Hole Geometry Research Articles

Geometry of obstacle marks at instream boulders—integration of laboratory investigations and field observations

AbstractObstacle marks are instream bedforms, typically composed of an upstream frontal scour hole and a downstream sediment accumulation in the vicinity of an obstacle. Local scouring at infrastructure (e.g. bridge piers) is a well‐studied phenomenon in hydraulic engineering, while less attention is given to the time‐dependent evolution of frontal scour holes at instream boulders and their geometric relations (depth to width, and length ratio). Furthermore, a comparison between laboratory studies and field observations is rare. Therefore, the morphodynamic importance of such scour features to fluvial sediment transport and morphological change is largely unknown. In this study, obstacle marks at boulder‐like obstructions were physically modelled in 30 unscaled process‐focused flume experiments (runtime per experiment ≥ 5760 min) at a range of flows (subcritical, clear‐water conditions, emergent and submerged water levels) and boundary conditions designed to represent the field setting (i.e. obstacle tilting, and limited thickness of the alluvial layer). Additionally, geometries of scour holes at 90in‐situboulders (diameter ≥ 1 m) located in a 50‐km segment of the Colorado River in Marble Canyon (AZ) were measured from a 1 m‐resolution digital elevation model. Flume experiments reveal similar evolution of local scouring, irrespective of hydraulic conditions, controlled by the scour incision, whereas the thickness of the alluvial layer and obstacle tilting into the evolving frontal scour hole limit incision. Three temporal evolution phases—(1) rapid incision, (2) decreasing incision, and (3) scour widening—are identified based on statistical analysis of spatiotemporal bed elevation time series. A quantitative model is presented that mechanistically predicts enlargement in local scour length and width based on (1) scour depth, (2) the inclination of scour slopes, and (3) the planform area of the frontal scour hole bottom. The comparison of field observations and laboratory results demonstrates scale invariance of geometry, which implies similitude of processes and form rather than equifinality.

Gravitational redshift/blueshift of light emitted by geodesic test particles, frame-dragging and pericentre-shift effects, in the Kerr\u2013Newman\u2013de Sitter and Kerr\u2013Newman black hole geometries

We investigate the redshift and blueshift of light emitted by timelike geodesic particles in orbits around a Kerr–Newman–(anti) de Sitter (KN(a)dS) black hole. Specifically we compute the redshift and blueshift of photons that are emitted by geodesic massive particles and travel along null geodesics towards a distant observer-located at a finite distance from the KN(a)dS black hole. For this purpose we use the killing-vector formalism and the associated first integrals-constants of motion. We consider in detail stable timelike equatorial circular orbits of stars and express their corresponding redshift/blueshift in terms of the metric physical black hole parameters (angular momentum per unit mass, mass, electric charge and the cosmological constant) and the orbital radii of both the emitter star and the distant observer. These radii are linked through the constants of motion along the null geodesics followed by the photons since their emission until their detection and as a result we get closed form analytic expressions for the orbital radius of the observer in terms of the emitter radius, and the black hole parameters. In addition, we compute exact analytic expressions for the frame dragging of timelike spherical orbits in the KN(a)dS spacetime in terms of multivariable generalised hypergeometric functions of Lauricella and Appell. We apply our exact solutions of timelike non-spherical polar KN geodesics for the computation of frame-dragging, pericentre-shift, orbital period for the orbits of S2 and S14 stars within the 1^{prime prime } of SgrA*. We solve the conditions for timelike spherical orbits in KN(a)dS and KN spacetimes. We present new, elegant compact forms for the parameters of these orbits. Last but not least we derive a very elegant and novel exact formula for the periapsis advance for a test particle in a non-spherical polar orbit in KNdS black hole spacetime in terms of Jacobi’s elliptic function sn and Lauricella’s hypergeometric function F_D.

Semiclassical backreaction on asymptotically anti–de Sitter black holes

We consider a quantum scalar field on the classical background of an asymptotically anti--de Sitter black hole and the backreaction the field's stress-energy tensor induces on the black hole geometry. The backreaction is computed by solving the reduced-order semiclassical Einstein field equations sourced by simple analytical approximations for the renormalized expectation value of the scalar field stress-energy tensor. When the field is massless and conformally coupled, we adopt Page's approximation to the renormalized stress-energy tensor, while for massive fields we adopt a modified version of the DeWitt-Schwinger approximation. The latter approximation must be modified so that it possesses the correct renormalization freedom required to ensure the semiclassical equations are consistent. Equipped with these approximations, the reduced-order field equations are easily integrated and the first-order (in $\ensuremath{\hbar}$) corrections to the metric are obtained. We also compute the corrections to the black hole event horizon, surface gravity, and minimum temperature as well as corrections to the photon sphere and quadratic curvature invariants. We pay particular attention to the temperature profiles of the semiclassical black holes compared with their classical counterparts, pointing out some interesting qualitative features produced by the backreaction. These results ought to provide reasonable approximations to the first-order (one-loop) quantum backreaction on the geometry of asymptotically anti--de Sitter black holes when the exact numerical stress-energy tensor sources the semiclassical equations.

Numerical analysis of biaxial elasto-plastic buckling of perforated rectangular steel plates applying the Constructal Design method

Thin plates are constantly used in many applications of the structural designs, like naval, aerospace, civil and offshore platforms. When the supported loading is compressive along the plane of plate, it can suffer with an instability phenomenon called buckling which can be elastic or elasto-plastic. In addition, many times the plated structures need to be designed with cutouts for the most varied reasons: access, maintenance, crossing pipes and reducing of weight, for example. The presence of holes affects the mechanical behavior of the plate and it must be investigated. This work used Finite Element Method associated to Constructal Design method and Exhaustive Search technique to find the optimal geometries, i.e. the ones that maximize the Normalized Ultimate Stress, for simply-supported rectangular steel plates under biaxial compressive loading. It was analyzed the size and geometry of the centered elliptical hole. It was observed that the presence of cutout reduces the mechanical strength of the plate and also, the same occurs when the hole size is increased. Constructal Design method has been proved as an effective method to analyze buckling problems conducting to the best geometry for each studied case. For the simulated cases it is evident the relevance of geometric evaluation of elliptical perforations, once the simply variation of geometry can provide differences until around 42% when comparing the optimum and the worst geometries, for the same hole size.

Stress Analysis of Hole Orientation and Laminate Geometry Impacting on Boron/Epoxy Composites Laminates

Boron/epoxy laminates are used in aircraft and space vehicles for their high strength. Evaluation of stresses and residual strength of the laminate with square cutout are not analyzed in the literature. The present work is focused on studying the effect of hole orientation and laminate geometry on Boron/Epoxy composites laminates under in-plane loading. The analytical solution for stresses around holes in laminates is derived using Savins’s complex variables method to consider a multilayered plate with different hole shapes and orientations of loading. The basic equations of failure criteria available for plain laminates are derived to calculate the residual strength of the laminates with hole using the stresses obtained from the analytical solution. The derived analytical solution is validated by reproducing exactly the same results of earlier researchers even by other formulations and also by the results of finite element analysis using ANSYS. The [0/0]s laminate is not preferred due to highest stress concentrations at the corners that range between 12 to 12.45. Similarly, [45/-45]s laminate is also not preferred due to its higher values of stress concentrations which range from 9.5 to 28. The normalized stress for [0/90]s underx-axis loading is 9.6 and fory-axis loading it is 9.5 which is almost the same. Even for equi-biaxial loading, it is 8.5 and for shear loading, it is 12.45. Except for shear loading, [0/90]s laminate seems to be a better choice for a reasonable value of stress concentration for any general case loading. The analytical solution derived in the present work is the most general and unique as it can yield the stresses around any shape of hole and laminate geometry and all types of in plane loading. This solution will be able to reproduce the results of all other solutions available in the literature by different formulations.

Parametric Study on the Effect of Aspect Ratio of Selected Cooling Hole Geometries on the Mechanical Response of an Automobile Aluminium Alloy Wheel

Aluminium alloy wheels are increasingly popular for their light weight and good thermal conductivity. Cooling Holes (CH) are introduced to reduce their weight without compromising structural integrity. Literature is sparse on the effect of aspect ratio (AR) of CHs on wheels. This, work, therefore, attempts to undertake a parametric study of the effect of aspect ratio (AR) on the mechanical response of an aluminium alloy wheel with triangular, quadrilateral and oval-shaped CHs. Three-dimensional wheel models (6JX14H2ET42) with triangular, quadrilateral and oval shaped CH (each with CH area of 2229 mm2) were generated, discretized, and analyzed by FEM using Creo Elements/Pro 5.0 to determine the mechanical response at the inboard bead seat at different ARs of 1, 0.5, 0.33 and 0.25, each for quadrilateral-CH and oval-CH, at a static Radial Load of 4750 N and Inflation Pressures of 0.3 and 0.15 MPa, respectively. The study shows that the magnitude of stress and displacement is affected by shape and AR of CH. From the results, it could be established that oval-shaped-CH wheel at AR of 0.5 offers greater prospect in wheel design as it was least stressed and deformed and, that the CH combination with highest integrity was the oval-CH and quadrilateral-CH at AR of 0.5.

Hybrid model of support vector regression and fruitfly optimization algorithm for predicting ski-jump spillway scour geometry

ABSTRACT Accurate prediction of the scour hole depth and dimensions downstream of ski-jump spillways has been an important issue among hydraulic researchers for decades. In recent years, computing methods such as Artificial Neural Networks (ANNs), Adaptive Neuro-Fuzzy Inference Systems (ANFISs) and Support Vector Regression (SVR) have shown a powerful performance in the prediction of scour characteristics owing to their flexibility and learning nature. In the present paper, a new hybrid approach has been proposed for the first time in order to improve the estimation power of the SVR tool for scour hole geometry prediction below ski-jump spillways. The principal characteristics of the scour hole pattern in the equilibrium phase have been predicted using SVR optimized with Fruitfly Optimization Algorithms (FOAs). The hybrid model is compared with the corresponding simple SVR model. To evaluate the proposed hybrid model further, it is also compared with other machine learning and empirical methods, such as ANNs, ANFISs and regression equations. The results show that the proposed SVR-FOA method performs well, improves remarkably on Support Vector Machines (SVMs) results, estimates scour hole geometrical parameters more accurately than the simple SVR model, and can be applied as an alternative reliable scheme for estimations on which simple SVR and other methods demonstrate shortcomings. The proposed hybrid method improves the precision level for scour depth prediction by about 8% compared with simple SVM in terms of the correlation coefficient.

Justification of vibrating hopper hole parameters during fine grained bulk material unloading

Purpose. The leakage process of the fine grained bulk material (BM) from the unloading hopper is considered. As known the BM behaviour during the unloading process is directly related to the material stress state (active or passive) inside the hopper, which depends on the physical and mechanical bulk material properties, as well as hopper geometric parameters. At the boundary of the transition from the cylindrical part to the conical part of the unloading hopper hole, the horizontal stresses that precede the leakage of the material increase sharply. The use of vibration reduces horizontal stresses in the hopper and thus improves the bulk product fluidity. Also, the use of vibration reduces the probability of the free-fall arch formation over the outlet. Therefore, the present paper is aimed at developing the mathematical model of the fine grained bulk material flow under the vibration action from the conical hopper hole. Methodology. It is used one of the methods of studying the BM behavior, namely the analysis of the stress state of the conditionally stationary (pseudo-stationary) layer of the product and the force balance equation in the free-fall arch is made for further study of the geometric parameters of the unloading hole. Findings. In this paper, the mathematical model of the BM behavior in the conical hopper hole is developed. Since the most determining factor influencing the hopper productivity is the outlet diameter, so based on the developed model, it is established relationships that allow determining all parameters that affect the diameter. Graphical dependences are obtained, which allow to estimate the influence of the angle inclination of the hopper hole walls on the value of the hopper outlet size at active and passive stress states. The dependence of the diameter of the unloading hopper hole on the BM properties is also established. The BM properties directly affect the initial shear resistance of the material. The influence of vibration on the unloading hole geometry is presented. Originality. The pseudo-immobile layer of bulk product is considered in the developed mathematical model, and it is investigated how vibration affects the BM behavior in this layer. Practical value. The practical value of this paper lies in the possibility of further mathematical modeling of the influence of the BM properties, hopper geometric dimensions and vibration on the product behavior in the material leakage process from the hopper. The results of the studies, presented in the form of graphs, can be used during the vibrating hopper design and the selection of rational modes of hopper operation.

Parametric optimization of hole geometry in laser drilled Inconel 825 by grey based response surface methodology

Laser micro drilling is a non-conventional machining process which uses thermal energy to remove material from the workpiece. This paper presents the parametric study on Nd:YAG laser micro drilling of 2 mm thickness INCONEL 825 plate a Nickel based super alloy which have found purpose in nuclear, aerospace, and production industries due its high strength and resistant to oxidation at high temperature. The present work is to improve the geometrical characteristic like hole taper and hole circularity. Integrated grey Taguchi based Response surface methodology (GT-RSM) was used to predict optimal cutting condition . The effect of process parameters such as air pressure, trepanning speed, frequency and lamp current on the output response hole circularity at entry and hole taper is studied by grey based response surface methodology. Lamp current and air pressure is determined most influential parameter on hole circularity and hole taper.

Compression deformation analysis of cellular lattice structure for structural optimization in additive manufacturing

Additive manufacturing has Cellular structures as its prominent component because of their ability to overshadow the solid ones on account of more strength-to-weight ratio, porous and light-weight nature. A lattice structure called vintile was designed and the effect of change in unit size, lattice kernel position, volume reduction coefficient, and cellular structure optimization on mechanical properties were discussed in this study. Samples with different cell sizes, lattice kernel positions, were 3-D printed using Polylactic acid (PLA) material on MakerBot Replicator Plus 3D printer. Finite element analysis (FEA) and experimentation work was performed on the designed cellular structures so as to make the estimation and evaluation of the mechanical properties of these cellular structures. Output of the work shown that the vin tile lattice topology cellular structure with lattice kernels on both sides of the central hole geometry bears less stress and very little deformation than the other cellular structures with kernels on only either side. Experimental results were in conformation with simulation results. The study does not limit itself to design of cellular structure only but also compared mechanical behavior through volume reduction coefficient (VRC) and surface area coefficient (SAC). Final testing of vin tile cellular structures was done using FEA and experimental work have been carried out on fabricated samples. The results of both concluded that the optimized cellular structure had less stress and deformation than the non-optimized cellular structure.

A simulation-based study on the disc brake temperature distribution for optimising hole geometry

A simulation-based study on the disc brake temperature distribution for optimising hole geometry

Injection lap riveting

This paper presents an injection lap riveting process to connect two sheets placed one on top of the other. The process is carried out at ambient temperature and differs from self-pierce riveting because its joining principle is based on plasticity and friction without fracture and formation of new surfaces. The working principle is based on two consecutive operations - first, a dovetail ring hole is machined in the lower sheet and then a semi tubular rivet is injected through the upper sheet into the dovetail ring hole of the lower sheet, by compression with a punch. The presentation is based on a combined experimental and numerical investigation and special emphasis is put on the influence of the dovetail ring hole geometry in material flow, riveting force, and pull-out and shear destructive forces. The last past of the paper includes details of a prototype cutting tool that was developed by the authors for producing the dovetail ring holes in-site and fostering the portability and applicability of the process.

Numerical Investigation on Film Cooling Mechanism with Different Coolant Delivery Configurations

Kidney vortex has significant impact on film cooling effectiveness, and different kinds of film cooling hole geometry and configuration are developed to weaken or eliminate kidney vortex. This paper is focus on the mechanism of eliminating kidney vortex by optimizing the coolant delivery configuration, seven coolant delivery configurations are designed to conduct a comparative study with different blowing ratios. At high blowing ratio, the strong kidney-shaped vortex is formed outside the film cooling hole causing the low cooling effectiveness for β≤0˚. For β>0˚, the coolant ejection interacts with mainstream hot gas, and the coolant gas in low momentum region of upstream bypasses the large jet momentum coolant to attach film cooling surface at downstream. It increases the distance between the vortexes to weaken mutually reinforcing effect, resulting in high film cooling effectiveness. When the blowing ratio is 1.5, the average adiabatic film cooling effectiveness of β=+15˚ and β=+30˚ is increased by about 130% and 70% compared to case of β=-60˚, respectively.

The Black Hole Entropy Distance Conjecture and Black Hole Evaporation

AbstractWe extend the recently proposed Black Hole Entropy Distance Conjecture to the case of charged black holes in de Sitter space. By systematically studying distances in the space of black hole geometries with multiple horizons, we find that the distance is generically related to the logarithm of the entropy. From the infinite distance conjecture this predicts the appearance of a massless tower of modes in the limit of infinite entropy. Further, we study the evaporation of these black holes and relate it to the geometric distance. We find that the corresponding distance to the final stage of evaporation is finite. We conclude that evaporation does not lead to the appearance of a light tower of black hole microstates.

Null hypersurfaces in Kerr–Newman–AdS black hole and super-entropic black hole spacetimes

A three-dimensional light-like foliation of a spacetime geometry is one particular way of studying its light cone structure and has important applications in numerical relativity. In this paper, we execute such a foliation for the Kerr–Newman–AdS black hole geometry and compare it with the lightlike foliations of the Kerr–AdS and Kerr–Newman black holes. We derive the equations that govern this slicing and study their properties. In particular, we find that these null hypersurfaces develop caustics inside the inner horizon of the Kerr–Newman–AdS black hole, in strong contrast to the Kerr–AdS case. We then take the ultra-spinning limit of the Kerr–Newman–AdS spacetime, leading to what is known as a super-entropic black hole, and show that the null hypersurfaces develop caustics at a finite distance outside the event horizon of this black hole. As an application, we construct Kruskal coordinates for both the Kerr–Newman–AdS black hole and its ultra-spinning counterpart.

Spectral extended finite element method for band structure calculations in phononic crystals

In this paper, we compute the band structure of one- and two-dimensional phononic composites using the extended finite element method (X-FEM) on structured higher-order (spectral) finite element meshes. On using partition-of-unity enrichment in finite element analysis, the X-FEM permits use of structured finite element meshes that do not conform to the geometry of holes and inclusions. This eliminates the need for remeshing in phononic shape optimization and topology optimization studies. In two dimensions, we adopt a rational Bézier representation of curved (circular) geometries, and construct suitable material enrichment functions to model two-phase composites. A Bloch-formulation of the elastodynamic phononic eigenproblem is adopted. Efficient computation of weak form integrals with polynomial integrands is realized via the homogeneous numerical integration scheme—a method that uses Euler's homogeneous function theorem and Stokes's theorem to reduce integration to the boundary of the domain. Ghost penalty stabilization is used on finite elements that are cut by a hole. Band structure calculations on perforated (circular holes, elliptical holes, and holes defined as a level set) materials as well as on two-phase phononic crystals are presented that affirm the sound accuracy and optimal convergence of the method on structured, higher-order spectral finite element meshes. Several numerical examples are presented to demonstrate the advantages of p-refinement made possible by the spectral extended finite element method. In these examples, fourth-order spectral extended finite elements deliver O(10−8) accuracy in frequency calculations with more than thirty-fold fewer degrees-of-freedom when compared to quadratic finite elements.

Black holes and gravitational waves sourced by non-linear duality rotation-invariant conformal electromagnetic matter

Maxwell's equations are invariant under both duality rotations and conformal transformations. Recently Bandos, Lechner, Sorokin, and Townsend have found a nonlinear generalisation of electrodynamics which possesses both of these symmetries. We couple this theory to General Relativity and explore self-gravitating configurations with a clear physical interpretation. We find charged black holes and exact gravitational waves. The black hole geometry is Reissner-Nordström, however, the non-linearity parameter acts as a screening factor allowing extremal configurations where the mass of the black hole is smaller than its charge. Furthermore, we also discuss the phenomenon of birefringence and determine the optical metrics associated to the propagation of photons.

Thermodynamic geometry of normal (exotic) BTZ black hole regarding to the fluctuation of cosmological constant

We construct the thermodynamic geometry of ([Formula: see text])-dimensional normal (exotic) BTZ black hole regarding the fluctuation of cosmological constant. We argue that while the thermodynamic geometry of black hole without fluctuation of cosmological constant is a two dimensional flat space, the three-dimensional space of thermodynamics parameters including the cosmological constant as a fluctuating parameter is curved. Some consequences of the fluctuation of cosmological constant will be investigated. We show that such a fluctuation leads to a thermodynamic curvature which is singular at the critical surface. Also, we consider the validity of first thermodynamics law regarding the fluctuation of the cosmological constant.

Large-Eddy Simulation Study of Ultra-High Fuel Injection Pressure on Gasoline Sprays

The development of gasoline spray at ultra-high injection pressures was analyzed using Large-Eddy simulation (LES). Two different nozzle hole geometries, divergent and convergent shape, were considered to inject the fuel at injection pressures ranging from 200 to 1500 bar inside a constant volume spray chamber maintained at atmospheric conditions. The discrete droplet phase was treated using a Lagrangian formulation together with the standard spray sub-models. The numerical results were calibrated by reproducing experimentally observed liquid penetration length and efforts were made to understand the influence of ultra-high injection pressures on the spray development. The calibrated model was then used to investigate the impact of ultra-high injection pressures on mean droplet size and droplet size distribution. In addition, the spray-induced large-scale eddies and entrainment rate were evaluated at different ultra-high injection pressures. Overall, simulation results showed a good agreement with available measurement data. At ultra-high injection pressures mean droplet sizes were significantly reduced and comprised very high velocities. Integral length scales of spray-induced turbulence and air entrainment rate into the spray were larger at higher injection pressure compared to lower ones.Graphic abstract

Resolving Black Hole Information Paradox: Revisited

Blackhole remnants are one of the most exotic remnants in our universe, leaving behind several unsolved paradoxes. Resolving the black hole information paradox, in particular, can direct us to numerous engrossing discoveries and provide a decent understanding of the unsolved conventional theories. We readdress the notions underlying the paradox explicitly, beginning from the basic principles. Various theories, explanations, conclusions, their advantages and disadvantages in several works of literature regarding the information paradox and black hole entropy are discussed. Recent developments in the interpretation of the black hole information paradox are reviewed. A congenital solution to this contradiction involves the transition of classical physics to quantum physics. At the centre of the black hole, the space-time theory by Einstein’s general theory of relativity fails. The research suggests that the solution obtained from considering the principles of quantum gravity is quite plausible. This approach also gives a decent explanation towards the recondite hypothesis of tunnelling of black holes to white holes and the interior geometries of white holes.