Circumferential Angle Research Articles

Fracture Initiation Model of Shale Fracturing Based on Effective Stress Theory of Porous Media

Unconventional oil and gas are important resources of future energy supply, and shale gas is the focus of the development of unconventional resources. Shale is a special kind rock of porous medium, and an orderly structure of beddings aligned in the horizontal direction where causing the strong elastic anisotropy of shale is easy. A new model has been established to calculate the fracture initiation pressure with the consideration of mechanical characteristics of shale and the anisotropic tensile strength when judging rock failure. The fracture initiation model established in this paper accurately reflects the stress anisotropy and matches well with the actual situation in porous media. Through the sensitivity analysis, the results show that σv/σH, Ev/EH, υv/υH, m/s, and A/B have a certain impact on the tangential stress when the circumferential angle changes, and there is a positive relationship between the initiation pressure and the above sensitive factors except for A/B. The results can provide a valuable and effective guidance for the prediction of fracture initiation pressure and fracture propagation mechanism under special stratum conditions of shale.

Experimental investigation of circumferentially non-uniform heat flux on the heat transfer coefficient in a smooth horizontal tube with buoyancy driven secondary flow

In this experimental investigation the influence of non-uniform heat flux distributions on the internal heat transfer coefficient in a horizontal circular tube was studied for liquid water. The tube had an inner diameter of 27.8 mm and a length to diameter ratio of 72. Different outer wall heat flux conditions were studied for Reynolds numbers ranging from 650 to 2600 at a Prandtl number of approximately 6.5. Heat flux distributions included fully uniform heating (which had a circumferential angle span of 360°) and different partial uniform heat flux distributions with angle spans of 180° or 90° at different circumferential positions. Depending on the angle span, local heat flux intensities ranging from 1658 W/m2 to 6631 W/m2 were tested. Results indicate that the average steady state Nusselt number is greatly influenced by the applied heat flux position and intensity. Highest average heat transfer coefficients were achieved for cases where the applied heat flux was positioned on the lower half (in terms of gravity) of the tube circumference, while the lowest heat transfer coefficients were achieved when the heating was applied to the upper half of the tube. Smaller angle spans produced lower heat transfer coefficients. The relative thermal performance of the different heating scenarios where characterised and described by means of newly developed heat transfer coefficient correlations for angle spans of 180° and 90° which correlated 92% and 96% of the data respectively within 3% of the measured Nusselt number.

A Design Method of HTS Bulks Array for Decreasing Rotation Loss in a Superconducting Maglev Microthrust Stand

Rotation losses at low frequency is very crucial to the microthrust stand depending on high temperature superconductors (HTS) maglev. HTS bulks arrays are sources of levitation forces and have an influence on declination angle of the levitation platform during rotation. Changes of declination angle can lead to variation of external magnetic field on HTS bulk arrays, which then affect rotation losses of the microthrust stand. An experimental setup has been established to investigate influence of HTS bulk arrays and eccentric loads on rotation losses. Space ratio is applied to describe the dispersion degree of HTS bulk arrays with different geometrical configurations. Experimental results show that Arrays with smaller space ratio help diminish rotation losses of the HTS maglev stand. Presetting eccentric loads with proper amount and initial circumferential angle could decrease rotation losses for arrays with smaller space ratio. For microthrust measurement using HTS maglev stand, HTS bulk arrays should be optimized to achieve lower rotation losses and better adjustability.

Measurement of surface shear stress vector beneath high-speed jet flow using liquid crystal coating

The shear-sensitive liquid crystal coating (SSLCC) technique is investigated in the high-speed jet flow of a micro-wind-tunnel. An approach to measure surface shear stress vector distribution using the SSLCC technique is established, where six synchronous cameras are used to record the coating color at different circumferential view angles. Spatial wall shear stress vector distributions on the test surface are obtained at different velocities. The results are encouraging and demonstrate the great potential of the SSLCC technique in high-speed wind-tunnel measurement.

Calculation of stress intensity factor in two-dimensional cracks by strain energy density factor procedure

In order to calculate the stress intensity factor (SIF) of crack tips in two-dimensional cracks from the viewpoint of strain energy density, a procedure to use the strain energy density factor to calculate the SIF is proposed. In this paper, the procedure is presented to calculate the SIF of crack tips in mode I cracks, mode II cracks and I+II mixed mode cracks. Meanwhile, the results are compared to those calculated by traditional approaches or other approaches based on strain energy density and verified by theoretical solutions. Furthermore, the effect of mesh density near the crack tip is discussed, and the proper location where the strain energy density factor is calculated is also studied. The results show that the SIF calculated by this procedure is close to not only those calculated by other approaches but also the theoretical solutions, thus it is capable of achieving accurate results. Besides, the mesh density around the crack tip should meet such requirements that, in the circular area created, the first layer of singular elements should have a radius about 0.05 mm and each element has a circumferential directional meshing angle to be 15°–20°. Furthermore, for a single element around the crack tip, the strain energy density factor is suggested to be calculated in the location where half of the sector element’s radius from the crack tip.

Prevalence of Calcification in Human Femoropopliteal Arteries and its Association with Demographics, Risk Factors, and Arterial Stiffness.

Arterial calcification and stiffening increase the risk of reconstruction failure, amputation, and mortality in patients with peripheral arterial disease, but underlying mechanisms and prevalence are unclear. Fresh human femoropopliteal arteries were obtained from n=431 tissue donors aged 13 to 82 years (mean age, 53±16 years) recording the in situ longitudinal prestretch. Arterial diameter, wall thickness, and opening angles were measured optically, and stiffness was assessed using planar biaxial extension and constitutive modeling. Histological features were determined using transverse and longitudinal Verhoeff-Van Gieson and Alizarin stains. Medial calcification was quantified using a 7-stage grading scale and was correlated with structural and mechanical properties and clinical characteristics. Almost half (46%) of the femoropopliteal arteries had identifiable medial calcification. Older arteries were more calcified, but small calcium deposits were observed in arteries as young as 18 years old. After controlling for age, positive correlations were observed between calcification, diabetes mellitus, dyslipidemia, and body mass index. Tobacco use demonstrated a negative correlation. Calcified arteries were larger in diameter but had smaller circumferential opening angles. They were also stiffer longitudinally and circumferentially and had thinner tunica media and external elastic lamina with more discontinuous elastic fibers. Although aging is the dominant risk factor for femoropopliteal artery calcification and stiffening, these processes seem to be linked and can begin at a young age. Calcification is associated with the presence of certain risk factors and with elastic fiber degradation, suggesting overlapping molecular pathways that require further investigation.

Influence of squeezing and interface slippage on the performance of water‐lubricated tilting‐pad thrust bearing during start‐up and shutdown

AbstractThe film thickness varied because of the swing of the tilting‐pad thrust bearing, which introduced the squeezing effect in the start‐up and shutdown periods. The interface slippage might occur between the water and the pad surface, because of the effects of water polarity and surface energy of the material. To study the performance of the water‐lubrication tilting‐pad thrust bearing during start‐up and shutdown, a transient model considering the effects of squeezing and interface slippage was established. The effects of squeezing and interface slippage on film‐thickness distribution, nondimensional minimum film thickness, circumferential angle, and friction torque were studied. The theoretical friction torque was consistent with the experimental result quite well. The result demonstrated that the effect of squeezing was higher in the opening process than in the closing process; the interface slippage effect influenced the start‐up and shutdown significantly, blocking the formation of the water film. The friction torque of the bearings increased if the interface slippage existed, because the solid contact friction‐force increase was higher than the fluid shear‐force decrease in the mixed lubrication. When both effects worked simultaneously, the interface slippage dominated in the start‐up period. During the shutdown situation, as the rotational speed sustained a loss, the interface slippage was abated, where the influence of the squeezing effect dominated gradually.

Buckling Analysis of Cylindrical Shells Subjected to Liquid Pressures

The finite element method is applied to buckling analysis of cylindrical shells subjected to axisymmetric external and internal liquid pressures. The axisymmetric shell element is used and buckling displacements are represented by Fourier series expansion in the circumferential angle. The linear and nonlinear buckling analyses are performed for cylindrical shells and model tanks. The results of linear and nonlinear buckling analyses are compared and the effects of geometric nonlinearity are investigated.

Effect of groove texture on the dynamic characteristics of water-lubricated thrust bearing

In this study, the effects of groove texture on the dynamic characteristics of water-lubricated thrust bearing are theoretically investigated. The turbulent Reynolds equation and its perturbation equations for water-film lubrication are derived and solved by using finite difference method. Dynamic characteristics including the stiffness and damping coefficients of the bearing are calculated. The effects of rotary speed, film clearance and geometrical parameters including groove texture depth and circumferential angle on the dynamic characteristics of the bearing have been investigated.

Anisotropic drop spreading on superhydrophobic grates during drop impact.

We study the influence of geometric anisotropy of micro-grate structures on the spreading dynamics of water drops after impact. It is found that the maximal spreading diameter along the parallel direction to grates becomes larger than that along the transverse direction beyond a certain Weber number, while the extent of such an asymmetric spreading increases with the structural pitch of grates and Weber number. By employing grates covered with nanostructures, we exclude the possible influences coming from the Cassie-to-Wenzel transition and the circumferential contact angle variation on the spreading diameter. Then, based on a simplified energy balance model incorporating slip length, we propose that slip length selectively enhances the spreading diameter along the parallel direction, being responsible for the asymmetric drop spreading. We believe that our work will help better understand the role of microstructures in controlling the drop dynamics during impact, which has relevance to various engineering applications.

Investigation on asymmetric flow over a blunt-nose slender body at high angle of attack

The asymmetric vortices over a blunt-nose slender body are investigated experimentally and numerically at a high angle of attack (AoA, α = 50°) and a Reynolds number of ReD = 1.54 × 105 on the basis of an incoming free-stream velocity and diameter (D) of the model. A micro-perturbation in the form of a hemispherical protrusion with a radius of r = 0.012D is introduced and attached on the nose of the slender body to control the behavior of the asymmetric vortices. Given the predominant role of micro perturbation in the asymmetric vortex pattern, a square wave, which is singly periodic, is observed for side-force variation by setting the circumferential angle (θ) of the micro perturbation from 0° to 360°. The asymmetric vortex pattern and the corresponding side force are manageable and highly dependent on the location of perturbation. The flow structure over the blunt-nose slender body is clarified by building a physical model of asymmetric vortex flow structure in a regular state at a high AoA (α = 50°). This model is divided into several regions by flow structure development along the model body-axis, i.e., inception region at x/D ≤ 3.0, triple-vortex region at 3.0 ≤ x/D ≤ 6.0, four-vortex region at 6.0 ≤ x/D ≤ 8.5, and five-vortex region at 8.5 ≤ x/D ≤ 12. The model reveals a complicated multi-vortex system. The associated pressure distributions and flow characteristics are discussed in detail.

Constitutive modeling of human femoropopliteal artery biaxial stiffening due to aging and diabetes.

We have analyzed n=744 human femoropopliteal artery (FPA) specimens using biaxial tensile testing to derive constitutive description of FPA aging in diabetic and non-diabetic subjects. The proposed model allows determination of FPA mechanical properties for subjects of any given age in the range of 13-82years. These results contribute to understanding of FPA pathophysiology and can help improve fidelity of computational models investigating device-artery interaction in peripheral arterial disease repair by providing more personalized arterial properties. In addition, they can guide the development of new materials tunable to diabetic and non-diabetic arteries.

Three new models for evaluation of standard involute spur gear mesh stiffness

Time-varying mesh stiffness is one of the main internal excitation sources of gear dynamics. Accurate evaluation of gear mesh stiffness is crucial for gear dynamic analysis. This study is devoted to developing new models for spur gear mesh stiffness evaluation. Three models are proposed. The proposed model 1 can give very accurate mesh stiffness result but the gear bore surface must be assumed to be rigid. Enlighted by the proposed model 1, our research discovers that the angular deflection pattern of the gear bore surface of a pair of meshing gears under a constant torque basically follows a cosine curve. Based on this finding, two other models are proposed. The proposed model 2 evaluates gear mesh stiffness by using angular deflections at different circumferential angles of an end surface circle of the gear bore. The proposed model 3 requires using only the angular deflection at an arbitrary circumferential angle of an end surface circle of the gear bore but this model can only be used for a gear with the same tooth profile among all teeth. The proposed models are accurate in gear mesh stiffness evaluation and easy to use. Finite element analysis is used to validate the accuracy of the proposed models.

Static error model of a three-floated gyroscope with a rotor supported on gas-lubricated bearings

Three-floated gyroscope with the advantages of high accuracy has been widely used in platform inertial navigation system. To investigate the influence of specific force on the measured angular velocity of a gyroscope with a rotor supported on gas-lubricated bearings, a static error model considering three-degrees-of-freedom displacement of the rotor is proposed through numerical computation. Firstly, the conical Reynolds equation incorporated with the Fukui and Kaneko’s slip model is adopted and solved by the finite difference method, and the bearing force, caused by specific force, are obtained for each rotor displacement. Secondly, the error of gyroscope measured angular velocity is calculated from bearing force and rotor displacement. Finally, the relationship between the error and specific force is obtained by regression analysis, and the static error model of the gyroscope is proposed. To simplify the ternary regression analysis to binary, two intermediate parameters, radial interference torque and circumferential angle between interference torque and specific force, are introduced. Numerical results show that interference torque is approximately π/2 ahead of specific force in circumferential direction with fz > 0, and π/2 behind specific force with fz < 0, and that a large interference torque is produced when the specific force in radial and axial direction are both large. The error model provides a rapid prediction of the error caused by rotor displacement by three-degrees-of-freedom specific force.

Frequency-domain method for multistage turbomachine tone noise calculation

A method of frequency-domain calculation of the multistage turbomachinery tone noise is presented. The method is based on the kinematic relations featuring dependence of flow fields in a turbomachine on time and circumferential angle. It solves the flow in several blade passages inside each row and can be used in conjunction with nonlinear equations. The method is developed at Central Institute of Aviation Motor and implemented in the Three Dimensional Acoustics Solver in-house solver. The multi-passage method is verified on two numerical problems. One is the tone noise generation by a 2D two stage turbine. The other is the problem of nonlinear interaction of circumferential modes in a 2D cylindrical channel.

Circumferential Trabeculotomy Versus Conventional Angle Surgery: Comparing Long-term Surgical Success and Clinical Outcomes in Children With Primary Congenital Glaucoma

This study compares the long-term efficacy of circumferential trabeculotomy to that of conventional angle surgeries in primary congenital glaucoma (PCG), as judged by glaucoma and visual outcomes. Retrospective observational case series. Setting: Emory Eye Center, Atlanta, Georgia. This was a single-institution retrospective study involving children with PCG who underwent circumferential trabeculotomy, standard trabeculotomy, or goniotomy with ≥2-year follow-up. Postoperative success (intraocular pressure [IOP] < 22mm Hg ± glaucoma medications, without glaucoma progression/additional IOP-lowering surgery), Snellen-equivalent visual acuity (VA), and IOP at last follow-up. Kaplan-Meier method estimated the probability of glaucoma control vs time postoperatively, and values were compared between angle surgery cohorts using Wilcoxon signed rank tests, Mann-Whitney U tests, and Fisher exact tests. Included were 58 eyes (33 children) after circumferential trabeculotomy and 42 eyes (27 children) after standard trabeculotomy/goniotomy, with mean follow-up of 7.2 ± 4.0 and 8.2 ± 4.5 years, respectively. Postoperative success at last follow-up in the circumferential vs conventional cohorts was 81% (47 of 58 eyes) vs 31% (13 of 42 eyes) (P < .0001). At last follow-up, the circumferential cohort had better median VA than the conventional cohort (20/30 (interquartile range [IQR] 20/25 to 20/70) vs 20/70 (IQR 20/40 to 20/200), P= .009), required fewer glaucoma medications (0.55±1.2 vs 1.61 ± 1.51, P < .0001), had lower IOP in first operated eye (15.2 ± 3.6 vs 18.2 ± 7.0, P= .048), and had comparable incidence of devastating complications (P= .065). In this retrospective study, circumferential trabeculotomy afforded better long-term success and visual outcomes than conventional angle surgery for children with PCG.

Convection induced by vibrating rod in fine-powder bed

In this study, vibration-induced convection was studied experimentally using a fine powder with a mass median particle diameter of 8μm. A cylindrical rod arranged vertically in a powder container was vibrated horizontally with simple harmonic motion at a frequency of 300Hz using a piezoelectric vibrator. For a vibration amplitude of 10μm, particles around the cylindrical rod were consolidated to a certain extent due to gravity; however, for a vibration amplitude of 70μm or more, a pair of convection rolls formed on both sides of the vibrating rod. The strength of the convection was quantified from the particle velocity distribution in the convection rolls, and the relationship between the convection strength and vibration amplitude was elucidated. In addition, the air-pressure distribution in the powder bed was measured showing that the convection strength correlates with the characteristic positive pressure, i.e., the average value of positive pressure measurements. Elliptical motion and circular motion as well as simple harmonic motion were applied to the cylindrical rod by adding two harmonic motions in directions orthogonally crossing each other with a phase difference of π/2rad. The convection of the particles varied according to the Lissajous trajectory of the cylindrical rod. Even for simple harmonic motion, heaps of a pair of convection cells overlapped each other. In the case of elliptical motion, the overlapping portion of the heaps became larger. In the case of circular motion, the two heaps were integrated into one circular heap, and there were no effects of the circumferential angle on the particle velocity and the characteristic positive pressure.

Experimental Investigation on Propagation Characteristics of PD Radiated UHF Signal in Actual 252 kV GIS

For partial discharge (PD) diagnostics in gas insulated switchgears (GISs) based on the ultra-high-frequency (UHF) method, it is essential to study the attenuation characteristics of UHF signals so as to improve the application of the UHF technique. Currently, the performance of UHF has not been adequately considered in most experimental research, while the constructive conclusions about the installation and position of UHF sensors are relatively rare. In this research, by using a previously-designed broadband sensor, the output signal is detected and analyzed experimentally in a 252 kV GIS with L-shaped structure and disconnecting switch. Since the relative position of the sensor and the defect is usually fixed by prior research, three circumferential angle positions of the defect in cross section are performed. The results are studied by time, statistics and frequency analyses. This identifies that the discontinuity conductor of DS will lead to a rise of both the peak to peak value (Vpp) and the transmission rate of the UHF signal. Then, the frequency analysis indicates that the reason for the distinction of signal amplitude and transmission rate is that the mode components of the PD signal are distinctively affected by the special structure of GIS. Finally, the optimal circumferential angle position of the UHF Sensor is given based on the comparison of transmission rates.

Experimental analysis of the thermal field and heat transfer characteristics of a pebble-bed core in a high-temperature gas-cooled reactor

Identifying the locations of hot spots in a pebble-bed reactor core and analyzing the thermodynamic characteristics in the core are critical tasks. Although various numerical simulations have been conducted in this regard, experimental analyses are rarely found in the literature. Therefore, in this study, experiments are conducted with the pebbles packed in a face-centered-cubic (FCC) structure inside the test section. The local heat transfer characteristics of a pebble are analyzed, and it is found that the heat transfer varies with the location; areas with φ=36° and 117° are the strongest heat transfer zones (φ is the circumferential angle from the z-axis to the hole), while areas with φ=0°, 90°, and 180° are the weakest heat transfer zones. The experiments are performed under five different conditions of air inlet velocity, and the corresponding surface thermal profiles and maximum temperature differences between two pebbles are obtained. It is found that the maximum surface temperature difference between two pebbles is 15.3°C when the Reynolds number is 1.46×104 and 7.8°C when the Reynolds number is 3.30×104. In addition, the heat transfer coefficients and the Nusselt number are also obtained and they are correlated with the Reynolds number as hAVG=0.03677Re0.8, Nu=0.194Re0.8Pr0.4, respectively. These findings can not only provide a deeper understanding of the thermodynamics in a pebble-bed reactor core but also facilitate safer reactor design.

Fatigue life estimation of screws under multiaxial loading using a local approach

The fatigue life estimation of screws usually applies a nominal approach on the basis of normal forces. For time-dependent, multiaxial loading of screws this method is not accurate enough; a related method has not been specified yet. In this regard, the current contribution discusses the incorporation of a local approach to predict durability. Therefore, Schneider’s method is enhanced to generate an efficient procedure for calculating the fatigue-induced damage at the screws. The failure criterion is the technical relevant incipient crack length in the first load-bearing thread turn of the screw. By incorporating a submodelling technique, the presented method leads to damage values over the circumferential angle of the thread.In order to validate the method, the computed damage values are compared with experimentally determined results. In the experiments, the incipient crack length in the thread of the screws is measured by an advanced technique using a rod-type strain gauge.