Fluid Rotation Research Articles

Time-dependent squeezing flow of Casson-micropolar nanofluid with injection/suction and slip effects

Time-dependent and incompressible squeezing flow of Casson and micropolar nanofluids is analyzed. The non-Newtonian liquids are confined through parallel disks. The bottom disk is saturated in the plane z = 0 and the fluid is squeezed by the movement of the upper disk along axial direction. Nanofluid theory (Buongiorno model) is accomplished in the flow phenomenon. A uniform injection/suction is act upon at the lower disk. Velocity, thermal and concentration slip effects are also incorporated at the bottom fixed disk. The similarity functions are first accomplished in order to achieve the governing system of ordinary differential equations and then the system is solved in numerical manner using Runge-Kutta-Fehlberg fourth fifth (RKF-45) order numerical procedure. Results are disclosed in tabular and graphical forms against the various physical quantities. For the validation of our numerical technique, the results are compared well with the literature work under limiting case. It is perceived that increased squeezing Reynolds number pushed the radial velocity profiles towards the upper disk. The micropolar parameter tends to the fluid rotation in opposite way due to which microrotational field first enhanced and then reduced by the vortex viscosity parameter.

The effects of Coriolis force and radial stretch on the convective instability characteristics of the Bödewadt flow

The Bödewadt boundary-layer flow is induced by the rotation of a viscous fluid rotating with a constant angular velocity over a stationary disk. In this paper, the Bödewadt boundary-layer flow has been studied in the presence of the Coriolis force to observe the effect of radial stretch of the lower disk on the flow. For the first time in the literature, a numerical investigation of the effects of both stretching mechanism and the Coriolis force on the flow behaviour and on the convective instability characteristics of the above flow has been carried out. In this paper, the Kármán similarity transformations have been considered in order to convert the system of PDEs representing the momentum equations of the flow into a system of highly non-linear coupled ODEs and solved numerically to obtain the velocity profiles of the Bödewadt flow. Then, a convective instability analysis has been performed by using the Chebyshev collocation method in order to obtain the neutral curves. From the neutral curves it is observed that radial stretch has a globally stabilising effect on both the inviscid Type-I and the viscous Type-II instability modes. This underlying physical phenomena has been verified by performing an energy analysis of the flow. The results obtained excellently supports the previous works and will be prominently treated as a benchmark for our future studies.

New fluid kinematics

Fluid kinematics describes the fluid motion without consideration of any force. Classical fluid kinematics adopts Helmholtz velocity decomposition, which is equivalent to Cauchy-Stokes (CS) velocity gradient tensor decomposition. CS decomposes the velocity gradient tensor into a strain-rate (symmetric) tensor and a vorticity (anti-symmetric) tensor. However, several questions arise: (1) since vorticity cannot represent fluid rotation, the vorticity tensor is a mixture of vorticity shear and rigid rotation, (2) since the strain-rate tensor cannot represent fluid shear, the strain-rate tensor is a mixture of stretching and shear, (3) the stretching and shear in the CS decomposition are dependent on the selection of coordinate system and are therefore not Galilean invariant. On the other hand, Liutex is a new physical quantity to represent the rigid fluid rotation and a principal coordinate system can be set up based on Liutex. A principal decomposition of the velocity gradient tensor, or the rotation-stretching-shear decomposition, can be easily carried out in the principal coordinate system with a clear physical meaning, which represents the rigid rotation, stretching (compression) and shear (symmetric and anti-symmetric shear). In the principal decomposition, all elements in three sub-tensors are Galilean invariant and, therefore, the principal decomposition is unique, Galilean invariant and independent of coordinate system. The principal decomposition is then transformed back to the original xyz coordinate system. The Liutex-based principal decomposition creates the new fluid kinematics which is ready for building up new fluid dynamics. Since fluid kinematics is the foundation of the fluid dynamics, the new fluid kinematics could replace the classical fluid kinematics, Helmholtz or CS decomposition, and open a new gate to develop new fluid dynamics especially for vortex science and turbulence research.

Experimental study on the effect of tube rotation on performance of horizontal shell and tube latent heat energy storage

As latent heat energy storage (LHES) represents a solution for many problems of energy, therefore it has become under focus for enhancement. The main reason that pushes scientists to enhance LHES is the non-uniform melting occurring inside phase change material (PCM) field. The rotation of heat transfer fluid (HTF) tube is proposed in shell and tube LHES as a method to treat this problem. The present work investigated the effect of tube rotation on the performance of LHES. Paraffin wax was used as PCM while water was used as HTF. The experiments were implemented at three rotation speeds 3, 6 and 9 rpm, then results were compared with still case (zero rpm). It is concluded that tube rotation with above range of speeds gave liquid fraction enhancement percentage that did not exceeded 8.12% at best after about 11 working hrs.

Insight into the dynamics of fluid conveying tiny particles over a rotating surface subject to Cattaneo–Christov heat transfer, Coriolis force, and Arrhenius activation energy

This article addressees the dynamics of fluid conveying tinny particles and Coriolis force effects on transient rotational flow toward a continuously stretching sheet. Tiny particles are considered due to their unusual characteristics like extraordinary thermal conductivity, which are significant in advanced nanotechnology, heat exchangers, material sciences, and electronics. The main objective of this comprehensive study is the enhancement of heat transportation. The governing equations in three dimensional form are transmuted in to dimensionless two-dimensional form with implementation of suitable scaling transformations. The variational finite element procedure is harnessed and coded in Matlab script to obtain numerical solution of the coupled non-linear partial differential problem. It is observed that higher inputs of the parameters for magnetic force and rotational fluid cause to slow the primary as well as secondary velocities, but the thermophoresis and Brownian motion raise the temperature. However, thermal relaxation parameter reduces the nanofluid temperature. The velocities for viscosity constant case are faster than that for the variable viscosity, but temperature and species concentration depict opposite behavior.

Study of double-diffusive convection in a rotating couple-stress ferromagnetic fluid in the presence of varying gravitational field and horizontal magnetic field saturating in a porous medium

The results of double-diffusive convection on the liquid coatings of ferromagnetic liquids is studied by researchers by various theoretical and hydrodynamics concepts of hydrodynamics. However this study is done in presence of varying gravitational field. The study of such couple-stress ferromagnetic fluids in presence of fluctuating gravitational field is still not explored. As we know that gravitational field varies on different points on the earth; for this reason the study of couple-stress ferromagnetic liquids in presence of variable gravity fields is highly required. In this paper we studied the impact of medium permeability, stable solute gradient, couple-stress, rotation, magnetic field, and magnetization of a couple-stress ferromagnetic fluid in presence of variable gravitational field. For this study a coating of couple-stress ferromagnetic fluid saturating in a porous medium when fluid layer is heated and soluted. We examined the results of the magnetic field on couple-stress ferromagnetic fluids, its thermosolutal instability during rotation. A linearized concept and normal mode technique are used to acquire the dispersion relation. For the case of stationary convection, medium permeability, couple-stress, and magnetic field have both stabilizing and destabilizing results under certain conditions. A stable solute gradient has a stabilizing result on the system. Also, the rotation has a stabilizing result for λ>0 and destabilizing result for λ 0 and λ<0. The critical Rayleigh number for the onset of instability is decided numerically and graphically also. The principle of exchange of stabilities is observed to keep genuine in the absence of rotation, magnetic field, and stable solute gradient under certain conditions.

Stretching and shearing contamination analysis for Liutex and other vortex identification methods

The newly developed vortex-identification method, Liutex, has provided a new systematic description of the local fluid rotation, which includes scalar, vector, and tensor forms. However, the advantages of Liutex over the other widely used vortex-identification methods such as Q, ∆, λ2, and λci have not been realized. These traditional methods count on shearing and stretching as a part of vortex strength. But, in the real flow, shearing and stretching do not contribute to fluid rotation. In this paper, the decomposition of the velocity gradient tensor is conducted in the Principal Coordinate for uniqueness. Then the contamination effects of stretching and shearing of the traditional methods are investigated and compared with the Liutex method in terms of mathematical analysis and numerical calculations. The results show that the Liutex method is the only method that is not affected by either stretching or shear, as it represents only the local fluid rigid rotation. These results provide supporting evidence that Liutex is the superior method over others.

Transient growth, edge states, and repeller in rotating solid and fluid.

For the classical problem of the rotation of a solid, we show a somehow surprising behavior involving large transient growth of perturbation energy that occurs when the moment of inertia associated to the unstable axis approaches the moment of inertia of one of the two stable axes. In that case, small but finite perturbations around this stable axis may induce a total transfer of energy to the unstable axis, leading to relaxation oscillations where the stable and unstable manifolds of the unstable axis play the role of a separatrix, an edge state. For a fluid in solid-body rotation, a similar linear and nonlinear dynamics apply to the transfer of energy between three inertial waves respecting the triadic resonance condition. We show that the existence of large transient energy growth and of relaxation oscillations may be physically interpreted as in the case of a solid by the existence of two quadratic invariants, the energy and the helicity in the case of a rotating fluid. They occur when two waves of the triad have helicities that tend towards each other, when their amplitudes are set such that they have the same energy. We show that this happens when the third wave has a vanishing frequency which corresponds to a nearly horizontal wave vector. An inertial wave, perturbed by a small-amplitude wave with a nearly horizontal wave vector, will then be periodically destroyed, its energy being transferred entirely to the unstable wave, although this perturbation is linearly stable, resulting in relaxation oscillations of wave amplitudes. In the general case we show that the dynamics described for particular triads of inertial waves is valid for a class of triadic interactions of waves in other physical problems, where the physical energy is conserved and is linked to the classical conservation of the so-called pseudomomentum, which singles out the role of waves with vanishing frequency.

Optimization of Flow Rate and Pipe Rotation Speed Considering Effective Cuttings Transport Using Data-Driven Models

Effectively transporting drilled cuttings to the surface is a vital part of the well construction process. Usually, mechanistic models are used to estimate the cuttings concentration during drilling. Based on the results from these model, operational parameters are adjusted to mitigate any nonproductive time events such as pack-off or lost circulation. However, these models do not capture the underlying complex physics completely and frequently require updating the input parameters, which is usually performed manually. To address this, in this study, a data-driven modeling approach is taken and evaluated together with widely used mechanistic models. Artificial neural networks are selected after several trials. The experimental data collected at The University of Tulsa–Drilling Research Projects (in the last 40 years) are used to train and validate the model, which includes a wide range of wellbore and pipe sizes, inclinations, rate-of-penetration values, pipe rotation speeds, flow rates, and fluid and cuttings properties. It is observed that, in many cases, the data-driven model significantly outperforms the mechanistic models, which provides a very promising direction for real-time drilling optimization and automation. After the neural network is proven to work effectively, an optimization attempt to estimate flow rate and pipe rotation speed is introduced using a genetic algorithm. The decision is made considering minimizing the required total energy for this process. This approach may be used as a design tool to identify the required flow rate and pipe rotation speed to acquire effective hole cleaning while consuming minimal energy.

Size-dependent stability analysis of a functionally graded cylindrical shell subjected to swirling annular flow including the fluid viscosity

In this paper, the stability and dynamics of a functionally graded materials (FGMs) cylindrical micro-shell subjected to swirling annular fluid through the annulus between the inner shell and the outer shell are firstly investigated. The fluid perturbation pressure related to the shell vibration is determined by the potential flow theory. The steady viscous forces are derived based on the fully developed turbulent flow. The shell motion equations are established on the basis of the Hamilton's principle along with the Donnell shell theory. To capture the size effect of micro-shell, the zero-level contour method is adopted to obtain the solutions of shell motion equations. First, the system subjected to an ideal annular flow is studied. The results show effects of the fluid rotation, material length-scale parameter, and material properties on the fluid-micro-shell system stability. Furthermore, the coupling effect of the fluid rotation and the material length-scale parameter on the dynamical stability of the system is evaluated. Second, the system subjected to a viscous annular flow is further studied. A more impressive result is observed that the fluid viscosity effect renders the system subjected to an annular flow more unstable, and the physical explanation for the phenomenon is presented.

Modeling and analysis of a novel rotational magnetorheological abrasive flow finishing process

The present work proposes a new non-conventional machining process. The proposed method is a combination of magneto-rheological finishing and rotational abrasive flow finishing process. The modeling of the new process was done on the brass workpiece at different magnetic field strengths and at different rotational speeds to observe its effect on final surface roughness and volumetric material removal. From the results, it was inferred that the value of surface roughness decreases with the increase in rotational speed and magnetic field for the constant number of cycles. This decrease in surface roughness value authenticates the active participation of the centrifugal force and rheological behavior of polishing fluid. The present study shows that with the rotation of magneto-rheological polishing fluid, an extra component of centrifugal force adds up to the resultant force which increases the volumetric removal rate and surface finish as compared to other finishing processes.

Thermally developed generalized Bödewadt flow containing nanoparticles over a rotating surface with slip condition

Recent advanced nanotechnology trends have developed thermal implications of nanoparticles as they are more and more important in different engineering and thermal extrusion technologies. Nanofluids are the best substitute to improve the thermal conductivity of conventional heat transfer base liquids. Therefore, the present article addresses the comparative study for the heat transfer phenomena in the thermal boundary layer due to a generalized VF of NF over an infinite rotating disk with generalized SC. The motion is generated by the fluid rotation like a solid body with a constant angular velocity Ω at a sufficiently extensive distance from the disk's surface. The nanoparticles Cu and TiO2 are considered with water-based NF subjected to thermal radiation. Finite difference-based method bvp4c is employed to solve the obtained non-linear ODEs numerically. The analysis of various flow parameters on the velocity components and temperature fields at the surface of the disk is outlined through graphical and tabular outcomes. The findings reveal that suction reduces the velocity overshoot and dampens the fluctuation.

Effect of pipe rotation velocity on the flow rate in the automated coating system

The article is devoted to the study of the viscous fluid rotation in the confined space of an inclined rotating pipe in the automated system for applying a silicate coating to the inner surface of steel pipes. The authors proposed an automated coating method when the product is installed at the sloping position and rotates around its axis while processing. The thickness of the coating depends on the rotation velocity of the material. The dependence of the flow velocity of a viscous fluid on the angle of inclination of the pipe and the rotation velocity is obtained. It ensures the coating uniformity along the entire length of the product. The study of the rotation velocity dependence of the viscous fluid along the inner surface of the rotating pipe on the velocity of its rotation is carried out.

Couette flow of viscoelastic dusty fluid in a rotating frame along with the heat transfer

Viscoelastic fluid is an advanced fluid which exhibits both elastic and viscous properties. Whereas rotation of viscoelastic fluid is a very complex phenomenon and has an immense amount of applications in engineering and product making industries. Due to various applications in real life researchers are working to understand the rheology of viscoelastic fluids. Viscoelastic dusty fluids are used in gas cooling systems. In nuclear reactors, dusty fluids are used to lower the temperature of the system. Such fluids are also used in centrifugal separators, which separate solid particles from the liquid state, etc. Therefore, in the present study, viscoelastic dusty fluid is analyzed. More precisely free convective Couette flow under the influence of the transversely applied uniform magnetic field in a rotating frame is considered. The subject fluid is driven by the sine oscillations of the upper plate along with the effect of free convection. Due to rotation, the fluid and dust particles have complex velocities which is the sum of primary velocity and secondary velocity. The flow regime is modeled in terms of partial differential equations. To non-dimensionalize the system of governing equations, dimensionless variables have been derived through Buckingham-Pi theorem. The system of partial differential equations is solved through assumed periodic solutions (Poincare-Light Hill Technique). The expressions for skin friction (shear stresses at y = 0) and Nusselt number (the rate of heat transfer) are also calculated. Moreover, parametric influence on Nusselt number, and velocity profile of the fluid and the dust particles, is discussed. It is observed that increase in rotation parameter η causes retardation in the velocity of dust particles and the fluid. This is due to the fact that the increase in η enhances the Coriolis forces that are in fact inertial forces, causing a retardation in the velocity of the fluid phase and the dust phase.

New Formulas and Mechanism for the Spiral Arm Formation of Galaxies

A rotating double-side sprinkle emission model is proposed to describe mechanism for the spiral arm formation of galaxies and various types of spiral patterns. The spiral galaxy can be treated as an ideal fluid system with a universal flat rotation curve; a rotating black hole is located at the center of the galaxy with rotating axis perpendicular to the galactic disc. Inside the black hole, the matter is transformed into new type of matter with anti-gravitational property and emitted by the black hole through two opposite directions in the galactic rotating plane similar to the lighthouse beams, it is then converted to non-gravitational matter. The new matter moves in straightly confined route for certain distance, and then it moves freely with its momentum combining the fluid rotation of the galaxy. The new matter will be transformed to hydrogens on its way of motion, increases the local hydrogen density, refuels the local stars and promotes young star formation, the luminosity of the area is temporarily enhanced, brighter than other areas, such enhanced luminosity area is what seen as the galactic bar and spiral arms. New formulas with one parameter and one variable are derived in three different cases. Different categories of theoretical spiral patterns have been produced and various real images of the spiral galaxies have been precisely simulated by the new formulas. This model seems a universal model and can be applied to most (if not all) spiral galaxies. Galaxies with special spiral patterns like Hoag’s object and arms not meeting the end of galactic bars can be naturally explained by this model. This model is the first attempt to think the spiral arm formation with the hydrogen originated from inside of the galactic center to outside. The proposed mechanism of the hydrogen production seems highly speculative, but the result of the simulations is very satisfactory, this indicates that the idea for the hydrogens originated from inside the bar is a promising approach, may lead us to re-think about the property of the black holes and hope to serve as a trigger to promote the future research in this direction.

Study of double-diffusive convection in a rotating couple-stress ferromagnetic fluid in the presence of varying gravitational field and horizontal magnetic field saturating in a porous medium

The results of double-diffusive convection on the liquid coatings of ferromagnetic liquids is studied by researchers by various theoretical and hydrodynamics concepts of hydrodynamics. However this study is done in presence of varying gravitational field. The study of such couple-stress ferromagnetic fluids in presence of fluctuating gravitational field is still not explored. As we know that gravitational field varies on different points on the earth; for this reason the study of couple-stress ferromagnetic liquids in presence of variable gravity fields is highly required. In this paper we studied the impact of medium permeability, stable solute gradient, couple-stress, rotation, magnetic field, and magnetization of a couple-stress ferromagnetic fluid in presence of variable gravitational field. For this study a coating of couple-stress ferromagnetic fluid saturating in a porous medium when fluid layer is heated and soluted. We examined the results of the magnetic field on couple-stress ferromagnetic fluids, its thermosolutal instability during rotation. A linearized concept and normal mode technique are used to acquire the dispersion relation. For the case of stationary convection, medium permeability, couple-stress, and magnetic field have both stabilizing and destabilizing results under certain conditions. A stable solute gradient has a stabilizing result on the system. Also, the rotation has a stabilizing result for λ&gt;0 and destabilizing result for λ&lt;0 the system. It is likewise observed that in the absence of a stable solute gradient, magnetization has a stabilizing result on the system for both λ&gt;0 and λ&lt;0. The critical Rayleigh number for the onset of instability is decided numerically and graphically also. The principle of exchange of stabilities is observed to keep genuine in the absence of rotation, magnetic field, and stable solute gradient under certain conditions.

Rigid vorticity transport equation and its application to vortical structure evolution analysis in hydro-energy machinery

Vortex is the dominant flow structure in hydro-energy machinery, and its swirling features are mainly determined by the rigid rotation part of vorticity. In this study, the rigid vorticity transport equation is proposed based on the vorticity decomposition. The vortex spatial evolution is described by the stretching term RST, the dilatation term RDT, the Lamb term RCT and the viscous term RVT. The shape change of a vortex tube is mainly affected by RST and RDT, while vortex production and dissipation are mainly reflected by RCT and RVT. Compared with the traditional vorticity transport equation, this new theoretical tool can distinguish between rigid rotation and shearing motion of local fluids, and it can better reveal the intuitive evolution characteristics of vortical structures. Two cases with clear engineering demands are analysed by using the transport equation, and the results show that it can provide a practical method for the analysis and control of vortical flows in hydro-energy machinery.

1+3 formulation of Newton’s equations

We present in this paper a 4-dimensional formulation of the Newton equations for gravitation on a Lorentzian manifold, inspired from the 1+3 and 3+1 formalisms of general relativity. We first show that the freedom on the coordinate velocity of a general time-parametrised coordinate system with respect to a Galilean reference system is similar to the shift freedom in the 3+1-formalism of general relativity. This allows us to write Newton's theory as living in a 4-dimensional Lorentzian manifold $M^N$. This manifold can be chosen to be curved depending on the dynamics of the Newtonian fluid. In this paper, we focus on a specific choice for $M^N$ leading to what we call the \textit{1+3-Newton equations}. We show that these equations can be recovered from general relativity with a Newtonian limit performed in the rest frames of the relativistic fluid. The 1+3 formulation of the Newton equations along with the Newtonian limit we introduce also allow us to define a dictionary between Newton's theory and general relativity. This dictionary is defined in the rest frames of the dust fluid, i.e. a non-accelerating observer. A consequence of this is that it is only defined for irrotational fluids. As an example supporting the 1+3-Newton equations and our dictionary, we show that the parabolic free-fall solution in 1+3-Newton exactly translates into the Schwarzschild spacetime, and this without any approximations. The dictionary might then be an additional tool to test the validity of Newtonian solutions with respect to general relativity. It however needs to be further tested for non-vacuum, non-stationary and non-isolated Newtonian solutions, as well as to be adapted for rotational fluids. One of the main applications we consider for the 1+3 formulation of Newton's equations is to define new models suited for the study of backreaction and global topology in cosmology.

Hall and ion slip effects on magnetohydrodynamic convective rotating flow of Jeffreys fluid over an impulsively moving vertical plate embedded in a saturated porous medium with Ramped wall temperature

AbstractIn the present study, it is explored theoretically Hall and ion slip effects on the unsteady magnetohydrodynamic (MHD) rotating flow of a viscous, incompressible electrically conducting, and optically thick radiating Jeffreys fluid over an impulsively, moving vertical plate embedded in a saturated porous medium, when the temperature of the plate has a provisionally ramped profile. The exact solutions of the governing equations for the flow domain are attained by making use of the Laplace transform method. The specified analytical solutions are also acquired for some limiting cases. The research phrases of engineering curiosity for skin friction and Nusselt number are originated for both ramped wall temperature and the isothermal plate. Sherwood number is also obtained. The numerical results of velocity, temperature, and concentration distributions are exhibited graphically whereas skin friction, Nusselt number, and also Sherwood number are mentioned in a table form. It is observed that on either cases of ramped wall temperature and isothermal plate, the resultant velocity enhances with an increase in Hall and ion slip parameters. Reversal behavior is observed with an increase in magnetic field parameter, Jeffreys fluid parameter and Prandtl number. Thermal and concentration buoyancy forces and thermal radiation tend to accelerate the resultant velocity throughout the boundary layer region. The temperature reduces with an increase in Prandtl number and reverse effect is observed with an increase in thermal radiation parameter. Mass diffusion tends to enhance to species concentration. The rotation and Jeffreys fluid parameters tend to enhance both stress components. Nusselt number enables to lessen with growing in thermal radiation parameter and is magnified on escalating in time. The Sherwood number is improved with increasing in Schmidt number at the plate and it is refused on increasing in time.

Turbulent entrainment into a cylinder wake from a turbulent background

Abstract