Azimuthal Stress Research Articles

Energy optimization of aluminum alloys on engine oil-based nanofluid flow

The growing demand for energy calls for efficient utilization of natural energy resources in developing useful work. Thermodynamic irreversibility deals with the disorderliness in any system. This work investigates the energy optimization of a cylinder experiencing stretching and rotation immersed with aluminum alloys (AA7072-AA7075) in engine oil-based nanofluid. The Maxwell nanofluid model is employed to check the thermophysical properties of nanofluids. Heat transfer occurred at the cylinder’s surface by considering the constant and prescribed temperature. Forced convection is due to a stretchable rotating boundary, while natural convection is owing to a thermal gradient in the system. The dimensionless ordinary differential equations are obtained by using the appropriate ansatz and solved numerically through the bvp4c technique. A comparison profile of constant wall temperature and prescribed surface temperature shows that entropy generation and Bejan number are reduced for the former and increased for the latter, while thermal transport exhibits an opposite behavior. The axial and azimuthal wall stress parameters diminished due to an increment in Reynolds number. The heat transport rate is comparatively higher for AA7075/Engine oil than AA7072/Engine oil.

Mean flow and Convective instability analysis of the BEK and related rotating boundary layer flows subject to a uniform static magnetic field

This study examines the convective instability of the hydromagnetic Bödewadt, Ekman, and von Kármán (BEK) rotating system under the low magnetic Reynolds number approximation. The computations for the mean flow are carried out for different magnetic parameters using MATLAB for several flows of the BEK family. The equations for the linear instability are derived and then solved through the Chebyshev-spectral method for both Type-I (Inviscid) and Type-II (viscous) modes. It is observed that the Rossby number, the Reynolds number, and the magnetic parameter characterize the stability of the hydromagnetic BEK flows. The Reynolds number is based on the dimensionless radial location at the disk while the Rossby number is the ratio of the difference between the angular speeds of fluid and disk and the angular speed of the disk. The magnetic number is the ratio of magnetic field strength and the system rotation rate. The analysis reveals a stabilizing effect of the magnetic parameter on the Type-I modes for Rossby numbers in the range [−1,1]. Further, the Type-II modes disappear upon elevating the magnetic parameter in the aforementioned range of the Rossby number. The growth rates, |αi|, also diminish upon increasing the magnetic parameter. The computations for mean flow reveal that the radial wall shear stress diminishes upon elevating the strength of the applied magnetic field. However, a reverse trend is noted for the azimuthal wall shear stress which indicates an increase in the torque on the disk with enhancing the intensity of the magnetic field.

Study of thermophoresis and Brownian motion phenomena in radial stagnation flow over a twisting cylinder

This article deals with the analysis of nanofluid flow and its thermal energy transport in the stagnation region, impinged radially on a rotating circular cylinder with magnetohydrodynamic (MHD) effect. The swirling flow is driven by the rotational motion of a circular cylinder along the z -direction. A two-phase nanofluid model, namely the Buongiorno model is utilized to determine the thermal characteristics of nanoparticles, which highlights the influence of Brownian diffusion and thermophoresis on temperature and concentration distributions. Numerical outcomes are computed by applying the built-in program bvp5c in MATLAB. The focus of this manuscript is to determine the numerical interpretations of wall stresses with their asymptotic behavior, Nusselt number, and Sherwood number against relevant parameters. The axial and azimuthal wall stress parameters are obtained as a function of twist rate at various values of Reynolds number. Furthermore, the asymptotic behavior for small Reynolds number is compared with their corresponding numerical solutions. The comparison of our result as a special case for non-electrically conducting flow is found in exact agreement with the ones in the literature. It is noticed that wall stresses are greatly affected due to an increment in Reynolds number. The thermal and mass transport phenomena is reduced due to increment in the twisting rate of the cylinder. However, the momentum of the system is inclined, and consequently, an increase in the axial and azimuthal velocities is observed. Moreover, the numerical values of heat and mass transfer rates deteriorate because of thermophoresis; however, owing to the Brownian diffusion, the former declines, and the latter progress significantly.

A Primer on CFD-DEM for Polymer-Filled Suspensions

This work reports on an evaluation of the computational fluid dynamics–discrete element method (CFD-DEM) numerical approach to study the behavior of polymer-filled suspensions in a parallel-plate rheometer. For this purpose, an open-source CFD-DEM solver is used to model the behavior of such suspensions considering different particle volume fractions and different types of fluid rheology. We first validate the numerical approach for the single-phase flow of the continuum phase (fluid phase) by comparing the fluid’s azimuthal velocity and shear stress components obtained from the open-source solver against the analytical expressions given in cylindrical coordinates. In addition, we compare the numerical torque given by the numerical procedure with analytical expressions obtained for Newtonian and power law fluids. For both cases, there is a remarkable agreement between the numerical and analytical results. Subsequently, we investigated the effects of the particle volume fraction on the rheology of the suspension. The numerical results agree well with the experimentally measured ones and show a yield stress phenomenon with the increase of the particle volume fraction.

Mathematical modeling and analysis of the thermomechanical behavior of a bimetallic spherical element during technological processing with an electromagnetic impulse

The initial-boundary problem of thermomechanics for a bimetallic spherical element under homogenous non-stationary electromagnetic action is formulated. The azimuthal component of the magnetic field strength vector, temperature, and the radial component of the displacement vector were selected as key functions. To find the key functions, the approximation of their distributions in the constituent layers of the spherical element by quadratic polynomials in the radial variable is proposed. This approximation makes it possible to accurately satisfy the specified boundary conditions both on the surfaces of this element and on the surface of the connection of the component layers, where ideal electromagnetic, thermal and mechanical contacts take place. The coefficients of the polynomials approximating the key functions in the component layers of the spherical element are given by a linear combination of functions describing all given boundary conditions and integral characteristics of the key functions on both component layers. As a result, the original initial-boundary value problems for the defining functions are reduced to Cauchy problems for their integral (summed over the package of layers) characteristics. With the use of Laplace transformation in time, the general solutions of these problems under homogeneous non-stationary electromagnetic action are recorded. The change in time of radial and azimuthal stresses and stress intensity was numerically analyzed by technological processing with an electromagnetic impulse, as well as the performance and properties of the contact connection of the bimetallic spherical element were investigated.

Radial stagnation flow of a micropolar fluid over a twisting cylinder

AbstractAn investigation is accomplished to analyze the problem of radial stagnation flow of micropolar fluid radially impinging over a twisting cylinder. The impact of the twisting rate σ, Reynolds number R on the flow under the concentration of rotation of microelements on the flow is predicted in this research. By utilizing similarity variables, the leading flow equations of micropolar fluid are transformed into ordinary ones. A numerical scheme called the Keller–Box technique is applied to acquire the numerical results. The consequences of the micro rotational components on the twisting parameter are analyzed. Important characteristics of this flow are studied for different values of and σ. The wall shear stresses are also obtained. The interesting feature of axial and azimuthal wall shear stress parameters under the concentration of micro rotation of fluid elements are obtained and discussed.

Multi-scale nonlinear stress analysis of Nb3Sn superconducting accelerator magnets

A multi-scale nonlinear procedure to analyze the stress in Nb3Sn superconducting accelerator magnets is presented to address one of the most challenging obstacles currently facing the successful development of high-field superconducting magnets—the issue of stress management. The study demonstrates that gasket materials (special nonlinear materials) are capable of modeling the complex nonlinear deformation behavior of insulation layers within the Nb3Sn coil block and that Hill materials (orthotropic materials utilizing the Hill yield criterion) are suitable to enable homogenization of the filamentary regions and the resin-impregnated Nb3Sn Rutherford cables. With the whole magnet under preload, cool-down, and Lorentz forces, the nonlinear behavior of the Nb3Sn coil was simulated, in three orthongonal axes, using the combined properties of the gasket materials (insulation layers) and Hill materials (resin-impreganted cable). The procedure makes very few assumptions with regard to material properties because it incorporates actual measured stress–strain curves in the analysis. The coil was simulated to the level of detail of the insulation layers and resin-impregnated cables. The computed compressive azimuthal stresses of the cables were used to assess stress-induced performance degradation. Through submodeling, the area-weighted average axial strains of the strands were computed and employed to evaluate the strain-induced performance degradation. The overall performance degradation of the Nb3Sn coil was thus obtained, and this information was subsequently used to guide the design of the overall magnet. Besides Nb3Sn magnets, this versatile procedure can also be employed in the design of LTS, HTS, and room temperature magnets or of any structures ultilizing composite materials; specifically, it can be used to manage the stress and strain of HTS fusion magnets.

Thermal case study on linearly twisting cylinder: A radial stagnation point flow of nanofluid

The thermal case study is performed to inspect heat transfer aspects for radial stagnation point flow. For this phenomenon, the study assumes a linear twisting cylinder for the heated viscous nanofluid and the arrangement is investigated among the torsionally rotating cylinders and radial stagnation point flow. The dimensionless torsion rate σ , the volume fraction of nanoparticles φ and the Wangs Reynolds number R are three possible parameters that are articulated in the study. The BVP-Midrch routine integrated with the Maple software is used to obtain numerical results of the governing flow field equations. It is found that the axial wall stress f ″ ( 1 ) is a very weak function of σ , a weak function of φ and a strong function of R . Also, the azimuthal wall stress g ′ ( 1 ) is a strong function of R and shows a practically decreasing behavior and is linear with σ for the starting value g ′ ( 1 ) = 0 at σ = 0 . It is seen that the temperature gradient admits trifling variation for the positive iteration in torsional rate. Furthermore, the heat flux at surface admits direct relation towards volume fraction of nanoparticles.

Irreversibility process analysis for SiO2-MoS2/water-based flow over a rotating and stretching cylinder

Entropy is the measure of the amount of energy in any physical system that is not accessible for the useful work, which causes a decrease in a system's thermodynamic efficiency. The idea of entropy generation analysis plays a vital role in characterizing the evolution of thermal processes and minimizing the impending loss of available mechanical power in thermo-fluid systems from an analytical perspective. It has a wide range of applications in biological, information, and engineering systems, such as transportation, telecommunication, and rate processes. The analysis of the entropy generation of axisymmetric magnetohydrodynamic hybrid nanofluid /water flow induced by rotating and stretching cylinder in the presence of heat radiation, ohmic heating, and the magnetic field is focus of this study. Thermal energy transport of hybrid nanofluids is performed by applying the Maxwell model. Heat transport is carried out by using convective boundary condition. The dimensionless ordinary differential equations are acquired by similarity transformations. The numerical solution for these differential equations is obtained by the bvp4c program in MATLAB. A comparison between nanofluid and hybrid nanofluid is made for flow field, temperature, and entropy generation. Comparison of nanofluid flow with hybrid nanofluid flow exhibits a higher rate of heat transmission, while entropy generation exhibits the opposite behavior. It is observed that the flow and heat distribution increase as the solid volume fraction's value grows. An increase in entropy is indicated by augmentation in the Brinkman number and temperature ratio parameter, but the Bejan number shows a declining trend. Furthermore, outcomes of the Nusselt number for hybrid nanofluid and nanofluid are calculated for various parameters. It is noticed that the Nusselt number is reduced for enlarging the magnetic field and Eckert number. The axial and azimuthal wall stress parameters are declined by augmenting the Reynolds number.

Stability of an oscillatory Taylor–Couette flow in an upper convected Maxwell fluid

The stability of pulsed bi-dimensional flow between two co-oscillating cylinders in a linear Maxwell fluid was studied by Riahi et al. [J. Soc. Rheol. 42, 321–327 (2014)]. In the present paper, we revisit this flow configuration with emphasis on the effect of the non-linear terms in the constitutive equation of the model, measured by the Weissenberg number, on the dynamics of the system. Under these assumptions and using the upper convected Maxwell derivative, we examine this model to large amplitude oscillatory shear giving rise to the appearance, in comparison to the linear Maxwell model, of the azimuthal normal stress in the basic state. Using the spectral method and the Floquet theory for the spatiotemporal resolution of the obtained eigenvalue problem, numerical results exhibit numerous classes of Taylor vortex flows depending on the order of magnitude of the fluid elasticity. The resulting stability diagram consists of several branches intersecting at specific frequencies where two different Taylor vortex flows simultaneously branch off from the basic state. This feature is accompanied by the occurrence of several co-dimension two bifurcation points besides jumps/drops in the corresponding critical wave number. In addition, it turns out that the elasticity produces strong destabilizing and stabilizing effects in the limit of high and low frequency regimes, respectively, attributed solely to the non-linearities considered by the rheological model.

ГИДРОДИНАМИКА ТУРБУЛЕНТНЫХ ПОТОКОВ В ТВС БЫСТРЫХ РЕАКТОРОВ (ПОЛЕ СКОРОСТИ И МИКРОСТРУКТУРА ТУРБУЛЕНТНОСТИ)

The article describes the factors under the influence of which the formation of thermohydraulic characteristics occurs in the fuel assemblies of the core of fast reactors with liquid metal cooling. It is shown that one of the most important factors is a complex multiply connected geometry of a stochastic nature, subject to deformation during the campaign under the influence of temperature irregularities and radiation effects. The paper presents and analyzes the results of experimental and computational studies of the velocity field and shear stress, the microstructure of turbulence, momentum transfer in the central and peripheral regions of fuel assemblies without and with displacers, as well as in the case of deformation of the lattice of rods. The intensification of turbulent momentum transfer in the channels in the azimuthal direction in the area of the gaps between the rods is demonstrated. The anisotropy coefficient of turbulent momentum transfer reaches 30-40 units. The performed analysis indicated a significant difference in the calculated in the framework of semi-empirical models of turbulent transfer and experimental dependences of the coefficients of turbulent transfer of momentum in the radial and azimuthal directions and the coefficients of anisotropy of turbulent transfer of momentum in rod bundles. The results of an open benchmark on the thermohydraulics of fuel assemblies showed that common commercial computational thermohydraulic codes only approximately describe the experimental data. It is shown that the intensification of turbulent momentum transfer in the channels of rod assemblies is due to the appearance of large-scale turbulent momentum transfer (secondary flows). The contribution of large-scale turbulent momentum transfer to the kinetic energy of turbulent pulsations, azimuthal turbulent shear stresses, and turbulent momentum transfer coefficients in rod assemblies is calculated. An empirical dependence of the coefficient of interchannel turbulent impulse exchange in bundles of smooth rods is obtained, on the basis of a semi-empirical model, data on interchannel turbulent impulse exchange in assemblies of smooth rods are generalized, and the intensification of interchannel turbulent exchange in close lattices of rods is explained. Data on hydraulic resistance in bundles of smooth rods are analyzed. The tasks of further research are discussed.

Influence of Diamond Smoothing on the Surface Layer of a 30ХГСН2А-ВД High-Strength Steel Workpiece

The influence of the smoothing force, the tool radius, the machining speed, and the supply on the distribution of azimuthal and axial residual stress, the microhardness, and the depth of strain hardening is analyzed for the machining of 30ХГСН2А-ВД steel by ASB-1 synthetic diamond. Empirical equations for these parameters are presented.

Analysis of asymptotic solutions for non-Newtonian fluid flow between two parallel discs with dissimilar in-plane motion

The investigation on the flow of non-Newtonian (Casson) fluid is made between parallel discs, executing in-plane motion in different manners. The fluid motion is induced due to upper radially stretching or shrinking disc at the rate a and lower rotating disc at an angular velocity Ω, with plate separation h. The nondimensional Navier–Stokes (NS) equations are reduced to coupled ordinary differential equations (ODEs) by using a suitable similarity reduction. The effects of the Casson parameter, Reynolds number and rotation parameter are discussed. The numerical solutions of radial pressure gradient and shear stresses are found and compared with low R series solutions and large R asymptotic manners. Velocity profiles indicate the regions of zero azimuthal and radial shear stresses which are also discussed in detail. This paper represents the first study of non-Newtonian (NN) fluid flow in this geometry i.e. flow between parallel discs in which both execute in-plane motion in different manners.

Measurements of the Effects of Compressive Loading on the Narrow Side of the HTS TAPE

Brookhaven National Laboratory (BNL) is involved in building high field magnets wound using Second Generation (2G) High Temperature Superconductor (HTS) tape. Certain magnet designs demand a load on the narrow edge of the tape approaching 170 MPa. While significant experimental data is available on the performance of the 2G HTS tape under radial and azimuthal stresses [1] , limited experimental data is available for the load on the narrow edge of the tape. To validate the design of a 25 Tesla, 100 mm cold bore Non-Insulated (NI) HTS solenoid, a series of compressive tests were performed on coils wound using 12 mm 2G HTS tape from SuperPower with an Hastelloy substrate thickness of 50 µm and varying copper stabilizer layer thicknesses of 65 μm, 40 μm, and 20 μm. This paper summarizes the initial design, several iterations, and results in the development of this test to simulate the conditions of the coils in a solenoid energized to 25 Tesla.

Modeling the axially symmetric fracture evolution in deep-hole blasting

When blasting deep-hole charges in a brittle rock mass, rock disintegration mainly proceeds due to development of radial fractures induced by dramatic tensile azimuthal stresses in the vicinity of a charge and along its surface. Coincidently, appreciable tensile stresses are generated by blasting nearby ends of deep charges along their axes. Such stresses can initiate a rise and development of axially symmetric fractures. In the present paper the computational model is set forth for development of axially symmetric fractures nearby free surface in the vicinity of a charge end. Calculations of a fracture shape and size are reported.

Direct numerical simulation of low Reynolds number turbulent swirling pipe flows

Direct numerical simulation of swirling pipe flows is performed to investigate the effects of swirl on turbulence statistics as well as the inertial regime. The swirling motion is imposed via a constant azimuthal body force coupled with a body force in the axial direction that drives the flow. The friction Reynolds number is Re τ ≈ 170 with a pipe length of 8 π δ (where δ is the pipe radius). The simulations are performed at various swirl numbers. The swirling motion introduces additional drag into the flow and reduces the bulk flow rate for the swirl strengths investigated in this study. We also show from our data as well as via the mean equations that similar to the total axial stress, the total azimuthal stress when normalized by the azimuthal friction velocity follows a linear decrease from wall to the pipe centerline independent of swirl strength. In the inertial regime, with negligible viscous effects, the linear relationship holds for the turbulent shear stresses. We derive the modified axial mean momentum equation, which when studied alongside the azimuthal momentum equation shows that increasing the swirl strength increases the inertial region in the pipe by pushing the beginning of the inertial region closer to the wall. This effect is governed by the axial viscous forces rather than the azimuthal ones.

Radial Stagnation Flow on a Twisting Cylinder

The problem of stagnation-point flow impinging radially on a linearly twisting cylinder is considered. This advances previous work on the motion outside a cylinder undergoing linear torsional motion. The problem is governed by a Reynolds number R and a dimensionless torsion rate σ. Numerical calculations are carried out using the ODEINT program, and convergence of the shooting method is obtained using the MNEWT program. The radial and azimuthal wall shear stresses are found over a range of R and σ, and radial and azimuthal velocity profiles at σ={0,1,2} are presented for various values of R. The interesting feature is that the axial wall shear stress parameter f″(1) is a very weak function of σ while the azimuthal wall shear stress parameter g′(1) is a strong function of σ although both stress parameters are a strong function of R.

Hydrodynamics of a weakly curved channel

The underlying mechanism of curvature induced helicoidal flow in a weakly curved channel intrigues researchers. Here, we explore the hydrodynamics of weakly curved channels, defined by the limiting values of the curvature ratio (ratio of channel half-width to radius of curvature) and aspect ratio (ratio of channel half-width to average flow depth) as 0.1 and 10, respectively. The three-dimensional continuity and momentum equations are solved analytically, involving the appropriate boundary conditions and closing the system by means of the turbulence closure model and the indispensable fluid constitutive formulations. The skewed filament of the azimuthal velocity component, emanating from the effects of curvilinear streamlines, is introduced into the analysis, for the first time, to address the flow asymmetry across the flow cross section. The modification of the radial slope due to the presence of the stress term in the radial momentum balance is accomplished by a slope correction factor, which turns out to be a weak function of the reciprocal of the power-law exponent. The attenuation of the azimuthal shear stress component, resulting from the skewed velocity profile, is characterized by the damping function to provide a quantitative insight into the redistribution of the primary flow momentum. The velocity field reveals that the flow circulation (on the flow cross-sectional plane) about the azimuthal axis and the flow helicity strengthen with an increase in the curvature ratio. The variation of the radial free surface profile is more sensitive to the flow Froude number than to the curvature ratio. The evolutions of the stress field with several key parameters are also examined.

Assessing shale mineral composition: From lab to seismic scale

Shales have always been a difficult target for drilling of deviated and horizontal wells. In the presence of azimuthal stress fields, inclined boreholes in smectite-rich shales exhibit geomechanical instabilities and can result in borehole failure. The complex geology of the major gas fields in the Northern Carnarvon Basin on the North West Shelf of Australia makes it necessary to drill deviated wells through the smectite-rich shale seal extending more than 1 km in thickness. Predicting the mineralogical composition of shales in the area is therefore crucial for the success of drilling operations related to hydrocarbon exploration and production. Here we introduce a novel workflow that combines seismic data, well logs, and laboratory measurements to rapidly infer smectite content in shale. The workflow is applied to the Duyfken 3D seismic survey in the central part of the Northern Carnarvon Basin. The results of our quantitative interpretation are verified against the laboratory X-ray diffraction measurements from the test well that was not used for interpretation, and they match the test data well within the determined uncertainty bounds.

Rock heterogeneity at the centimeter scale, proxies for interfacial weakness, and rock strength-stress interplay from downhole ultrasonic measurements

Analysis of data acquired with an ultrasonic rotating device lowered inside a vertical well of a highly laminated, kerogen-rich, carbonate source formation reveals centimeter-scale rock heterogeneities. The high-frequency (50–600 kHz) measurement used consists of a pulse-echo modality that yields a high-resolution (millimeter-scale) borehole shape and a pitch-catch modality with one transmitting and two receiving transducers that provide compressional (P) and shear (S) slownesses (depth-versus-azimuth) images estimated from signals propagating in the near-wellbore region as compressional head waves and pseudo-Rayleigh surface waves. The slownesses are compared with their counterparts estimated from a lower-frequency (1–15 kHz) sonic measurement logged in the same well interval. The sonic P and S logs are seen to average the centimeter-scale slowness spatial variation between compliant and stiff laminates at a scale larger than 30 cm (1 ft). This is also accompanied by a reduction in resolution of the slowness contrast, which markedly reduces the spectrum of rock-mechanical property variations that are estimated from the ultrasonic data. Further, ultrasonic images of the P and S slownesses and borehole acoustic caliper reveal a host of features associated with rock geomechanics in the near-wellbore and that inform on a first-order basis the interplay between rock strength and local stress regime, as affected by the lamination. The features include breakouts present in the stiffer limestone layers and their arrest at the intersection with the compliant siltstone layers, as well as azimuthal P and S slowness variations indicative of azimuthal stress concentrations, but without the appearance of breakouts. The ultrasonic borehole shape data also identify compliant thin layers that retract into the formation by amounts that are commensurate with their Young’s modulus, suggesting a proxy for detecting and characterizing thin-layer weakness in situ.