextiles,geomembranes,and geocells.However,the elastic-viscoplastic behaviors of novel-developed geocell sheets are still poorly understood.Therefore,this paper investigates the elastic-viscoplastic behaviors of PBGS to gain a comprehensive understanding of their mechanical properties.Furthermore,the tensile load-strain history under various loading conditions is simulated by numerical calculation for widespread utilization.To achieve this goal,monotonic loading tests,short-term creep and stress relaxation tests,and multi-load-path tests(also known as arbitrary loading history tests)are performed using a universal testing machine.The results are simulated using the nonlinear three-component(NLTC)model,which consists of three nonlinear components,i.e.a hypo-elastic component,a nonlinear inviscid component,and a nonlinear viscid component.The experimental and numerical results demonstrate that PBGS exhibit significant elastic-viscoplastic behavior that can be accurately predicted by the NLTC model.Moreover,the tensile strain rates significantly influence the tensile load,with higher strain rates resulting in increased tensile loads and more linear load-strain curves.Also,parametric analysis of the rheological characteristics reveals that the initial tensile strain rates have negligible impact on the results.The rate-sensitivity coefficient of PBGS is approximately 0.163,which falls within the typical range observed in most geosynthetics.

The influence of inter-band rock on rib spalling in longwall panel with large mining height

In order to improve rib stability,failure criteria and instability mode of a thick coal seam with inter-band rock layer are analysed in this study.A three-dimensional mechanical model is established for the rib by considering the rock layer.A safety factor is defined foy the rib,and it is observed that the safety factor exhibits a positive correlation with the thickness and strength of the inter-band rock.A calculation method for determining critical parameters of the rock layer is presented to ensure the rib stability.It is revealed that incomplete propagation of the fracture at the hard rock constitutes a fundamental prerequisite for ensuring the rib stability.The influence of the position of the inter-band rock in the coal seam on failure mechanism of the rib was thoroughly investigated by developing a series of physical models for the rib at the face area.The best position for the inter-band rock in the coal seam is at a height of 1.5 m away from the roof line,which tends to provide a good stability state for the rib.For different inter-band rock positions,two ways of controlling rib by increasing supports stiffness and flexible grouting reinforcement are proposed.

Toward understanding the microstructure characteristics,phase selection and magnetic properties of laser additive manufactured Nd-Fe-B permanent magnets

Nd-Fe-B permanent magnets play a crucial role in energy conversion and electronic devices.The essential magnetic properties of Nd-Fe-B magnets,particularly coercivity and remanent magnetization,are significantly infuenced by the phase characteristics and microstructure.In this work,Nd-Fe-B magnets were manufactured using vacuum induction melting(VIM),laser directed energy deposition(LDED)and laser powder bed fusion(LPBF)technologies.Themicrostructure evolution and phase selection of Nd-Fe-B magnets were then clarified in detail.The results indicated that the solidification velocity(V)and cooling rate(R)are key factors in the phase selection.In terms of the VIM-casting Nd-Fe-B magnet,a large volume fraction of theα-Fe soft magnetic phase(39.7 vol.%)and Nd2Fe17Bxmetastable phase(34.7 vol.%)areformed due to the low R(2.3×10-1?C s-1),whereas only a minor fraction of the Nd2Fe14B hard magnetic phase(5.15 vol.%)is presented.For the LDED-processed Nd-Fe-B deposit,although the Nd2Fe14B hard magnetic phase also had a low value(3.4 vol.%)as the values of V(<10-2m s-1)and R(5.06×103?C s-1)increased,part of theα-Fe soft magnetic phase(31.7vol.%)is suppressed,and a higher volume of Nd2Fe17Bxmetastable phases(47.5 vol.%)areformed.As a result,both the VIM-casting and LDED-processed Nd-Fe-B deposits exhibited poor magnetic properties.In contrast,employing the high values of V(>10-2m s-1)and R(1.45×106?C s-1)in the LPBF process resulted in the substantial formation of the Nd2Fe14B hard magnetic phase(55.8 vol.%)directly from the liquid,while theα-Fe soft magnetic phase and Nd2Fe17Bxmetastable phase precipitation are suppressed in the LPBF-processed Nd-Fe-B magnet.Additionally,crystallographic texture analysis reveals that the LPBF-processedNd-Fe-B magnets exhibit isotropic magnetic characteristics.Consequently,the LPBF-processed Nd-Fe-B deposit,exhibiting a coercivity of 656 k A m-1,remanence of 0.79 T and maximum energy product of 71.5 k J m-3,achieved an acceptable magnetic performance,comparable to other additive manufacturing processed Nd-Fe-B magnets from MQP(Nd-lean)Nd-Fe-Bpowder.

A methodology for damage evaluation of underground tunnels subjected to static loading using numerical modeling

We have proposed a methodology to assess the robustness of underground tunnels against potential failure.This involves developing vulnerability functions for various qualities of rock mass and static loading intensities.To account for these variations,we utilized a Monte Carlo Simulation(MCS)technique coupled with the finite difference code FLAC^(3D),to conduct two thousand seven hundred numerical simulations of a horseshoe tunnel located within a rock mass with different geological strength index system(GSIs)and subjected to different states of static loading.To quantify the severity of damage within the rock mass,we selected one stress-based(brittle shear ratio(BSR))and one strain-based failure criterion(plastic damage index(PDI)).Based on these criteria,we then developed fragility curves.Additionally,we used mathematical approximation techniques to produce vulnerability functions that relate the probabilities of various damage states to loading intensities for different quality classes of blocky rock mass.The results indicated that the fragility curves we obtained could accurately depict the evolution of the inner and outer shell damage around the tunnel.Therefore,we have provided engineers with a tool that can predict levels of damages associated with different failure mechanisms based on variations in rock mass quality and in situ stress state.Our method is a numerically developed,multi-variate approach that can aid engineers in making informed decisions about the robustness of underground tunnels.

Numerical simulation on sand sedimentation and erosion characteristics around HDPE sheet sand barrier under different wind angles

For the safety of railroad operations,sand barriers are utilized to mitigate wind-sand disaster effects.These disasters,characterized by multi-directional wind patterns,result in diverse angles among the barriers.In this study,using numerical simulations,we examined the behavior of High Density Polyethylene(HDPE)sheet sand barriers under different wind angles,focusing on flow field distribution,windproof efficiency,and sedimentation erosion dynamics.This study discovered that at a steady wind speed,airflow velocity varies as the angle between the airflow and the HDPE barrier changes.Specifically,a 90°angle results in the widest low-speed airflow area on the barrier’s downwind side.If the airflow is not perpendicular to the barrier,it prompts a lateral airflow movement which decreases as the angle expands.The windproof efficiency correlates directly with this angle but inversely with the wind’s speed.Notably,with a wind angle of 90°,wind speed drops by 81%.The minimum wind speed is found at 5.1H(the sand barrier height)on the barrier’s downwind side.As the angle grows,the barrier’s windproof efficiency improves,extending its protective reach.Sedimentation is most prominent on the barrier’s downwind side,as the wind angle shifts from 30°to 90°,the sand sedimentation area on the barrier’s downwind side enlarges by 14.8H.As the angle grows,sedimentation intensifies,eventually overtakes the forward erosion and enlarges the sedimentation area.