Numerical Simulation Test Research Articles

“Subvolume Splitting” DVC applied for accurate discontinuous deformation measurement and fracture parameter extraction

As a powerful experimental tool for quantifying internal full-field mechanical response, digital volume correlation (DVC) has been increasingly used for extracting crucial fracture parameters. Nevertheless, due to the limitations of its regularly-used shape functions in describing discontinuous deformation, routine subvolume-based DVC encounters challenges in accurately capturing displacement maps around discontinuities, thus impeding reliable and accurate extraction of fracture parameters. To address this issue, a “subvolume splitting” DVC (SS-DVC) method is proposed. SS-DVC first splits subvolumes into two subblocks along a pre-calculated fitted crack plane and then only tracks the subblock with continuous deformation, thereby circumventing the limitations associated with discontinuities. Additionally, a straightforward and effective computational strategy is devised to ensure correct displacement measurements around discontinuities. For validation, both numerical simulation and real three-point bending tests were conducted to examine the performance of SS-DVC in terms of displacement measurement accuracy and extraction of fracture parameters. The experimental results demonstrate that, in comparison to routine DVC, SS-DVC exhibits a significant reduction in measurement errors of displacement around discontinuities, thus enabling more accurate determination of material fracture mechanical properties.

FRP bending-active gridshells: Numerical simulation and model test

Bending-active gridshells are a distinct category of grid structures achieved through elastic bending of initially straight profiles arranged in perpendicular layers and interconnected by hinge joints. These joints permit free in-plane rotation, thereby enabling the progressive transformation from the initial planar configuration to the desired curved shape. Rigorous modelling of hinge joint behavior is crucial for an accurate simulation of bending-active gridshells. Nevertheless, prior numerical studies have relied on oversimplified approximations in this regard. To overcome these limitations, this study developed an explicit dynamic numerical procedure, where the hinge joints are modelled as rigid links characterized by paired nodes that represent the actual hinge length. The proposed procedure incorporates all six nodal degrees of freedom (DoFs). This not only facilitates modelling the spatial behavior of the constituent profiles but, more importantly, allows for independent treatment of the in-plane rotational DoFs of a hinge joint’s paired nodes. Simultaneously, it addresses the joint’s coupling behavior in relation to the translational and out-of-plane rotational DoFs. The proposed procedure was verified through benchmark numerical tests. Furthermore, validation was conducted through forming and loading tests on a 4.60-m-span bending-active gridshell model constructed from carbon fiber-reinforced polymer (CFRP) strips.

Influence of Mining Sequence of Branch on Stope Pressure Behaviour on Continuous Mining and Continuous Backfilling

Instability in coal pillars and filling bodies is a common occurrence during the mining process of continuous mining and continuous backfilling (CMCB). In view of this, combining numerical simulation, similarity simulation, and on-site testing approaches, backfill mining models were established in Flac3d5.01 software, similarity model test bench, and “two-stage”, “three-stage”, and “four-stage” mining sequences were conducted; the stress characteristics of coal pillar-filling body and the displacement evolution law of surrounding rock have been compared under three typical mining sequences. The results show that compared to two-stage mining sequence, three-stage and four-stage mining sequences provide sufficient time for the solidification of the filling body. The coal pillar exhibits better stability in the early stage of mining, but the stress concentration phenomenon is more significant in the later stage of mining. The stress concentration coefficient is the highest when the width of the coal pillar is 10 m. The integrity of the overburden is intact in different mining sequences, with only a small amount of separation and longitudinal cracks. Increasing the number of mining stages significantly reduces the roof subsidence, with the maximum roof subsidence in the three- and four-stage mining sequences being only 62.0% and 33.9% of that in the two-stage mining sequence. “Two stages”, “three stages”, and “four stages” of mining sequences are implemented in response to the requirements of weak and thick coal seam mining in Haoyuan Coal Mine and gangue disposal in Chahasu Coal Mine. Good engineering applications are achieved, enabling the realisation of safe, green, and efficient coal mining.

Effect of inlet velocity on the hydraulic and filtering performance of a Y‐type screen filter

AbstractUneven sediment distribution affected by inlet velocity, particle size distribution and flow field characteristics leads to local clogging in a Y‐type screen filter. This study revealed the detailed flow field characteristics and distribution of sediments on the screen via computational fluid dynamics combined with the discrete element method (CFD–DEM) simulations and experimental tests. The results showed that the distribution of the flow rate on the filter screen was extremely uneven, with the maximum flow rate being 11.72 times greater than the minimum rate. The flow rate was distributed symmetrically on the two sides along the outlet centreline, as shown by the unfolded drawing of the filter core. Numerical simulation and experimental tests using sandy water showed that the number and average particle diameter on the screen decreased, and the number and average particle diameter in the plug increased, with increasing inlet velocity. The sediments on the screen were distributed intensively, and the plugging extent coefficient and the anti‐clogging performance improved. However, this process was more likely to cause local clogging and worsen the filtration performance. Therefore, low‐speed filtering should be applied if the filtering effect is needed, and high‐speed filtering should be applied if the filtering efficiency is favourable but the flushing frequency increases.

Leveraging the depolarization of scattered light for holography with the Stokes correlation

A correlation holography technique for quantitative phase imaging from scattered depolarized light is proposed and experimentally demonstrated. To implement this technique, we exploit the depolarization of scattered light with the higher-order Stokes correlation. The higher-order Stokes correlation along with the two-step phase-shifting method is utilized to retrieve the complex Fourier coefficient, this subsequently supports the recovery of the phase in the correlation holography with the fourth-order correlation. A detailed theoretical framework is developed and is also supported by numerical simulation and experimental tests. The applicability of the proposed technique is experimentally demonstrated by quantitatively reconstructing different phase objects from the scattered depolarized light.

Numerical simulation and experiment of a blade management device in microgravity

Currently, most satellite propulsion systems are mainly chemical propulsion, and liquid propellant is the necessary power fuel for the propulsion system. The working environment of microgravity occurs when the satellite is in orbit. According to the working characteristics of the satellite, a propellant management device of vane type is designed. The PMD is composed of a vertical guide plate and a liquid accumulator, which is applied to the propellant tank to store and manage the propellant. In this paper, the microgravity gas-liquid management and control mechanism of a propellant management device of vane type is studied by numerical simulation and tower drop test. The results of numerical simulation and tower drop test are consistent, which verifies the good fluid management characteristics of this type of propellant management device, and provides references for its engineering application and the design of this type of structure.

Study on cavitation performance improvement of high-power centrifugal pump impeller

High power centrifugal pump is frequently used in large project for water resources allocation. Cavitation phenomenon causes noise and vibration and affects the centrifugal pump unit stability. The impeller model was used an initial impeller to be developed, and the impeller geometry, the blade profile, blade inlet edge were optimized by design method based on numerical simulation technique to improve cavitation performances. The 3D model with the initial and optimized impeller were simulated to obtain cavitation characteristic. The results of optimization impeller are compared and verified by model test. The numerical simulation results show that the pressure distribution is distributed on the blade surface is uniform and the location of lowest pressure is reasonable. The test results show that the optimized design significantly increases the ratio of plant cavitation coefficient σp to incipient cavitation coefficient σi and critical cavitation coefficient σ1 of the impeller under normal operation conditions, the safety margin of cavitation is increased. It was confirmed from numerical simulation and model test results that the impeller blade optimization is a reasonable and effective method for cavitation performance improvement. The study results provides design reference for the cavitation performance improvement and safe operation of high power centrifugal pump.

Particle distribution and two-phase flow characteristics of twin-screw pump during solid-liquid transfer

The twin-screw pump is a kind of positive displacement machinery with smooth pressure and flow pulsation and strong self-priming ability, which is widely used in the fields of oilfield production, marine engineering, and other fields. However, in the process of conveying liquid-phase media, it is difficult to avoid the inclusion of solid impurities and grit, resulting in wear of the pump casing and rotor, and the pump’s pressurization capacity is reduced or even shut down. At present, the solid-liquid two-phase flow characteristics within the twin-screw pump have not been clarified, which hinders the study of particle wear in the pump. In this paper, a solid-liquid two-phase flow study is carried out on a twin-screw pump through numerical simulation and experimental testing. The distribution of particles with different diameters in the rotor domain with the liquid-phase transport process is explored by simulating the two-phase flow under different differential pressures and particle concentrations. The results show that the particles in the rotor domain are mainly distributed in the region away from the male and female rotor engagement, and the number of particles near the engagement is small but the velocity is higher under the influence of the clearance jets; the elevation of the differential pressure and the particle concentration increase the risk of the particles to collide with the rotor more frequently and at higher velocity; at different particle concentrations, new localized vortices are caused by particle conveying which compared to pure liquid transport, but there are also cases where the original vortices are suppressed. The results will provide a theoretical basis for further research on particle wear characteristics in twin-screw pumps.

Research on the bearing characteristics of brackets in thick hard roof mining sites and the effect of blasting on roof control

Deep mining stress increase and thick hard rock layer endowment drive rock body fissure expansion, leading to sudden fracture of the roof plate accidents. The roof slab of 11,129 working face in Zhangji Mine is a 16 m thick sandstone composite roof slab, whose compressive strength reaches 89.8 MPa. The hardness of the roof slab is high, its bearing capacity is high, and it is difficult to collapse. The hardness of the roof plate is high, its bearing capacity is high, and it is difficult to fall. If the roof plate does not fall in time, it will lead to the energy accumulation of itself, and the sudden fracture and fall will make the working face and the two roadways show the drastic mine pressure, which will lead to the risk of the coal wall appearing the slice of gangs, the roof falling and the pressure frame. Therefore, for the 11,129 working face thick hard sandstone roof plate direct cover and mining technology conditions. It is very necessary and imperative to research the artificial roof release technology of deep hole pre-cracking blasting to improve the adventitious fall of the thick hard roof plate, reduce the overhanging roof area of the mining hollow area, and reduce the incoming pressure strength of the roof plate. This paper adopts the research method combining theory, physical experiment, numerical simulation and field test, focusing on research and analysis of the deflection change of the roof plate after pre-cracking and blasting, the relationship between the roof plate and the role of the bracket, and the effect of artificial blasting to release the roof. The results show that the theoretical part deduces and analyzes the relationship equation of the influence of the rotating and sinking of the roof plate on the pressure of the support, and combined with the law of the roof plate-support action can be divided into three stages: (1) Initial stage of mining, (2) Rotating and sinking stage, and (3) Breakdown and fragmentation stage. The deep stress increase and the rock layer's own characteristics (hardness and thickness) are the main controlling factors to determine the bearing capacity of the stent. As the depth of coal mining increases, the pressure at the minimum roof control distance of the stent gradually increases from 11.5 to 34.6 MPa. The increase of rock hardness relatively reduces the force acting on the stent, and the stent bearing capacity decreases by 75% when the hardness increases from 8 to 32 GPa. The 11,129 engineering geological parameters are brought into the calculation to obtain the pressure in the stent control distance of 13.5–20.5 MPa. The simulation part analyzes the stress relief degree of the roof plate before and after the roof blasting, and the peak stress in front of the coal wall is reduced from 46.7 to 30.9 MPa, which is an obvious effect of pressure relief, and the simulation results are analyzed in comparison with the theoretical results to validate the reliability of the simulation results. Further, the physical similarity experiments were conducted to analyze the deformation behavior of mining instability and crack evolution characteristics of the overburden rock of the quarry after cutting the roof, and the peak stress of the coal wall was in the range of 22.7–27.8 MPa after the blasting decompression, which was mutually verified with the theoretical analysis and the simulation results to ensure the reliability of the calculation results. Combined with the geological conditions of the mine area, the "fan-shaped" blasting hole arrangement is proposed to carry out segmental blasting, and the specific parameters of different locations of the holes are given. The effect of pre-cracking blasting was examined, and it was found that the rock mass at the hole opening had a high degree of fragmentation, and the ring and strike cracks appeared alternately in the middle and lower part of the drilling holes, and the polygonal energy slit played a very effective role, and achieved the purpose of artificially releasing the roof. At the same time, it is improved the load-bearing environment of the mining support, which further improves the safety and efficiency production of the coal mine.

Numerical Simulation Study on Mechanical Bearing Behavior of Arch Steel–Concrete Composite Sandwich Roof

In order to study the mechanical bearing behavior of arched sandwich roof structures, a full combination and independent action mode of concrete sandwich composite panels was constructed using the finite element method, and an arched steel–concrete composite sandwich roof with a span of 18 m was subjected to a numerical simulation test under a full-span vertical uniformly distributed load, with the bearing characteristics of the arched sandwich roof discussed in depth. The results show that the cross-sections of l/16 and l/2 of the elliptical arch sandwich roof are weak sections, and the tensile cracking of concrete appears for the first time in the upper and lower wythes of the elliptical arch sandwich roof, the von Mises stress level of the lower wythe of the l/16 section is higher under the ultimate load, and the roof shows four-part form failure characteristics. With the expansion of the cracking range of the upper and lower concrete wythes of the steel–concrete composite sandwich arch roof, the load–displacement curve of the roof structure does not decrease significantly, and the bearing capacity of the structure is high and the vertical deformation is small. The steel–concrete composite segment at the end of the roof effectively strengthens the edge constraint of the roof and improves the integrity of the sandwich roof. The upper and lower concrete wythes of the sandwich roof show a fully combined action mode in the elastic working stage and, when the concrete cracks, it shows a partial combined action mode.

Numerical simulation and experimental testing for static failure prediction in additively manufactured below-knee prosthetic sockets.

The socket of a transtibial prosthesis is a structural part customized to a patient's amputated residual lower limb. The free-form geometry of the socket can be suitable for additive manufacturing (AM) to save time and cost. However, the mechanical fracture of additively manufactured lower limb prostheses is not yet fully understood. A novel experimental method and numerical approach by finite element method (FEM) to test the strength and fracture behavior of a lower limb prosthetic socket of acrylonitrile butadiene styrene (ABS), reverse-engineered using computer-aided design (CAD) from the actual amputee's residual limb and manufactured using fused filament fabrication (FFF) are proposed in the present work. The mechanical behavior, von Mises stress distribution, and the damage status of layered AM sockets of different thicknesses were simulated by FEM using Hashin's transversely isotropic mechanical damage model, initially developed for composite materials. The experimental work showed that the fracture failure initiated at the corner of the lobe in the 4 mm thickness socket at a failure load of 918.5 N. The FEM results predicted this failure load to be 896.6 N, with only a 2.45% error as compared to the experiment. The failure loads predicted by FEM in the sockets with thicknesses of 3, 5, and 6 mm were 618.1, 1008.6, and 1105.2 N, respectively. The present work provides a dependable method for testing a below-knee prosthetic socket against static failure and arriving at a factor-of-safety (FoS) based socket thickness selection for any amputee.

Anomaly Detection Method for Rocket Engines Based on Convex Optimized Information Fusion.

The power system, as a core component of a launch vehicle, has a crucial impact on the reliability and safety of a rocket launch. Due to the limited measurement information inside the engine, it is often challenging to realize fast and accurate anomaly detection. For this reason, this paper introduces the rocket flight state data to expand the information source for anomaly detection. However, engine measurement and rocket flight state information have different data distribution characteristics. To find the optimal data fusion scheme for anomaly detection, a data set information fusion algorithm based on convex optimization is proposed, which solves the optimal fusion parameter using the convex quadratic programming problem and then adopts the adaptive CUSUM algorithm to realize the fast and accurate anomaly detection of engine faults. Numerical simulation tests show that the algorithm proposed in this paper has a higher detection accuracy and lower detection time than the traditional algorithm.

The vibroacoustic characteristic of beam-plate coupled structure in similitude

Similitude theory can be used to extrapolate the experimental data of a small, inexpensive, and easily tested model into design information for a large prototype. Scaling laws provide the relationship between a full-scale structure and its scale models. However, one challenging issue is the similitude of complex structure. To address the problem, an energy similarity method is presented based on the principle of conservation of power flow. The emphasis is to predict the vibroacoustic characteristic of beam-plate coupled structure in an effective and convenient way. The vibration response and radiated sound are investigated on the beam-plate coupled structure under random excitation. Numerical simulation and model test are both implemented, which validate the effectiveness and efficiency of the proposed method. Both aluminum and honeycomb materials are considered in beam-plate coupled structures. In addition, the comparison between the classic similitude method and the presented method (energy similarity) is illustrated. The results show that the energy similarity presented in this study can achieve a better performance in reproducing the vibroacoustic characteristic of beam-plate coupled structure than the classic similarity method.

Application research on composite support technology of concrete-filled steel tube support in high stress and large deformation soft rock roadway: A case study

Aiming at the surrounding rock control problem of high stress and large deformation soft rock roadway. This article takes the 141712 coal haulage uphill as the engineering background in Guizhou Panjiang Mining Area. Through field investigation, theoretical calculation, numerical simulation, and industrial tests, the deformation characteristics of surrounding rock and the mechanism of roadway instability and failure were revealed. And a composite support scheme of "bolt (cable) + grouting + concrete-filled steel tube support" was designed. A strengthening support mechanical model of “Three-arch” based on the concrete-filled steel tube support technology was established. The ultimate bearing capacity of the design scheme above is calculated, which meets the support load and can maintain the stability of the soft rock roadway. Through numerical simulation analysis, the distribution characteristics of the plastic zone, stress field and displacement field of the design scheme are obtained, and the rationality of the scheme is verified. The industrial tests were successfully applied and the field monitoring results show that the deformation is within the controllable range, effectively controls the deformation of the 141712 roadway. The research results can provide a reference case for the control of soft rock roadway with high stress and large deformation under similar complex conditions.

Research on the inflation process of underwater parachute by numerical simulation and model test

In order to meet the application requirements of the underwater parachute, the underwater inflation performance of a drag parachute is investigated based on numerical simulation and water tank test. A method for simulating the inflation process of underwater parachute based on Arbitrary Lagrangian Eulerian (ALE) method is proposed. The variation of axial force in the numerical simulation exhibits a similar trend to that observed in the model test, and the discrepancy of value between them is relatively insignificant. The purpose of this paper is to provide a basis for the evaluation and design of underwater parachutes for underwater applications. The effects of parameters such as permeability and flow velocity on the inflation performance are discussed in detail, and the analysis is carried out for parameters such as axial force and structural deformation. The results show that the high-stress zone and high-pressure intensity zone of the underwater parachute were found to be mainly concentrated in the center of the canopy and the joint. It can be observed both in model test and numerical simulation that, during the inflation process, vortexes are generated inside and outside the canopy. After the inflation shape of the canopy has stabilized under steady flow, lateral forces are generated on the parachute due to asymmetric vortex shedding, which cause the parachute to rotate around the axis.

Research on the technology of gob-side entry retaining by pouring support beside the roadway in “three soft” coal seam: A case study

This paper's goal is to investigate if a gob-side entry retention technique combined with a surrounding rock support system is feasible in three soft coal seams. Field engineering confirmed the results of numerical simulation tests and similar simulation tests, which were conducted in accordance with the actual geological conditions of Zhaojiazhai Mine. The following conclusions are reached after studying the technology and process parameter of the gob-side entry retaining in three soft coal seams in conjunction with theoretical calculations: the coal seam of Zhaojiazhai Coal Mine's 12 209 working face is a part of the soft coal seam, and its loose circle is approximately 1.8 m. The expansion roadway size is 3.5 m, and the potential loose circle range is 1.32 m, according to the same model and numerical simulation test. The support scheme after the expansion of the road working face is determined to be the “anchor rod + anchor cable + hydraulic lifting shed” support method. Furthermore, this article suggests a building method for the reinforcement and enlargement of gob-side entry retaining in three-soft thick coal seam by theoretical analysis and numerical simulation. Roadway shotcrete, advance grouting, building of a large deformation anchor cable and continuous resistance, single column lifting shed, hydraulic lifting shed, and roadway enlargement in advance are all steps in the procedure. Furthermore, an analysis is conducted on the deformation features of the surrounding rock in gob-side entry retention. The study highlights the significance of actively supporting the surrounding rock, fortifying the roof support, guaranteeing the stiffness compatibility between the shoulder filling body and the surrounding rock on the roof, boosting the wall's strength and stability, and enhancing the roadway's stability.

Research on the impact and control techniques of gangue rib in hard roof

Blocking gangue support is a key link in gob-side entry retaining by roof cutting and pressure release (GERRC), and its stability is related to the success or failure of the retained roadways. Due to the severe dynamic pressure and high hardness of the gangue during hard roof collapse, serious bending and toppling instability of the section steel can easily occur. Since potential safety hazards exist in gangue ribs, the 1105 panel of the Qiuji Coal Mine is used as the engineering background, a mechanical model of gangue impact is constructed based on four forms of gangue motions, and the failure of a blocking gangue support structure under hard roof conditions is explored with ABAQUS software. The results indicate the following: (1) Section steel experiences transient bending by gangue impact, and will further bending failure or toppling instability occurs under roadway roof subsidence and gangue compression. (2) This impact causes the steel bar mesh to generate a significant transient lateral force, which couples with gangue compression, resulting in instability and slip of the section steel. To this end, three optimized components have been proposed, sliding yield I-steel, reinforced bolts and link components, and the optimal parameters are obtained. The results of the numerical simulation and field tests suggest that the new blocking gangue support structure has a good support effect, and the field deformation of the gangue rib is reduced by 86%. No failure of I-steel occurs with the new blocking gangue support structure. This study can provide a reference for the control of gangue ribs in GERRC under similar geological conditions.

Low-velocity impact and post-impact compression properties of carbon/glass hybrid yacht composite materials

In the field of maritime engineering, low-velocity impact (1-10 ms−1) is typically regarded as a quasi-static event. During navigation, yachts are inevitably subjected to low-velocity impact from floating objects in the water, and may also encounter compression after low-velocity impact. This study employs a combined approach of numerical simulation and experimental testing, aiming to investigate the damage and failure mechanisms of yacht composite laminates under conditions of low-velocity impact and post-impact compression (CAI), and by SEM and ultrasonic C-scanning the damage characteristics of different layup samples was studied in impact and compression tests. In order to conduct a more in-depth study on the damage evolution and failure mechanisms of yacht composite laminates, a three-dimensional damage model is established based on the continuum damage mechanics, and a physico-mechanical failure criterion combining the 3D Hashin and Puck criteria is employed. This criterion is used to capture the initiation points of damage in both fibers and matrix. Additionally, a bi-linear damage constitutive relationship is utilized to describe the damage evolution. Interlayer delamination is addressed through simulating the bonding behavior of interfaces. The numerical results show good correlation with the experimental results, which validates the effectiveness and rationality of the proposed numerical model. The study shows that laying carbon fiber cloth in the middle of the sample exhibits excellent impact resistance; laying carbon fiber cloth at the bottom exhibits better deformation resistance and stronger residual compression performance. Considering the three aspects of deformation, residual strength, and damage area, laying carbon fiber cloth in the first layer exhibits better mechanical properties, which provides useful reference for the design and manufacture of yacht materials and helps to improve the safety and reliability of yachts.

Cross-coupling indirect iterative learning control method for batch processes with time-varying uncertainties

For batch time-varying processeswith non-repetitive disturbances, a cross-coupling indirect iterative learning control (CC-iILC) is proposed. The set trajectory of the system on the single axis is accurately tracked by an indirect iterative learning control strategy with a PI controller for its time direction and a closed-loop feedback control strategy for the batch direction. Under the asymptotically stable condition of the two-dimensional (2D) dynamic model, the optimal control law is obtained by optimizing the H-infinity control function. To avoid the contour error during coupling, the cross-coupling technique is used to distribute the contour error to each axis for compensation. The stability condition of the indirect iterative learning controller is analyzed by a two-dimensional Fornasini-Marchesini (FM) batch dynamics model and two-dimensional robust H-infinity control theory. The feasibility and superiority of the proposed control method are verified by numerical simulation and experimental tests.

Optimization of low-head shaft tubular pumping systems based on entropy production theory

In order to improve the operation efficiency of low-head tubular pump, this paper studies the influence of shaft type in the shaft tubular pump on the flow characteristics and energy characteristics of the pump. To optimize the shaft structure of shaft tubular pumping systems and realize the efficient use of energy, numerical simulation and model test was employed to study the optimization of the entire pumping system. In this paper, the CFD method was used to numerically simulate the whole pumping system, and the effect of changing the shaft length, shaft head profile, and shaft tail profile on the internal flow and entropy production characteristics of the inlet passage and impeller position were analyzed. It is found that the tapered tail profile can make the inlet passage overflow area change more smoothly and thus make the flow pattern more favorable. The wall entropy production dissipation at the inlet passage position dominates the total entropy production, and the high-value area of mainstream entropy production at this position is distributed periodically. The mainstream entropy production dissipation at the impeller section accounts for a relatively large proportion. After the entropy production dissipation analysis, it is believed that the tapered can reduce the entropy production dissipation of the pumping systems. The change of the shaft tail profile will make the entropy production dissipation change more noticeable compared with other optimization factors. Therefore, the tapered tail profile with better transition in the actual project is recommended.