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One of the most frequently used governing equations underpinning engineering flow analysis is the renowned Navier–Stokes (NS) equation. Several references regarding the derivation of equation of motion in Cartesian coordinates are available in standard textbooks. However, derivation of above equation in rotational frame is missing in literatures. Flow analysis using NS equation in rotational frame is a prerequisite for analysis of various engineering problems like rotational flow dynamics in chemical reactors, lubricating oil behavior in various rotating machines, electrolyte flow behavior in electrochemical reactors with rotating electrodes, etc. Systematic understanding of each terms in the equation is essential to develop a suitable governing mathematical model of any physical flow problem with various level of complexities. This is possible only if same can be derived from fundamentals, detailing terms behind the equation. A systematic approach is made here to derive NS equation in rotational frame from basic Cartesian form.

Using CFD simulation, we first investigated the flow field distribution of the tridimensional rotational flow sieve tray (TRST) under different structural parameters (i.e. number of the blades, twist angle of the blades, tray height and sieve hole diameter) and installation methods (forward and backward) when gas flows downward through the TRST. Secondly, we carried out a comparative study of three modified structures of the tray, i.e. no supporting ring, a closed internal cylinder and no sieve holes present. Finally, we studied the transformed situations of the rotational flow and propose a dimensionless correlation to evaluate the performance of the tray. The results show that, apart from the tray with a smaller twist angle of the blade, the gas flow field distributions for all the other types of trays are similar. When two trays are installed, the gas flow field of the second tray in a forward installation is obviously different to that of a backward installation. The transformed position of the rotational flow for most types of trays is about half the depth of the tray. After comprehensive evaluation, the optimized tray structures are identified as a configuration with 8 blades, a 90° twist angle of the blades, a tray height of 40 mm, and sieve holes of 5 mm diameter. In addition, the tray should have open internal cylinder without a supporting ring. When a multi-tray is installed, the backward installation method should be adopted.

A novel column internal is proposed, named the tridimensional rotational flow sieve tray (TRST), which has a three-dimensional hollow structure that can make the gas form two kinds of flow pattern coupled with each other: one is rotational flow and the other is flow through the perforations. Using an air-liquid system, we experimentally measured the pressure drops (dry and wet) when gas-liquid flows concurrently downwards through the TRST. We also examined the effects of gas-liquid flux, various geometric parameters of the TRST (i.e. number of blades, twist angles of the blades, tray heights and sieve hole diameters), tray installation methods (forward and backward) and number of installed trays on the pressure drop. The results indicate that the pressure drop increases with increasing gas-liquid flux, number and twist angles of the blades, but decreases with increasing tray heights and sieve hole diameters. The pressure drop of the tray is largest in backward installation, smaller in first installed location and smallest in forward installation. Compared with other new types of trays, the pressure drop of the TRST is lower and there is a significant resistance performance advantage. In addition, according to the mechanism of gas-liquid flow in the TRST, we established the mathematical model of TRST performance in the range of operating conditions. The fitting values agree well with the experimental values.

In this paper exact solutions corresponding to the rotational flow of a fractional Oldroyd-B fluid, in an annulus, are determined by applying integral transforms. The fluid starts moving aftert= 0+when pipes start rotating about their axis. The final solutions are presented in the form of usual Bessel and hypergeometric functions, true for initial and boundary conditions. The limiting cases for the solutions for ordinary Oldroyd-B, fractional Maxwell and Maxwell and Newtonian fluids are obtained. Moreover, the solution is obtained for the fluid when one pipe is rotating and the other one is at rest. At the end of this paper some characteristics of fluid motion, the effect of the physical parameters on the flow and a correlation between different fluid models are discussed. Finally, graphical representations confirm the above affirmation.

We present a rigorous mathematical treatment of water flow in saturated heterogeneous porous media based on the classical Navier-Stokes formulation that includes vorticity in a heterogeneous porous media. We used the mathematical approach proposed in 1855 by James Clark Maxwell. We show that flow in heterogeneous media results in a flow field described by a heterogeneous complex lamellar vector field with rotational flows, compared to the homogeneous lamellar flow field that results from Darcy’s law. This analysis shows that Darcy’s Law does not accurately describe flow in a heterogeneous porous medium and we encourage precise laboratory experiments to determine under what conditions these issues are important. We publish this work to encourage others to perform numerical and laboratory experiments to determine the circumstances in which this derivation is applicable, and in which the complications can be disregarded.

An electrically activated rotation-flow gripper uses rotating airflow to generate negative pressure and suction force on a workpiece. The rotational flow is directly driven by a fan connected to an electrical motor, so the gripper only consumes electrical power. Because the centrifugal force generated by the rotating flow helps prevent vacuum leakage, the gripper can handle workpieces with rough and uneven surfaces. In this study, the torque to drive the rotational flow in the rotating chamber and the suction force generated by the gripper are modeled, based on which the efficiency of the gripper can be obtained. The theoretical model shows efficiency could be improved by decreasing the suction force and increasing the size of the gripper. It is also found that adding a disc at the top end of the fan can improve the efficiency of the gripper by 35%. The disc could transform the flow between the fan and the upper shell wall into a turbulent plane Couette flow, thus reducing the driving torque by 24%. In addition, the disc isolated the insufficiently rotating flow near the upper shell wall from the sufficiently rotating flow below it, thereby further increasing the efficiency by increasing the suction force. The theoretical model and the efficiency improvement are verified by experiments.

A model of the distribution of laminar temperature and dynamic boundary layers is considered. An integral relation is derived for the energy equation of the temperature spatial boundary layer, that allows integration over the surface of any shape, which is necessary for determining the thickness of the energy loss., The expressions for the thickness of the energy loss of the temperature spatial boundary layer are defined for the laminar flow. The expressions for the thickness of the energy loss are necessary to determine the local heat transfer coefficients for the characteristic cases of flow, taking into account heat transfer. Analytically, expressions are obtained for determining the local heat transfer coefficient in the form of the Stanton criterion for the rotational flow according to the law of a solid and the rotational flow of a free vortex. Local heat transfer coefficients are determined for laminar rotational flows.

Wire wrapped fuel pins, typical of sodium fast reactor designs, introduce a strong secondary rotational flow and enhanced mixing compared to bare pins found in many other nuclear reactor designs. The transverse flow is created by deflection off of the helical wires, exerting a force onto the wires. The resulting pressure field can be more intricate than found for bare fuel pins. There is an increased concern for fluid structure interactions such as twisting, bending, and vibration due to the fluid deflection and increased transverse flow. The present study uses LES to simulate the fluid flow in a wire-wrapped fuel pin bundle. The simulation is performed using Nek5000, a spectral element LES/DNS code. The time-dependent, fluctuating pressure field at the surface of select fuel pins are specifically captured for analysis. Statistical analysis is performed on the pressure data to find areas of persistent force or bending moment, which over large periods of time may result in deformation of the pins. Further, the pressure data is analyzed in search of areas with large fluctuations in pressure, which may result in flow induced vibrations. Frequency spectra of the force fluctuations are analyzed.

An experimental investigation shows that the small ellipticity of a precessing spheroidal cavity has a significant impact on the flow transition from solid-body rotational flow to developed turbulence of a confined fluid. In contrast, the developed turbulence in the spheroid is almost identical to that in the sphere.

In this article, an effort has been made to compute and inspect the rotational flow of Oldroyd-B fluid between two co-axial circular cylinders. As novelty, the rotation of both cylinders produces motion of the fluid. The velocity field and tangential stress corresponding to the motion of an Oldroyd-B fluid with fractional derivatives have been obtained using Laplace and Hankel integral transforms. The velocity profiles of the respective model are graphically presented and deliberated for the pertinent parameters. Corresponding solutions are also obtained for ordinary Oldroyd-B fluid, ordinary and fractional Maxwell fluids, ordinary and fractional second-grade fluids, and Newtonian fluid as limiting cases of our general solutions.

Five basic flow regimes between coaxial cylinders are analyzed for a fluid with solidification effect. The dependences of the angular velocity of the inner cylinder on the torque applied to it are obtained. It is shown that this dependence does not increase monotonically. As the torque exceeds a certain critical value, the angular velocity decreases.

Recently, a vector named Rortex was proposed to represent the local fluid rotation [C. Liu et al., “Rortex—A new vortex vector definition and vorticity tensor and vector decompositions,” Phys. Fluids 30, 035103 (2018)]. In this paper, a universal Rortex based velocity gradient tensor decomposition is proposed and the relevant local velocity increment decomposition is provided. Vortex structures in boundary layer transition on a flat plate are analyzed to quantify the local rotational, compression-stretching, and shearing effects. The results demonstrate that vorticity is shearing-dominant, while the rotational part or Rortex in general occupies a small part of vorticity in most areas of this case. In other words, vorticity is a quality representing shearing rather than rotation or vortex in most regions of this case.

The impacts of rotational velocity and inertia on velocity gradients and stresses are addressed under present study. The non-Newtonian behaviour of inelastic rotating flows is predicted by employing Power law model. A numerical model has been developed for mixing flow within a cylindrical vessel along a couple of stirrers. A time marching FEM (Finite Element Method) is employed to predict the required solution. Predicted solutions are presented for minimum to maximum values in terms of contour plots of velocity gradients and shear stresses, over the range. The long term application of this research will be used to improve the design of mixers and processing products. The predicted results are used to generate the capability and are in good agreement with numerical results to the mixer design that will ultimately effect the processing of dough products

A new model for calculation of the velocity field in a pump meridian is presented in this paper. It is a parameterized rotational flow model providing the pump designer with an option to simulate various flow conditions at the blade leading edge using a single parameter, which leads to different blade designs. Despite being rotational, this flow model does not allow for creation of helical swirl structures, a feature that is usually sought to be suppressed in a pump impeller. A condition for a flow pattern suitable for a pump hydraulic design is derived using curvilinear coordinates. The variation of the meridional velocity for different choices of the parameter is demonstrated, and the meridional flow field is compared against the turbulent flow. The resulting velocity field is easy to obtain and provides a unified approach to determine the distribution of the blade inlet angles along the leading edge for a range of design requirements.

We considered the unsteady flow of a fractional Oldroyd-B fluid through an infinite circular cylinder with the help of infinite Hankel and Laplace transforms. The motion of the fluid is produced by the cylinder that, at time t=0+ is subject to a time-dependent angular velocity. The established solutions have been presented under series form in terms of the generalized G functions satisfy all imposed initial and boundary conditions. The corresponding solutions for ordinary Oldroyd-B, ordinary and fractional Maxwell, ordinary and fractional second-grade, and Newtonian fluids, performing the same motion, are acquired as limiting cases of general solutions. The keynote points regarding this work to mention are that (1) we extracted the expressions for velocity field and shear stress corresponding to the motion of fractional second-grade fluid as a limiting case of general solutions; (2) the expressions for velocity field and shear stress are in the most simplified form in contrast with the studies of Siddique and Sajid (2011), in which the expression for the velocity field involves the convolution product as well as the integral of the product of generalized G functions. Finally, numerical results are presented graphically and discussed in order to reveal some physical aspects of obtained results.

When deployed as large arrays, wind turbines significantly interact among themselves and with the atmospheric boundary layer. In this study, we integrate a three-dimensional large-eddy simulation with an actuator line technique to examine the characteristics of wind-turbine wakes in an idealized wind farm inside a stable boundary layer (SBL). The wind turbines, with a rotor diameter of 112 m and a tower height of 119 m, were "immersed" in a well-known SBL case that bears a boundary layer height of approximately 175 m. Two typical spacing setups were adopted in this investigation. The super-geostrophic low-level jet near the top of the boundary layer was eliminated owing to the energy extraction and the enhanced mixing of momentum. Non-axisymmetric wind-turbine wakes were observed in response to the non-uniform incoming turbulence, the Coriolis effect, and the rotational effects induced by blade motion. The Coriolis force caused a skewed spatial structure and drove a part of the turbulence energy away from the center of the wake. The SBL height was increased, while the magnitude of the surface momentum flux was reduced by more than 30%, and the magnitude of the surface buoyancy flux was reduced by more than 15%. The wind farm was also found to have a strong effect on vertical turbulent fluxes of momentum and heat, an outcome that highlights the potential impact of wind farms on local meteorology. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3589857]

The deformation and orientation of droplets during transient shear flow is studied in a counterrotating device using microscopy. The effect of the degree of confinement and viscosity ratio is systematically investigated. The system consists of polydimethylsiloxane droplets of varying sizes and viscosities dispersed in a polyisobutylene matrix. The observations are compared with the predictions of an adapted version of the Maffettone and Minale model [Maffettone, and Minale, J. Non-Newtonian Fluid Mech. 78, 227-241 (1998)] which includes confinement effects [Minale, Rheol. Acta 47, 667-675 (2008)]. For flow start-up at low capillary numbers, the deformation of confined droplets and their orientation towards the flow direction are increased with respect to the unconfined situation for all viscosity ratios under investigation. The confined model results for start-up and the experimental data at low capillary numbers are in good agreement both showing similar monotonous transients. At high degrees of confinement and high shear rates, one or more overshoots in the droplet deformation are experimentally observed, depending on the viscosity ratio. In addition, droplets become sigmoidal when highly confined. Under these conditions, the confined Maffettone and Minale model, which assumes an ellipsoidal droplet shape, cannot be used to predict the droplet behavior. The relaxation of confined droplets upon cessation of steady-state shear flow is also studied. It is experimentally observed that confinement only affects the relaxation at degrees of confinement above 60% of the gap spacing. Highly confined droplets experience a slightly slower relaxation with respect to bulk conditions. The relaxation predictions of the confined model are in rather good agreement with the experimental data. ispartof: Journal of rheology vol:52 issue:6 pages:1459-1475 status: published

Two linear eddy-viscosity models, the v2-f and k-ω models, have been combined with an algebraic structure-based algorithm for the evaluation of the Reynolds stresses. This closure was originally designed as an integral part of the algebraic structure-based model (ASBM) to capture the turbulent anisotropy occurring in rotating wall bounded flows. It is shown that the algebraic structure-based evaluation of the Reynolds stresses can be used directly with conventional turbulence models sensitizing them to rotation. Significant improvement in the prediction of anisotropic turbulent flow can be achieved without an additional tuning of the closure coefficients. The models are evaluated in spanwise rotating channel flow and in flat plate boundary layers. The sensitivity to the Reynolds and rotation numbers is investigated. The results are compared with DNS data. © 2006 Elsevier Inc. All rights reserved. 27 653 660 653-660

A new algorithm using polar coordinate system similarity (PCSS) for tracking particle in particle tracking velocimetry (PTV) is proposed. The essence of the algorithm is to consider simultaneously the changes of the distance and angle of surrounding particles relative to the object particle. Monte Carlo simulations of a solid body rotational flow and a parallel shearing flow are used to investigate flows measurable by PCSS and the influences of experimental parameters on the implementation of the new algorithm. The results indicate that the PCSS algorithm can be applied to flows subjected to strong rotation and is not sensitive to experimental parameters in comparison with the conventional binary image cross-correlation (BICC) algorithm. Finally, PCSS is applied to images of a real experiment.

The present paper mainly focuses on the generation and development of lee vortices for the low Froude number density stratified flow passing over an isolated obstacle. A series of laboratory experiments were carried out by towing-tank equipments to simulate the airflow passing over a large terrain. Based on the similarity principle, the Froude number of the stratified flow, the stratified condition, and the rotation parameter are chosen in the specified scope. Our studies show that the lee vortices can appear in the non-rotational and rotational cases. For the non-rotational fluid, the lee vortices generate only under the condition of strong stratification and the small Froude number (0.1

In the presented study a special test pump with two-dimensional curvature blade geometry was investigated in cavitating and noncavitating conditions using different experimental techniques and a three-dimensional numerical model implemented to study cavitating flows. Experimental and numerical results concerning pump characteristics and performance breakdown were compared at different flow conditions. Appearing types of cavitation and the spatial distribution of vapor structures within the impeller were also analyzed. These results show the ability of the model to simulate the complex three-dimensional development of cavitation in a rotating machinery, and the associated effects on the performance.

We consider stationary and nonstationary problems of viscous incompressible fluid flows with slip boundary conditions in a rotating bounded domain. We show a geometrical representation of the slip conditions where principal curvatures of its boundary surfaces are characteristic coefficients. When the domain is axisymmetric, it is proved that a steady flow exists if external force f→ in equations of motion is orthogonal to rigid rotational flows, and that a nonstationary flow converges to a steady flow depending on its initial flow as time tends to infinity, if f→ is independent of time and orthogonal to rigid rotational flows and if the L2-norm of f→ is sufficiently small.

It is shown that for a body which is swimming at low Reynolds number and is spherical at some time of its motion the mean surface flow velocity and the mean surface rotational flow velocity in the laboratory frame vanish at that time. The instantaneous translational and rotational swimming velocities are the opposite of the mean surface flow velocity and the mean surface rotational flow velocity in the rest frame. The swimming velocities are calculated for an example of spherical squirming motion. In the example, the translational swimming velocity oscillates in time about a steady value and the rotational swimming velocity is steady.

Numerical simulations of interfacial stability for miscible droplet in a rotating Hele–Shaw cell by means of high-accurate numerical schemes are presented. The interfacial instability is dominated by four control parameters, such as rotating speed, viscosity contrast, diffusion between the species and injecting strength. More vigorous interfacial fingerings are found at higher rotating speed and lower viscosity contrast. The effect of stronger diffusion is not significant to the fingering patterns, but leads only to milder instability. Injection in general reinforces viscous stabilization. For the case of annulus, different mechanisms of instability are observed on the inner and outer fronts. The injecting strength tends to stabilize the outer interface, and perturbs the inner.

A sound wave propagating in an inhomogeneous duct consisting of two semi-infinite uniform ducts with a smooth transition region in between and which carries a steady flow is considered. The duct walls may be rigid or compliant. For an irrotational sound wave it is shown that the three properties of the title are closely related, such that the validity of any two implies the validity of the third. Furthermore it is shown that the three properties are fulfilled for lossless locally reacting duct walls provided the impedance varies at most continuously. For piecewise-continuous wall properties edge conditions are essential. By an analytic continuation argument it is shown that reciprocity remains true for walls with loss. For rotational flow, energy conservation theorems have been derived only with the help of additional potential-like variables. The inter-relation between the three properties remains valid if one considers these additional variables to be known. If only the basic gasdynamic variables in both half-ducts are known, one cannot formulate an energy conservation equation; however, reciprocity is fulfilled.

Weak solutions to the Stokes and Navier-Stokes problems are proved to exist in domains which, outside a ball, coincide with the three-dimensional layer ℝ2 × (0,1). Apart from solutions with the finite Dirichlet integral, solutions to the linear problem are constructed with a prescribed behavior at infinity such that the plane-parallel Poiseuille and Couette flows, the rotational flow. A solution to the nonlinear problem is found that drives a nonzero flux to infinity and becomes unique under the data smallness assumption. Estimates for weighted norms of the pressure are derived as well

In the field of tissue engineering, it is called for to automate generation of various-shaped spheroids. We propose a micro fluidic device that generates rotational flow for producing toroidal-like spheroid. This paper reports the concept of construction of toroidal-like spheroid, designs of microchannels, and fundamental verification about generation of rotational flow in the device using simulation and experiment using created microchannels. Concept of construction is non-contact operation in a continuous flow stimulus by using centrifugal force of rotational flow. Designs of the micro fluidic device was optimized to generate micro-rotational flow, and the results of flow simulation models show that rotational flow is generated at the flow velocity more than fixed. We made these designs. The large size channel was made with 3D printer and the small channel was made by poly-dimethysiloxane (PDMS) molding, and generation of rotational flow was observed in an experiment using particles. In both types of channels, particles were rotated similar to the simulations.

The characteristics of the air-core vortex formed during free draining of liquids from tanks strongly depend on the size and shape of the drain ports used. In order to understand the role of the drain-port in influencing the air-core vortex, the flow currents induced while draining a rotating column of liquid with different drain-port diameters is assessed. The flow currents are monitored using nets and tufts. It is shown that for small drain ports, for which an air-core vortex is spontaneously formed, the rotational flow currents are concentrated along the central core. With larger drain ports, the rotational flow currents are smaller and are diffused over larger radii leading to weak air-core vortex.

Explicit expressions are derived for the matrices determining the mean translational and rotational swimming velocities and the mean rate of dissipation for Stokesian swimming at low Reynolds number of a distorting sphere in a viscous incompressible fluid. As an application, an efficient helical propeller-type stroke is found and its properties are calculated.

We present a parametric space study of the decay of turbulence in rotating flows combining direct numerical simulations, large eddy simulations, and phenomenological theory. Several cases are considered: (1) the effect of varying the characteristic scale of the initial conditions when compared with the size of the box, to mimic "bounded" and "unbounded" flows; (2) the effect of helicity (correlation between the velocity and vorticity); (3) the effect of Rossby and Reynolds numbers; and (4) the effect of anisotropy in the initial conditions. Initial conditions include the Taylor-Green vortex, the Arn'old-Beltrami-Childress flow, and random flows with large-scale energy spectrum proportional to $k^4$. The decay laws obtained in the simulations for the energy, helicity, and enstrophy in each case can be explained with phenomenological arguments that separate the decay of two-dimensional from three-dimensional modes, and that take into account the role of helicity and rotation in slowing down the energy decay. The time evolution of the energy spectrum and development of anisotropies in the simulations are also discussed. Finally, the effect of rotation and helicity in the skewness and kurtosis of the flow is considered., Sections reordered to address comments by referees

We studied the properties of the large-scale circulation (LSC) in turbulent Rayleigh-B\'enard (RB) convection by using results from direct numerical simulations in which we placed a large number of numerical probes close to the sidewall. The LSC orientation is determined by either a cosine or a polynomial fit to the azimuthal temperature or azimuthal vertical velocity profile measured with the probes. We study the LSC in \Gamma=D/L=1/2 and \Gamma=1 samples, where D is the diameter and L the height. For Pr=6.4 in an aspect ratio \Gamma=1 sample at $Ra=1\times10^8$ and $5\times10^8$ the obtained LSC orientation is the same, irrespective of whether the data of only 8 or all 64 probes per horizontal plane are considered. In a \Gamma=1/2 sample with $Pr=0.7$ at $Ra=1\times10^8$ the influence of plumes on the azimuthal temperature and azimuthal vertical velocity profiles is stronger. Due to passing plumes and/or the corner flow the apparent LSC orientation obtained using a cosine fit can result in a misinterpretation of the character of the large-scale flow. We introduce the relative LSC strength, which we define as the ratio between the energy in the first Fourier mode and the energy in all modes that can be determined from the azimuthal temperature and azimuthal vertical velocity profiles, to further quantify the large-scale flow. For $Ra=1\times10^8$ we find that this relative LSC strength is significantly lower in a \Gamma=1/2 sample than in a \Gamma=1 sample, reflecting that the LSC is much more pronounced in a \Gamma=1 sample than in a \Gamma=1/2 sample. The determination of the relative LSC strength can be applied directly to available experimental data to study high Rayleigh number thermal convection and rotating RB convection., Comment: 12 pages, 15 figures

International audience; Temperature depression within the leading edge cavities on a space inducer is measured in Refrigerant 114 using miniature thermocouples mounted on the rotating blades. Time-averaged values of cavity temperature depression are determined all along the descent in cavitation number and correlated with the extent of cavities. In addition to mean values, temperature fluctuations are analyzed with respect to the onset of cavitation instabilities, namely, alternate blade cavitation and supersynchronous rotating cavitation. Temperature spectra relative to a rotating frame of reference are compared with pressure spectra obtained in a fixed frame of reference. Temperature oscillations issued from different blades are compared, and phase shifts between consecutive and opposite blades are evaluated in the case of the supersynchronous instability regime.

International audience; The thermodynamic effect on a cavitating inducer is investigated from joint experiments in cold water and Refrigerant 114. The analysis is focused on leading edge cavitation and cavitation instabilities, especially on alternate blade cavitation and supersynchronous rotating cavitation. The cavity length along cylindrical cuts at different radii between the hub and casing is analyzed with respect to the local cavitation number and angle of attack. The similarity in shape of the cavity closure line between water and R114 is examined and deviation caused by thermodynamic effect is clarified. The influence of rotation speed on cavity length is investigated in both fluids and analyzed on the basis of a comparison of characteristic times, namely, the transit time and a thermal time. Thermodynamic delay in the development of leading edge cavities is determined and temperature depressions within the cavities are estimated. Thresholds for the onset of cavitation instabilities are determined for both fluids. The occurrence of cavitation instabilities is discussed with respect to the extent of leading edge cavitation. The thermodynamic delay affecting the occurrence of cavitation instabilities is estimated and compared with the delay on cavity development.

International audience; Two different approaches are used for evaluating two-time correlations of Fourier velocity modes in isotropic, and in rotating, homogeneous incompressible turbulence. A synthetic model is proposed and compared with the results of direct numerical simulations. This kinematic model presents the advantage to incorporate different sources of unsteadiness, from arbitrary timescales to linear dynamics of rotating flows. The two main timescales characterizing the various processes involved in the dynamics of isotropic turbulence can be included: the sweeping effect, in which small scales of the flow are advected by the large scale motion, and the straining hypothesis–also called Kolmogorov or eddy turnover timescale. In the rotating case, the dispersion relation of inertial waves can also be included. Using Lighthill's theory, the effect of these different timescales on the sound emitted by such a model is also examined, and compared with direct numerical simulations.

The effect of rotation on the boundary layers (BLs) in a Rayleigh-Benard (RB) system at a relatively low Rayleigh number, i.e. $Ra = 4\times10^7$, is studied for different Pr by direct numerical simulations and the results are compared with laminar BL theory. In this regime we find a smooth onset of the heat transfer enhancement as function of increasing rotation rate. We study this regime in detail and introduce a model based on the Grossmann-Lohse theory to describe the heat transfer enhancement as function of the rotation rate for this relatively low Ra number regime and weak background rotation $Ro\gtrsim 1$. The smooth onset of heat transfer enhancement observed here is in contrast to the sharp onset observed at larger $Ra \gtrsim 10^8$ by Stevens {\it{et al.}} [Phys. Rev. Lett. {\bf{103}}, 024503, 2009], although only a small shift in the Ra-Ro-Pr phase space is involved., Comment: 17 pages, 13 figures

WOS: 000273877000005, The turbulent flow inside a low-speed centrifugal compressor at design condition is investigated using large-eddy simulation (LES) comprising of up to 26x10(6) computational volume cells. Unlike in the past, the current study's special emphasis is placed on the turbulence field evolution inside the impeller. LES predictions suggest that the Boussinesq hypothesis does not seem to be valid, especially near the exit of the impeller where the blade unloading takes place. Reynolds stress variations show a tendency toward an "axisymmetric expansion" type of turbulence after the impeller exit for which the subgrid-scale stress contribution shows a monotonic decrease. Probability density function analysis for the leakage flow show that instantaneous velocities in the wake region are less intermittent as compared with those in the jet. Time spectra analysis display also another feature that the energy cascade proceeds at a higher rate and lasts longer in the wake region than in the tip jet region., NASA, The authors would like to thank to Dr. Michael D. Hathaway from NASA for providing the experimental data for the centrifugal compressor.

We report the formation of a ringlike structure in the flow of particular non-Newtonian liquids coating a rotating vertical disk. Experiments were performed with a known volume of the liquid and at varying rotation rates such that the inertial effects were negligible. The liquid injected on the rotating disk initially coats the surface uniformly, which then redistributes itself such that at steady state a significant amount collected into a circular ring, off center with the axis of rotation. Beyond a critical rotation speed and for a given liquid volume, the ring formation did not occur. The ring formation was not observed in the case of Newtonian liquids. Rheological measurements along with the shear rate calculations suggest that the shear thinning nature of the liquids could be responsible for the observed ring formation.

The instabilities of fluid flows between coaxial differentially rotating cones are considered in the limit of the small gap approximation as function of the cone angle. As in the experimental study of Wimmer (presented at the 10th International Couette-Taylor Workshop, Paris, 15–17 July 1997), a transition from Taylor vortexinstabilities to Ekman-type instabilities is found at a cone angle of about 45°.

This article deals with fluid flow in a rotating coordinate frame and how to make the characteristics of the flow visible to lecture‐demonstration‐size audiences. This is a sequel to an earlier article [H. A. Daw, Am. J. Phys. 55, 1010–1014 (1987)] dealing with a rolling ball in the rotating frame. Basically, the same apparatus is used. The path of the fluid flow in a uniformly rotating system in two dimensions is made visible using food coloring, and observation is made by using a video camera. A simple derivation of the flow path is given. The article concludes with the description of a demonstration showing the formation of whirlpools.

This paper reports the flow of elastico-viscous liquid embedded with particles in an oscillating cylinder. Explicit expressions are obtained for the velocities of liquid and dust particles by the technique of Laplace transforms. Numerical computations of the velocity fields are carried out for different values of mass concentration and relaxation time of the dust particles and varying elastic elements in the liquid.

The transition from the two-dimensional (2D) longitudinal roll cell state to 3D flows in the rotating plane Couette system, predicted by the theoretical investigation [M. Nagata, J. Fluid Mech. 358, 357 (1998)], is examined experimentally. The streamwise and spanwise wave numbers of observed steady 3D flows seem to agree with those predicted by the theory when the rotation rate is relatively large. However, we observe unsteady 3D states in the region where the theory predicts stable steady 3D flows when the rotation rate is small.

In the present study, we investigate, using inviscid rapid distortion theory, the evolution of sheared turbulence in a rotating frame as a function of the rotation rate (including stable, transitional, and unstable regimes), and examine the sensitivity of the results for various nonisotropic initial conditions. Analytical solutions are derived for the evolution of the stresses and the structure dimensionality tensor components for three one-dimensional and three two-dimensional initializations. From these solutions, we calculate the asymptotic states of the turbulence, which are compared to the exact numerical solution of the three-dimensional initially isotropic case. From the investigation it is shown that the qualitative characteristics of the isotropic solution in the unstable regime are represented quite accurately when the initial turbulence is dependent at least on the axis of the rotation of the frame. For the transitional and the stable regimes, though, the initial dependence of the turbulence on the axis of the mean flow is also crucial. © 2007 American Institute of Physics. 19

We apply inviscid rapid distortion theory to the generalized case of turbulent hyperbolic flow in a rotating frame and investigate the dependence of the evolution of the turbulent kinetic energy on the frame rotation rate. We derive an analytical two-dimensional solution which allows for an accurate approximation of the three-dimensional initially isotropic problem. From the analytical solutions we determine a new generalized stability criterion for the evolution of the turbulent kinetic energy in this class of flows. © 2007 American Institute of Physics. 19

We report a numerical study on the vaneless diffuser core flow instability in centrifugal compressors. The analysis is performed for the purpose of better understanding of the rotating stall flow mechanism in radial vaneless diffusers. Since the analysis is restricted to the two-dimensional core flow, the effect of the wall boundary layers is neglected. A commercial code with the standard incompressible viscous flow solver is applied to model the vaneless diffuser core flow in the plane parallel to the diffuser walls. At the diffuser inlet, rotating jet-wake velocity pattern is prescribed and at the diffuser outlet constant static pressure is assumed. Under these circumstances, two-dimensional rotating flow instability similar to rotating stall is found to exist. Performed parameter analysis reveals that this instability is strongly influenced by the diffuser geometry and the inlet and outlet flow conditions.

We report a numerical study on the vaneless diffuser core flow instability in centrifugal compressors. The analysis is performed for the purpose of better understanding of the rotating stall flow mechanism in radial vaneless diffusers. Since the analysis is restricted to the two-dimensional core flow, the effect of the wall boundary layers is neglected. A commercial code with the standard incompressible viscous flow solver is applied to model the vaneless diffuser core flow in the plane parallel to the diffuser walls. At the diffuser inlet, rotating jet-wake velocity pattern is prescribed and at the diffuser outlet constant static pressure is assumed. Under these circumstances, two-dimensional rotating flow instability similar to rotating stall is found to exist. Performed parameter analysis reveals that this instability is strongly influenced by the diffuser geometry and the inlet and outlet flow conditions.

A review of asymptotic analyses for the study of the motion and decay of a vortex filament submerged in a background potential flow is presented. Emphasis is placed on physical intuitions motivating the analyses and on the physical interpretation of the asymptotic solutions. The extension of the analyses to a vortex filament submerged in a rotational flow is outlined.

A theoretical analysis of the thermal effects on the dynamics of a thin nonuniform film of a nonvolatile incompressible viscous fluid on a heated rotating disk has been considered and the effects of temperature-dependent viscosity and surface tension have been analyzed. A nonlinear evolution equation describing the shape of the film interface has been derived as a function of space and time and its stability characteristics have been examined using linear theory. It has been observed that the infinitesimal disturbances decay for small wave numbers and are transiently stable for large wave numbers, for both zero and nonzero values of Biot number. ? 2005 American Institute of Physics.

International audience; Both direct numerical simulation and theoretical stability analysis are performed together in order to study the transition process to turbulence in a flow between a rotating and a stationary disk. This linear stability analysis considers the complete rotor-stator flow and then extends the results of Lingwood [J. Fluid Mech. 299, 17 (1995); 314, 373 (1996)] obtained in a single disk case. The present linear analysis also extends the former two-disk computations of Itoh [ASME FED 114, 83 (1991)], only limited to a hydrodynamic spatial instability analysis. Moreover, in the present work, this approach is completed by discussing the effects of buoyancy-driven convection on the flow stability and by absolute/convective analysis of the flow. Coupled with accurate numerical computations based on an efficient pseudo-spectral Chebyshev-Fourier method, this study brings new insight on the spatio-temporal characteristics of this flow during the first stages of transition. For instance, an exchange of stability from a steady to a periodic flow with spiral structures is observed for the first time numerically in such cavity of large aspect ratio. The nature of the first bifurcation is discussed as well as the influence on it of disturbances coming from the end-wall boundary layer. Annular and spiral patterns are observed in the unstable stationary disk layer with characteristic parameters agreeing very well with the present theoretical results. Then, these structures are interpreted in terms of type I and type II generic instabilities. Moreover, the absolute instability regions which are supposed to be strongly connected with the turbulent breakdown process are also identified and the critical Reynolds numbers of the convective/absolute transition in both Ekman and Bödewadt layers are given.

In 1957 Metzner and Otto proposed a simplified way of calculating the power consumption in impeller-driven systems for power-law type of fluids. Assuming a proportionality between the shear rate and rotational speed of the impeller, they reported that the proportionality constant was independent of the geometric and fluid properties of the mixing system. This was later contested by a number of researchers, and different correlations have been given to evaluate the proportionality constant. An in-depth investigation of the Metzner–Otto concept is discussed with the help of computational fluid dynamics (CFD) techniques to calculate the flow field created by an anchor impeller. Fundamentally, both of the assumptions are broadly valid for typical operating parameters used in anchor-driven impeller systems. A new correlation, based on the Metzner–Otto concept and making use of the present CFD simulations, was developed to calculate power consumption in anchor-driven mixing systems.

The initial-boundary value problem for the PDE of a composite type of the 4-th order is investigated. This problem simulates the process of distribution of non-stationary interior waves in a stratified rotating liquid excited by a progressive wave on a sloping bottom.