Tangential Coefficient Research Articles

Nanofluid Flow over a Rotating Disk with Prescribed Heat Flux

An analysis is carried out to study the problem of the steady flow and heat transfer over a rotating disk with a prescribed heat flux in nanofluid. Nanofluid considered is Copper (Cu) with water as the base fluid. The governing partial differential equations are transformed into a set of nonlinear ordinary differential equations using similarity transformation, which are then solved using the Nachtsheim-Swigert Shooting iteration technique along with the fourth order Runga Kutta method. The features of the flow and heat transfer characteristics are analyzed and discussed. The radial velocity, tangential velocity and the axial velocity for copper-water nanofluid are calculated and are represented graphically. Numerical results for dimensionless temperature, the radial skin friction coefficient and the tangential skin friction coefficient of the nanofluid flows are obtained and computations are carried out for the various values of Prandtl number. It is found that for the prescribed heat flux case (PHF case), the effect of Prandtl number is to reduce the temperature as it increases for copper-water nanofluid.

Comparative Analysis of Movement Characteristics of Lancelet and Fish Spermatozoa Having Different Morphologies

The movement characteristics of the sperm and their flagella obtained from a lancelet and 35 species from almost all orders of fishes were examined using high-speed video microscopy. The aim was to clarify the relationship between the motility parameters of the spermatozoa having different morphologies and how these motility parameters affect the swimming speed of the spermatozoa. The motility parameters representing the flagellar waveform, the wavelength, and the amplitude were neither very different between the spermatozoa of the different species nor related to the swimming speed. In contrast, the beat frequency was remarkably changed in the different spermatozoa and was proportional to the swimming speed. The maximum shear angle of the flagellar wave, which is directly related to the maximum sliding displacement between the doublet microtubules, remained nearly constant while the beat frequency varied widely; therefore, the spermatozoa beat in the constant sliding displacement mode. An analysis of the relationship between swimming speed and flagellar length revealed that short flagella were at a disadvantage in developing swimming speed; however, so were extra-long flagella. The ratio of the swimming speed to the wave velocity calculated from the wavelength and the beat frequency depended on the distance from the glass surface. The swimming speeds calculated using the original resistive-force theory were greater than the measured values. To rationalize the measured values, the ratio between the normal and tangential drag coefficient in the resistive-force theory was corrected; namely, 1.99 at 1 μm and 1.63 at 3 μm from the glass surface.

Tangential Momentum Accommodation Coefficient measurements for various materials and gas species

The tangential momentum accommodation coefficient was measured from the gaseous flow through a single microtube. The mass flow rate was measured by the constant volume technique, where the rate is related to time rate of pressure variation in a fixed volume tank. The measured mass flow rate was fitted by the theoretical mass flow rate expressed by the slip velocity at the surface to deduce the slip coefficient, which can be related to the tangential accommodation coefficient. The mean Knudsen number, which is determined as the mean pressure of the inlet and the outlet, was set to be below 0.32, where the second-order slip boundary condition was suggested to be valid. The measurement system was designed to allow using a microtube with large diameter of several hundred micrometers. Since low pressure environment was essential for large Knudsen number condition for the flow through such large microtube, a low leakage measurement system realized by applying the UHV technology is needed. Applicability of sub millimeters size microtubes allowed us to measure the tangential momentum accommodation coefficients on various materials. In this study, we measured the tangential momentum accommodation coefficients on an engineering metal surface for various gas species.

Analysis of beam on elastic foundation using the radial point interpolation method

The concept of beam on an elastic foundation has been extensively used by geotechnical engineers for foundation design and analysis. However, most numerical solutions for beam on an elastic foundation are obtained by mesh based methods, such as finite element or finite difference methods. Mesh based methods suffer from some deficiencies, mostly related to mesh definition. In this paper, a mesh-free method, called the radial point interpolation method, is implemented for the analysis of a beam on two parameter elastic foundation. The beam and the elastic foundation are modeled separately. The geometry of the beam is simulated by a set of nodes that are aligned on two or three parallel lines. The displacement field along the beam is constructed by radial basis functions, and the discretized system of equations is derived by substitution of the displacement field into the weak form of the governing equation. The elastic foundation is simulated by the concept of the linkage element and there is no need for nodes or elements in the traditional sense. The stiffness of the foundation has been taken into account by defining normal and tangential stiffness coefficients along the foundation layer. The displacement of each point across the foundation layer is tied to the displacement of the beam nodes. The final system of equations is derived by a combination of equations for both the beam and the elastic foundation in the global coordinate. Based on the derived equations, a computer code has been developed and the results of analysis with the mesh-free method are compared with the results of the exact solution and results obtained from finite element analysis.

Effects of Thermal Radiation on Hydromagnetic Flow due to a Porous Rotating Disk with Hall Effect

Radiation effect on steady laminar hydromagnetic flow of a viscous, Newtonian and electrically conducting fluid past a porous rotating infinite disk is studied taking Hall current into account. The system of axisymmetric nonlinear partial differential equations governing the MHD flow and heat transfer are reduced to nonlinear ordinary differential equations by introducing suitable similarity variables introduced by von Karman and the resulting nonlinear equations are solved numerically using Runge-Kutta based shooting method. A parametric study of all parameters involved was conducted and a representative set of results showing the effect of the magnetic field, the radiation parameter, the uniform suction/injection parameter and Hall parameter are illustrated graphically. The numerical values of the radial and tangential skin-friction coefficient and Nusselt number are calculated and displayed in the tables showing the effects of various parameters. Finally, a good comparison between the present numerical predictions and the previously published data are presented in the absence of magnetic field and radiation.

Analysis of a generalized kinematic impact law for multibody-multicontact systems, with application to the planar rocking block and chains of balls

In this paper, we analyze the capabilities of a generalized kinematic (Newton’s like) restitution law for the modeling of a planar rigid block that impacts a rigid ground. This kinematic restitution law is based on a specific state transformation of the Lagrangian dynamics, using the kinetic metric on the configuration space. It allows one to easily derive a restitution rule for multiple impacts. The relationships with the classical angular velocity restitution coefficient r for rocking motion are examined in detail. In particular, it is shown that r has the interpretation of a tangential restitution coefficient. The case when Coulomb’s friction is introduced at the contact impulse level together with an angular velocity restitution is analyzed. A simple chain of aligned balls is also examined, illustrating that the impact law applies to various types of multibody systems.

Non-Modal Stability and Optimal Perturbations in Unbounded Granular Shear Flow: Three-Dimensionality and Particle Spin

The effects of three-dimensional perturbations and particle rotations are analyzed on the non-modal stability characteristics of an unbounded granular shear flow for which the stability problem is solved as an initial value problem. A kinetic-theory constitutive model is used that incorporates the spin degrees of freedom along with certain micro-polar effects of granular materials. The singular values of the underlying non-normal linear operator play a central role in the non-modal analysis in contrast to the standard modal analysis where the eigenvalues determine the asymptotic (in)stability of the flow. For linearly stable flows, it is shown that the perturbation energy can be amplified by a few orders of magnitude at short times before decaying in the asymptotic time limit. Optimal perturbations, that correspond to maximum energy growth over all possible initial conditions, are found to be two-dimensional in a smooth granular fluid. The effect of particle rotation has been assessed by varying the tangential restitution coefficient (β) for smooth particles (β = −1) to perfectly rough particles (β = 1), with significant enhancement of maximum energy for rough particles. Since the non-modal mechanism can significantly amplify perturbation energy, this provides a viable alternate route for pattern formation in a sheared granular fluid.

CFD simulation of bubbling fluidized beds using kinetic theory of rough sphere

Flow behavior of particles is simulated using an Eulerian–Eulerian two-fluid model based on the kinetic theory of rough spheres. The interactions of the short and fast collisions of particles are incorporated to consider the redistribution of momentum and kinetic energy between the collision and friction interactions. The fluctuating kinetic energy by collisions of particles has taken the transfer of particle kinetic energy between the rotational and translational degrees of freedom and also the energy losses into account. Two coefficients, normal restitution coefficient and tangential restitution coefficient, are used to characterize the collisions of particles. The friction coefficient is used to predict the frictional stresses caused by the enduring contacts of particles. The collisional and frictional constitutive relations are used to predict the stresses of rough spheres. The solid pressure and viscosity are obtained in terms of the normal and tangential restitution coefficients and empirical friction constants. Distributions of concentrations and velocities of particles are predicted in the 2-D bubbling fluidized bed. The influence of bed temperature and particle diameter on fluctuation kinetic energy is analyzed in the bubbling fluidized beds. Simulated results are compared with measured axial velocity of particles and bubble diameter published in literature.

In situ rockfall testing in New South Wales, Australia

Despite the significance of rockfall hazards in Australia, this phenomenon is still poorly characterised in many regional environments. In particular, the relationship between slope/rock properties and rockfall motion parameters needs better definition. In the context of rockfall prediction, it is important to quantify the normal and tangential restitution coefficients (referred to as k n and k t ) and the equivalent rolling coefficient ( μ), which are site-specific. Several series of rockfall tests have been conducted in three different geological environments in New South Wales. The results of the tests show a large variability of the motion parameters, which is due to the natural variability of the blocks and to the randomness of the impact positions. Also, values of k n consistently and systematically higher than the benchmark values from the literature have been inferred. Despite there being no clear correlation between the restitution coefficients and the rotational energy, rotational phenomena are believed to be at the origin of such results.

Effects of shear keys on nonlinear seismic responses of an arch-gravity dam

In the paper, the added tangential nonlinear springs are introduced to represent the effects of one-way and two-way shear keys. The added tangential stiffness coefficient is relative to the joint opening and the relative tangential movement and determined numerically by using a refined model of shear keys. The user subroutine of nonlinear spring elements has been implemented into ABAQUS program. The seismic responses of an arch-gravity dam are mainly examined. It is shown by the results that a significant increase of about 17%–30% in joint opening can be observed for the dam with one-way shear keys; the two-way shear keys are beneficial to restrain the sliding displacement along both the radial and vertical directions, whereas the one-way shear keys mainly restrain the displacement along the radial direction; for the dam with shear keys, the maximum arch stress is increased, the cantilever stress is reduced, and the location of the maximum cantilever stress is also moved from the dam heel to the midheight of the cantilever.

Mixed-flow vertical tubular hydraulic turbine: determination of proper design duty point

A new vertical single-regulated mixed-flow turbine with conical guide apparatus and without spiral casing is presented in this paper. Runner blades are fixed to the hub and runner band and resemble to the Francis type runner of extremely high specific speed. Due to lack of information and guidelines for the design of a new turbine, a theoretical model was developed in order to determinate the design duty point, i.e. to determine the optimum narrow operation range of the turbine. It is not necessary to know the kinematic conditions at the runner inlet, but only general information on the geometry of turbine flow-passage, meridional contour of the runner and blading, the number of blades and the turbine speed of rotation. The model is based on the integral tangential lift coefficient, which is the average value over the entire runner blading. The results are calculated for the lift coefficient 0.5 and 0.6, for the flow coefficient range from 0.2 to 0.36, for the number of the blades between 5 and 13, and are finally presented in the Cordier diagram (specific speed vs. specific diameter). Calculated results of the turbine optimum operation in Cordier diagram correspond very well to the adequate area of Kaplan turbines with medium and low specific speed and extends into the area of Francis turbines with high specific speed. Presented model clearly highlights the parameters that affect specific load of the runner blade row and therefore the optimum turbine operation (discharge—turbine head). The presented method is not limited to a specific reaction type of the hydraulic turbine. The method can therefore be applied to a wide range from mixed-flow (radial-axial) turbines to the axial turbines. Applicability of the method may be considered as a tool in the first stage of the turbine design i.e. when designing the meridional geometry and selecting the number of blades according to calculated operating point. Geometric and energy parameters are generally defined to an extent that these parameters are considered in detailed design using turbulent viscous flow CFD solver.

Hydrodynamic modeling of particle rotation in bubbling gas-fluidized beds

A kinetic theory for flow of dense, slightly inelastic, slightly rough sphere (KTRS) is proposed on the basis of kinetic theory of gases and kinetic theory of granular flow. The fluctuation kinetic energy of particles is introduced to characterize the random motion of particles as a measure of the translational and rotational velocities fluctuations. The kinetic energy transport equation is proposed with the consideration of the redistribution of particle kinetic energy between the rotational and translational modes and kinetic energy dissipation by collisions. The models for solid pressure, conductivity of fluctuating energy and viscosity are presented in terms of the tangential restitution coefficient and normal restitution coefficient. Thus, present kinetic theory for rough spheres (KTRS) has the same structure as that for frictionless spheres, i.e., only conservation of mass, mean translational velocity and fluctuation energy are considered. The partition of the kinetic energy of inelastic rough particles between rotational and translational modes is shown to be affected by the particle roughness and inelasticity. Hydrodynamics of gas–solid bubbling fluidized beds are numerically simulated on the basis of the kinetic theory for flow of rough spheres. Computed profiles of particles velocity are in agreement with the experimental measurements in a bubbling fluidized bed. The effect of tangential restitution coefficient on the distribution of energy dissipation, fluctuation kinetic energy and viscosity of particles is analyzed.

Spatial Diffusion of Water in Carbon Nanotubes: From Fickian to Ballistic Motion

We investigate the spatial variation of the axial, radial, and tangential diffusion coefficients in carbon nanotubes (CNTs) of various diameters. The effect of confinement and CNT wall on the diffusion coefficient is studied. On the basis of the spatial variation of the diffusion coefficient, the diffusion mechanisms in different regions of the nanotube are identified. The dependence of the diffusion coefficient on the carbon-water interaction parameter is investigated. The average diffusion coefficient in the nanotube as a function of the nanotube diameter is computed, and the diffusion mechanisms, including the transition regimes, are identified. The results are analyzed via hydrogen bonds and water orientations.

Effect of Coulomb friction on orientational correlation and velocity distribution functions in a sheared dilute granular gas

From particle simulations of a sheared frictional granular gas, we show that the Coulomb friction can have dramatic effects on orientational correlation as well as on both the translational and angular velocity distribution functions even in the Boltzmann (dilute) limit. The dependence of orientational correlation on friction coefficient (μ) is found to be nonmonotonic, and the Coulomb friction plays a dual role of enhancing or diminishing the orientational correlation, depending on the value of the tangential restitution coefficient (which characterizes the roughness of particles). From the sticking limit (i.e., with no sliding contact) of rough particles, decreasing the Coulomb friction is found to reduce the density and spatial velocity correlations which, together with diminished orientational correlation for small enough μ, are responsible for the transition from non-gaussian to gaussian distribution functions in the double limit of small friction (μ→0) and nearly elastic particles (e→1). This double limit in fact corresponds to perfectly smooth particles, and hence the maxwellian (gaussian) is indeed a solution of the Boltzmann equation for a frictional granular gas in the limit of elastic collisions and zero Coulomb friction at any roughness. The high-velocity tails of both distribution functions seem to follow stretched exponentials even in the presence of Coulomb friction, and the related velocity exponents deviate strongly from a gaussian with increasing friction.

The normal and oblique impact of three types of wet granules

Impact tests against a hardened steel plate have been carried out to obtain the coefficient of restitution of three types of spherical granules. The dominant elastic γ-Al2O3, the elastic-plastic zeolite 4A and the dominant plastic sodium benzoate have been chosen as granule samples. An electromagnetic canon has been constructed to accelerate the granules and to measure the normal coefficient of restitution. The moisture content of the granules has been varied so that the pore saturation ranges between of S = 0–1. Thereby, the influence of the moisture content on the normal coefficient of restitution could be determined. A free fall apparatus, on which the impact angle is changeable in the range of ΘA = 0–80°, has been used to investigate the tangential coefficient of restitution. A high speed digital camera has been used to record the events of impact and rebound. The record frequency of the camera has been varied between 4,000 and 8,000 frames per second.

Aplicações do método de ensaio esclerométrico em peças de eucalipto saligna sm

Neste trabalho é avaliada a tendência de correlações entre as resistências a compressão paralela e normal às fibras, por meio de ensaios destrutivos normalizados e parâmetros do ensaio do método esclerométrico. Também se fez comparação com o método de ensaio não destrutivo de ultrassom. Três séries de corpos de prova foram extraídas de uma tora de Eucalyptus saligna e ensaiadas na condição de madeira saturada. Dos resultados dos impactos esclerométricos para as três direções anatômicas avaliadas (paralela às fibras, radial e tangencial) foram verificados coeficientes de variação inferiores a 9%. Da análise das tendências de correlações de resistência a compressão com os resultados da esclerometria e ultrassonografia, foram constatados os melhores ajustes para a direção paralela às fibras. Tendo em vista os resultados obtidos, pode-se concluir que a técnica de esclerometria mostrou-se capaz para identificar a homogeneidade do lote ensaiado, justificando haver possibilidades de aplicações do método à madeira.

Collisions in a liquid fluidized bed

Collisional phenomena in a solid–liquid flow were studied in terms of two parameters: the collision frequency and the coefficient of restitution. Experimental measurements of these parameters were conducted inside a liquid fluidized bed by particle tracking in an index-matched array. Collision detection was based on the use of a peak acceleration threshold of the instantaneous speed of colored tracers. The measurements of collision frequency were compared with the theoretical expression derived from the kinetic theory for granular flow (KTGF). The normal and tangential restitution coefficients were measured from the trajectories before and after contact for both particle–particle and particle–wall collisions. A comparison with previous theoretical and experimental works is presented and discussed.

Near-wall turbulent characteristics along very long thin circular cylinders

Understanding the salient physics within the turbulent boundary layer of towed thin cylinders is paramount to the Navy sonar array communities. However, the required long array length to achieve wide acoustic aperture creates unique and consistent flow characteristics that suggest simplified tangential forcing expressions suitable for design purposes. One well-known fact is that the majority of the array surface experiences very thick turbulent boundary layers (TBL) and large Reynolds numbers. The resultant statistics are most commonly dependent on the inner and outer length scales. Herein, we resolve the near-wall TBL structure under those flow conditions by large-eddy simulation. The turbulent mean-flow statistics showed near-wall consistency using only inner scaling. But both inner and outer variables were found necessary to properly scale the turbulent fluctuations. An expression for the tangential wall-friction coefficient ( C t ) indicates two distinct flow regimes as characterized by the near-wall turbulent flow structure. The respective parameters appear independent of the outer length scale. Thickening (or thinning) the cylinder near their common threshold (defined by a radius-based Reynolds number) transitioned the turbulent character between the two regimes.

The Normal and Tangential Coefficient of Restitution of Different Types of Granules

AbstractDie normale und tangentiale Stoßzahl von dominant elastischen γ‐Al2O3‐, elastisch‐plastischen Zeolith 4A‐ und dominant plastischen Natriumbenzoatgranulaten wurden mit einer elektromagnetischen Schussapparatur und einer Fallapparatur experimentell ermittelt. Der Einfluss der Feuchtebeladung auf das Stoßverhalten wurde ebenfalls bestimmt. Die normale Stoßzahl zeigte sich im untersuchten Geschwindigkeitsbereich als annähernd unabhängig von der Aufprallgeschwindigkeit während mit zunehmender Feuchtebeladung der Granulate die Stoßzahl abnahm.

Caracterização anatômica, química e física da madeira de candeia (Eremanthus erythropappus (DC.) Macleish)

Neste trabalho, objetivou-se a caracterização anatômica, química e física da madeira de candeia (Eremanthus erythropappus (DC.) Macleish). Coletaram-se cinco árvores na região de Carrancas-MG, e retirados discos ao DAP para confecção dos corpos-deprova. Realizou-se a descrição e mensuração dos principais elementos anatômicos da madeira (fibras, vasos e parênquima radial). Para a análise química, determinou-se a quantidade de extrativos totais, holocelulose, lignina e constituintes inorgânicos. O estudo físico consistiu na determinação da densidade básica e aparente da madeira e assim como a determinação das contrações tangencial, radial e volumétrica total, dos coeficientes de anisotropia e de retratibilidade. Os principais resultados encontrados para características macroscópicas foram: odor desagradável, decorrente da presença de óleo-resina, grã revessa e dura ao corte; características microscópicas: parênquima axial escasso e radial bastante fino, elementos de vasos com pontoações numerosas e muito pequenas, placas de perfuração simples, fibras libriformes curtas com parede celular espessa e presença de células de óleo no raio. Composição química: 20,89% de extrativos totais; 50,52% de holocelulose; 28,59% de lignina e 0,39% de constituintes inorgânicos. A densidade aparente foi de 0,98 g/cm³ e a básica de 0,79 g/cm³. O coeficiente de anisotropia foi igual a 1,91 e o coeficiente de retratibilidade volumétrica, 0,28%.