A Study of the Dependence of the Mach Stem Height on the Trailing Edge Height

The Mach stem height is an important parameter in the Mach reflection of steady supersonic flow. Various experimental, numerical, and theoretical works have been conducted to study this parameter in the past. However, much of the established work focuses around a single set of trailing edge heights. Here, we perform a study to show the dependence of Mach stem height on the trailing edge height for a wider range of geometry. Through numerical simulation for a set of trailing edge heights, we found that the normalized Mach stem height is almost linear with respect to the normalized wedge trailing edge height. The parameter used for normalization can be either the inlet height or the length of the lower wedge surface. The observation of this linear trend is justified through a simplified analysis, which leads to an expression of the Mach stem height that linearly depends on the trailing edge height. The present study extends our knowledge about how the geometry affects the Mach stem height, and provides a basis for future work to elaborate analytical models for Mach stem height.

Numerical and Theoretical Study on the Varying Speed Impact of Wedge Bodies on a Water Surface

The varying speed impact of wedge bodies on a water surface is studied numerically and theoretically to provide a fast and accurate prediction of the pressure on the wedge surface and the motion of wedge bodies during the free impact, which can be a two-dimensional (2D) model for the strip theory or 2D + t strategy. The fluid is assumed to be incompressible, inviscid, with negligible gravity effect and surface tension effect. The computational fluid dynamics (CFD) method is based on the volume of fluid (VOF) method and global moving mesh (GMM) method. Various cases of a varying speed impact are shown for the CFD method, and a linear relationship between the pressure coefficient Cp and a dimensionless variable K is observed. To clearly explain the linear relationship between Cp and K, we follow the potential theory to derive the Cp expression based on several assumptions on the free surface drawn from the CFD results. The Cp expression and the motion of wedge bodies for a free impact derived from it are considered as an approximate solution for a varying speed impact. The approximate solution is compared with the existing analytical models and the published experimental data. The approximate solution can work well for different deadrise angles, while the existing analytical models can only be used for small deadrise angles. Good agreement is also obtained between the approximate solution and the experimental test results, including the time history of wedge acceleration and the pressure on the wedge surface.

Predicting the propagation and interaction of frontal accretionary thrust faults with work optimization

<p>This study assesses the ability of work optimization to predict the spatial and temporal initiation of faults. We focus on the growth of flaws that develop into thrust faults at the toe of accretionary prisms because observations from physical laboratory accretion experiments provide rich data with which to validate the models, and the processes of accretionary thrust fault initiation remain unclear. In order to model these systems, we apply new implementations to the fault growth code GROW that improve its prediction of fault interaction using work optimization, including: 1) CPU parallelization, 2) a new growth algorithm that propagates only the most efficient fault in each growth increment, the single run mode, and 3) a new growth algorithm that only considers fault propagation from fault tips that host high sums of modes I and II stress intensity factors, K<sub>G</sub>, the limiting mode. The single and limiting mode produce the geometries that best match the observed geometries, rather than the previous algorithm that allows all the faults to propagate simultaneously, regardless of K<sub>G</sub>, the multiple and non-limiting mode. The single limiting models predict that frontal accretionary thrusts initiate at the midpack or shallower depths, consistent with findings of previous studies. The thrusts propagate upward, link with the surface, and then propagate downward and link with the detachment. The backthrust tends to propagate before the forethrust, and then influence the forethrust propagation. This temporal and spatial sequence of faulting arises from the lower compression, higher shear strain, higher Coulomb stress and higher strain energy density that develop near the wedge surface and the inflection of the wedge slope. The models reveal that the final slip distributions do not reliably indicate the initiation location of the faults, in contrast to the assumptions of previous analyses.</p>

IMPROVING THE ENERGY EFFICIENCY OF OPERATION OF MOBILE CRUCIFORM KNIVES GRINDERS OF FOOD

Рассмотрены конструкции крестообразных ножей измельчителей пищевого сырья. На основе анализа сил, действующих на лопасть ножа в процессе его вращения, и расчетов показано, что при прочих равных условиях уменьшением величины угла заострения клина можно уменьшить значение горизонтальной составляющей силы резания и силу трения между поверхностью клина и решеткой, тем самым повысить энергоэффективность процесса измельчения. Предложена конструкция крестообразного подвижного ножа, лопасти которого имеют во всех поперечных сечениях форму классического клина с углом альфа при вершине величиной не более 612. Оптимальная величина угла альфа между поверхностью лопасти и решеткой 23. По предложенной конструкции были изготовлены подвижные крестообразные ножи. Проведенные испытания показали, что энергозатраты на процесс измельчения мяса при использовании подвижных крестообразных ножей предложенной конструкции были на 3032 ниже по сравнению с энергозатратами на процесс измельчения подвижными ножами, имеющими форму параллелограмма. The designs of mobile cruciform knives grinders of food are considered. Based on the analysis of the forces acting on the blade of the knife in the process of its rotation and calculations, it is shown that, ceteris paribus, a decrease in the value of the wedge sharpening angle can reduce the horizontal component of the cutting force and the friction force between the wedge surface and the grid, thereby increasing the energy efficiency of the grinding process. The design of a mobile cruciform knife, the blades of which have in all cross sections the shape of a classical wedge with an angle alpha at the top of no more than 612, is proposed. The optimum value of the angle alpha between the surface of the blade and the grid is 23. Movable cruciform knives were made according to the proposed design. Tests have shown that the energy consumption of the grinding process the meat when using a movable cruciform knives of the proposed construction was on a 3032 lower compared to the energy consumption of the grinding process with movable blades having the shape of a parallelogram.

Wedge Surface Plasmon Polariton Waveguides Based on Wet-Bulk Micromachining

In this paper, we propose and investigate the modal characteristics of wedge surface plasmon polariton (SPP) waveguides for guiding surface plasmon waves. The wedge SPP waveguides are composed of a silver layer deposited onto the surface of a wedge-shaped silicon dielectric waveguide. The wedge-shaped silicon dielectric waveguides are explored from the anisotropic wet etching property of single crystal silicon. The wedge SPP waveguides are embedded in a dielectric medium to form the metal–dielectric interface for guiding the surface plasmon waves. The propagation characteristics of the wedge SPP waveguides at the optical telecommunication wavelength of 1.55 μm are evaluated by a numerical simulation. The influence of the physical parameters such as the dimensions of the wedge SPP waveguide and the refractive index of the dielectric medium on the propagation of the surface plasmon wave is investigated. In addition, by comparing the propagation characteristics, we derive the wedge SPP waveguide with the optimal performance.

Solar Radiation Energy Issues on Nanoparticle Shapes in the Potentiality of Water Based Cu, Al2O3 and SWCNTs

<p>Energy is an extensive view for industrial advancement. Solar thermal energy is designed by light and heat which is radiated by the sun, in the form of electromagnetic radiation. Solar energy is the highest promptly and sufficiently applicable authority of green energy. Impact of nanoparticle shapes on the Hiemenz nanofluid (water-based Cu, Al2O3 and SWCNTs) flow over a porous wedge surface in view of solar radiation energy has been analyzed. The three classical form of nanoparticle shapes are registered into report, i.e. sphere (m=3.0), cylinder (m=6.3698) and laminar (m=16.1576). Nanoparticles in the water-based Cu, Al₂O₃ and SWCNTs have been advanced as a means to boost solar collector energy through explicit absorption of the entering solar energy. The controlling partial differential equations (PDEs) are remodeled into ordinary differential equations (ODEs) by applying dependable accordance alteration and it is determined numerically by executing Runge Kutta Fehlberg method with shooting technique. It is anticipated that the lamina shape SWCNTs have dynamic heat transfer attainments in the flow improvement over a porous wedge surface as compared with the other nanoparticle shapes in different nanofluid flow regime.</p><p> </p>

Sensitivity Analysis on Thermal Conductivity Characteristics of a Water-Based Bionanofluid Flow Past a Wedge Surface

Thermobioconvection boundary layer flow in a suspension of water-based bionanofluid holding both nanoparticles and motile microorganisms past a wedge surface was studied. The governing nonlinear partial differential equations on reference of the Buongiorno model were transformed into a set of coupled nonlinear ordinary differential equations. Shooting technique was then used to solve the transformed nonlinear ordinary differential equations numerically. The solutions were found to be contingent on several values of the governing parameters. As highlighted, the velocity profile as well as the skin friction coefficient was affected by the pressure gradient parameter, the function of the wedge angle parameter. On the other hand, the temperature, nanoparticle concentration, and density of motile microorganism’s distributions together with its corresponding local Nusselt number, local Sherwood number, and local density of the motile microorganisms change with the thermophoresis and Brownian motion parameter and so Lewis number, Schmidt number, and bioconvection Péclet number. An experimental scheme together with sensitivity analysis on the basis of Response Surface Methodology (RSM) was applied to examine the dependency of the response parameters of interest to the input parameters’ change. Obviously, local Nusselt number was more sensitive towards the Brownian motion parameter when the Brownian motion parameter was at 0.2 and 0.3. However local Sherwood number was more sensitive towards the Lewis number for all values of Brownian motion parameter. Compatibility found by comparing results between RSM and shooting technique gave confidence for the model’s accuracy. The findings would provide initial guidelines for future device fabrication. Finally, the numerical results obtained were thoroughly inspected and verified with the existing values reported by some researchers.

Classical Boundary-Layer Theory

Chapter 1 discusses the flows that can be described in the framework of Prandtl’s 1904 classical boundary-layer theory, including the Blasius boundary layer on a flat plate and the Falkner–Skan solutions for the boundary layer on a wedge surface. It presents Schlichting’s solution for the laminar jet and Tollmien’s solution for the viscous wake. These are followed by analysis of Chapman’s shear layer performed with the help of Prandtl’s transposition theorem. It also considers the boundary layer on the surface of a fast rotating cylinder with the purpose of linking the circulation around the cylinder with the speed of its rotation. It concludes discussion of the classical boundary-layer theory with analysis of compressible boundary layers, including the interactive boundary layers in hypersonic flows.