Effects of multiple shapes for steady flow with transformer oil+Fe_(3)O_(4)+TiO_(2) between two stretchable rotating disks

In this study,we examine the effects of various shapes of nanoparticles in a steady flow of hybrid nanofluids between two stretchable rotating disks.The steady flow of hybrid nanofluids with transformer oil as the base fluid and Fe_(3)O_(4)+TiO_(2)as the hybrid nanofluid is considered.Several shapes of Fe_(3)O_(4)+TiO_(2)hybrid nanofluids,including sphere,brick,blade,cylinder,and platelet,are studied.Every shape exists in the same volume of a nanoparticle.The leading equations(partial differential equations(PDEs))are transformed to the nonlinear ordinary differential equations(ODEs)with the help of similarity transformations.The system of equations takes the form of ODEs depending on the boundary conditions,whose solutions are computed numerically by the bvp4c MATLAB solver.The outputs are compared with the previous findings,and an intriguing pattern is discovered,such that the tangential velocity is increased for the rotation parameter,while it is decreased by the stretching values because of the lower disk.For the reaction rate parameter,the concentration boundary layer becomes shorter,and the activation energy component increases the rate at which mass transfers come to the higher disk but have the opposite effect on the bottom disk.The ranges of various parameters taken into account are Pr=6.2,Re=2,M=1.0,φ_(1)=φ_(2)=0.03,K=0.5,S=-0.1,Br=0.3,Sc=2.0,α_(1)=0.2,γ=0.1,E_(n)=2.0,and q=1.0,and the rotation factor K is within the range of 0 to 1.

Finite deformation analysis of the rotating cylindrical hollow disk composed of functionally-graded incompressible hyper-elastic material

The deformations and stresses of a rotating cylindrical hollow disk made of incompressible functionally-graded hyper-elastic material are theoretically analyzed based on the finite elasticity theory.The hyper-elastic material is described by a new micro-macro transition model.Specially,the material shear modulus and density are assumed to be a function with a power law form through the radial direction,while the material inhomogeneity is thus reflected on the power index m.The integral forms of the stretches and stress components are obtained.With the obtained complicated integral forms,the composite trapezoidal rule is utilized to derive the analytical solutions,and the explicit solutions for both the stretches and the stress components are numerically obtained.By comparing the results with two classic models,the superiority of the model in our work is demonstrated.Then,the distributions of the stretches and normalized stress components are discussed in detail under the effects of m.The results indicate that the material inhomogeneity and the rotating angular velocity have significant effects on the distributions of the normalized radial and hoop stress components and the stretches.We believe that by appropriately choosing the material inhomogeneity and configuration parameters,the functionally-graded material(FGM)hyper-elastic hollow cylindrical disk can be designed to meet some unique requirements in the application fields,e.g.,soft robotics,medical devices,and conventional aerospace and mechanical industries.

Novel scheme of high precision inertial measurement for high-speed rotating carriers

In order to satisfy the requirement of high precision measurement in a high dynamic environment, a kind of gyro aided multi-accelerometer inertial measurement unit （GAMA-IMU） with six accelerometers and two gyros （6A2G） was proposed in this paper. The available configurations have the problem of low measurement precision In a high dynamic environment due to channel coupling. The three channels were decoupled when calculating the angular velocity in the proposed configuration. The yawing and pitching angular velocity were directly measured by gyros, while only the rolling angular velocity was obtained by the GAMA-IMU indirectly from the rolling angular acceleration and quadratic component of rolling angular velocity. Then a single channel rolling angular velocity calculation model was established and the extended Kalman filter （EKF） was used to do state esti- mation. Simulations were carried out and results indicated that the calculation precision of the proposed 6A2G configuration could meet the demand of high precision measurement for a high-speed rotating carrier.

Comprehensive evaluations of heat transfer performance with conjugate heat dissipation effect in high-speed rotating free-disk modeling of aero-engines

Thermal boundary conditions of the turbine disk cavity system are of great importance in the design of secondary air systems in aero-engines.This study aims to investigate the complex heat transfer mechanisms of a rotating turbine disk under high-speed conditions.A high-speed rotating free-disk model with Dorfman empirical solutions is developed to evaluate the heat transfer performance considering various factors.Specifically,the influence of compressibility,variable properties,and heat dissipation is determined using theoretical and numerical analyses.In particular,a novel combined solution method is proposed to simplify the complex heat transfer problem.The results indicate that the heat transfer performance of a free disk is primarily influenced by the rotating Mach number,rotating Reynolds number,Rossby number,and wall temperature ratio.The heat transfer temperature and Nusselt number of the free disk are strongly correlated with the rotating Mach number and rotating Reynolds number.Analysis reveals that heat dissipation is a critical factor affecting the accurate evaluation of the heat transfer performance of the turbine disk.Thus,the combined solution method can serve as a reference for future investigations of flow and heat transfer in high-speed rotating turbine disk cavity systems in aero-engines.

CO2 absorption performance in a rotating disk reactor using DBU-glycerol as solvent

Gas–liquid mass transfer of rotating disk reactor was studied in CO2 absorption using 1,8-diazabicyclo-[5.4.0]-undec-7-ene(DBU)-glycerol solution as solvent. Effects of the rotating disk structure and various operation parameters on the CO2 absorption rate and CO2 removal efficiency were investigated. The rotating disk with optimal holes is conducive to mass transfer of CO2 and the formation of thin liquid film at the opening increases the gas–liquid contact area. With the increase of rotating speed, the liquid flow pattern on the rotating disk surface changes from thin film flow to separated streams and creates extra liquid lines attached to the rim of the disk,which leads to a very complicated change on the CO2 absorption rate and CO2 removal efficiency. The overall gas-phase mass transfer coefficient increases 138% as the rotating speed increasing from 250 to 1400 r·min^-1.Increasing temperature from 298 to 338 K can enhance the CO2 absorption rate due to lowering the viscosity of the solvent. The rate-determined step for the absorption is focused on the gas side. The rotating disk reactor can effectively enhance the absorption of CO2 with viscous DBU-glycerol solvents.

Numerical Solution for Accelerated Rotating Disk in a Viscous Fluid

The problem of a disk rotating in a viscous fluid has been investigated. The disk is accelerated with angular velocity proportional to time. Employing suitable similarity transformations the governing partial differential equations are transformed in to ordinary differential form. The resulting equations are solved numerically using SOR method and Simpson’s (1/3) rule. The results have been improved by using Richardson’s extrapolation. The effect of the non-dimensional parameter s which measures unsteadiness is observed on velocity components, skin friction coefficient and torque of the disk.

Chemically reactive and radiative von Kármán swirling flow due to a rotating disk

A new mathematical model is presented to study the heat and mass transfer characteristics of magnetohydrodynamic(MHD) Maxwell fluid flow over a convectively heated stretchable rotating disk. To regulate the fluid temperature at the surface, a simple isothermal model of homogeneous-heterogeneous reactions is employed. The impact of nonlinear thermal radiative heat flux on thermal transport features is studied. The transformed nonlinear system of ordinary differential equations is solved numerically with an efficient method, namely, the Runge-Kutta-Felberg fourth-order and fifth-order(RKF45)integration scheme using the MAPLE software. Achieved results are validated with previous studies in an excellent way. Major outcomes reveal that the magnetic flux reduces the velocity components in the radial, angular, and axial directions, and enhances the fluid temperature. Also, the presence of radiative heat flux is to raise the temperature of fluid. Further, the strength of homogeneous-heterogeneous reactions is useful to diminish the concentration of reaction.

Mass Transfer of MHD Nanofluid in Presence of Chemical Reaction on A Permeable Rotating Disk with Convective Boundaries, Using Buongiorno’s Model

This communiquéis opted to study the flow of nanofluid because of heated disk rotation subjected to the convective boundaries with chemical reaction of first order.Wherein Buongiorno’s model for nanofluids is used due to its wide range of applications and the rotating disk under investigation is permeable.Small magneto Reynolds parameter and boundary layer assumptions are carried out to formulate the problem.The system of nonlinear partial differential equations governing the flow problem is converted into the set of ordinary differential equations by using particular relations known as Von Karman transformations.The complicated set of coupled ordinary differential equations with complicated boundary conditions is set to solve by an analytical technique Homotopy Analysis Method(HAM).Whereby the results obtained by the aforementioned method are provided analytically and analyzed graphically.Also validation of the work is confirmed by providing comparison of previous works in tabular form.Effect of chemical reaction parameter on mass transfer rate is also highlighted tabularly for its increament.Nusselt and Sherwood numbers calculated and compared to the like literature and found in good agreement.

Prediction of mass transfer coefficients in an asymmetric rotating disk contactor using effective diffusivity

Mass transfer characteristics have been investigated in a 113 mm diameter asymmetric rotating disk contactor of the pilot plant scale for two different liquid–liquid systems. The effects of operating parameters including rotor speed and continuous and dispersed phase velocities on the volumetric overall mass transfer coefficients are investigated. The results show that the mass transfer performance is strongly dependent on agitation rate and interfacial tension, but only slightly dependent on phase flow rates. In this study, effective diffusivity is used instead of molecular diffusivity in the Grober equation for estimation of dispersed phase overall mass transfer coefficient.The enhancement factor is determined experimentally and there from an empirical expression is derived for prediction of the enhancement factor as a function of Reynolds number. The predicted results compared to the experimental data show that the proposed correlation can efficiently predict the overall mass transfer coefficients in asymmetric rotating disk contactors.

Comprehensive investigation of stress intensity factors in rotating disks containing three-dimensional semi-elliptical cracks

Initiation and propagation of cracks in rotating disks may cause catastrophic failures. Therefore, determination of fracture parameters under different working con- ditions is an essential issue. In this paper, a comprehensive study of stress intensity factors （SIFs） in rotating disks containing three-dimensional （3D） semi-elliptical cracks subjected to different working conditions is carried out. The effects of mechanical prop- erties, rotational velocity, and orientation of cracks on SIFs in rotating disks under cen- trifugal loading are investigated. Also, the effects of using composite patches to reduce SIFs in rotating disks are studied. The effects of patching design variables such as mechanical properties, thickness, and ply angle are investigated separately. The modeling and analytical procedure are verified in comparison with previously reported results in the literature.

Analytical and Numerical Solutions for a Rotating Annular Disk of Variable Thickness

In this paper, the analytical and numerical solutions for rotating variable-thickness solid disk and numerical solution for rotating variable-thickness annular disk are presented. The outer edge of the solid disk and the inner and outer edges of the annular disk are considered to have clamped boundary conditions. Two different cases for the radially varying thickness of the solid and annular disks are given. The numerical solution as well as the analytical solution is available for the first case of the solid disk while the analytical solution is not available for the second case of the annular disk. Both analytical and numerical results for displacement and stresses will be investigated for the first case of radially varying thickness. The accuracy of the present numerical solution is discussed and its ability of use for the second case of radially varying thickness is investigated. Finally, the distributions of displacement and stresses will be presented and the appropriate comparisons and discussions are made at the same angular velocity.

Visualization of Traveling Vortices in the Boundary Layer on a Rotating Disk under Orbital Motion

The objective of this study is to experimentally visualize traveling vortices in the boundary layer on a rotating disk under orbital motion. The orbital radius is half of the disk’s diameter (200 mm) and the maximum speed of orbital motion is 500 revolutions per minute. The Reynolds number in the pure-rotation case is 2.77 × 105. The characteristics of two types of traveling vortices are visualized by a smoke-wire method. The first type is transition vortices. In the pure-rotation case, they arise at circumferentially equal intervals, and are not traveling but stationary relative to the rotational disk. The result of visualization of this type shows that the intervals between transient vortices change in a circumferential direction, or in an orbital radial direction, on the rotating disk under orbital motion. The second type is new arc-shaped vortices that correspond to low-frequency disturbances. As orbital speed increases, the radial traveling velocities of the low-frequency disturbances increase and the intervals between low-frequency disturbances decrease.

An Evaluation of Metronidazole Degradation in a Plasma-Assisted Rotating Disk Reactor Coupled with TiO2 in Aqueous Solution

Pollution involving pharmaceutical components in bodies of water is an increasingly serious environmental issue.Plasma discharge for the degradation of antibiotics is an emerging technology that may be relevant toward addressing this issue.In this work,a plasma-assisted rotating disk reactor(plasma-RDR)and a photocatalyst—namely,titanium dioxide(TiO_(2))—were coupled for the treatment of metronidazole(MNZ).Discharge uniformity was improved by the use of a rotating electrode in the plasma-RDR,which contributed to the utilization of ultraviolet(UV)light radiation in the presence of TiO_(2).The experimental results showed that the degradation efficiency of MNZ and the concentration of generated hydroxyl radicals respectively increased by 41%and 2.954 mg∙L^(-1) as the rotational speed increased from 0 to 500 r∙min^(-1).The synergistic effect of plasma-RDR plus TiO_(2) on the generation of hydroxyl radicals was evaluated.Major intermediate products were identified using three-dimensional(3D)excitation emission fluorescence matrices(EEFMs)and liquid chromatography-mass spectrometry(LC-MS),and a possible degradation pathway is proposed herein.This plasma-catalytic process has bright prospects in the field of antibiotics degradation.

Recovery of Hg(Ⅱ)from aqueous solution by complexation-ultrafiltration using rotating disk membrane and shear stability of PMA-Hg complex

Copolymer of acrylic acid and maleic acid(PMA)was used to remove Hg^2+from aqueous solution by complexation-ultrafiltration(C-UF)through rotating disk membrane(RDM).The effects of P/M(mass ratio of PMA to metal ions),pH and rotation speed(N)on the interception of Hg^2+were investigated.The interception could reach 99.7%at pH 7.0,P/M 6 and N less than 1890 r/min.The shear stability of PMA-Hg complex was studied by RDM.The critical rotation speed,at which the interception starts to decrease,was 1890 r/min,and the critical shear rate,the smallest shear rate at which PMA-Hg complex begins to dissociate,was 2.50×10^5s^-1 at pH 7.0.Furthermore,the critical radii were obtained at different rotation speeds and pHs.The results showed that the critical radius decreased with the rotation speed and increased with pH.Shear induced dissociation coupling with ultra?ltration(SID-UF)was efficiently used to recover Hg^2+and PMA.

Flow of a Second-Grade Fluid between Eccentric Rotating Porous Disks in the Presence of a Magnetic Field

This paper is concerned with the steady flow of a second-grade fluid between two porous disks rotating eccentrically under the effect of a magnetic field. A perturbation solution for the velocity field is presented under the assumption that the second-grade fluid parameter β is small. It is also studied the effect of all the parameters on the horizontal force per unit area exerted by the fluid on the disks. It is found that the x- and y-components of the force increase and decrease, respectively, when the second-grade fluid parameter β and the Hartmann number M increase. It is seen that the forces in the x- and y-directions on the top disk increase with the increase of the suction/injection velocity parameter P but those on the bottom disk decrease. It is shown that the force acting on the top disk is greater than that acting on the bottom disk in view of the axial velocity in the positive z-direction. It is observed that the increase in the Reynolds number R leads to a rise in the horizontal force.

Model of Rotation Accuracy of High-Speed Spindles on Ball Bearings

For the purpose to improve a design quality of high-speed spindle units, we have developed mathematical models and software to simulate a rotation accuracy of spindles running on ball bearings. In order to better understand the mechanics of ball bearings, the dynamic interaction of ball bearings and spindle unit, and the influence of the bearing imperfections on the spindle rotation accuracy, we have carried out computer aided analysis and experimental studies. When doing this, we have found that the spindle rotation accuracy can vary drastically with rotational speed. The influence of bearing preload has a secondary importance. Comparison of the results of these studies has demonstrated adequacy of the models developed to the real spindle units.

A class of exact solutions for the incompressible viscous magnetohydrodynamic flow over a porous rotating disk

The present paper is concerned with a class of ex- act solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous electrically conducting fluid flow due to a porous disk rotating with a constant angu- lar speed. The three-dimensional hydromagnetic equations of motion are treated analytically to obtained exact solutions with the inclusion of suction and injection. The well-known thinning/thickening flow field effect of the suction/injection is better understood from the constructed closed form veloc- ity equations. Making use of this solution, analytical formu- las for the angular velocity components as well as for the permeable wall shear stresses are derived. Interaction of the resolved flow field with the surrounding temperature is fur- ther analyzed via the energy equation. The temperature field is shown to accord with the dissipation and the Joule heating. As a result, exact formulas are obtained for the temperature field which take different forms corresponding to the condi- tion of suction or injection imposed on the wall.

Numerical Simulations of Snow Accumulation in the Bogie Region of a Train Considering Snow Particle Rotation

To investigate the influence of snow particle rotational motion on the accumulation of snow in the bogie region of high-speed trains,an Euler‒Lagrange numerical approach is adopted.The study examines the effects of snow particle diameter and train speed on the ensuing dynamics.It is shown that considering snow particle rotational motion causes significant deviation in the particle trajectories with respect to non-rotating particles.Such a deviation increases with larger snow particle diameters and higher train speeds.The snow accumulation on the overall surface of the bogie increases,and the amount of snow on the vibration reduction device varies greatly.In certain conditions,the amount of accumulated snow can increase by several orders of magnitudes.

INTELLIGENT INTEGRATION CONTROL OF ROTATING DISK VIBRATION

The rotating disk is a basic machine part that is u sed widely in industry. The motion equation is transformed into the dynamic equa tion in real modal space. The personating intelligent integration is introduced to improve the existing control method. These modes that affect the transverse vibration mainly are included to simulate the vibration of rotating disk, and two methods are applied separately on condition that the sensor and the ac tuator are collocated and non collocated. The results obtained by all sided si mulations show that the new method can obtain better control effect, especially when the sensor and the actuator are non collocated.

Darcy-Forchheimer flows of copper and silver water nanofluids between two rotating stretchable disks

This investigation describes the nanofluid flow in a non-Darcy porous medium between two stretching and rotating disks. A nanofluid comprises of nanoparticles of silver and copper. Water is used as a base fluid. Heat is being transferred with thermal radiation and the Joule heating. A system of ordinary differential equations is obtained by appropriate transformations. Convergent series solutions are obtained. Effects of various parameters are analyzed for the velocity and temperature. Numerical values of the skin friction coefficient and the Nusselt number are tabulated and examined. It can be seen that the radial velocity is affected in the same manner with both porous and local inertial parameters. A skin friction coefficient depicts the same impact on both disks for both nanofluids with larger stretching parameters.