Dimensionless Rotational Speed Research Articles

Entropy generation due to mixed convective transport from a rotating porous cylinder inside a shear-driven cavity

The mixed convective transport in a vertically shear-driven square cavity with a rotating circular porous cylinder is investigated numerically in two dimensions. This study aims to enhance the understanding of heat distribution within a closed environment containing intricate electronic systems and heat exchangers by employing a porous media modeling approach. The vertical walls of the enclosure are kept isothermal, while both the horizontal walls are assumed to be adiabatic. Upward progress is being made by the left wall at a constant translational speed. The porous circular cylinder is inserted within the square cavity concentrically, which is then rotated both clockwise and counter-clockwise. While the Reynolds number based on the motion of the lid is maintained constant at Re = 100, the porosity of the cylinder fluctuates in accordance with the Darcy number range 10−6 ≤ Da ≤ 10−2 The streamline and the isotherm patterns for a range of controlling factors, including the Richardson number (0.5 ≤ Ri ≤ 10) and the dimensionless rotational speed ( − 5 ≤ Ω ≤ 5 ) are used to show how the flow and the thermal fields within the enclosure evolve. Additionally, the entropy generation is calculated and compared for the above mentioned parameters. The irreversibility generation as well as the flow and the heat transfer phenomena are observed to be significantly influenced by the rotation and the porosity of the cylinder.

Experimental and numerical investigation on the wake flow and vortex shedding of a rotating circular cylinder

When fluid passes through a still cylinder, alternate shedding vortices are formed on the two sides of the cylinder in the wake. Regarding a rotating circular cylinder, the rotation can affect the wake flow and vortex shedding pattern. To investigate the wake flow and surface pressure characteristics of a rotating cylinder at different rotational speeds, wind tunnel tests and numerical simulation methods through Fluent were used. The dimensionless rotational speed was discussed for its impact on the vortex shedding intensity and pattern. Additionally, the correlation between the cylinder surface wind pressure and the vortex shedding pattern was analyzed. The results of this study provide useful insights into the mechanisms underlying the vortex shedding phenomenon and the effects of rotational speed on the wake flow and surface pressure of a rotating cylinder. The results show that an increase in the dimensionless rotational speed will change the characteristics of the wind pressure distribution, leading to the variation in aerodynamic coefficients. On the other hand, the vortex shedding characteristics of the wake flow will also be affected, with changes in the vortex shedding pattern and direction, thereby changing the characteristics of the wake deviation angle and correlation. Based on the analysis of wake flow speed power spectrum characteristics and the Reynolds number effect, the mechanism of the vortex shedding change caused by flow transitions is speculated and verified by numerical simulation of the vorticity field.

The Numerical Identification of Basins of Attraction for the Vibration Response of the Rigid Rotor with Squeeze Film Dampers

The article deals with the computational study of the rigid rotor coupled with squeeze film dampers. Various techniques such as the method of computation of the synchronous response with a circular centred orbit, the harmonic balance method, and the direct time integration method are used to analyse the nonlinear behaviour of the rotor system. The results indicate that the rotor system can exhibit both a synchronous circular response with a large orbit radius and a nonsynchronous response with a quasiperiodic character. However, both responses are undesirable in rotating machinery and should be avoided. The new results are presented to provide insight into the impact of initial conditions on the vibration response via basins of attraction. The simulations show that: (i) the basins of attraction are more sensitive to the choice of the initial velocities than displacements, (ii) the basins of attraction are noticeably dependent on the rotor speed in the region of a nonsynchronous response, and (iii) the border between the basins of attraction can be smooth or without a clear structure. The research brings clear conditions defined by parameters such as the dimensionless SFD constant, unbalance, and rotational speed for the suppression of undesirable nonlinear phenomena. The results suggest that the damper can effectively improve the vibration response of high-speed rotating machinery, but its design must be chosen appropriately.

Effect of rotation and cross thermal buoyancy on the nanofluidic transport around a circular cylinder

We numerically explore the coupled effect of a primary free stream nanofluid flow and secondary induced flows due to rotation and thermal buoyancy around a rotating and heated circular cylinder. The free stream flow of the Cu–H2O nanofluid is considered for a Reynolds number range 10≤Re≤30. The solid fraction (Cu-nanoparticles) varies in the base fluid (H2O) in the range 0%≤φ≤10%. The rotation and thermal buoyancy induced flows are considered for the range of dimensionless rotational speed, 0≤Ω≤3, and Richardson number, 0≤Ri<5. We estimate the first and the second critical rotational speeds characterizing the complete suppression of the steady and unsteady wakes. We also demonstrate a second vortex shedding mode originated at high rotational speeds. Furthermore, this study determines the critical thermal buoyancy to initiate the vortex shedding. The critical buoyancy parameter is found to increase with the increasing rotation rate and decrease with the increasing Reynolds number. However, it drops, rises, or remains constant depending on the solid fraction present in the base fluid.

Study of Rotation Effect on Nanofluid Natural Convection and Heat Transfer by the Immersed Boundary-Lattice Boltzmann Method

Aiming to investigate the rotation effect on the natural convection and heat transfer of nanofluid, which has an important application in the control of heat transfer, the velocity field and temperature distribution inside the square cylinder with the rotating heat source in the center were numerically studied and presented in detail at different Hartman numbers and aspect ratios using the immersed boundary-lattice Boltzmann method. Then, the average Nusselt number on the surface of the heat source was calculated to compare the heat transfer rate in different cases. The results showed that the rotation would reduce the effect of gravity on the flow and suppress the heat transfer between the rotating heat source and nanofluid, while the external magnetic field would reduce the rotation effect on the flow and suppress or promote the heat transfer depending on the rotational speed and aspect ratio. Moreover, the smaller aspect ratio of the heat source to the square cylinder would enhance the heat transfer rate and make the retarding effect of magnetic field on rotation more apparent. In addition, the dimensionless rotational speed was proposed in this work, by which much computational time could be saved during the calculation of the immersed-boundary lattice Boltzmann method for the problem of rotation.

Experimental Investigation on the Effect a Rotational Shaft on the Thermal Behavior of a Circular Tube under Constant Heat Flux

Active and passive methods are two main mechanisms of heat transfer improvement. The active methods use external forces to improve heat transfer. This investigation evaluates the thermal and frictional behavior of a circular tube containing a rotational shaft. Constant heat flux was exerted to the circular tube. The fluid inlet and outlet temperature as well as wall temperature of tubes were measured to calculate the hat transfer coefficient. The Re (Reynolds) number was between 800-2000. Also, the dimensionless rotational speed (Rs) had the values of 1,1.5, 2, 2.5 and 3. Results revealed that the rotational shaft could increase the Nu number. Up to %18. Also, the results showed that the rotational shaft could significantly increase the pressure drop and friction factor. The maximum increment of %78 was achieved for friction factor. It was revealed that the use of rotational shaft could be more efficient at low Re numbers and low dimensionless rotational speeds. Also, it was found that by the increment of Reynolds number and being in the transient regime the efficiency of the system would improve.

Free vibration of rotating pretwisted FG-GRC sandwich conical shells in thermal environment using HSDT

The free vibration behavior of rotating pretwisted sandwich conical shell panels with functionally graded graphene-reinforced composite (FG-GRC) face sheets and homogenous core is investigated in uniform thermal environment using finite element method in conjunction with a higher-order shear deformation theory (HSDT). The volume fraction distribution of the graphene in the face sheets is considered to be uniform or layer-wise functionally graded across its thickness. The temperature-dependent effective elastic moduli of the FG-GRC face sheets are computed employing the refined Halpin-Tsai model, while the effective Poison’s ratio, density, and thermal expansion coefficients are obtained using the mixture-rule. The effects of non-linearity arising out of the initial stresses due to thermal and centrifugal loads are incorporated via geometric stiffness based on Green-Lagrange’s strains. The governing equations for sandwich conical shell panels are derived using Lagrange’s equation of motion at moderate rotational speeds. The influence of graphene distribution patterns on the fundamental frequencies of FG-GRC sandwich conical shells under different thermal conditions is studied with emphasis on triggering parameters like pretwist angle, cone length-to-thickness ratio, core-to-face sheets thickness ratio, and dimensionless rotational speed.

Size dependent flapwise vibration analysis of rotating two-directional functionally graded sandwich porous microbeams based on a transverse shear and normal deformation theory

Within this study, the free vibration behavior of rotating two-directional functionally graded porous sandwich microbeams is studied based on the modified couple stress theory by employing a transverse shear-normal deformation beam theory. The effects of the thickness to material length scale parameter accompanying with the porosity volume fraction coefficient, boundary condition, aspect ratio, hub ratio, dimensionless rotation speed and gradient index on the dimensionless fundamental frequencies of the two-directional functionally graded porous sandwich microbeams are investigated. It is found that the dimensionless fundamental frequencies are significantly affected by the variation of the thickness to material length scale parameter, hub ratio, dimensionless rotation speed and porosity volume fraction coefficient. The normal deformation effect is very important especially while the variations of the dimensionless rotation speed, hub ratio and gradient index are considered. Moreover, the mode shapes of the rotating two-directional functionally graded porous sandwich microbeams are also influenced with respect to the variation of the porosity volume fraction coefficient. As a result, the optimum design of the microstructures accompanying with the lightweight and low-cost objectives can be achieved by controlling the material and porosity distribution through the body of the microstructure.

Large-eddy simulation of flow over a rotating cylinder: the lift crisis at

We present wall-resolved large-eddy simulation (LES) of flow with free-stream velocity $\boldsymbol{U}_{\infty }$ over a cylinder of diameter $D$ rotating at constant angular velocity $\unicode[STIX]{x1D6FA}$ , with the focus on the lift crisis, which takes place at relatively high Reynolds number $Re_{D}=U_{\infty }D/\unicode[STIX]{x1D708}$ , where $\unicode[STIX]{x1D708}$ is the kinematic viscosity of the fluid. Two sets of LES are performed within the ( $Re_{D}$ , $\unicode[STIX]{x1D6FC}$ )-plane with $\unicode[STIX]{x1D6FC}=\unicode[STIX]{x1D6FA}D/(2U_{\infty })$ the dimensionless cylinder rotation speed. One set, at $Re_{D}=5000$ , is used as a reference flow and does not exhibit a lift crisis. Our main LES varies $\unicode[STIX]{x1D6FC}$ in $0\leqslant \unicode[STIX]{x1D6FC}\leqslant 2.0$ at fixed $Re_{D}=6\times 10^{4}$ . For $\unicode[STIX]{x1D6FC}$ in the range $\unicode[STIX]{x1D6FC}=0.48{-}0.6$ we find a lift crisis. This range is in agreement with experiment although the LES shows a deeper local minimum in the lift coefficient than the measured value. Diagnostics that include instantaneous surface portraits of the surface skin-friction vector field $\boldsymbol{C}_{\boldsymbol{f}}$ , spanwise-averaged flow-streamline plots, and a statistical analysis of local, near-surface flow reversal show that, on the leeward-bottom cylinder surface, the flow experiences large-scale reorganization as $\unicode[STIX]{x1D6FC}$ increases through the lift crisis. At $\unicode[STIX]{x1D6FC}=0.48$ the primary-flow features comprise a shear layer separating from that side of the cylinder that moves with the free stream and a pattern of oscillatory but largely attached flow zones surrounded by scattered patches of local flow separation/reattachment on the lee and underside of the cylinder surface. Large-scale, unsteady vortex shedding is observed. At $\unicode[STIX]{x1D6FC}=0.6$ the flow has transitioned to a more ordered state where the small-scale separation/reattachment cells concentrate into a relatively narrow zone with largely attached flow elsewhere. This induces a low-pressure region which produces a sudden decrease in lift and hence the lift crisis. Through this process, the boundary layer does not show classical turbulence behaviour. As $\unicode[STIX]{x1D6FC}$ is further increased at constant $Re_{D}$ , the localized separation zone dissipates with corresponding attached flow on most of the cylinder surface. The lift coefficient then resumes its increasing trend. A logarithmic region is found within the boundary layer at $\unicode[STIX]{x1D6FC}=1.0$ .

Bifurcation and Chaos Analysis of Gear Pair System Based on Crack Rotor-Bearing System with Rub-Impact Effect

This study performs a systematic analysis of the dynamic behavior of a crack rotor-bearing system with rub-impact effect. The dynamic orbits of the system are observed using bifurcation diagrams plotted using the dimensionless damping coefficient, the dimensionless unbalance parameter and the dimensionless rotational speed ratio as control parameters. The analysis methods employed in this study include the dynamic trajectories of the crack rotor-bearing system, power spectra, Poincaré maps and bifurcation diagrams. Lyapunov exponent and fractal dimensional analysis are also used to identify the onset of chaotic motion. The numerical results reveal that the system exhibits a diverse range of periodic, sub-harmonic, quasi-periodic and chaotic behaviors. The results presented in this study provide an understanding of the operating conditions under which undesirable dynamic motion takes place in a crack rotor-bearing system and therefore serve as a useful source of reference for engineers in designing and controlling such systems.

Size-dependent three-dimensional free vibration of rotating functionally graded microbeams based on a modified couple stress theory

A size-dependent three-dimensional dynamic model of rotating functionally graded (FG) microbeams is developed based on the Euler–Bernoulli beam theory. A two-constituent material varying along the thickness is considered following the power law. In addition, Poisson's ratio is assumed constant in the present model. Hamilton's principle is adopted in conjunction with a modified couple stress theory to derive the governing equations with the von Kármán geometric nonlinearity incorporated. The Galerkin method is utilized to solve these equations in which the coupling of the axial, chordwise and flapwise deformations is included. The centrifugal stiffening effect of the rotating FG microbeam is captured by the nonlinear coupling deformations. The convergence, accuracy and validity of the present method are confirmed by several examples. The influence of the size-dependency on modal characteristics is investigated combined with the material gradient index, dimensionless rotational speed and hub radius ratio. Finally, the achieved results of dynamic responses indicate that the deformations of rotating FG microbeams are greatly affected by the size-dependency and material gradient variation.

Free Vibration Analysis of Rotating Mindlin Plates with Variable Thickness

The modal analysis of rotating cantilevered rectangular Mindlin plates with variable thickness is studied. The Ritz method is used to derive the governing eigenfrequency equation by minimizing the energy functional of the plate. The admissible functions are taken as a product of the Chebyshev polynomials multiplied by the boundary functions, which enable the displacements and rotational angles to satisfy the geometric boundary conditions of the plate. The Chebyshev polynomials guarantee the numerical robustness, while the Ritz approach provides the upper bound of the exact frequencies. The effectiveness of the present method is confirmed through the convergence and comparison studies. The effects of the dimensionless rotational speed, taper ratio, aspect ratio and thickness ratio on modal characteristics are investigated in detail. The frequency loci veering phenomenon along with the corresponding mode shape switching is exhibited and discussed.

Increment of mixed convection heat transfer and decrement of drag coefficient in a lid-driven nanofluid-filled cavity with a conductive rotating circular cylinder at different horizontal locations: A sensitivity analysis

Since in most industrial rotating equipment, increasing thermal efficiency and reduction of drag has always been subject of interest, in this paper, a 2-D numerical investigation on mixed convection heat transfer and drag coefficient in a lid-driven square cavity filled with Al2O3 Nanofluid is done under the effect of an inner rotating cylinder. To analyze effective parameters on heat transfer and drag coefficient on movable wall, a sensitivity analysis is carried out utilizing the Response Surface Methodology. Simulations are performed for effective parameters of the Richardson number (0.1≤Ri≤10), dimensionless rotational speed (0≤Ω≤5), a/b ratios (0.5≤S≤1), and the Nanoparticle volume fraction (0.00≤Ф≤0.03) with a constant Grashof number of 104. It is found that the mean Nusselt number enhances with Ri number and Ф and decreases with increasing of Ω and S. Additionally, increasing the Ri number and Ω increases the drag coefficient but it reduces as Ф and S increase. The sensitivity analysis results showed that to maximize the mean Nu number and minimize the drag coefficient simultaneously, the effective parameters must be Ω=0, Ri=0.13636, Ф=0.03 and S=0.5.

Effect of Prandtl number and rotation on vortex shedding behind a circular cylinder subjected to cross buoyancy at subcritical Reynolds number

We perform a two-dimensional numerical simulation following a finite volume approach to understand the vortex shedding (VS) phenomena around a circular cylinder subjected to cross thermal buoyancy at a subcritical Reynolds number, Re=40. The flow is considered in an unbounded medium. The cylinder may either be stationary or rotating about its centroidal axis. At the subcritical Reynolds number, the flow and thermal fields are steady without the superimposed thermal buoyancy (i.e. for pure forced flow). However, as the buoyancy parameter (Richardson number, Ri) increases, flow becomes unstable, and eventually, at some critical value of Ri, periodic VS is observed to characterize the flow and thermal fields. An extended Stuart–Landau model is used in this work for the accurate quantitative estimation of the critical Richardson number for the onset of VS. The above phenomena of VS with imposed buoyancy is strongly dependent on the type of the fluid being used. We quantify here the minimum heating requirement for the initiation of VS by choosing three different types of fluids having Prandtl numbers, Pr=0.71, 7, and 100. The dimensionless rotational speed (Ω) ranges between 0 and 4. It is revealed that as Pr increases, heating requirement also increases for the initiation of VS. A possible explanation for the observation is provided.

Magnetoconvective Transport in a Lid-Driven Square Enclosure with Two Rotating Circular Cylinders

Numerical analysis of hydromagnetic mixed convective transport in a differentially heated vertical lid-driven square enclosure is performed in this article. Two heat-conducting solid circular cylinders of identical shape are placed within the enclosure. The cylinders may be either stationary or rotating about their centroidal axes. Two different combinations of cylinder rotations are considered: one when the top cylinder rotates and the bottom one is kept stationary, and the other when the bottom cylinder rotates and the top one is kept stationary. Simulations are performed for a range of controlling parameters such as the Richardson number (1 to 10), Hartmann number (0 to 50), and dimensionless rotational speed (0 to 5), keeping the Reynolds number based on the lid velocity fixed as 100. Furthermore, three different Prandtl numbers, 0.02, 0.71, and 7, are considered. The flow and thermal fields are analyzed through streamline and isotherm plots for various Hartmann and Richardson numbers and rotational speeds. Additionally, the Nusselt number and the bulk fluid temperature are also computed to understand the effects of Hartmann and Richardson numbers and rotational speeds on them. It is observed that the heat transfer greatly depends on the rotational speed of the cylinder.

Free vibration analysis of rotating axially functionally graded-tapered beams using Chebyshev–Ritz method

The modal analysis of rotating axially functionally graded tapered Euler–Bernoulli beams with various boundary conditions is studied. The Chebyshev polynomials multiplied by boundary functions are chosen as the admissible functions in the Ritz minimisation procedure, which is called the Chebyshev–Ritz method. The Chebyshev polynomials guarantee the numerical robustness while the boundary functions satisfy the geometric boundary conditions and the Ritz approach provides the upper bound of the exact frequencies. The effectiveness of the method is verified through the convergence and comparative studies. The effects of hub radius ratio, dimensionless rotational speed ratio, taper ratios for height and breadth and gradient parameters of material on natural frequencies and mode shapes are studied in detail.

Magneto-Convective Transport of Nanofluid in a Vertical Lid-Driven Cavity Including a Heat-Conducting Rotating Circular Cylinder

Numerical simulations are performed for the two-dimensional magneto-convective transport of Cu–H2O nanofluid in a vertical lid-driven square cavity in the presence of a heat-conducting and rotating circular cylinder. The left wall of the cavity is allowed to translate at a constant velocity in the vertically upward direction. Both left and right walls are maintained at isothermal but different temperatures. The top and bottom walls of the enclosure are thermally insulated. At the central region of the cavity is a heat-conducting circular cylinder which can rotate either clockwise or counterclockwise. A constant horizontal magnetic field of amplitude B0 is applied perpendicular to the vertical walls. The nanofluid is electrically conducting, while the solid walls are considered electrically insulated. Simulations are performed for various controlling parameters, such as Richardson number (0.01 ≤ Ri ≤ 10), Hartmann number (0 ≤ Ha ≤ 50), dimensionless rotational speed of the cylinder (Ω = ±1), and nanoparticle concentration (0 ≤ ϕ ≤ 0.3), while Reynolds number based on lid velocity is fixed at a specific value (Re = 100). The flow and thermal fields are found to be susceptible to changes in the magnetic field and mixed convective strength, as well as nanoparticle concentration. However, the direction of cylinder rotation is observed to have little or no influence quantitatively on global hydrodynamic and thermal parameters.

Convective Transport Around a Rotating Square Cylinder at Moderate Reynolds Numbers

Two-dimensional numerical simulation is performed to analyze the thermofluidic transport around a rotating square cylinder in an unconfined medium. The convective transport originates as a consequence of the interaction between a uniform free-stream flow and the flow evolving due to the rotation of the sharp-edged body. A finite volume-based method and a body-fitted grid system along with the moving boundaries are used to obtain the numerical solution of the incompressible Navier–Stokes and energy equations. The Reynolds number based on the free-stream flow is considered in the range 10 ≤ Re ≤ 200, and the dimensionless rotational speed of the cylinder is kept 0 ≤ Ω ≤ 5. Depending on the Reynolds number and the rotational speed of the cylinder, the transport characteristics change. For the range 10 ≤ Re < 50, the flow remains steady irrespective of the rotational speed. In the range 50 ≤ Re ≤ 200, regular low-frequency Kármán vortex shedding (VS) is observed up to a critical rate of rotation (Ωcr ). Beyond Ωcr , the global convective transport shows a steady nature. The rotating circular cylinder also shows likewise degeneration of Kármán VS at some critical rotational speed. However, the heat transfer behavior varies significantly with a rotating circular cylinder. Such thermofluidic transport around a spinning square in an unconfined free-stream flow is reported for the first time.

A Parametric Study of Functionally Graded Rotating Annular Fin

Performance analysis of the rectangular annular fins made of functionally graded material subjected to rotation is reported in the present work. The governing differential equation for the fins has been derived to study the temperature distribution of the fins with insulated tip. A parametric study is then carried out by varying grading parameters along with the parameter of dimensionless rotational speed of the shaft in the governing equation to investigate the effect of on fin performance. The results are presented in graphical form. The formulation is validated with benchmark results and good agreement is observed.

Numerical Study of the Laminar Flow Past a Rotating Square Cylinder at Low Spinning Rates

The fluid dynamic interaction between a uniform free stream flow and the rotation induced flow from a sharp edged body is numerically investigated. A two-dimensional (2D) finite volume based computation is performed in this regard to simulate the laminar fluid flow around a rotating square cylinder in an unconfined medium. Body fitted grid system along with moving boundaries is used to obtain the numerical solution of the incompressible Navier–Stokes equations. The Reynolds number based on the free stream flow is kept in the range 10≤Re≤200 with a dimensionless rotational speed of the cylinder in the range 0≤Ω≤5. At low Re=10, the flow field remains steady irrespective of the rotational speed. For 50≤Re≤200, regular low frequency Kármán vortex shedding (VS) is observed up to a critical rate of rotation (Ωcr). Beyond Ωcr, the global flow shows steady nature, although high frequency oscillations in the aerodynamic coefficients are present. The rotating circular cylinder also shows likewise degeneration of Kármán VS at some critical rotational speed. However, significant differences can be seen at higher rotation. Such fluid dynamic transport around a spinning square in an unconfined free stream flow is reported for the first time.