Effects Of Coriolis Forces Research Articles

Combined effects of Coriolis force and nanoparticle properties on the dynamics of gold–water nanofluid across nonuniform surface

AbstractInvention of nanofluid has proved revolutionary in the enhancement of fluid thermal and electrical conductivity. Industrial applications of gold–water nanofluids over rotating surface include, but not limited to, heat transfer fluids, as a solar absorber, in medieval medicine for the diagnosis of syphilis, and so forth. Gold–water nanofluid is useful in colorant of glass and silk, nonlinear optics, and molecular recognition. Studies have been carried out mostly across stationary or stretching flat surfaces. This paper studies the flow of gold–water nanofluids over the rotating upper horizontal surface of a paraboloid of revolution. The relevant body forces are added to the Navier–Stokes equations to formulate appropriate equations for the flow of gold–water nanofluids over a surface with nonuniform thickness under the action of Coriolis force. Appropriate Blasius similarity transformation is used to nondimensionalize the governing equations and thereby reducing the nonlinear partial differential equations to nonlinear ordinary differential equations. The numerical method used is the Runge–Kutta–Gills method with shooting technique and the three‐stage Lobatto IIIa collocation method, and the results are illustrated graphically. Coriolis force is found to have reduced the coefficient of skin friction in the x‐direction but enhances the coefficient of skin friction in the z‐direction. The haphazard motion of the nanoparticles and the nanoparticle volume fraction are found to enhance the skin friction coefficient in the x‐ and y‐directions.

Linear and weakly non-linear stability analysis of oscillatory convection in rotating ferrofluid layer

In the present paper, the problem of ferroconvection in the presence of uniform vertical rotation is considered to investigate the linear and weakly non-linear oscillatory stability. Two-dimensional convective roll instability is discussed with finite-amplitude disturbances. For linear stability, as a first-order problem, the expressions for Rayleigh numbers for stationary and oscillatory convection are derived and the effects of Coriolis force and magnetic parameters on the onset of ferromagnetic convection are studied, numerically. In weakly nonlinear oscillatory analysis, the second-order and third-order stability problems are discussed and the complex Ginzburg-Landau equation describing the amplitude of convection cell in rotating ferrofluid is derived and consequently, the expression for Nusselt number representing the heat transfer rate is obtained. From the present analysis, we observed that the rotation has the usual stabilizing effect on the linear stability in ferroconvection, however, the magnetic number (M1) and the measure of nonlinearity of magnetization (M3) both have a destabilizing effect on the onset of linear instability. Also, we found that for non-linear convection, the heat transfer rate (the Nusselt number) increases with increasing values of Taylor number, magnetic number, and the measure of nonlinearity of magnetization.

Investigating the Effect of Coriolis Force In A Vibrating Pipeline

Pipelines conveying fluids are bound to vibrate during operation and if not properly handled from the design stage, there will be tendency of failure. This paper aims at studying the behavior of a pipe under the influence of a coriolis force for when conveying crude oil and natural gas only. A pipe under fixed ends condition was considered using finite element method based on Hamilton principle to determine the deformation mode shape behavior pattern, and this was validated using ANSYS software simulations. It was observed that the pipe exhibited the same behavioral pattern for crude oil when Coriolis force was enabled in both the finite element method and the ANSYS software simulation method. On the other hand, it was observed that the pipe exhibited the same behavioral pattern for crude oil when coriolis force was not enabled in both the finite element method and the ANSYS software simulation method, though the ANSYS simulation method tend to exhibit a more uniform and accurate pattern than the finite element method because of the two elements considered in the finite element method. It is a known fact that the higher the number of elements, the more accurate the finite element results would be. In view of this limitation, it was recommended that for similar works to be carried out in future, the number of elements should be increased more than two for more accurate results. Keywords: Coriolis Force, Finite Element Analysis, ANSYS Simulation

The structure of turbulence in rotating rough-channel flows

Direct numerical simulation (DNS) of rib-roughened turbulent channel flow rotating about its spanwise axis, by Narasimhamurthy and Andersson [Turbulence statistics in a rotating ribbed channel. International Journal of Heat and Fluid Flow 51, 29–41. (2015)], is revisited to seek complementary insights into the combined effects of roughness and Coriolis force on the turbulence. Flow in the channel was maintained at a friction Reynolds number, Reτ=400 and the non-inertial reference frame was rotated at different speeds quantified by the dimensionless rotation number, Ro=0, 2 and 6. Both the aforementioned parameters are based on the friction velocity uτ and half-height of the channel h. The channel walls were symmetrically mounted with transverse square ribs with cross-section of side k=0.1h and pitch λ=8k. Rotation causes preferential aligning of the near-wall vortical structures. The Taylor-Görtler–like roll-cells similar to those found in the rotating smooth-channel flows, survive the presence of the transverse ribs, but exhibit transient behavior. Increased transport of turbulent kinetic energy from the pressure side at higher Ro is evident from the variation of the vertical transport velocity Vk. The rotational production rates assume increasingly significant roles in distributing the kinetic energy in different directions. Anisotropy invariant maps and Taylor microscales show that the structure of turbulence is affected by rotation in a significant manner.

Spin dynamics of a long tethered sub-satellite system in geostationary orbit

A long tethered sub-satellite system (LTSS) has a promising application for earth observation, which requires that the LTSS spins towards the earth. Due to the long flexible tethers and the spinning of the LTSS, the system exhibits dynamics of high nonlinearity and high complexity. While most previous studies did not consider more than three satellites in a tethered satellite system, the computational method developed in this work allows considering an arbitrary number of satellites as demonstrated by the numerical examples presented. First of all, a nonlinear flexible multibody dynamic model of the spinning LTSS in the orbital coordinate frame is established and the corresponding dynamic analysis is studied. Here, the absolute nodal coordinate formulation (ANCF) and the natural coordinate formulation (NCF) are used to accurately describe the large deformations and large overall motions of the flexible tethers and rigid satellites, respectively. Afterwards, through coordinate transformation, the orbital dynamics of the LTSS is obtained and the effects of Coriolis force, centrifugal force, and gravity gradient are analytically derived. Finally, several numerical examples are presented, and the vibrations and stabilities of the LTSS are analyzed via parameter study.

Numerical study of a novel curved pin fin for heat transfer enhancement within aeroengine turbine blade

This paper introduces and develops a novel curved pin fin for heat transfer enhancement of aeroengine turbine blade. The effects of inclination angle and vertical segment length of curved pin fin on heat transfer performance are studied under stationary and rotating condition. Four cases with different inclination angle (90°, 75°, 60° and 45°) and four cases with different vertical segment length (9, 7, 5 and 3) are studied for rotation number varying from 0 to 0.5. Numerical results show that curved pin fins with smaller inclination angle and shorter vertical segment are characterized by lower friction factor and better thermal performance. Compared to upright pin fin, the thermal performance factors for curved pin fins with inclination angle γ=45° and vertical segment length Hv=3 are improved by 6.1% and 14.4%, respectively. Under rotating frame, the effects of Coriolis force are suppressed by curved pin fin, and lower heat transfer enhancement is produced consequently. Moreover, curved pin fin with smaller inclination angle and shorter vertical segment is featured with relatively lower sensitivity with respect to rotation number.

Coriolis force effects on radial convection in a cylindrical annulus

Thermal convection under the influence of rotation appears in a wide range of engineering and geophysical applications, and has been investigated extensively both experimentally and numerically utilizing different canonical configurations. The problem of radial convection in a cylindrical annulus, studied in the present work, has received less attention than other configurations, such as rotating Rayleigh-Bénard convection. It has long been known that rotation has a stabilizing effect and, in the limit of strong rotation, a two-dimensional flow emerges, resulting in reduced heat transfer rates. Here, direct numerical simulations are performed for buoyancy-driven flows in a cylindrical annulus bounded by two parallel disks with and without rotation. By maintaining a radial gravity term analogous to a centrifugal acceleration even in the stationary cases, it is possible to isolate the effect of the Coriolis force on the flow. As expected, when rotation is imposed the flow is characterized by large-scale structures and the heat transfer rates are significantly reduced. Turbulence statistics are presented for the mean temperature profiles, temperature and velocity fluctuations, turbulent kinetic energy budgets, and Reynolds stress anisotropy tensor. It is shown that rotation significantly affects the distribution of turbulent kinetic energy throughout the radial direction, in particular away from the cylindrical surfaces. The anisotropy maps reveal that the turbulence is quasi-two-dimensional in the rotating cases, even for the highest value of Ra considered, whereas without rotation the core region approaches the isotropic limit with increasing Ra.

Increasing effects of Coriolis force on the cupric oxide and silver nanoparticles based nanofluid flow when thermal radiation and heat source/sink are significant

When radiation of thermal energy, either internal generation of heat or absorption are significant, the increasing effects of Corriolis force on the cupric oxide and silver tiny particles based nanofluid flow must be determined. The differential equation that models the dynamics of the hybrid nanofluid was used to investigate the fluctuation in the aforementioned transport, friction, and temperature. The constitutive equations are translated and non-dimensionalized using appropriate transformations. Following that, the Variational Parameter Method (VPM) was used to generate numerical solutions to the dimensionless governing equations. The analysis of results shows that an increasing in the rotation parameter corresponds to enhancement of the Corriolis force is capable to boost the temperature distribution. Meanwhile, a higher stretching ratio parameter causes decrement in the temperature distribution. Both radiation of the thermal energy and the generation of heat energy are found to cause the temperature distribution to increase.

Activation energy with exothermic/endothermic reaction and Coriolis force effects on magnetized nanomaterials flow through Darcy–Forchheimer porous space with variable features

Nanomaterials have a remarkable role in contributing to industrial and medical applications like cooling of compressors, domestic refrigerators, brain tumors, and engines. Therefore, this report develops the theoretical investigation of magnetized nanomaterials Darcy–Forchheimer flow with zero mass flux. Rotation and stretching of disk cause the flow. Variable permeability and porosity are explored via Darcy–Forchheimer expansion. Activation energy with exothermic/endothermic reaction, Joule heating, exponential, and thermal heat source are additionally added to the energy equation. For the analysis of nanomaterials, Boungiorno model is considered. The modeled equations are altered to systems of ordinary differential equations by using Von Karman variables. ND-Solve scheme numerically approximated the converted system. Variation of physical quantities against distinct parameters is interpreted. It is noted that exothermic/endothermic reaction improves the temperature of nanomaterials.

Impacts of Rotation on Unsteady Fluid Flow and Energy Distribution through a Bending Duct with Rectangular Cross Section

A depth understanding of fluid flow past a curved duct having rectangular cross-section with different aspect ratios (l) are essential for various engineering applications such as in chemical, mechanical, bio-mechanical and bio-medical engineering. So highly ambitious researchers have given significant attention to study new characteristics of fluid flow in a curved duct. The flow characterization in the rectangular duct has been studied over a wide range of numerical and selective experimental studies. However, proper knowledge with the effects of Coriolis force for different aspect ratios is important for better understanding of the transitional behaviour and the subsequent heat generation, which is required to improve further. The purpose of this study is to reveal insight into the transitional flow pattern and heat transfer in a curved rectangular domain. The Navier-Stokes equations are solved using the spectral method, while the Crank-Nicolson method is used to solve the energy equation. An in-house FORTRAN code is developed to get the numerical solution. For post-processing purposes, Tecplot-360 and Ghost-script tools are used. The present study exposes development of Dean vortices that affect heat generation as well as thermal enhancement in the flow with underlying the flow controlling parameters, the Dean number (Dn), the Grashof number (Gr) and the Taylor number (Tr). Time-dependent results followed by phase spaces show that transient flow undergoes in the scenario ‘chaotic → multi-periodic→ periodic→ steady-state’ generating 2- to 8- vortices for the periodic/multi-periodic flow at 2000 ≤ Tr ≤ 2205 for l = 2, whereas similar sort of flow is observed in the range of 3100 ≤ Tr ≤ 3195 for l = 3. More complicated 4- to 13-vortex solutions are obtained for the chaotic flow regime at l = 2 in the range of 0 ≤ Tr < 2200 and at l = 3 in the range of 0 ≤ Tr < 3100. The chaotic flow that occurs at the certain range of Tr proficiently intensifies the heat transfer than the unperturbed, periodic or multi-periodic flow. The overall investigation reveals that in the rotating duct, the temperature-influenced buoyancy compulsion and centrifugal-coriolis joint forces are dominant, influencing the characteristic of the fluid and thus optimizing the transfer of heat. The present investigation will contribute to enhancing the understanding of fluid flow and heat transfer of internal heating/cooling/gas turbines, electric generators, biological systems, and some separation processes.

Rotational heat transfer in a rectangular cooling channel with compound turbulators of pin-fins and dimples

The convective heat transfer characteristics in a rotating trailing edge channel roughened with compound turbulators of pin-fin and dimple arrays were experimentally investigated via copper plate technique. The effects of Reynolds number (Re), rotation number (Ro) and buoyancy number (Buo) on the local and averaged heat transfer for the leading and trailing walls of current pin fin-dimpled channel were studied at conditions of 12,000 ≤ Re ≤ 20,000, 0 ≤ Ro ≤ 0.89 and 0 ≤ Buo ≤ 1.32. Both the static-to-rotating Nusselt number ratio (Nu/Nus) and the normalized Nusselt number ratio (Nu/Nu0) were compared with that in a similar pin-fin channel. To examine the coupling and individual Coriolis force and centrifugal buoyancy effects in current compound channel, experiments were designed and performed with three density ratios (d.r. = 0.05, 0.08, 0.10) for each given Re and Ro. In the static cases, it was found that heat transfer at most of the measured locations was promoted by adding dimples onto the pin-fin wall, including the high radius region where the worst heat transfer level was observed in the traditional pin-fin channel. The overall averaged heat transfer was respectively enhanced by 15.8% and 21.0% at Re = 12,000 and 20,000. In the rotating compound channel, the heat transfer augmentation in the high radius region reduced with rotation, and the reduction expanded towards the low radius with ascending Ro. A turning point at each location were observed after which heat transfer stopped decreasing and started to recover with rotation. Those turning points were diverse at various locations, but they appeared to be approximately 1.0 once the local rotation number were adopted. Moreover, the heat transfer data indicated that the centrifugal buoyancy abated or promoted heat transfer at lower or higher Ro, respectively. Further study revealed that the local parameters were more instructive than the inlet ones to analyze the coupling and isolated Coriolis force and centrifugal buoyancy effects in current compound channel.

Instabilities of thermocapillary-buoyant-Coriolis flow of medium Prandtl fluid in a slowly rotating annular pool

In differently heated slowly rotating annular pools, the thermocapillary force, buoyancy force, and Coriolis force drive fluid flows and induce various flow instabilities. To understand these complex flow instabilities, the linear stability of axisymmetric thermocapillary-buoyant-Coriolis flow was investigated for medium Prandtl number fluid in an annular pool slowly rotating in a counter-clockwise direction. The neutral states for the incipience of instabilities were determined by a linear stability analysis, and the underlying mechanisms were clarified using energy budgets. Three types of flow instabilities were identified for Taylor numbers ranging from 0 to 60. The results showed that the sign of the temperature perturbation in the bulk and that on the surface right above it governed the mechanisms of the stationary and oscillatory instabilities. This work can be helpful for understanding the combined effects of thermocapillary force, buoyancy force, and Coriolis force on flow instabilities.

Thermo‐electrokinetic rotating non‐Newtonian hybrid nanofluid flow from an accelerating vertical surface

AbstractThis paper explores the combined effects of Coriolis force and electric force on the rotating boundary layer flow and heat transfer in a viscoplastic hybrid nanofluid from a vertical exponentially accelerated plate. The hybrid nanofluid comprises two different types of metallic nanoparticles, namely silver (Ag) and magnesium oxide (MgO) suspended in an aqueous base fluid. The Casson model is deployed for non‐Newtonian effects. An empirical model is implemented to determine the thermal conductivity of the hybrid nanofluid. Rosseland's radiative diffusion flux model is also utilized. An axial electrical field is considered and the Poisson–Boltzmann equation is linearized via the Debye–Hückel approach. The resulting coupled differential equations subject to prescribed boundary conditions are solved with Laplace transforms. Numerical evaluation of solutions is achieved via MATLAB symbolic software. A parametric study of the impact of key parameters on axial velocity, transverse velocity, nanoparticle temperature and Nusselt number is conducted for both the hybrid (Ag–MgO)–water nanofluid and also unitary (Ag)–water nanofluid. With increasing volume fraction of silver nanoparticles, there is a reduction in both axial velocity and temperatures, whereas there is a distinct elevation in transverse velocity for both unitary and hybrid nanofluids. Elevation in the heat absorption parameter strongly decreases axial velocity, whereas it enhances transverse velocity. Increasing the radiation parameter strongly boosts temperatures. Increasing the heat absorption parameter significantly accelerates the transverse flow. Negative values of Helmholtz–Smoluchowski velocity decelerate the axial flow whereas positive values accelerate it; the opposite behavior is observed for transverse velocity. Increasing Taylor number significantly damps both the axial (primary) and transversal (secondary) flow. Increasing thermal Grashof number strongly enhances the axial flow but damps the transverse flow. The unitary nanofluid achieves higher Nusselt numbers than the hybrid nanofluid but these are decreased with greater radiative effect (due to greater heat transport away from the plate surface), Prandtl number and heat absorption. Nusselt number is significantly reduced with greater time progression and values are consistently higher for the unitary nanofluid compared with hybrid nanofluid. The computations provide insight into more complex electrokinetic rheological nanoscale flows of relevance to biomedical rotary electro‐osmotic separation devices.

Effect of Coriolis force on the linear stability of subaqueous dunes with erodible and non-erodible beds

Dunes, are wavy-shaped structures, that can be found on river shores and underwater. We aim to investigate the influence of Coriolis effect on the linear stability of subaqueous dunes using a simple model based on the three-dimensional shallow water equations written in rotating frame of reference. The analysis is performed for both erodible and non-erodible beds. Our analytical results in the absence of Coriolis force are verified with published results. The wave speed and growth rate of disturbances are presented for different Coriolis parameter, Froude number and erodibility. A new mode is observed, which becomes unstable beyond a threshold value of Coriolis parameter.

Faraday–Fresnel rotation and splitting of orbital angular momentum carrying waves in a rotating plasma

Rotational Fresnel drag – or orbital Faraday rotation – in a rotating magnetised plasma is uncovered and studied analytically for Trivelpiece–Gould and whistler–helicon waves carrying orbital angular momentum (OAM). Plasma rotation is shown to introduce a non-zero phase shift between OAM-carrying eigenmodes with opposite helicities, similarly to the phase shift between spin angular momentum eigenmodes associated with the classical Faraday effect in a magnetised plasma at rest. By examining the dispersion relation for these two low-frequency modes in a Brillouin rotating plasma, this Faraday–Fresnel rotation effect is traced back to the combined effects of Doppler shift, centrifugal forces and Coriolis forces. In addition, the longitudinal group velocity in the presence of rotation is shown to depend both on rotation and azimuthal mode, therefore predicting the Faraday–Fresnel splitting of the envelope of a wave packet containing a superposition of OAM-carrying eigenmodes with opposite helicities.

Effects of Coriolis Force on the Nonlinear Interactions of Acoustic-Gravity Waves in the Atmosphere

The nonlinear theory of acoustic-gravity waves ( AGWs ) in the atmosphere is revisited with the effects of the Coriolis force. Previous theory in the literature [Phys. Scr . 90 (2015) 055001] is advanced. Starting from a set of fluid equations modified by the Coriolis force, a general linear dispersion relation is derived which manifests the coupling of the high-frequency acoustic-gravity waves ( AGWs ) and the low-frequency inertial gravity waves ( IGWs ). The frequency of IGWs is enhanced by the Earth's angular velocity. The latter also significantly modifies the nonlinear coupling of AGWs and IGWs whose evolutions are described by the Zakharov approach as well as the Wigner- Moyal formalism. The consequences of the two equivalent evolution equations modified by the Coriolis force are briefly discussed.

Computational modeling of axial rotation for the evolution of temperature in horizontal toroidal cans under pasteurization conditions

Axial rotation mechanism has been widely used during thermal processing of liquid containing cans. Besides this can geometry modification might be an innovative approach to increase heat transfer rates. Therefore, the objective of this study was to determine temperature distribution and effect of rotation rate in axially rotating toroidal cans. For this purpose, experimental and numerical modeling studies were carried out. In the experimental studies, toroidal cans including distilled water were processed in hot water, and temperature data were used for computational model validation and mesh independency. Then, the second set of simulations were conducted to determine the rotational effects on temperature evolution. Effects of gravitational buoyancy, centrifugal and Coriolis forces were determined, and Coriolis forces increased up to 4 times with increased rotation rates (20–160 rpm). With this aspect, process time for 70 °C increase was reduced by ≈40 and 33.3% at 80 and 160 rpm compared to conventinal cylindrical cans. This study is an introduction to modify can geometry and process parameters to reduce quality losses and decrease energy use. However, industrial practice has still significant challenge for manufacturing and using in the process line.

Heat transfer in an impingement cooling channel under isothermal boundaries at high rotation numbers

The jet impingement cooling technology is usually applied in the turbine blade leading edge which suffers the highest heat flux and needs priority protection. Therefore, heat transfer performances in a rotating impingement cooling channel under an isothermal boundary are experimentally studied. Both the jet-to-target surface spacing and the jet-to-jet spacing are 3 times the jet hole diameter. The effects of Coriolis force and buoyancy force on heat transfer are focused. And the maximum rotation number and buoyancy number reaches 1.63 and 8.06, respectively. The Reynolds number varies from 7119 to 21,358. Besides, numerical simulations are conducted to predict the flow field. The results show that the heat transfer in the impingement channel is determined by the radial mass-flowrate distribution of supply channel in both static and rotating states. Moreover, the rotation enhances the heat transfer at both ends but decreases the heat transfer in the middle-radius due to the stagnant zone induced by Coriolis force in the supply channel, resulting in large thermal stress on the target surface. However, the heat transfer is insensitive to the rotational effects when the rotation number exceeds 0.42. There is a critical rotation number for each location, before which the effect of buoyancy force could be neglected. Once the rotation number is greater than this value, the effect of buoyancy force increases with the wall-to-fluid temperature ratio.

A control-oriented large eddy simulation of wind turbine wake considering effects of Coriolis force and time-varying wind conditions

A control-oriented large eddy simulation (LES) code is developed to predict wind turbine wake and is validated by laboratory-scale and utility-scale wind turbines. Firstly, the wind turbine control algorithms including torque, pitch and yaw controls are implemented in LES with Actuator Line Model (ALM). Two sets of numerical simulations under uniform inflow with time-varying wind speeds and wind directions are performed. The simulated thrust and torque forces agree well with those calculated by the aeroelastic code, FAST. The predicted mean velocity and turbulence intensity in the wake of a laboratory-scale wind turbine show favorable agreement with those measured in wind tunnel experiments. The blade rotation induced dynamic effects on wake flows and rotor loading are well reproduced by ALM. Finally, numerical simulations for a utility-scale wind turbine are conducted, in which the ambient flow filed with time-varying wind speeds and wind directions are generated based on the wind condition measured by the Met-mast and the Coriolis force effect is incorporated as well. The predicted time series of control signals and power production agree well with the wind turbine SCADA data and the predicted mean wind speed in the wake region show favorable agreement with those measured by Doppler scanning LiDAR.

Direct numerical simulation of turbulent elliptical pipe flow under system rotation about the major axis

The effect of Coriolis forces on the turbulent flow in an elliptical pipe subjected to spanwise rotation has been studied using direct numerical simulations (DNS). In response to the system rotation, large-scale secondary flows appear in the cross-stream plane as a pair of counter-rotating vortices, which significantly impact the turbulence statistics and structures of the flow. The characteristics of the turbulence field is investigated in both physical and spectral spaces through analyses of the first- and second-order statistical moments, as well as the budget balance of the Reynolds stress transport equation and coherent flow structures.